NUREG- 1746

System-Level Repository 

Sensitivity Analyses, Using TPA 

Version 3.2 Code 

Center for Nuclear Waste Regulatory Analyses 

Swedish Nuclear Power Inspectorate 

U.S. Nuclear Regulatory Commission 

Office of Nuclear Material Safety and Safeguards o". FE 

Washington, DC 20555-0001
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NUREG-1746

System-Level Repository 

Sensitivity Analyses, Using TPA 

Version 3.2 Code 

Manuscript Completed: June 2001 

Date Published: August 2001 

Prepared by 

R. B. Codell, M. R. Byrne, T. J. McCartina 

S. Mohanty, J. Weldy, M. Jarzemba, G. W. Wittmeyerb 

Y. LuC 

R. W. Riced 

'Division of Waste Management 

Office of Nuclear Material Safety and Safeguards 

U.S. Nuclear Regulatory Commission 

Washington, DC 20555-0001 

bCenter for Nuclear Waste Regulatory Analyses 

6220 Culebra Road 

San Antonio, TX 78238-5166 

'Office of Nuclear Waste Safety 

Swedish Nuclear Power Inspectorate 

(Statens Kidrnkraftinspektion) 

S-106 58 Stockholm, Sweden 

dIndependent Consultant 

307 Quincy 

El Paso, TX 79922
For sale by the Superintendent of Documents, U.S.Government Printing Office 

Internet: bookstore.gpo.gov Phone: (202) 512-1800 Fax: (202) 512-2250 

Mail: Stop SSOP, Washington, DC 20402-0001 

ISBN 0-16-050907-6
ABSTRACT 

To review and quantitatively evaluate the safety case in a potential license application by the 

U.S. Department of Energy (DOE) for the proposed Yucca Mountain (YM) repository, the U.S. Nuclear 

Regulatory Commission (NRC), with technical assistance from the Center for Nuclear Waste Regulatory 

Analyses (CNWRA), developed a Total-system Performance Assessment (TPA) code. The most recent 

versions of the TPA code used in evaluation and calculation of YM performance are 3.2 and 3.2.3. This 

report describes a series of computations performed using these codes for determining the confidence in the 

estimation of future repository performance in light of the uncertainty in conceptual models and parameters 

of those models. This report primarily presents: (i) the system-level and process-level results 

(e.g., intermediate results) to demonstrate trends and variabilities in outputs; (ii) the results of system-level 

sensitivity and uncertainty analyses using a variety of analysis techniques to determine the paiameters that 

have the most influence on repository performance; and (iii) the relative importance of the integrated 

subissues in reviewing the DOE total-system performance assessment. An influential parameter is one that 

either drives uncertainty in performance, or one to which performance is sensitive. The sensitivity and 

uncertainty analyses were conducted using numerous TPA code runs (several thousand realizations) for each 

sensitivity analysis technique. Results of system-level analyses are based on peak dose and peak expected 

dose to a receptor group 20 km (12.4 mi) from the repository at two time periods of interest (TPIs): 10,000 

yr (the likely compliance period in the draft regulation) and either 50,000 or 100,000 yr [a longer period for 

investigating any significant effects that may not be evident because of the calculated long waste package 

(WP) life]. 

Using the basecase, which included the seismic disruptive event scenario, peak expected doses of 

0.003 mrem/yr and 4 mrem/yr were obtained for the 10,000- and 100,000-yr TPIs, respectively. The faulting 

scenario changed the peak expected dose negligibly. The igneous activity scenario increased the peak 

expected dose to 0.6 mrem/yr. For both TPIs, it was found that the most influential parameters were: (i) the 

fraction of the repository wetted by infiltrating water; (ii) the fraction of water entering the WP; (iii) the well 

pumping rate at the 20-km receptor group location; (iv) alluvium retardation factors for radionuclides 

(specifically, 9Tc and 1291), and (v) the present-day infiltration. The most influential parameters for the 

10,000-yr TPI, but not for the 50,000-yr TPI, were the initially defective fraction of WPs and the factor that 

focuses flow onto the WP. The most influential parameters for the 50,000-yr TPI, but not for the 

10,000-yr TPI, were the alluvium retardation factors for radionuclides (specifically, 234

U and 237

Np). The 

influential parameters were then compared to the current integrated subissues, which are used by the NRC 

to focus work on items important to repository performance. Nine out of 14 of the integrated subissues 

reflected at least one influential parameter. 

The analyses and results are limited by the use of simplifying assumptions, models, and sparse data in certain 

areas. As a consequence, these results are preliminary. However, the estimates resulting from this study 

allowed the staff to focus attention on what are likely to be the most important phenomena relative to 

repository performance and point out deficiencies in the current state of knowledge. The manner in which 

these analyses were conducted or the assumptions and approaches used should not be construed to express 

the views, preferences, or positions ofthe NRC staffregarding the nature of site-specific regulations for YM.

iii
CONTENTS 

Section Page 

AB STRA CT ........................................................................ iii 

TABLE OF CONTENTS .............................................................. v 

FIGU RES .......................................................................... ix 

TA BLES ......................................................................... xiii 

EXECUTIVE SUMMARY ........................................................... xv 

ACKNOWLEDGMENTS ........................................................... xviii 

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

1.1 BACKGROUND ...................................................... 1-2 

1.1.1 Previous IPA Analyses ........................................... 1-2 

1.1.2 IPA Phase 1 Sensitivity and Uncertainty Analyses ..................... 1-4 

1.1.3 IPA Phase 2 Sensitivity and Uncertainty Analyses ..................... 1-4 

1.1.4 TPA Version 3.1 Sensitivity and Uncertainty Analyses .................. 1-5 

1.2 PURPOSE OF CURRENT ANALYSIS .................................... 1-5 

1.3 REPORT ORGANIZATION ............................................. 1-7 

1.4 CAVEATS ........................................................... 1-7 

2 OVERVIEW OF THE TOTAL-SYSTEM PERFORMANCE ASSESSMENT 

CONCEPTUAL MODELS IN THE TPA VERSION 3.2 CODE ....................... 2-1 

2.1 CONCEPTUALIZATIONS OF REPOSITORY AND GEOLOGIC SETTING ...... 2-1 

2.2 CONCEPTUAL MODELS IMPLEMENTED IN THE TOTAL-SYSTEM 

PERFORMANCE ASSESSMENT COMPUTER CODE ....................... 2-5 

2.2.1 Infiltration and Deep Percolation ................................... 2-5 

2.2.2 Near-Field Environment .......................................... 2-6 

2.2.3 Radionuclide Releases from the EBS ................................ 2-7 

2.2.4 Treatment of Aqueous-Phase Transport in the Unsaturated and 

Saturated Zones ................................................ 2-9 

2.2.5 Airborne Transport from Direct Releases ............................ 2-9 

2.2.6 Exposure Pathways and Reference Biosphere ........................ 2-10 

2.3 BASECASE DEFINITION AND ALTERNATIVE CONCEPTUAL MODELS ... 2-11 

2.3.1 Basecase ..................................................... 2-11 

2.3.2 Alternative Conceptual Models ................................... 2-11 

2.3.2.1 Fuel-Dissolution M odels ........................................ 2-11 

2.3.2.2 Fuel-Wetting Assumptions ....................................... 2-12 

2.3.2.3 Transport Alternatives .......................................... 2-13 

3 ANALYSIS OF TOTAL-SYSTEM BEHAVIOR ................................... 3-1 

3.1 SINGLE-REALIZATION DETERMINISTIC ANALYSES .................... 3-1 

3.1.1 Unsaturated Zone Flow ........................................... 3-1 

3.1.2 Near-Field Environment .......................................... 3-2 

3.1.2.1 Repository-Scale Thermohydrology ................................. 3-2 

3.1.2.2 Drift-Scale Thermohydrology ...................................... 3-5 

3.1.2.3 Near-Field Geochemical Environment ............................... 3-5

v
CONTENTS 

Section Page 

3.1.3 W P Degradation ................................................ 3-9 

3.1.4 Releases from W P .............................................. 3-11 

3.1.4.1 Cladding Degradation ........................................... 3-11 

3.1.4.2 SF Dissolution and Mobilization .................................. 3-11 

3.1.4.3 Transport in the EBS ........................................... 3-14 

3.1.5 UZ Transport ................................................. 3-14 

3.1.6 SZ Flow and Transport .......................................... 3-19 

3.1.7 Dose to the Receptor Group ...................................... 3-19 

3.2 RESULTS FROM THE MEAN VALUE DATA SET ........................ 3-20 

3.2.1 10,000-Year Releases and Dose ................................... 3-23 

3.2.2 100,000-Year Releases and Dose .................................. 3-28 

3.3 MULTIPLE-REALIZATION ANALYSIS ................................. 3-35 

3.3.1 UZ Flow ..................................................... 3-36 

3.3.2 Near-Field Environment ......................................... 3-4 1 

3.3.3 W P Degradation ............................................... 3-41 

3.3.4 W P Release ................................................... 3-4 1 

3.3.5 UZ Transport ................................................. 3-4 8 

3.3.6 SZ Flow and Transport .......................................... 3-48 

3.4 COMPARISON OF DOSES FROM MEAN VALUE DATA SET AND 

MULTIPLE-REALIZATION CASES ..................................... 3-53 

3.5 ALTERNATIVE CONCEPTUAL MODELS ............................... 3-55 

3.5.1 Fuel-Dissolution Models ........................................ 3-60 

3.5.1.1 Fuel-Dissolution Model 1 ........................................ 3-60 

3.5.1.2 Fuel-Dissolution Model 3 (Natural Analog) .......................... 3-60 

3.5.1.3 Fuel-Dissolution Model 4 (Schoepite Dissolution) .................... 3-61 

3.5.2 Fuel-W etting Assumptions ....................................... 3-61 

3.5.2.1 Flowthrough Model with Fuel-Dissolution Model 2 ................... 3-61 

3.5.2.2 Flowthrough Model with Fuel-Dissolution Model 1 ................... 3-61 

3.5.2.3 Focused Flow ................................................. 3-61 

3.5.2.4 Cladding Credit with Model 1 .................................... 3-62 

3.5.2.5 Grain-Size Model with Fuel Dissolution Model 1 ..................... 3-62 

3.5.3 Transport Alternatives .......................................... 3-62 

3.5.3.1 No Retardation of Pu, Am, and Th ................................. 3-62 

3.5.3.2 No-Invert M odel ............................................... 3-62 

3.5.3.3 M atrix Diffusion ............................................... 3-62 

3.6 DISRUPTIVE EVENTS ............................................... 3-63 

3.6.1 Single-Realization Analysis of Disruptive Events ..................... 3-63 

3.6.2 Multiple-Realization Analysis of Disruptive Events ................... 3-72 

3.7 CALCULATION OF RISK ............................................. 3-72 

3.7.1 Scenarios Other Than Extrusive Igneous Activity .................... 3-72 

3.7.2 Extrusive Igneous-Activity Scenario ............................... 3-76 

3.7.3 Combining Conditional Risks into an Overall Risk .................... 3-78

vi
CONTENTS 

Section Page 

4 SYSTEM-LEVEL SENSITIVITY STUDIES ...................................... 4-1 

4.1 SENSITIVITY ANALYSIS TECHNIQUES ................................. 4-1 

4.1.1 Regression Analyses Methods ..................................... 4-3 

4.1.1.1 Scatter Plot/Single Linear Regression on One Variable .................. 4-3 

4.1.1.2 Variable Transformations and Their Attributes ........................ 4-5 

4.1.1.3 Stepwise Multiple Linear Regression ................................ 4-8 

4.1.1.4 Application of the Kolmogorov-Smirnov and Sign Tests for Determining 

Important Parameters ........................................... 4-10 

4.1.2 Differential Analysis Technique ................................... 4-10 

4.1.3 Morris Method Technique ....................................... 4-12 

4.1.4 The Fourier Amplitude Sensitivity Test Method ...................... 4-13 

4.1.5 Parameter Tree Method ......................................... 4-14 

4.2 ANALYSIS OF SENSITIVITY FROM MONTE CARLO RUNS ............... 4-16 

4.2.1 Procedure for Screening Monte Carlo Sensitivity Results ............... 4-16 

4.2.1.1 Sensitivity Results from Monte Carlo Analysis ....................... 4-17 

4.2.1.2 Parameter Sensitivity at High End of Peak Doses ..................... 4-22 

4.3 ANALYSIS OF SENSITIVITY FROM NONSTATISTICAL METHODS ........ 4-26 

4.3.1 Results from Differential Analyses ................................ 4-26 

4.3.2 Results from the Morris Method .................................. 4-28 

4.3.3 Results from the FAST Method ................................... 4-31 

4.4 RESULTS FROM THE PARAMETER TREE METHOD ..................... 4-31 

4.4.1 Parameter Trees Using Different Branching ......................... 4-36 

4.4.2 Stepwise Implementation of the Technique .......................... 4-39 

4.5 ALTERNATIVE CONCEPTUAL MODELS AND SCENARIO CASES 

STUDIED AT THE SYSTEM LEVEL ................................... 4-41 

5 SYNTHESIS OF SENSITIVITY RESULTS AND LINKAGE OF SENSITIVE 

PARAMETERS TO INTEGRATED SUBISSUES .................................. 5-1 

5.1 SELECTION OF INFLUENTIAL PARAMETERS ........................... 5-1 

5.2 COMPARING INFLUENTIAL PARAMETERS WITH 

INTEGRATED SUBISSUES ............................................ 5-3 

5.2.1 Key Integrated Subissues for 10,000-yr TPI ........................... 5-5 

5.2.2 Key Integrated Subissues for 50,000-yr TPI ........................... 5-7 

6 CONCLUSIONS ............................................................ 6-1 

6.1 BASECASE RESULTS ................................................. 6-1 

6.2 ALTERNATIVE CONCEPTUAL MODELS ................................ 6-1 

6.3 SENSITIVITY ANALYSES ............................................. 6-2 

6.4 IMPORTANCE OF RADIONUCLIDES ................................... 6-3 

6.5 INTEGRATED SUBISSUES REQUIRING FURTHER STUDIES ............... 6-4 

7 REFERENCES ............................................................. 7-1

vii
CONTENTS 

Section Page 

APPENDIX A DESIGN MATRIX FOR THE MORRIS METHOD ................... A-1 

APPENDIX B FORMALISM OF FOURIER AMPLITUDE SENSITIVITY 

TEST TECHNIQUE ......................................................... B-1 

APPENDIX C FORMALIZATION OF PARAMETER TREE SENSITIVITY 

ANALYSIS APPROACH ..................................................... C-1 

APPENDIX D DESCRIPTION OF ABBREVIATIONS USED FOR TPA VERSION 3.2 

CODE INPUT PARAMETERS ............................................... D-1 

APPENDIX E DETAILED RESULTS FROM DIFFERENTIAL ANALYSES ............ E-1

viii
FIGURES 

Figure Page 

1-1 Flowdown diagram showing the subsystems and the integrated subissues ................ 1-3 

2-1 Flow diagram for TPA Version 3.2 code .......................................... 2-2 

2-2 Conceptualization of the repository system ........................................ 2-4 

3-1 Mean annual precipitation and infiltration at the repository horizon averaged over 

all subareas and encompassing both the current and pluvial periods for the mean value 

data set .................................................................... 3-3 

3-2 Effect of the thermal perturbation on the near-field seepage rate in each subarea for the 

mean value data set ........................................................... 3-3 

3-3 Subarea average infiltration rate, flow into the drift, and amount of water entering the WP 

for the mean value data set ..................................................... 3-6 

34 WP surface temperature in each subarea for the mean value data set .................... 3-6 

3-5 WP surface relative humidity in each subarea for the mean value data set ................ 3-7 

3-6 Time history of chloride concentration computed by MULTIFLO ...................... 3-7 

3-7 WP wall thickness as a function of time for the mean value data set .................... 3-10 

3-8 Cumulative number of failed WP for the mean value data set ......................... 3-10 

3-9 Thickness of subarea stratigraphic units .......................................... 3-15 

3-10 36C1 normalized release rates from the EBS, UZ and SZ for the mean value data set ....... 3-20 

3-11 SZ streamtubes assigned to each subarea ......................................... 3-21 

3-12 Groundwater dose to an average individual as a function of time at the receptor location 

20 km (12.4 MI)downgradient of the repository, for the mean value data set in the: 

(a) 10,000-yr, and (b) 100,000-yr, time periods of interest ........................... 3-24 

3-13 Release rates in the 10,000-yr time period of interest from the: (a) EBS; (b) UZ; and (c) SZ 

for the mean value data set .................................................... 3-25 

3-14 Groundwater dose in 10,000-yr time period of interest with and without: (a) faulting; and 

(b) igneous-activity disruptive events, for the mean value data set, without 

probability weighting ......................................................... 3-27 

3-15 Release rates in 100,000 yr from the: (a) EBS, (b) UZ, and (c) SZ for the mean value 

data set ................................................................... 3-29 

3-16 237Np and 9Tc total release and releases by subarea in 100,000 yr from the: (a) EBS; (b) UZ; 

and (c) SZ for the mean value data set ........................................... 3-31 

3-17 9Tc groundwater doses, total and by subarea, in 100,000 yr, for the mean value data set ... 3-32 

3-18 Groundwater dose, total and by subarea, in: (a) 10,000 and (b) 100,000 yr, for the mean 

value data set ............................................................... 3-33 

3-19 Groundwater dose in 100,000 yr with and without: (a) faulting, and (b) igneous activity 

disruptive events for the mean value data set, without probability weighting ............ 3-34 

3-20 Groundwater dose in: (a) 10,000, and (b) 100,000 yr, including the average dose, for 

250 realizations ... .. ....................................................... 3-37 

3-21 Mean, maximum, and minimum infiltration rates in the UZ for each subarea ............ 3-38 

3-22 Cumulative release rates of '9Tc and 3Np from the EBS plotted with the maximum flow 

rate of water into the repository, for 250 realizations ................................ 3-39

ix
FIGURES (cont'd) 

Figure Page 

3-23 Peak groundwater dose in: (a) 10,000, and (b) 100,000 yr, plotted with the maximum flow 

rate of water into the repository, for 250 realizations ................................ 3-40 

3-24 WP surface temperature: (a) averaged over the repository and for each subarea; and (b) in 

subarea 1, the average, minimum, and maximum values, for 250 realizations ............ 3-42 

3-25 Fraction of WPs failed by corrosion for each of the 250 realizations, and the average fraction 

of failed WPs ........................................................ 3-43 

3-26 Average WP failure time by corrosion plotted with: (a) peak groundwater dose; and (b) time 

of the peak groundwater dose, for 250 realizations ................................. 3-44 

3-27 Peak groundwater dose, and the: (a) 99Tc, and (b) 237

Np, peak release rates from subarea 1, 

for 250 realizations .......................................................... 3-45 

3-28 Peak release rates from the EBS and time of the peak release for: (a) 99Tc, and (b) 237

Np, in 

250 realizations ............................................................. 3-46 

3-29 9Tc release rates from the EBS over: (a) 10,000, and (b) 100,000 yr, including the average 

release rate, in subarea 1, for 250 realizations ..................................... 3-47 

3-30 Cumulative releases from the EBS, the UZ, and the SZ, together with the initial inventory 

in the repository ............................................................ 3-4 9 

3-31 UZ average release rates of 99Tc, 237

Np, and 239pu, for 250 realizations .................. 3-49 

3-32 UZ release rates of 99Tc over: (a) 10,000, and (b) 100,000 yr, including the average release 

rate, in subarea 1, for 250 realizations ........................................... 3-50 

3-33 CCDF of UZ groundwater travel times, for 250 realizations .......................... 3-51 

3-34 SZ average release rates of 99

Tc, 2 7Np, and 2 9

Pu, for 250 realizations .................. 3-51 

3-35 SZ release rates of 9Tc over: (a) 10,000; and (b) 100,000 yr, including the average release 

rate, in subarea 1, for 250 realizations ........................................... 3-52 

3-36 CCDF of UZ GWTTs, for 250 realizations ....................................... 3-54 

3-37 Peak groundwater dose of: (a) 9Tc; and (b) 237

Np; and time of the peak dose, for 

250 realizations ............................................................. 3-56 

3-38 Percent each radionuclide contributes to the peak groundwater dose, for 250 realizations... 3-57 

3-39 Average groundwater dose in (a) 10,000, and (b) 100,000 yr, for each nuclide, including the 

total dose, for 250 realizations ................................................. 3-58 

3-40 Peak groundwater dose and the volume of well water pumped, for 250 realizations ........ 3-59 

3-41 Groundwater dose from the basecase and the fuel-dissolution alternative conceptual models, 

for: (a) 10,000, and (b) 100,000 yr, using the mean value data set ..................... 3-64 

3-42 Groundwater dose from the basecase and the fuel-wetting alternative conceptual models, 

for: (a) 10,000; and (b) 100,000 yr, using the mean value data set ..................... 3-65 

3-43 Groundwater dose from the basecase and the transport alternative conceptual models, for: 

(a) 10,000; and (b) 100,000 yr, using the mean value data set ......................... 3-66 

344 Seismic hazard curve comprises ground accelerations and recurrence times used to 

determine the time of seismic events ............................................ 3-67 

3-45 Vertical extent of rockfall associated with the 5 rock types and 10 seismic events defined 

by the seismic hazard curve ................................................... 3-67 

3-46 Joint spacing of the 5 rock types and 10 seismic events .............................. 3-68 

3-47 Fraction of the area with ground motion for each of the 10 seismic events defined by the 

seismic hazard curve ......................................................... 3-68

X
FIGURES (cont'd) 

Figure Page 

3-48 Groundwater dose in 10,000 and 100,000 yr with and without: (a) faulting, and (b) igneous 

activity, in 10,000 yr, for 250 realizations ........................................ 3-73 

3-49 Mean dose arising from extrusive igneous-activity shown with various times for the volcanic 

event in 400 realizations ...................................................... 3-79 

3-50 Contribution of extrusive igneous-activity to the total dose, weighted by an annual 

probability for the volcanic event of 10 . ......................................... 3-79 

4-1 A diagram illustrating the use of the Monte Carlo method in performance assessment ...... 4-2 

4-2 Example of a scatter plot/single linear regression ................................... 4-4 

4-3 Normal probability plot of dose for 10,000 yr in the 1,000-vector basecase ............... 4-7 

4-4 Figure showing a close fit to normal distribution after using p = 0.1 transforms ........... 4-7 

4-5 General parameter tree ....................................................... 4-15 

4-6 Plot of the residual sum of squares versus number of parameters included in the fit for 

the basecase, with a time period of interest of 10,000 yr ............................. 4-23 

4-7 Plot of the residual sum of squares versus number of parameters included in the fit for the 

basecase with a time period of interest of 50,000 yr ................................ 4-23 

4-8 Results from the Morris method from the basecase with a time period of interest 

of 10,000 yr ................................................................ 4-32 

4-9 Results from the Morris method from the basecase with a time period of interest 

of 50,000 yr ................................................................ 4-33 

4-10 Median-based parameter tree describing the technique for examining system sensitivity to 

groups of parameters ......................................................... 4-35 

4-11 Mean-based parameter tree describing the technique for examining system sensitivity to 

groups of parameters ......................................................... 4-37 

4-12 Mean-percentile-based parameter tree describing the technique for examining system 

sensitivity to groups of parameters; input parameters divided based on their median values, 

and output variable divided based on its 90' percentile value from all 4000 realizations .... 4-38 

4-13 Tree developed using a stepwise implementation of the technique, based on the 

importance factor ........................................................... 4-40 

4-14 Bar chart showing the effects of alternative conceptual models at 10,000 yr ............. 4-43 

4-15 Bar chart showing the effects of alternative conceptual models at 50,000 yr ............. 4-43

xi
TABLES 

Table Page 

3-1 Mean values and sampled distributions of parameters for infiltration calculations .......... 3-4 

3-2 Mean values and sampled distributions of parameters for determining repository-scale and 

drift-scale thermo-hydrology ................................................... 3-4 

3-3 Parameters for determining the corrosion failure of WP .............................. 3-8 

3-4 Parameters used in determining radionuclide releases from the engineered barrier system .. 3-12 

3-5 Distributions of solubility limits ................................................ 3-13 

3-6 Radionuclide decay chains .................................................... 3-13 

3-7 Initial inventory, gap inventory, and half-life of radionuclides in spent nuclear fuel for 

groundwater release ......................................................... 3-14 

3-8 Mean values and sampled distributions of sorption coefficient, Kd (m3

/kg), parameters .... 3-16 

3-9 Parameter values used for SZ flow and radionuclide transport in TPA .................. 3-22 

3-10 Biosphere dose conversion factors for groundwater at the 20-km receptor location ........ 3-23 

3-11 Correlated parameters and correlation coefficients for the multiple realizations .......... 3-38 

3-12 Average, maximum, and minimum SZ groundwater travel times, by subarea and average, 

for all subareas, from 250 realizations ........................................... 3-53 

3-13 Primary radionuclides contributing to peak expected dose ........................... 3-54 

3-14 Parameters used in determining seismic failure of WPs ............................. 3-69 

3-15 Faulting disruptive event parameters ............................................. 3-69 

3-16 Igneous activity parameters ................................................... 3-70 

3-17 Initial inventory and half-life of additional radionuclides considered for ground-surface 

release, but not for groundwater release .......................................... 3-71 

3-18 Parameters used in computing ash and radionuclide removal from the ground surface ..... 3-74 

3-19 Biosphere dose conversion factors of all 43 nuclides for ground surface at the 20-km 

receptor location . ........................................................... 3-75 

4-1 Summary of regression and screening for basecase, 10,000-yr time period of interest ...... 4-18 

4-2 Summary of regression and screening for basecase, 50,000-yr time period of interest ...... 4-20 

4-3 Standardized sensitivities for basecase, 10,000-yr time period of interest ................ 4-24 

4-4 Standardized sensitivities for basecase, 50,000-yr time period of interest ................ 4-24 

4-5 t-test on means of high- and low-dose categories for 50,000-yr time period of interest ..... 4-25 

4-6 Top 10 influential parameters (standardized) from statistical and nonstatistical analyses, for 

10,000-yr time period of interest ............................................... 4-29 

4-7 Top 10 influential parameters from statistical andnonstatistical analyses, for 50,000-yrtime 

period of interest ............................................................ 4-30 

4-8 Most influential parameters from differential analysis for disruptive event scenarios ...... 4-31 

4-9 Statistical information about the 4000 realizations ................................. 4-36 

4-10 Sensitivity coefficients calculated for various parameter trees ........................ 4-39 

5-1 Influential parameters for 10,000-yr time period of interest, from sensitivity analysis studies . 5-2 

5-2 Influential parameters for 50,000-yr time period of interest, from sensitivity analysis studies . 5-2

xiii
TABLES (cont'd) 

Table Page 

5-3 A crosswalk between the integrated subissues, alternative conceptual models, and the 

influential param eters ......................................................... 5-4

xiv
EXECUTIVE SUMMARY 

To review and quantitatively evaluate the safety case in a potential license application by the 

U.S. Department of Energy (DOE) for the proposed Yucca Mountain (YM) repository, the U.S. Nuclear 

Regulatory Commission (NRC), with technical assistance from the Center for Nuclear Waste Regulatory 

Analyses (CNWRA), developed a Total-system Performance Assessment (TPA) code. To date, the NRC staff 

has written three reports on performance assessment (PA) for the proposed YM repository. The first, referred 

to as iterative performance assessment (IPA) Phase 1 (Codell, et al., 1992), assembled and demonstrated the 

NRC assessment methodology. The second NRC Total System Performance Assessment (TSPA), IPA Phase 

2 (Wescott, et al., 1995), used the TPA Version 2.0 code to investigate the features, events, and processes 

influencing isolation performance of the proposed YM repository. Information obtained in these IPA analyses 

was used in NRC reviews of early DOE TSPAs for YM. The third NRC TSPA (U.S. Nuclear Regulatory 

Commission, 1999) used the TPA Version 3.1 code (Mohanty and McCartin, 1998) to determine whether 

the NRC would be able to quantitatively evaluate the soundness of the conclusions reached by the DOE in 

its viability assessment (VA). Revisions were made to the TPA code, leading to the development of the most 

recent version of the code, TPA Version 3.2 code (Mohanty and McCartin, 1998), which was used in 

evaluating the TSPA-VA. This report documents the most recent system- and process-level sensitivity and 

uncertainty analyses performed by the NRC and the CNWRA in conjunction with the review of the 

TSPA-VA. This report presents: 

A brief description of the conceptual models implemented in the TPA code; 

An in-depth discussion ofbasecase results for a single realization, using the mean parameter 

values, as well as for a full Monte Carlo run; deterministic results from alternative 

conceptual models; deterministic results from disruptive scenarios; and a proposed method 

for combining basecase and disruptive scenario results; 

The results of system-level sensitivity and uncertainty analyses, using statistical and 

nonstatistical techniques to determine the parameters that have the most influence on 

repository performance; 

The results from the comparative studies of alternative conceptual models and combinations 

of models explicitly incorporated in the TPA Version 3.2 code or that can be mimicked, 

through adjustment of input parameters, to determine model and parameter uncertainties; 

An estimation of the relative importance of the integrated subissues, to focus staff effort; 

and 

A documentation of improvements in NRC staff capabilities in PA, based on the insights 

gained from process- and system-level results and sensitivity analyses. 

Most calculations were made using the basecase data set in which 246 out of 838 parameters were sampled 

from specified ranges and distributions that represent data uncertainty and variability. To develop a better 

understanding of the trends of the outputs at a process level, results from a single realization (using the mean 

value data set) were also analyzed. Calculations to date, using the basecase data set (the basecase is defined 

as the undisturbed scenario along with the effects of rockfall, from seismicity with multiple realizations) 

indicate peak expected doses of 3 x 10' mSv/yr (0.003 mrem/yr) in 10,000 yr (the proposed compliance

xv
period) and 4 mrem/yr in 100,000 yr1. For a time period of interest (TPI) of 10,000 yr, primarily six 

radionuclides (

237

Np, 1291, 9 9

Tc, 2 34

U, 36

C1, and 79Se) contributed to the peak expected dose. For a TPI of 

100,000 yr, four radionuclides (

237

Np, 234

U, 99Tc, and 1291) were the primary contributors to peak expected 

dose, with 92 percent of the contribution coming solely from 237Np. Igneous activity is the primary 

contributor to the peak expected dose during the 10,000-yr TPI, estimated to be 0.006 mSv/yr (0.6 mrem/yr). 

The faulting disruptive event is a negligible contributor to the peak expected dose. 

The sensitivity and uncertainty analyses were conducted using numerous (several thousands for each analysis 

method) TPA code runs. The sensitivity and uncertainty of repository performance to specific parameters 

were evaluated using a number of different statistical tests. The statistical tests examined the sensitivity of 

repository performance to individual parameters in an effort to identify, as comprehensively as possible, 

those parameters most important for understanding repository performance. This helped to focus the review 

of the VA and prepare for the forthcoming review of the TSPA-site recommendation (SR). Sensitivity 

analyses used peak dose, expressed as total effective dose equivalent, for each TPA run as the performance 

measure. The use of peak dose eliminated the time dependency of the performance measure, thus simplifying 

the analyses. Alternative conceptual model studies used case-by-case analyses, with peak expected dose from 

multiple realizations as the performance measure. 

This report identifies and presents influential parameters for twoTPIs--10,000 and 50,000 yr. An influential 

parameter is one that either drives uncertainty in performance, or one to which the estimated performance 

is sensitive. For both TPIs, several parameters were found most influential for the basecase. The influential 

parameters include: 

Areal fraction of the repository wetted by water infiltrating into the repository; 

The fraction of water infiltrating into the repository from the unsaturated zone above the 

repository that will enter the waste package (WP) and contribute to the release 

of radionuclides; 

Well-pumping rate at the 20-kin (12.3 mi) receptor group location; 

Alluvium sorption properties (i.e., RdS) for 99Tc and 1291; 

Present-day areal average mean annual infiltration above the repository. 

In addition, the parameters influential for the 10,000-yr TPI, but not influential for the 50,000 yr TPI, are: 

Initially defective fraction of WPs; and 

A flow-focusing factor that expresses the flow reaching a wetted WP. 

The only parameters significant for the 50,000-yr TPI, but not influential for the 10,000 yr TPI, are the 

alluvium Rds for 234

U and 237

Np. 

'The time period of interest of 100,000 yr used in presenting the basecase results is different from that used in the sensitivity 

analyses (10,000 and 50,000 yr), primarily because the basecase results were also used in reviewing the DOE TSPA-VA results. 

which extended to 100,000 yr and beyond.

xvi
The influential parameters were used to focus the review of the VA and were also traced back to the 

integrated subissues used by the NRC to focus its high-level waste program on aspects important to 

repository performance (U.S. Nuclear Regulatory Commission, 1998). Nine out of 14 integrated subissues 

have at least one influential parameter (including the integrated subissues related to disruptive scenarios), 

based on the results of the TPA Version 3.2 code. It should be noted that the staff has not yet developed 

appropriate techniques for conducting sensitivity analyses of results from the disruptive scenarios with 

appropriate consideration of probability weighting. Therefore, the sensitivity analyses results from disruptive 

scenarios are used as such (i.e., without probability weighting) for crosswalking the influential parameters 

with the integrated subissues. The integrated subissues deserve careful examination because the current 

models delay any significant radionuclide releases past the 1 0,000-yr TPI. The delay is primarily attributable 

to: (i) corrosion-resistant material of the inner overpack pushing the WP failure time beyond 10,000 yr; 

(ii) thermal reflux delaying the onset of flow into the repositor; (iii) WP filling time delaying the radionuclide 

release time by hundreds to thousands of years; and (iv) radionuclide sorption in the alluvium causing 

significant delay in the arrival time of radionuclides. 

This TSPA serves to aid the NRC staff in focusing its review of DOE TSPAs, especially those for the VA 

and SR, on those models and parameters that could significantly influence the estimated system performance. 

It should be noted that the results presented in the following chapters are based on numerous simplifying 

assumptions and use only limited site-specific data. Consequently, the numerical results should not be taken 

as representative of the performance of the proposed repository at Yucca Mountain, Nevada. Conclusions 

drawn from the analyses presented in this report may change as the models and assumptions are updated 

based on revised design, ongoing site characterization, recommendations from reviewers and experts, new 

regulatory requirements, and improved model conceptualization and data interpretation by staff. The analysis 

also contains uncertainties regarding conceptual models for consequences and scenarios. Finally, this report 

should be considered as an interim demonstration of some of the methods that the NRC staff has developed 

to review a PA submitted by the DOE as part of any potential license application. Thus, at the conclusion 

of some future TSPA effort, instructions to the NRC staffwill be developed and documented regarding which 

specific compliance determination methods will be used to review a DOE PA. Neither the manner in which 

these analyses were conducted nor the assumptions and approaches used should be construed to express the 

views, preferences, or positions of the NRC staff regarding the nature of site-specific regulations for YM.

xvii
ACKNOWLEDGMENTS 

This report was prepared to document work performed by the Center for Nuclear Waste Regulatory Analyses 

(CNWRA) for the Nuclear Regulatory Commission (NRC) under Contract No. NRC-02-97-009. The 

activities reported here were performed on behalf of the NRC Office of Nuclear Material Safety and 

Safeguards, Division of Waste Management. The report is an independent product of the CNWRA and does 

not necessarily reflect the views or regulatory position of the NRC. 

The authors wish to thank B. Sagar (CNWRA) and C. Lui (NRC) for their technical reviews and W. Patrick 

(CNWRA) and K. McConnell (NRC) for their programmatic reviews. Technical support provided by R. Rice 

(consultant) at various stages of this report is gratefully acknowledged. The effort of J. Firth (NRC), program 

element manager for the Total System Performance Assessment and Integration (TSPA&I) key technical 

issue, and C. Lui (NRC) in coordinating the multidisciplinary discussions leading to the identification of 

important integrated subissues is also recognized. Thanks to R. Janetzke for code quality assurance (QA), 

and debugging the code when needed, to 0. Pensado for observing during the analyses of Total System 

Performance Assessment-Viability Assessment (TSPA-VA) results and providing insights into Total-system 

Performance Assessment code outputs behavior, and to M. Smith for helping to regenerate several output 

tables. Thanks are also expressed to K. Poor of Portage Environmental, Inc. for an informal technical review 

of the document; J.M. Menchaca, Southwest Research Institute (SwRI), for assistance in debugging and 

testing the computation of several sensitivity analysis methods; M. Muller (SwRI) for help in generating 

some of the outputs and plotting results. Some staff also tested the initial version of the code. Their 

contributions are acknowledged and much appreciated. Thanks are also expressed to B. Long, A. Woods, 

C. Gray and C. Cudd for editorial reviews and C. Weaver, C. Garcia and A. Ramos for their 

secretarial support. 

QUALITY OF DATA, ANALYSES, AND CODE DEVELOPMENT 

DATA: CNWRA-generated data contained in this report meet QA requirements described in the CNWRA 

QA Manual. Data from other sources are freely used. The respective sources of non-CNWRA data should 

be consulted for determining levels of QA. 

ANALYSES AND CODES: The TPA Version 3.2,3.2.3, and 3.2MM codes have been developed following 

the procedures described in the CNWRA Technical Operating Procedure (TOP), TOP-018, which 

implements the QA requirements contained in the CNWRA QA Manual. The TPA Version 3.2MM code 

reflects a minor modification to the Version 3.2 code for use in conjunction with the Morris method. Codes 

used in conducting the Morris method and Fourier Amplitude Sensitivity Test have also been developed 

following procedures described in TOP-018.

xviii
1 INTRODUCTION 

In accordance with the provisions of the Nuclear Waste Policy Act (NWPA) of 1982, as amended, and the 

Energy Policy Act (EnPA) of 1992, the U.S. Nuclear Regulatory Commission (NRC) is responsible for 

evaluating the license application for a proposed geologic repository constructed for emplacement of high

level nuclear waste (HLW) [i.e., commercial spent fuel (SF); several types of U.S. Department of Energy 

(DOE) and U.S. Navy SF; and vitrified HLW] at Yucca Mountain (YM), Nevada. In support and preparation 

of its regulatory review activities outlined in the NWPA and EnPA, the NRC staff is conducting detailed 

technical performance assessments (PAs) to understand and identify the potentially important isolation 

characteristics and capabilities of the proposed repository system at the YM site, based on the available 

information. 

This PA activity, which is part of an ongoing process at the NRC to prepare for the review of a potential 

DOE license application for the proposed HLW disposal facility at YM, includes regular interactions 

between the NRC and the DOE on the topic of PA. For example, NRC staff comments on model abstraction 

related to the Total System Performance Assessment-Viability Assessment (TSPA-VA) were relayed to the 

DOE in a letter to Dr. S. Brocoum dated July 6, 1998 (Bell, 1998). Furthermore, the DOE, NRC, and various 

stakeholders regularly interact on the topic of PA through technical exchanges. 

As part of these Iterative Performance Assessment (IPA) activities, the NRC and its support contractor, the 

Center for Nuclear Waste Regulatory Analyses (CNWRA), are usingthe enhanced Total-system Performance 

Assessment (TPA) computer code. The TPA code, which evolves with each IPA phase, is designed to 

simulate the behavior of the geologic repository, taking into account the essential characteristics of the 

natural and engineered barrier systems (EBS), and changes in knowledge about the geologic setting and 

design. This document presents system-level sensitivity and uncertainty analyses using the latest version of 

the TPA code, Version 3.2. 

The NRC previously conducted analyses of repository performance (Codell, et al., 1992; Wescott, et al., 

1995). For the latest iteration, Version 3.2 of the TPA code was developed as a more general and versatile 

computer code that more readily can accommodate changes to the design of the proposed YM repository. 

This version: (i) accommodates the repository design outlined in the TSPA-VA (U.S. Department of Energy, 

1998) [e.g., repository layout and waste package (WP) emplacement and design]; (ii) quantifies total system 

performance related to the proposed compliance performance measure [the peak expected dose, expressed 

as total effective dose equivalent (TEDE), in the time period of interest (TPI)] expected in the forthcoming 

U.S. Environmental Protection Agency (EPA) standard and as proposed in the draft NRC site-specific 

regulations (Nuclear Regulatory Commission, 1999a); and (iii) includes recent site data and improved 

conceptual models. In addition, because approaches to estimate the performance of geologic repositories and 

site and repository design data continue to evolve, the TPA Version 3.2 code was developed with the 

flexibility to perform alternative calculations. Some of the examples include: 

* Evaluate alternative repository and design features; 

• Analyze the effect of different areal mass loadings; 

° Assess the significance of various disruptive scenario classes; 

° Evaluate radionuclide dilution in the saturated zone (SZ); 

* Compute the dose as a function of time for a 10,000-yr or longer TPI; and 

* Evaluate alternative SF dissolution models.

1-1
Introduction

1.1 BACKGROUND 

The PAs for geologic repositories are based on conceptual models of physical processes (embodied 

in computer codes) and parameters derived from field and laboratory data or expert elicitation. Because of 

the variability and sparsity of measured data and the underlying uncertainty involved with modeling physical 

processes for many thousands of years, the results of any PA are uncertain. Therefore, an important aspect 

of conducting a PA is quantifying the sensitivity of the results to, and the uncertainty associated with, the 

input parameters. An analysis of PA code output sensitivity and uncertainty will provide information 

delineating which input parameters most affect the model results. A better understanding of the parameters 

that have the most influence on model results can be used to improve the code and build confidence in the 

numerical results produced by the code. Likewise, identification of the most influential parameters and those 

parameters that drive uncertainty provides a means of comparing and evaluating different PA models and 

indicates where future design, site characterization, and analysis activities should be focused. 

The staff developed a systematic approach to reviewing the DOE TSPAs. As currently envisioned, 

the approach is hierarchical, as illustrated in Figure 1-1. The focal point is the overall repository system 

where the performance measure is anticipated to be the expected annual dose to the average member of the 

critical group during the performance TPI. To facilitate review of the DOE TSPAs, staff will examine the 

contribution to performance from each of three repository subsystems-engineered, geosphere, and 

biosphere-as shown in the second tier of Figure 1-1. Each of these subsystems is further subdivided into 

discrete components of the respective subsystems-engineered barriers that make up the engineered system; 

unsaturated zone (UZ) flow and transport, SZ flow and transport, and direct release to the biosphere; and the 

dose calculation for the biosphere. This characterization of components is not strictly based on the physical 

aspects of the system but stems from the perspective of dose or risk calculations for total system performance 

evaluation. Recognizing there are many different ways of dividing the overall system into smaller and 

analyzable components, this particular division is primarily based on the natural progress of radionuclide 

release and transport to a receptor group at the YM site and takes advantage of the results of past NRC IPA 

and reviews of the DOE TSPAs. At the base of the hierarchy are the key elements of the repository system 

that need to be appropriately abstracted into a TSPA. These key elements of subsystem abstraction (KESAs), 

in general, are the integrated processes, features, and events that could affect system performance. In 

conformance with recently proposed changes to the structure of the NRC program for resolving issues related 

to the HLW repository program, the KESAs are now known as the integrated subissues. 

1.1.1 Previous IPA Analyses 

To date, the NRC staff has written three reports on PA for the proposed YM repository. The first, 

referred to as IPA Phase 1 (Codell, et al., 1992), assembled and demonstrated the NRC assessment 

methodology. IPA Phase 1 examined the sensitivity and uncertainty in radionuclide releases to the accessible 

environment for a geologic repository in unsaturated tuff. The second NRC TSPA, IPA Phase 2 (Wescott, 

et al., 1995), was performed using the TPA Version 2.0 code to investigate the features, events, and 

processes influencing isolation performance of the proposed YM repository. Information obtained in these 

IPA analyses was used in NRC reviews of early DOE TSPAs for YM. The overall performance measures 

for the geologic repository used in IPA Phase 2 were cumulative total releases of radionuclides (normalized 

release) to the accessible environment and radiation dose (effective dose equivalent) to the exposed 

population. The third NRC TSPA (U.S. Nuclear Regulatory Commission, 1999b) was performed using the

1-2
Total 

System 

Subsystems 

Components 

of Subsystems

Integrated 

Subissues

Waste package degradation 

(temperature, humidity, and .!emist) 

Mechanical disruption of waste packages 

(seismicity, faulting, 

rockfafU, and dike intrusion 

Quantity and chemistry 

of water contacting 

waste packages and 

waste form 

Radionuclide release 

rates and solubility limits

'-9 

0

Figure 1-1. Flowdown diagram showing the subsystems and the integrated subissues.

I

I

I I II I

I

I
Introduction

TPA Version 3.1 code, to determine whether the NRC would be able to quantitatively evaluate the 

conclusions reached by the DOE in its VA. Subsequent to developing and testing the TPA Version 3.1 code, 

detailed sensitivity and uncertainty analyses were undertaken (U.S. Nuclear Regulatory Commission, 1999b) 

that indicated the need for further refinement of the TPA code before its use to evaluate the DOE TSPA-VA 

(U.S.Department of Energy, 1998). Revisions were made to the TPA code leading to the development of the 

current TPA Version 3.2 code, which was used in the evaluation of the TSPA-VA. 

In addition, the TSPA analyses are used to better focus NRC activities on those factors of greatest 

importance to repository performance. The draft site-specific rule developed by the NRC for the proposed 

YM repository is a risk-informed, performance-based rule. Therefore, the NRC review of a potential license 

application to build and operate a deep geologic repository at YM necessarily will focus on those physical 

aspects of the repository system of greatest importance to radiological safety. The results from this study, 

in part, will be used to focus and direct the review strategy outlined by the NRC in its Yucca Mountain 

Review Plan (YMRP). 

1.1.2 IPA Phase 1 Sensitivity and Uncertainty Analyses 

Four sensitivity or uncertainty analyses were performed for IPA Phase 1 (Codell, et al., 1992): 

(i) demonstration of the effect of individual parameters on the resultant complementary cumulative 

distribution function (CCDF) for cumulative release to the accessible environment; (ii) use of stepwise linear 

regression to estimate sensitivity ofkey parameters in the consequence models; (iii) determination of relative 

importance of individual radionuclides in the waste; and (iv) sensitivity of CCDFs to performance of the 

natural and engineered barriers. The sensitivity and uncertainty analyses considered only groundwater 

pathway releases, not those from human intrusion or airborne release through igneous activity. Gaseous 

release of radionuclides was not part of the IPA Phase 1 TSPA results, but was included as an auxiliary 

analysis. 

Although IPA Phase I conducted full sensitivity and uncertainty analyses for the groundwater 

pathway, only CCDFs for cumulative release were generated for the scenario cases (basecase, basecase with 

human intrusion, and basecase with pluvial conditions with and without human intrusion). Cumulative 

release refers to the sum of releases of all radionuclides during the TPI. The CCDFs reflected the uncertainty 

in the sampled parameters propagated through the analysis. Peak dose was not calculated as a performance 

measure for the IPA Phase 1 study. 

1.1.3 WPA Phase 2 Sensitivity and Uncertainty Analyses 

In IPA Phase 2 (Wescott, et al., 1995), model results were evaluated to develop regression equations 

describing TSPA model output and to analyze input parameter sensitivity. Techniques used to develop a 

regression equation that emulated the TPA model included transformation of data (Iman and Conover, 1979; 

Seitz, et al., 1991); test for heteroscedasity (residual variation-Draper and Smith, 1981; Bowen and Bennett, 

1988; Sen and Srivastava, 1990); and Mallows' Cp statistic (Sen and Srivastava, 1990). In addition to 

techniques used in previous PA work (e.g., the stepwise linear regression), several techniques were evaluated 

to determine parameter importance and sensitivity, including Kolmogorov-Smirnov (K-S) and Signs tests 

(Bowen and Bennett, 1988) and differential analysis (Helton, et al., 1991). 

Phase 2 IPA included a number of disruptive scenarios. These scenarios included igneous activity, 

seismicity, faulting, climate change, and exploratory drilling. Sensitivity and uncertainty analyses were

1-4
Introduction

conducted on the undisturbed case as well as on the other scenario cases. These analyses were conducted 

with radionuclide release to the accessible environment and integrated population dose as the output 

variables, in contrast to peak expected dose described in this report. 

1.1.4 TPA Version 3.1 Code Sensitivity and Uncertainty Analyses 

For the TPA Version 3.1 code (U.S. Nuclear Regulatory Commission, 1999b), a variety of analytical 

procedures was implemented to assess the sensitivity of the estimated peak dose caused by variations in the 

values of model parameters as well as by changes resulting from use of alternative conceptual models. Scaled 

sensitivity coefficients were obtained by univariate and stepwise, multiple linear regression, and by standard 

differential analysis. To make linear regression models as accurate as possible, the dependent (peak dose) 

and independent (sample parameter values) variables were transformed using four methods: 

(i) normalization, in which the variable is divided by its mean; (ii) standardization, in which the difference 

between the variable and its mean is divided by the standard deviation of the variable; (iii) rank 

transformation, in which the value of the variable is replaced by its numerical rank; and (iv) logarithmic 

transformation, in which a multiplicative model is converted to an additive model. The statistical significance 

of the scaled sensitivity coefficients obtained by stepwise regression was determined using Student's 

t-statistic. The importance or influence of each parameter was ranked by the order in which the stepwise 

procedure selected the parameter for inclusion as an explanatory variable in the regression equation and by 

the use of K-S and Sign tests. 

Sensitivity coefficients were calculated for both 10,000- and 50,000-yr TPIs and for waste canisters 

constructed with an inner corrosion-resistant layer of either Alloy 625 or Alloy C-22, leading to the 

identification of four distinct sets of important parameters. The effects of employing alternative conceptual 

models were also investigated for a number ofthe repository subsystems. Alternative conceptual models that 

were considered include: (i) backfilling of the repository; (ii) matrix diffusion in the rock matrix; (iii) credit 

for protection of the fuel provided by zircaloy cladding, (iv) focusing the flow of water to a smaller number 

of WPs; (v) use of the flowthrough model for SF dissolution and transport; (vi) radionuclide release rates 

based on natural analogs for SF; (vii) no credit for sorption of radionuclides; and (viii) instantaneous failure 

of all WPs. 

Based on the results of the sensitivity and uncertainty analyses, preliminary conclusions were drawn 

about the relative importance of the integrated subissues or KESAs. For the 10,000-yr TPI, the most 

important integrated subissues are those for WP corrosion and the quantity and chemistry of water contacting 

the WPs. When Alloy C-22 is used, corrosion of the WPs is minimal during the 10,000-yr TPI, and 

mechanical disruption of the WPs is the most important integrated subissue. For the 50,000-yr TPI, the 

integrated subissues related to dilution ofradionuclides in groundwater through well pumping and retardation 

in water production zones and alluvium are of increased importance. 

1.2 PURPOSE OF CURRENT ANALYSIS 

Similar to the sensitivity and uncertainty analyses conducted for previous IPA phases and the 

TPA Version 3.1 code, multiple sensitivity and uncertainty analyses have been conducted using the 

TPA Version 3.2 code. Sensitivity is defined as the relative change in output for a unit change of input, and 

uncertainty is the comparative change in overall output range because of input value uncertainty. Sensitivity 

and uncertainty analyses described in this report have been used to:

1-5
Introduction

Focus staff reviews of the DOE TSPA-VA on those factors most significant to 

total-system performance. 

Determine the input parameters in the TPA Version 3.2 code that are most influential to the 

estimated peak dose for the TPI at the receptor location by using a number of techniques. 

Although process-level sensitivity and uncertainty analyses have been conducted with the 

TPA code to determine the parameters most important in a given key technical issue (KTI) 

(e.g., unsaturated and saturated flow under isothermal conditions, igneous activity), this 

report summarizes analyses conducted to determine the most influential parameters at the 

total system level. 

Estimate the relative importance of the integrated subissues or KESAs. 

Continue improving staff capabilities, including improving the TPA code, for conducting 

independent evaluation of future DOE TSPAs for the site recommendation and license 

application for the proposed YM repository. 

Since the release of the TPA Version 3.1.4 code, which was used in the TPA Version 3.1 code 

sensitivity analyses (U.S. Nuclear Regulatory Commission, 1999b), several major improvements were 

incorporated into the TPA code and associated input data sets that may have a significant effect on the 

sensitivity analysis results. Most of these changes were based on new information provided by the DOE after 

the completion of the TPA Version 3.1.4 code. For example, the DOE decision to replace Alloy 625 with 

Alloy C-22 as the material for the inner overpack in WP required substantial changes to the TPA model 

abstraction and its associated model parameters. The second basis for improvements resulted from experience 

gained from the process- and system-level sensitivity analyses using TPA Versions 3.1.1-3.1.4. Specific 

changes that were made to the TPA Version 3.1.4 code to obtain the new TPA Version 3.2 code include: 

Accounting for the effect of secondary mineral formation on SF dissolution; 

Considering the effects of a concrete tunnel invert on the transport of radionuclides; 

Introducing correlation between sampled radionuclide sorption parameters for chemically 

similar species to reflect realization-to-realization homogeneity of water chemistry; 

Assessing the significance of the radionuclide inventory between the fuel pellet and the 

cladding (gap inventory); 

Refining the model used to estimate mechanical failure of the WP from seismically 

induced rockfall; 

Allowing the user to specify the volume of SF wetted (i.e., bathtub height) so that alternate 

WP failure modes can be better modeled; and 

Revising the code to implement parameter value distributions that reflect the most 

current data.

1-6
Introduction

1.3 REPORT ORGANIZATION 

This report documents the most recent system-level sensitivity and uncertainty analyses performed 

by the NRC and the CNWRA that were conducted using the TPA Version 3.2 code. Chapter 2 provides a 

brief description of the TPA Version 3.2 code. Chapter 3 presents an in-depth discussion of basecase results 

for a single realization using the mean parameter values, as well as for a full Monte Carlo run, deterministic 

results from alternative conceptual models, deterministic results from disruptive scenarios, and a proposed 

method for combining basecase and disruptive scenario results. 

Chapter 4 describes the system-level sensitivity studies, which were conducted in two parts. A set 

of alternative conceptual models and disruptive scenario cases were compared to evaluate the relative 

importance of specific components and assumptions used in the model. Evaluating the influence of individual 

components of the model in this way, where the full set of parameter values is used and a more 

comprehensive range of repository behavior is modeled, allows the relative importance of the components 

to be investigated. The sensitivity and uncertainty of repository performance to specific parameters were 

evaluated using a number of different statistical tests because no single test is completely comprehensive. 

The use of numerous statistical tests (described in this chapter and Appendices A-C and E) to examine the 

sensitivity of repository performance to individual parameters is intended to identify, as comprehensively 

as possible, those parameters most important for understanding repository performance. 

Evaluation of important parameters based on the system-level sensitivity studies is provided in 

Chapter 5. Here, the important parameters and the alternative conceptual model investigations are related 

to the NRC integrated subissues or KESAs. Conclusions resulting from this study are described in detail in 

Chapter 6. Appendix D describes the abbreviated parameter names used throughout the report. 

1.4 CAVEATS 

Because it is not possible to model a system as complex as a geologic repository in a complete and 

exhaustive manner, a number of assumptions and limitations are used directly, or are implicit, in the analyses 

conducted in this report. These assumptions and limitations are listed next. 

Any underlying assumptions, limitations, and bases used to construct the models in the 

TPA Version 3.2 code also apply to these analyses. These models are described in Chapter 2 

and discussed in greater detail in the TPA Version 3.2 code "User's Guide" (Mohanty and 

McCartin, 1998). 

The results are limited by the use of simplifying assumptions, models, and sparse data in 

certain areas. As a consequence, these results are preliminary. Moreover, the manner in 

which these analyses were conducted or the assumptions and approaches used should not 

be construed to express the views, preferences, or positions of the NRC staff regarding the 

ongoing efforts to develop site-specific regulations for YM.

1-7
2 OVERVIEW OF THE TOTAL-SYSTEM PERFORMANCE 

ASSESSMENT CONCEPTUAL MODELS IN THE 

TPA VERSION 3.2 CODE 

Analysis of repository performance is anticipated to be complex with substantial uncertainties because of 

the first-of-a-kind nature of the repository, extended period of performance, and reliance on engineered and 

natural barriers. The TPA analysis focuses on the postclosure performance of the proposed HLW repository 

at YM over long time periods (e.g., 10,000 yr). To attempt to quantify the uncertainty in estimating repository 

performance over long time periods, the TPA analysis is conducted in a probabilistic manner in which many 

realizations are calculated using input parameter sets sampled from probability distributions. Therefore, 

detailed simulation models that include all the process couplings, heterogeneities, and complexities are not 

incorporated into PA models to maintain reasonable computer execution times with modest hardware 

resources. Though a probabilistic code, the TPA analysis can also be performed in a deterministic mode. 

The TPA Version 3.2 code is used in this analysis to obtain deterministic and probabilistic estimates of dose 

for specified time periods (e.g., regulatory compliance TPI and beyond) at designated receptor locations 

[e.g., 20 km (12.4 mi) down gradient of YM]. The TPA Version 3.2 code, which is specifically tailored for 

evaluation of performance of the proposed repository at YM, is an update of the code used in the NRC IPA 

Phase 2 study. Conceptual models used in the previous version of the TPA code have been documented in 

Mohanty and McCartin (2001) and for the 3.2 version in Mohanty and McCartin (1998). 

A key part in developing the model used in the TPA Version 3.2 code is determining the level of detail in 

the processes, design, and attributes of the site necessary to produce a credible analysis that provides 

meaningful insights into performance without an unreasonable computational burden. A discussion of the 

repository system and the basecase conceptual models is presented in this section to provide a general 

overview of the TPA Version 3.2 code. This chapter also includes descriptions of the alternative conceptual 

models analyzed in Chapters 3 and 4. 

The TPA Version 3.2 code "User's Guide" contains more detailed information on the conceptual and 

mathematical models and the code structure (Mohanty and McCartin, 1998). A simplified flow chart 

illustrating the structure of the TPA Version 3.2 code is presented in Figure 2-1. The TPA input parameter 

values and the bases for their selection are presented in Appendix A of the same "User's Guide." 

2.1 CONCEPTUALIZATIONS OF REPOSITORY AND GEOLOGIC SETTING 

For ease of use and computational efficiency, the TPA Version 3.2 code replaces the intricate 

repository layout and the complex geologic setting with relatively simple conceptual representations. The 

repository layout, for example, is represented by an idealized planar feature discretized into a set of subareas, 

while the geology is replaced by a sequence of homogeneous layers. Properties and environmental conditions 

for each subarea are assumed uniform. Except for the influence of the thermal load, flow and transport 

processes in and below a given subarea are independent of processes in other subareas. Thus, flow is entirely 

vertical with no lateral diversion in the UZ.

2-1
Overview of the Total-system Performance Assessment Conceptual Models in the TPA Version 3.2 Code

Figure 2-1. Flow diagram for TPA Version 3.2 code.

2-2
Overview of the Total-system Performance Assessment Conceptual Models in the TPA Version 3.2 Code 

As illustrated in Figure 2-2, quadrilateral subareas of uniform thickness are used to represent 

individual subregions of the repository. In the current application, the repository is divided into seven 

subareas; however, the TPA Version 3.2 code has the capability to use much finer discretizations of both the 

repository and the geologic setting beneath it. The number of WPs in each subarea is assumed proportional 

to the fraction of the total repository area represented. Radionuclide releases from the EBS are calculated 

by modeling a single prototypical WP for each subarea and for each failure type. Performance characteristics 

of the WP and subsequent release in each subarea are calculated by considering the evolution of such 

characteristics as climatic conditions, water flux, thermal and chemical conditions, and geologic processes 

(e.g., seismicity, fault displacement, and igneous activity). Breaching of the WP by human intrusion and the 

associated release are not considered in the TPA Version 3.2 code. 

The geologic setting is composed of the UZ (i.e., geologic media between the ground surface and 

the water table) and the SZ (i.e., groundwater aquifer beneath the repository, extending to the location of the 

receptor group). For simplicity, the stratigraphy is assumed laterally continuous and uniform within a 

subarea, but differing from subarea to subarea. This simplification implies that, in general, flow in the UZ 

is primarily vertical with little or no lateral diversion of flow along hydrostratigraphic units. The geologic 

setting also includes features, events, and processes, such as seismicity, tectonism (faulting), and igneous 

activity (intrusive and extrusive) that may adversely affect the performance of the repository. Seismicity, 

tectonism, and intrusive igneous activity affect the performance characteristics of the WP and contribute to 

groundwater releases. 

To model flow and transport in the SZ, the TPA conceptual model consists of four distinct 

streamtubes over the width of the repository footprint normal to UZ flow. Each of the seven streamtubes in 

the UZ is connected to one of the four streamtubes in the SZ, based on proximity. Radionuclide releases from 

each of the UZ streamtubes provide the source term to the SZ streamtubes. The SZ streamtubes are treated 

as separate conduits and have flow velocities that vary along the individual flow paths. The mass flowrate 

of radionuclides exiting all SZ streamtubes at the well head is used to calculate annual dose to the average 

member of the receptor group. The annual dose computation accounts for all releases in the groundwater 

pathway at the location of the receptor group, the spatial extent of the releases in the SZ at the location of 

the receptor group, the extent of the production zone containing the radionuclides (all radionuclides are 

assumed released in one production zone), and the influence of the pumping rate attributed to water use by 

the receptor group. 

Direct release ofradionuclides to the accessible environment because of an extrusive igneous event 

is also modeled in the TPA Version 3.2 code. The physical characteristics of the extrusion and the 

assumption of a uniform distribution of WPs in the repository are used to determine the number of WPs 

affected by the event. Radionuclides are transported to the receptor location, based on characteristics of the 

eruption and meteorological conditions. The areal density of radionuclides in the soil, resulting from the 

deposition of volcanic ash containing SF particles, is then calculated. This soil concentration is used in 

computing the annual dose to the average member of the receptor group.

2-3
z I

. .... . . . . . . . . . . . . . . . . . ............ .

.............. .. ..... ... ................ 

Unsaturated Zone ................... ................... ..................... ................ ........... n

.; Saturated Zone

. . . . . . . .. . .. . . . . . . . . . . .I

. -. Hydrogeologlc 

. Units . ..S.. . . . . . . . •

. . . . . . . . . . . . . . 

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Discharge Point

Figure 2-2. Conceptualization of the repository system.

0 

0 

-t 

0

ir

i

I

&
Overview of the Total-system Performance Assessment Conceptual Models in the TPA Version 3.2 Code 

2.2 CONCEPTUAL MODELS IMPLEMENTED IN THE TOTAL-SYSTEM 

PERFORMANCE ASSESSMENT COMPUTER CODE 

In developing the TPA Version 3.2 code, several conceptual models were formulated, integrated, and 

implemented in various abstracted mathematical models. These basic conceptual models, which describe the 

interactions and couplings of the physical and chemical processes believed present in a proposed geologic 

repository at YM, can be grouped into the following generic categories: 

• Infiltration and deep percolation; 

* Near-field environment; 

* Radionuclide releases from the EBS; 

* Aqueous-phase radionuclide transport in the UZ and SZ; 

* Airborne transport from direct radionuclide releases; and 

• Exposure pathways and reference biosphere. 

These conceptual models are designed to apply to the current DOE repository design and specific 

site characteristics of the YM area and provide flexibility for examining alternative designs and uncertainties 

in site and engineered material performance. In some of these generic categories, alternative conceptual 

models also have been incorporated into the code. 

These conceptual models are used to represent a range of system states, including disruptive events. 

The consequences of disruptive events (e.g., seismicity, fault displacement, and igneous activity) are 

evaluated with the TPA Version 3.2 code by assessing the effects on EBS failure (producing releases to 

groundwater); direct releases of radionuclides (airborne releases to the biosphere); or both. The probability 

of occurrence of a disruptive event combined with the resulting consequences are used to calculate a risk 

curve separate from the TPA Version 3.2 code execution. 

The following discussion provides a general overview of the key aspects of the major conceptual 

models implemented in the TPA Version 3.2 code. More detailed descriptions of these models, including the 

mathematical basis, assumptions, and calculational methodologies, are presented in the TPA 

Version 3.2 code "User's Guide" (Mohanty and McCartin, 1998). 

2.2.1 Infiltration and Deep Percolation 

A one-dimensional (l-D) modeling approach is used in the TPA Version 3.2 code to describe the 

movement of meteoric water at the land surface vertically downward (i.e., without lateral flow) through the 

UZ, to the repository horizon, and ultimately to the water table. In the 1-D conceptual model, the deep 

percolation flux (qp,) is constrained to be equal to the shallow infiltration rate (q,,fil). The annual average 

q1,tfl is estimated based on 

* Present-day shallow-infiltration rate; 

* Change in climate with time; and 

• Elevation and soil depth over the repository subarea. 

Uncertainty in the present-day infiltration rate estimate is accounted for in the TPA Version 3.2 code 

by treating it as a statistically sampled input parameter. Temporal variations are incorporated by varying the 

present-day infiltration rate over the 100,000-yr TPI assumed for long-term climatic changes. The effects

2-5
Overview of the Total-system Performance Assessment Conceptual Models in the TPA Version 3.2 Code 

of site-specific soil cover thickness and elevation are used to reflect the spatial variation over each of 

the subareas. 

The temporal and spatial variations of qrnfl were developed through consideration of paleo-climatic information and results from detailed process-level auxiliary analysis (Stothoff, et al., 1997). The qnfil 

response function depends on two independent variables, present-day mean annual precipitation (MAP) and 

mean annual temperature, as well as the present-day infiltration rate. After computing qfi,, the water flux at 

the repository horizon is then partitioned into 

• Water flux diverted around the WP; and 

• Water flux entering the failed WP. 

Thus, for the purposes of the TPA Version 3.2 code, the net water flux carrying dissolved 

radionuclides is a fraction of the total water flux arriving at the repository. It is this net water flux that is used 

in the TPA Version 3.2 code to calculate the radionuclide source term for each subarea. 

2.2.2 Near-Field Environment 

Physical and chemical processes in the near field of the repository, such as heat transfer, water-rock 

geochemical interactions, and refluxing of condensate water, are expected to affect WP performance. In the 

TPA Version 3.2 code, a range of near-field characteristics is depicted in the abstracted mathematical models 

for heat and water flow and table look-ups for chemical parameters. To estimate WP failure times and 

radionuclide release rates, the near-field environment is characterized by 

Drift wall rock and WP surface temperatures; 

Relative humidity (RH) (defined in the TPA code as the ratio of vapor pressure at the drift 

rock wall to the vapor pressure at the WP surface); 

Water chemistry (e.g., pH, chloride concentration, and carbonate ion concentration); and 

Water reflux during the thermal phase. 

The average rock temperature in the repository horizon is calculated assuming a conduction-only model (i.e., the time history of temperature for each subarea is calculated accounting for the amount of 

emplaced waste) and no ventilation in the drifts. The WP surface temperature is calculated using a multimode 

heat transfer (i.e., conduction, convection, and radiation) model. Vapor pressure is computed using the 

standard thermodynamic equation relating vapor pressure to temperature. 

Estimates of the pH and chloride concentration histories of water films on the WP surface were 

developed in a separate process-level auxiliary analysis using the multicomponent geochemical module of 

the MULTIFLO code (Lichtner and Seth, 1996). MULTIFLO was applied to calculate the pH and chloride 

concentration for water percolating through the matrix of the tuffaceous rock. Because the chloride 

concentration in the water film is likely to be higher than that in the rock mass, the chloride history is scaled 

by a statistically sampled parameter that varies between I and 30, where 30 scales the peak chloride 

concentration to its solubility limit. The TPA Version 3.2 code provides the option of either using a look-up table that uses the temperature-dependent pH (not currently used) and chloride concentration generated with

2-6
Overview of the Total-system Performance Assessment Conceptual Models in the TPA Version 3.2 Code 

the MULTIFLO code, or specifying constant values in the input file. In general, the user selects code options 

by changing flag and variable values in the code input file. 

The amount of water percolating through the drifts varies over time primarily because of the coupled 

processes of heat transfer and fluid flow (e.g., vaporization, condensation, and refluxing). Water refluxing 

produced by these thermohydrologic effects is important during the first few thousand years, after which 

natural percolation determines the rate of water flow into the repository. Three water reflux models based 

on bulk flow balances are included in the TPA Version 3.2 code. The first model considers episodic reflux 

associated with time-dependent perching above the repository. The second model assumes that the volume 

of refluxing water will always be sufficient to depress the boiling isotherm in fractures and reach the WP 

during times when the surface temperature exceeds the boiling point of water. In the third model, the degree 

to which the boiling isotherm is depressed is a function of the temperature, the thickness of the dryout zone, 

and the volume of reflux water. These functions vary with time. Each reflux model produces estimates of 

the total water flux into the repository during the thermal period. 

2.2.3 Radionuclide Releases from the EBS 

In the TPA Version 3.2 code, the performance of a prototypical WP is modeled for each repository 

subarea, considering the failure time and radionuclide release rates for each of the WP failure categories. 

When this prototypical WP fails, all WPs in that subarea within a specified failure category are assumed to 

have failed. The estimation of both WP failure times and liquid releases is dependent on the nature and extent 

of corrosion, near-field environment, percolation flux in the drift, and external processes that may impose 

static loads, dynamic loads, or both. WP failures are grouped into three basic categories: (i) corrosion and 

mechanical; (ii) disruptive event; and (iii) initially defective. After determining the WP failure time, the 

TPA Version 3.2 code calculates the aqueous-phase radionuclide releases from the WP by considering the 

dissolution of radionuclides from the SF matrix, advective transport from the WP, and advective and 

diffusive transport through the invert directly to the UZ beneath the repository. 

Corrosion failure of the WP is defined to occur at the time when the inner overpack is fully 

penetrated by a single pit and the waste form is therefore accessible to water. The abstracted corrosion model 

uses a conceptual framework that assumes the formation of a water film containing a salt solution but does 

not explicitly consider water dripping on the container. The corrosion processes considered in the model 

abstraction are: 

* Dry air oxidation; 

* Humid air corrosion; and 

* Aqueous corrosion. 

WP surface temperature and the chloride concentration in the water film influence the mode, and hence, the 

rate, of corrosion. The predominant mode of corrosion, however, depends on the critical RH as well as the 

container material. Mechanical failure of the WP is considered the result of fracture of the outer steel 

overpack from thermal embrittlement arising from prolonged exposure at temperatures sufficiently elevated 

to cause substantial degradation of mechanical properties. 

Disruptive event failures are taken into account by modeling the effects of events such as seismicity, 

fault displacement, and igneous activity. In the case of seismicity, the drift is assumed to have no backfill 

that could prevent rockfalls from mechanically loading and deforming the WP. Because the DOE plans to

2-7
Overview of the Total-system Performance Assessment Conceptual Models in the TPA Version 3.2 Code 

not emplace WPs within a setback distance from known and well-characterized faults, displacements along 

yet undetected faults or new faults that exceed a preestablished threshold are assumed to fail WPs within the 

fault zone. For igneous activity, simulated magmatic intrusions intersecting the repository are assumed to 

cause WP failure; WPs within a dike but outside the vent hole are assumed to fail and expose the SF to water, 

whereas those within the vent hole (the diameter of which is a sampled parameter) are assumed entrained 

in the magma and released directly to the biosphere. For both igneous activity and fault displacement, failures 

are modeledby superimposingthe physical dimensions of the perturbation (i.e., length, width, and orientation 

of the fault and the igneous intrusion) on the repository footprint to determine the total number of WPs 

potentially affected in each repository subarea. Separate failure times are calculated for seismicity, fault 

displacement, and igneous activity. Because multiple seismic events occur during the 10,000- and 

100,000-yr TPIs, seismic failure occurrences are collected into four distinct failure times. 

In most applications of the TPA Version 3.2 code, it is assumed a small number of WPs is failed at 

the time of repository closure. These initially failed WPs are attributed to fabrication defects or damage to 

the WP as a result of improper emplacement. The average number of initially defective WPs is typically 

assumed to be 0.1 percent' of the total number of containers. 

Radionuclide releases from the WP are calculated by considering the alteration rate of SF (i.e., rate 

at which radionuclides in fuel become available for release); radionuclide solubility limits; and transport 

mechanisms out of the WP. The TPA Version 3.2 code incorporates a number of parameters [e.g., fraction 

of SF that is wet; particle size of the SF; alteration rate of (UO2+•), and credit for cladding] that control the 

release of radionuclides from the SF matrix. The effects of the formation of secondary minerals such as 

schoepite on SF dissolution are treated separately. After radionuclides are leached from the SF waste form, 

the calculated releases are adjusted to ensure consistency with the radioelement solubility limits. The gap 

fraction inventory of radionuclides is available for instantaneous release and therefore, may be a major 

contributor to peak dose. 

A parameter value in the code input file is used to specify the fraction of failed WPs that is wetted 

in the subarea. This value represents the number of failed WPs available to contribute to the source term. To 

compute the time-dependent source term, the TPA Version 3.2 code provides two alternative conceptual 

models: (i) a bathtub model-the WP must fill with water to a certain depth (up to the height of the outlet) 

before the radionuclides are released-and (ii) a flowthrough model-radionuclides are released by water 

dripping on the waste form and continuing immediately out of the bottom of the container. For the bathtub 

model, the WP is treated as a stirred tank, with the tank capacity dependent on the statistically sampled water 

outlet height. Water will fill the WP until the capacity (height) is reached and, thereafter, the amount of water 

entering the WP will equal the amount of water flowing out. Water leaving the WP transports dissolved 

radionuclides into the UZ below the repository. The water capacity of the bathtub is assumed unique to the 

failure modes and to subareas (except for faulting and igneous activity failures). Releases from WPs will 

travel through the invert before exiting the EBS. If the physical properties of the construction material for 

the invert are conducive, the radionuclide species could be sorbed, thus reducing the magnitude of 

radionuclide release from the near field. The flowthrough model is a variant of the bathtub model, except 

water does not have to first fill the bathtub before release; instead, radionuclides are released as soon as water 

enters the WP. 

'Tschoepe, E.C. et al. (1994) suggest fabricated metallic component reliabilities of 99.9-99.99 percent.

2-8
Overview of the Total-system Performance Assessment Conceptual Models in the TPA Version 3.2 Code 

2.2.4 Treatment of Aqueous-Phase Transport in the Unsaturated and 

Saturated Zones 

Movement of aqueous-phase radionuclides from the repository horizon, through the UZ, SZ, and 

ultimately to the receptor group, is modeled in the TPA Version 3.2 code, using the streamtube approach 

described in Section 2.1. Each streamtube encompasses one or more repository subareas and is composed 

of a vertical section from the repository to the water table and horizontal sections in the SZ. The transport 

module NEFTRAN II (Olague, et al., 1991) simulates the spectrum of processes (e.g., advection, dispersion, 

matrix diffusion, sorption, and decay) occurring within individual streamtubes. For the set of radionuclides 

specified in the code input file, the UZ and SZ modules simulate their vertical transport through the UZ and 

horizontal transport through the SZ. 

Time-dependent flow velocities in the UZ are calculated using the hydraulic properties of each major 

hydrostratigraphic unit. The UZ transport module simulates the transport ofradiocontaminants through either 

the porous rock matrix or fractures.2 Radionuclide retardation by chemical sorption in the rock matrix is also 

included in the model; however, retardation on fracture surfaces is neglected. 

Although groundwater flow in the SZ is assumed at steady state, radionuclide transport within 

individual streamtubes is time-dependent because the source term varies with time. Streamtubes in the SZ 

exhibit variable cross-sections along the flow path; this variable streamtube geometry was determined from 

a separate two-dimensional modeling study of the subregional flow (Baca, et al., 1996). The conceptual 

model of the SZ assumes that flow in the tuff aquifer is in localized conductive zones (i.e., permeable fracture 

zones) while flow in the alluvium is presumed uniformly distributed in the alluvial aquifer. Although the 

streamtube approach neglects dilution effects arising from lateral dispersion, credit is taken for sorption in 

the alluvium, which is likely to retard aqueous-phase transport of many radionuclides. Additionally, matrix 

diffusion from flowing pores and fractures into the more-or-less stagnant matrix pore water within the rock 

is included in the SZ transport model. 

2.2.5 Airborne Transport from Direct Releases 

Radiologic risks associated with the extrusive component of igneous activity are calculated in the 

TPA Version 3.2 code by modeling airborne releases of radionuclides for simulated extrusive events. The 

igneous activity module assumes that the magma intercepts WPs, moves upward to the land surface, and then 

ejects the ash and SF mixture into the atmosphere. The physical characteristics of each simulated extrusion 

(e.g., vent size, event energetics, and duration) and the atmospheric conditions are treated as statistical 

parameters in calculations of ash dispersal and deposition patterns, ash blanket thickness, and radionuclide 

soil concentrations. The three primary factors determining the ash plume geometry and transport rates are: 

* Power and duration (of the eruption); 

• Wind speed and direction; and 

* SF particle sizes. 

2

Transport though rock matrix takes place if the percolation rate, q,,, is less than the hydraulic conductivity of the rock 

matrix, K.,,,, or through fractures when qP.. exceeds K x.,

2-9
Overview of the Total-system Performance Assessment Conceptual Models in the TPA Version 3.2 Code 

The ash transport model developed by Suzuki (1983) was modified by Jarzemba, et al. (1997) and 

incorporated into the TPA Version 3.2 code to calculate distribution of the released radionuclides. The 

time-dependent radionuclide areal densities are calculated taking into account the thickness of the ash 

blanket, leaching and erosion rates, and radionuclide decay rates. The calculated doses attributed to direct 

releases are strongly influenced by the time of the event (early events result in larger doses, in part, because 

of the contribution to the estimated doses from short-lived fission products present in the SF). 

2.2.6 Exposure Pathways and Reference Biosphere 

Dose calculations are performed in the TPA Version 3.2 code for exposure pathways that consider 

an average person of a designated receptor group. These calculations express dose in rem/yr or mrem/yr. 

Alternative receptor groups are currently included in the exposure scenario. One receptor group is a farming 

community 20 km (12.4 mi) from the repository location whereas the second is a residential community at 

a specified distance, typically less than 20 km (12.4 mi). The average member of the designated receptor 

group is assumed exposed to radionuclides transported through the groundwater pathway, air pathway, or 

both, as a result of direct releases arising from the extrusive component of igneous activity. 

Geographic location and lifestyle characteristics assigned to each receptor group are two primary 

aspects defining the receptor group and are specified in the TPA Version 3.2 code by selection of appropriate 

input options. In addition, the farming community receptor group is assumed to include persons that use the 

contaminated water for 

* Drinking [i.e., 2 liters per day (0.5 gallons per day)]; and 

* Agriculture typical ofAmargosa Valley area practices (e.g., growing alfalfa and gardening). 

The farming community receptor group is assumed exposed to surface contamination through: 

* Consumption of contaminated farm products (i.e., ingestion); 

• Breathing air with ash-SF particles (i.e., inhalation); and 

* Direct contact. 

In contrast, the residential receptor group is assumed composed of persons who use contaminated 

groundwater only for drinking, but are also exposed to surface contamination (created by ash-SF particle 

deposition from the extrusive component of igneous activity) through inhalation and direct exposure. 

Site-specific dose conversion factors (DCFs) for each radionuclide and pathway are contained in 

TPA data files. These DCFs are used to convert radionuclide concentrations in the groundwater and soil to 

doses. The individual DCFs are mean values3 generated through separate pathway calculations using the 

GENII-S code (Leigh, et al., 1993). In the groundwater pathway, for example, the DCFs are applied to the 

concentrations at the well head. Two separate sets of DCFs are included in the TPA Version 3.2 code to 

represent two distinct reference biospheres associated with the present arid climate (nonpluvial) and the 

projected future pluvial climate. The determination of whether the climate is nonpluvial or pluvial is based 

on the K6ppen Geiger climate classification model (Strahler, 1969). In addition to computing the dose history 

for each stochastic simulation, the TPA Version 3.2 code scans these dose calculations to identify the 

magnitude and timing of the peak dose within a specified TPI. 

'The justification for using mean values can be found in Mohanty and McCartin (1998).

2-10
Overview of the Total-system Performance Assessment Conceptual Models in the TPA Version 3.2 Code 

2.3 BASECASE DEF1NITION AND ALTERNATIVE CONCEPTUAL MODELS 

The conceptual models available in the TPA Version 3.2 code are briefly presented in the previous 

sections. The option to evaluate alternatives to the basecase conceptual models is included in the 

TPA Version 3.2 code. The following sections list the set of conceptual models selected for the basecase 

studies and also describe the alternatives to the basecase models analyzed for mean input values in Chapter 3 

and sampled distributions in Chapter 4. 

2.3.1 Basecase 

The basecase input data set reflects current repository design features and likely parameter-range 

estimates for evaluation of processes affecting repository performance. The set of conceptual models that 

constitutes the basecase against which alternative conceptual models are evaluated in the 

sensitivity/uncertainty analyses include: 

No cladding protection; 

Dissolution of SF based on J-13 well-water chemistry; 

Bathtub model (i.e., pooling of water in the WP after failure) for determination of water 

mass balance and fuel wetting of the failed WP; and 

No matrix diffusion of contaminants in the UZ. 

A complete list of the input parameters used for the basecase can be found in Appendix A in the 

TPA Version 3.2 code "User's Guide" (Mohanty and McCartin, 1998). Climate change and seismicity are 

considered as integral components of the basecase and, therefore, alternative conceptual models to the 

components are not considered in the analyses. 

2.3.2 Alternative Conceptual Models 

Various alternative conceptual models are investigated to determine the sensitivity of repository 

performance to changes in WP design, radionuclide release mechanisms, and radionuclide transport models. 

These alternative model runs are conducted with the TPA Version 3.2 code and do not include disruptive 

events (faulting or igneous activity). The alternative models used in this analysis are grouped according to 

fuel wetting assumptions, fuel-dissolution models, and transport assumptions. For the analyses presented in 

this report, the repository performance is defined as dose for the mean value data set and as the peak of the 

expected dose from the multiple-realization results in the TPI. 

2.3.2.1 Fuel-Dissolution Models 

The TPA Version 3.2 code contains four models (Model 1-Model 4) for the dissolution rate of the 

SF that has come into contact with water. The basecase model uses Model 2 (Mohanty and McCartin, 1998), 

which is based on the dissolution rate of SF in J-13 water containing silica and calcium ions. The alternative 

dissolution models are listed next. Some of the alternatives are combined with fuel wetting alternatives 

as well.

2-11
Overview of the Total-system Performance Assessment Conceptual Models in the TPA Version 3.2 Code 

Fuel-Dissolution Model 1 

The first alternative fuel-dissolution model (IModel = 1) has an increased SF dissolution rate at high 

carbonate concentrations (Mohanty and McCartin, 1998) and reduced silicate and calcium concentrations 

in the water entering the WP. 

Fuel-Dissolution Model 3 (Natural Analog) 

In this alternative conceptual model, fuel dissolution and contaminant release rates are based on 

maximum likely rates inferred from measurements at the Pefia Blanca, Mexico, natural analog site 

(Mohanty and McCartin, 1998). For this alternative, the uranium dissolution rate for fully exposed fuel is 

24 kilogram/year (kg/yr) [53 pounds per year (lb/yr)] from the entire repository, but is further limited by the 

fraction of wetted WPs and the fuel wetting factors. The two factors range from 0 to 1 and are sampled. This 

alternative conceptual model is invoked by setting IModel = 3. 

Fuel-Dissolution Model 4 (Schoepite Dissolution) 

The schoepite-alternative conceptual model assumes that all radionuclides released from the 

SF matrix are captured in the secondary uranium mineral schoepite (Mohanty and McCartin, 1998) and are 

subsequently released at a limit controlled by schoepite solubility. This model is specified by 

setting IModel = 4. 

2.3.2.2 Fuel-Wetting Assumptions 

This grouping includes alternative conceptual models related to the way SF in the WP is contacted 

by water. These five alternative models use combinations of the flowthrough and dissolution-rate models, 

and also TPA input parameters for the amount of water and fraction of the subarea wetted by 

impinging water. 

Flowthrough Model with Fuel-Dissolution Model 2 

This alternative conceptual model evaluates the flowthrough option in which water enters WPs 

through corrosion pits but does not pool in the container. In the bathtub model used in the basecase, the 

fraction of fuel wetted is determined by the bathtub height (determined by the position of the exit port, which 

is a corrosion pit), which is sampled and ranges from 0 to 1. In the flowthrough model, the fraction of fuel 

wetted is unrelated to the water level in the WP. Additionally, the fraction of fuel wetted is likely much 

smaller and depends on poorly understood phenomena such as dripping patterns, surface tension, and 

vapor-phase wetting. This alternative conceptual model is invoked by specifying a smaller range for the 

parameter Fmult* (one-tenth of the normal range for the basecase),4 to simulate a smaller fraction of wet fuel 

surface. In this model, solubility limits for the radionuclides might become important because of the limited 

amount of water in contact with the fuel. 

4

Fmult* is the fraction of water, infiltrating to the repository from the unsaturated zone above the repository, that will enter 

the WP and contribute to the release of radionuclides. Water dripping toward the drifts may be diverted around the drift because of 

capillary action, may be diverted down the side of the drift, or may not enter the WP for other reasons.

2-12
Overview of the Total-system Performance Assessment Conceptual Models in the TPA Version 3.2 Code 

Flowthrough Model with Fuel-Dissolution Model 1 

This alternative conceptual model uses the flowthrough model and IModel = 1 (carbonate-dissolution 

model), which assumes that silicate and calcium will be depleted from much of the water entering the WP 

by reaction with the fuel and metal in its path. 

Focused Flow 

The basecase conceptual model assumes that all parts of a repository subarea will receive an equal 

quantity of infiltrating water. This alternative conceptual model accounts for the possibility that water 

infiltration reaching the WPs will be focused or funneled by discrete fractures, which will wet some of the 

WPs more heavily than others. This alternative model is evoked by increasing the range of Fmult* by a factor 

of 4 (from 0.01-0.2 to 0.04-0.8), while decreasing the fraction of WPs wetted by a factor of one-fourth (from 

0-1 to 0-0.25). This has the effect of funneling the same quantity of water for each subarea to one-fourth the 

number of WPs. 

Cladding Credit Plus SF Dissolution Model 1 

The basecase conceptual model assumes that once the inner and outer overpack containers have been 

breached, SF is exposed and available for dissolution and transport. This assumption ignores any protection 

afforded the fuel from intact and partially failed cladding. In this alternative model, the effect of cladding 

protection is simulated by setting the SF wetted fraction to a constant value of 0.005 for the entire TPI. 

Grain-Size Model with Fuel-Dissolution Model 1 

This conceptual model uses the grain size from the uranium dioxide fuel, instead of the particle size, 

to determine surface area, which leads to a higher dissolution rate because of the increased surface area. This 

alternative conceptual model combines the fuel-dissolution rate model 1 for relatively fast dissolution by 

carbonate water, with the large surface area provided by assuming that the fuel surface area is determined 

by the grain size. Both these assumptions are used in the DOE-TSPA-VA model (U.S. Department of Energy, 

1998) for radionuclide release from SF. 

2.3.2.3 Transport Alternatives 

The transport assumptions in the basecase UZ and SZ conceptual models are investigated with three 

alternative models. These assumptions affect the releases and time of release from the EBS, UZ, and SZ. 

No Retardation of Plutonium (Pu), Americium (Am), and Thorium (Th) 

This alternative conceptual model demonstrates the contribution, to repository performance, of 

retardation of Pu, Am, and Th in the geosphere, and the effect on the groundwater doses if this sorption were 

removed. Once released from failed WPs, Pu, Am, and Th are assumed to travel at the same speed as water 

through the EBS, UZ, and SZ to the receptor location. This alternative model is invoked by setting 

equilibrium coefficients (Kd) to zero and retardation coefficients (Rd) to unity for these elements. This model 

is a gross approximation of potential contribution from colloids that could move through the geosphere 

unretarded if filtration processes were not considered.

2-13
Overview of the Total-system Performance Assessment Conceptual Models in the TPA Version 3.2 Code 

No-Invert Model 

The TPA Version 3.2 code contains a model that takes into account the effect of flow and retardation 

through the invert material beneath the WPs. This function is normally activated. The no-invert alternative 

model negates the effect of the invert. This is accomplished by setting the variable InvertBypass equal to 1 

in the code input file. 

Matrix Diffusion 

This conceptual model assumes that matrix diffusion will occur in the tuff SZ transport legs where 

there is fracture flow. Matrix diffusion is specified by setting the parameter DiffisionRateSTFF as a 

loguniform distribution ranging from 0.01 to 1.0 yr-1. Two other factors involved in the matrix diffusion 

alternative are the immobile porosity and the retardation coefficients in the immobile phase. The default 

values in Appendix A of the TPA Version 3.2 code "User's Guide" (Mohanty and McCartin, 1998) are used 

to evaluate this conceptual mode.

2-14
3 ANALYSIS OF TOTAL-SYSTEM BEHAVIOR

In this chapter, the relationships between repository performance and the key input parameters and 

intermediate results are presented. The mean values and distributions for the uncertain TPA input parameters 

are summarized in Tables 3-1 to 3-18. 

In the single-realization case, mean values for the TPA input parameters are used and the results evaluated 

over the 10,000- and the 100,000-yr TPIs. The single-realization simulation establishes a baseline to 

investigate the behavior of the total system at the process level (e.g., WP lifetime and SZ travel time) and 

the repository performance as measured by groundwater dose. Additionally, the repository performance is 

related to the key input parameters and intermediate results in a deterministic mode. 

After the discussion of results from the single-realization simulation, a description of the variability in the 

TPA results from multiple realizations is presented. The variability in the behavior of the total system at the 

process level and the repository performance are analyzed in multiple realizations using distributions for the 

TPA input parameters. For example, the variability in dose is related to the release rate from the EBS. Both 

the single- and multiple-realization basecase analyses provide background information and form the 

framework to evaluate and quantify the sensitivity of repository performance to TPA input parameters 

presented in Chapter 4. After the multiple-realization results, the TPA outputs from alternative conceptual 

models and disruptive events are presented. This chapter concludes with a discussion of a methodology used 

to calculate risks from the disruptive events. 

3.1 SINGLE-REALIZATION DETERMINISTIC ANALYSES 

This section examines repository behavior for a single realization to illustrate how a component 

influences both the dose and the behavior of other components. For the single realization, all input 

parameters are specified at mean (or expected) values. It should be noted that the annual dose obtained from 

using the mean value data set most likely will not be the same as the expected annual dose (which is the 

performance measure) obtained from multiple-realizations because of the nonlinear dependency of dose on 

input parameters. 

The general representation of waste emplacement at YM is a total of 62,800 Metric Tons Uranium 

(MTUs) in an area of 3,060,000 meters2 (m2) [approximately 3,000 m (1.9 mi) long and 1,000 m (0.6 mi) 

wide]. Assuming a payload of 9.76 MTU per WP and an equivalence between the SF and other types of 

wastes, such as DOE waste and glass waste, approximately 6,427 WPs will be needed for waste disposal. 

The initial inventory activity is approximately 7.4 x 1018 Becquerel (Bq) [200 x 106 Curies (Ci)]. WVPs with 

a 5.682-m (18-6 ft) length and a 1.802-m (5.9-ft) diameter are emplaced in drifts 5 m (16.5 ft) in diameter, 

spaced 22.5 m (73.8 ft) apart. The average age of the SF is 26 yr. The descriptions of the mean values for the 

key parameters used in various process-level calculations are presented in each of the following sections. 

3.1.1 Unsaturated Zone Flow 

Detailed modeling (Stothoff, 1999) suggests that climate conditions could significantly affect the 

flow of water in the UZ and into the repository. As a consequence, the amount of water contacting a WP, 

which affects the release rate of radionuclides from the EBS and the transport of the radionuclides in the UZ, 

may also be significantly influenced.

3-1
Analysis of Total-system Behavior

In the TPA Version 3.2 code,5 precipitation is assumed to vary frompresent-dayto pluvial conditions 

over a period of 100,000 yr. For the mean value data set, Figure 3-1 shows the MAP changes from about 

160 to 330 mm/yr (0.52 to 1.08 ft/yr), whereas the infiltrating water enters the UZ from 5 to 110 mm/yr 

(0.016 to 0.36 ft/yr). Based on the K6ppen Geiger system of climate classification (Strahler, 1969) 

implemented in the TPA code to determine the onset of the pluvial period, approximately 90 percent of the 

100,000-yr TPI is characterized by pluvial conditions and 10 percent of the time is represented by the 

present-day climate. 

For higher flow rates, there are generally larger releases because of the greater amount of water 

available to dissolve and transport radionuclides out of the WP. Increasing flow rates in the UZ are not only 

expected to transport a larger mass of radionuclides from the EBS, but also lead to higher doses. The mean 

values of the parameters used to calculate the time-varying infiltration rates in the UZ are presented 

in Table 3-1. 

3.1.2 Near-Field Environment 

The near-field thermal conditions may alter the flow of water into the repository, which influences 

the quantity of water that contacts, dissolves, and transports the SF out of the EBS. The near-field chemical 

environment in conjunction with the thermal environment affects WP corrosion and determines quantity and 

time history of water entering the WP. These near-field conditions and the flow of water onto the WPs are 

discussed in the following sections. 

3.1.2.1 Repository-Scale Thermohydrology 

Radioactive decay of SF generates heat that perturbs ambient percolation conditions. The heat 

evaporates water and creates a dryout zone around the drift. Above the repository horizon, the water vapor 

condenses and flows back toward the repository, thus creating a reflux zone. The reflux zone is maintained 

until the near-field temperature falls below boiling. When the temperature falls below boiling or water from 

the condensate zone penetrates the dryout zone, water flows into the drift. Water entering the drift may 

impinge on the WP and contribute to WP corrosion failure. After the WP fails, water contacts the SF and is 

transported out of the EBS into the UZ. 

Of the three reflux models in the TPA code indicated in the previous chapter, the third model was 

used in the basecase. This model estimates the depth that water will penetrate the boiling isotherm as a 

function of dryout zone thickness and the volume of water flowing from the condensate zone. Table 3-2 

presents the mean values of parameters used in the reflux calculations. 

Figure 3-2 presents, except for early times, subarea-to-subarea variations in the volume of water 

contacting WPs, which behave similarly to the infiltration rates in Figure 3-1. Figure 3-2 also shows slight 

differences in the seepage flux between subareas and a consistency in the general behavior of the seepage 

flux for all seven subareas with subarea 3 having the largest seepage flux attributable to the effects of 

elevation and soil thickness. 

5

The specific version of the code used in developing this chapter is 3.2.3.

3-2
Analysis of Total-system Behavior

20000 40000 60000 80000 

Time (yr)

100000

Mean annual precipitation and infiltration at the repository horizon averaged over all 

subareas and encompassing both the current and pluvial periods for the mean value 

data set.

I I I I I I I I I I

Subarea I 

N

-2--- Subarea 2 

-*- Subarea 3 

--- Subarea 4 

- - Subarea 5 

I Subarea 6 

---- Subarea 7 

II I I , , , I , I I I I I I

20000 40000 

Time (yr)

60000 80000 100000

Effect of the thermal perturbation on the near field seepage rate in each subarea for the 

mean value data set.

3-3

0

350 

300 

250 

E 

E 200 

( 150 

o 100 

II

50 

0

Figure 3-1. 

101

S100 

%.0 

10-1 

1h 

1072

0

Figure 3-2.

. .. ~~~~~~3 1
Analysis of Total-system Behavior

Table 3-1. Mean values and sampled distributions of parameters for infiltration calculations

Parameter Mean Value Distribution 

Areally averaged mean annual infiltration for the initial 5.50 mm/yr Uniform; 1.0, 10.0 

(current) climate 

Mean average precipitation multiplier at glacial 2.00 Uniform; 1.5, 2.5 

maximum 

Mean average temperature increase at glacial maximum -7.50 0C Uniform; - 10.0, -5.0 

Table 3-2. Mean values and sampled distributions of parameters for determining repository-scale and 

drift-scale thermohydrology (The hyphen in the last column indicates a constant value for 

the parameter distribution.) 

Parameter Mean Value Distribution 

Y 1-nnrth ArA+r1fl-V WWI,- )o XP lo , r

Maximum flux in reflux zone 

Perched bucket volume per subarea-area 

Fraction of condensate removed 

Fraction of condensate toward repository 

Fraction of condensate toward 

repository removed 

Density of water at boiling 

Enthalpy of phase change for water 

Temperature gradient in vicinity of 

boiling isotherm 

Ambient repository temperature 

Mass density of Yucca Mountain rock 

Specific heat of Yucca Mountain rock 

Thermal conductivity of Yucca 

Mountain rock 

Emissivity of drift wall 

Emissivity of waste package 

Thermal conductivity of floor 

Effective thermal conductivity of 

unbackfilled drift 

Time of emplacement of backfill 

Effective thermal conductivity of backfill 

Thermal conductivity of inner stainless 

steel wall 

Thermal conductivity of outer carbon 

steel wall 

Effective thermal conductivity of basket and 

spent fuel in waste package 

Elevation of repository horizon 

Elevation of ground surface

1.00 x 10 9 m/s 

5.00 x 10-1 m3/m2 

1.00 x 10-4/yr 

5.00 x 10- /yr 

1.00 X 10-4 /yr 

9.61 x 102 kg/m3 

2.40 x 106 J/kg 

5.05 x 101 K/m 

2.00 x 10' °C 

2.58 x 103 kg/n3 

8.40 x 102 J/(kg-K) 

2.00 W/(m-K) 

8.00 x 10' 

7.00 x 10-1 

6.00 x 10-1 W/(m-°C) 

9.00 x 10-1 W/(m-°C) 

1.00 x 10 yr 

6.0 x 10-' W/(m-°C) 

1.50 x 101 W/(m-°C) 

5.00 x 101 W/(m-°C) 

1.00 W/(m-°C) 

1.07 x 103m 

1.40 x 103 M

Log-uniform; 1.0 x 10-, 1.0 

Uniform; 0.0, 1.0 

Log-uniform; 1.0 x 10', 1.0 

Uniform; 1.0, 100.0 

Uniform; 1.8, 2.2

3-4
Analysis of Total-system Behavior

The spike in Figure 3-2 at early times illustrates a large change in the seepage flux that occurs 

because of a higher thermal perturbation. Although this thermal perturbation takes place before to corrosion 

failures, the modified infiltration rate could affect releases from initially defective failures or seismically 

induced failures. The duration of the thermal perturbation is small compared with long simulation periods 

such as 105 yr; however, it may be significant for the 10,000-yr TPI. The subarea average infiltration rate 

in the UZ is provided in Figure 3-3. Water flowing into the drift and water entering the WP are also 

illustrated in this figure. The effects of the thermal perturbation on the flow rate are evident in this figure for 

approximately 3000 yr. Once the infiltration into the repository begins, the rate increases by a factor of 

approximately 5 compared with the ambient infiltration rate. The thermal augmentation of flow for the mean 

values data-set case lasts about 1000 yr. Significant infiltration into the repository is delayed until 

approximately 2000 yr. Afterward, the thermal effects no longer influence the UZ flow above the repository. 

3.1.2.2 Drift-Scale Thermohydrology 

WP surface temperature, drift wall temperature, and WP surface RH are computed for each subarea. 

The mean TPA input parameters used to compute these values are presented in Table 3-2. Figure 3-4 

illustrates the subarea-to-subarea differences in the WP surface temperature, and Figure 3-5 shows WP 

surface RH. For the mean value data set presented in Table 3-2, the highest temperature of approximately 

150 'C (302 'F) is observed at about 100 yr. The temperature remains above ambient temperature even at 

100,000 yr. Subareas 1 and 2 are the largest subareas and subarea 7 is the smallest, located away from the 

center of the repository and with an elongated shape. Thus, in subareas 1 and 2, WPs cool much more slower 

compared with subarea 7. Subarea 7 exhibits the greatest differences in temperature and RH when compared 

with subareas 1 through 6. 

Subarea-dependent temperature and RH values from the near field are also used by the WP 

degradation model to determine the WP failure time. Consequently, the WP failure time may be different for 

each subarea. For the drift-scale thermohydrology, the climatic conditions were considered irrelevant because 

fluid flow was not modeled in the temperature and RH calculations. Fluid flow was not accounted for in the 

temperature and RH calculations, because its effect was found to be insignificant in the detailed calculations 

using equivalent continuum modeling conducted outside the TPA code. 

3.1.2.3 Near-Field Geochemical Environment 

The near-field geochemical environment is represented bythe time-dependent chloride concentration 

that interacts with the WP and wasteform inside the drift. The parameters available to the TPA analysis are 

the chloride concentration, oxygen partial pressure, the solution pH, and the total dissolved carbonate. 

Figure 3-6 shows the time history of chloride concentration used by the TPA program, which was calculated 

with the MULTIFLO (Lichtner and Seth, 1996) computer program and supplied in tabular form to the 

TPA code. The chloride concentration is calculated based on an initial fluid composition corresponding to 

J-13 well water and represents the time-dependent composition of water available at the drift wall. The 

chloride multiplication factor in Table 3-3 (mean value of 15.5) modifies the time-dependent chloride 

concentration curve presented in Figure 3-6. The chloride multiplication factor is intended to account for the 

uncertainty in estimating the water chemistry; the parameter values (chloride concentration) and MULTIFLO 

results are considered to be the lower bound for chloride concentration.

3-5
Analysis of Total-system Behavior

102 

"101 

4) 0 o10 

• 10" 

•10-1 (U

102 102

Without Thermal 

Perturbation

103

I I t I I I I I I I I I I I I

With Thermal 

Perturbation I

I' 

S -- - -

- Flow Into 

Repository 

After Diversion

10 4

Time (yr)

Figure 3-3. Subarea average infiltration rate, flow into the drift, and amount of water entering the 

WP for the mean value data set.

250 

200 

0 

28 150 

•- 100 

E 

I5O

0 1 

100 101 102 103 104 

Time (yr)

101

Figure 3-4. WP surface temperature in each subarea for the mean value data set.

3-6

, a , , , , ,

C

10 5

'l 

I

, I , , . I , I I I I I I I I I
Analyses of Total-system Behavior

1.0 

0.8

Z% 

V 

4) 

M

0.6 

0.4 

0.2

0.0

16o

Time (yr)

Figure 3-5. WP surface relative humidity in each subarea for the mean value data set.

-j 

0 

C 

.2 0 

C 

C 

0 

0

10.2 

10 3

10 5

Time (yr)

Figure 3-6. Time history of chloride concentration computed by MULTIFLO

3-7
Analysis of Total-system Behavior

Table 3-3. Parameters for determining the corrosion failure of WPs

Mean Value 

1.00 x 10-1 m 

2.00 x 10-2 m 

1.38 x 101 gm 

7.00 x 10-4 Mm 

1.00 x 10-1 

5.50 x 10-1 

8.00 x 10-1 

2.00 x 10-3 m 

9.70 x 10' 0C 

-6.20 x 102

Parameter 

Outer waste package thickness 

Inner waste package thickness 

Metal grain radius 

Grain boundary thickness 

Dry oxidation constant 

Critical relative humidity humid 

air corrosion 

Critical relative humidity 

aqueous corrosion 

Thickness of water film 

Boiling point of water 

Outer overpack E, intercept 

Temperature coefficient of outer pack 

Er, intercept 

Outer overpack Erp slope 

Temperature coefficient of outer pack 

Ep slope 

Inner overpack Erp intercept 

Temp coef of inner pack Erp intercept 

Inner overpack Erp slope 

Temp coef of inner pack ErP slope 

Outer waste package beta kinetics 

parameter for oxygen 

Outer waste package beta kinetics 

parameter for water 

Inner waste package beta kinetics 

parameter for oxygen 

Inner waste package beta kinetics 

parameter for water 

Outer waste package rate constant for 

oxygen reduction 

Outer waste package rate constant for 

water reduction 

Outer waste package activation energy 

for oxygen reduction 

Outer waste package activation energy 

for water reduction 

Inner waste package rate constant for 

oxygen reduction 

Inner waste package rate constant for 

water reduction 

Inner waste package activation energy 

for oxygen reduction 

Inner waste package activation energy 

for water reduction

Distribution

Normal; 0.75, 0.85 

Uniform; 0.001, 0.003

Uniform; 1040.0, 1240.0

7.50 x 10-1 

5.00 x 10-' 

7.50 x 10-' 

5.00 x 10'1 

3.80 x 1012 C-m/m/yr 

1.60 x 10-1 C-m/m2/yr 

3.73 x 104 J/mol 

2.50 x 104 J/mol 

3.00 x 10'0 C-m/mol/yr 

3.2 C-m/m2/yr 

4.0 x 104 J/mol 

2.50 x 104 J/mol

3-8

4.70 x 10-1 

-9.52 x 10' 

8.80 x 10-1 

1.14 x 10' 

0.00 

0.00 

0.00
Analysis of Total-system Behavior

Table 3-3. Parameters for determining the corrosion failure of WPs (cont'd)

Parameter Mean Value Distribution 

Passive current density for waste 

package outer overpack 3.15 x 10' C/m2

/yr 

Passive current density for waste 

package inner overpack 4.15 x 10W Uniform; 2.0 x 104,6.3 x 104 

Measured galvanic couple potential -4.60 x 10-1 

Coefficient for localized corrosion of Uniform; 8.66 x 10-4, 

outer overpack 4.76 x 10-3 8.66 x 10-3 

Exponent for localized corrosion of 

outer overpack 4.5 x 10-1 

Humid air corrosion rate 1.16 x 10-nm/yr 

Localized corrosion rate of 

inner overpack 2.5 x 10-4 m/yr 

Fractional coupling strength 0.0 

Factor for defining choice of 

critical potential 0.0 

Critical chloride concentration for 

first layer 3.0 x 10-4 mol/L 

Critical chloride concentration for 

second layer 1.00 mol1/L 

Chloride multiplication factor 1.55 x 101 Uniform; 1.0, 30.0 

Reference pH 9.0 

Waste package surface scale thickness 0.0 m 

Tortuosity of scale on waste package 1.0 

Porosity of scale on waste package 1.0 

Yield strength 2.05 x 102 MPa 

Safety factor 1.4 

Fracture toughness 2.50 x 102 MPa/m2 

Note: mol/L-- moles per liter 

MPa-megapascal 

3.1.3 WP Degradation 

Because radionuclide releases begin only after WP failure, the lifetime of a WP significantly affects 

repository performance. The WP degradation rate is strongly dependent on the behavior of the inner and 

outer container materials. The inner and outer WP materials are specified as carbon steel and Alloy C-22, 

respectively, based on the DOE TSPA-VA design (U.S. Department of Energy, 1998). The mean values of 

the parameters used in computing the WP failure time are presented in Table 3-3. Figure 3-7 provides a time 

evolution of the WP wall thinning and shows WP failure occurring at about 16,500 yr. The two distinct lopes 

in this figure correspond to the different corrosion rates for the carbon steel and Alloy C-22 materials. The 

transition point corresponds to the penetration of the outer overpack at approximately 1700 yr. The figure 

indicates that an order of magnitude longer WP life is attributable to the inner overpack rather than the 

outer overpack. 

Figure 3-8 shows that, for the mean value data set, 31 WPs are initially defective at year zero. The 

number of initially defective failures ranges from one to nine WPs in the seven subareas. No seismically

3-9
Analysis of Total-system Behavior

0.12 

E 0.1 

0.08 

Ci 

0.06 

o o 4: Carbon Steel .E- 0.04 

(a 

M 0.02 .. __ .. Alloy C-22 

0 L 

4000 8000 12000 16000 

Time (yr) 

Figure 3-7. WP wall thickness as a function of time for the mean value data set.

IL 

E.

7000 

6000 

5000 

4000 

3000 

2000 

1000 

0

0 5000 10000 15000 20000 

Time (yr) 

Figure 3-8. Cumulative number of failed WPs for the mean value data set.

3-10

20000

25000
Analysis of Total-system Behavior

induced failure occurs for the mean value data set. The first corrosion failures take place in subareas 5 and 

7. A total of 928 WPs fail in these subareas at 16,300 yr. The next corrosion failure occurs in subareas 1 to 

4, and 6, with a total of 5468 WPs failing at 17,000 yr. 

3.1.4 Releases from WP 

After WP failure, radionuclide releases are modeled assuming advective mass transfer out of the WP 

from incoming water. The volume of water contacting the SF is computed from a combination of flow in the 

near-field environment and two flow factors. The first flow factor represents the fraction of dripping water, 

which may be focused to reach the WP. The second flow factor represents the fraction of the water reaching 

the WP that enters the WP. The flow rate into the WP is used in the bathtub model to determine radionuclide 

release rates. The mean value parameters used in the calculation of radionuclide release rates from the EBS 

are presented in Tables 3-4 and 3-5. 

Because radionuclides have different chemical, physical, and biological properties that affect the 

mobilization and radiotoxicity, not every radionuclide in the SF is an important contributor to dose. 

Furthermore, because modeling all radionuclides in the SF significantly increases the computation time, a 

screening process employing criteria such as contribution to dose was used to determine a list of 

11 radionuclides. The 11 radionuclides and the decay chains evaluated in the TPA analysis are presented 

in Table 3-6. 

3.1.4.1 Cladding Degradation 

Cladding must fail for water to contact the SF. Because of lack of adequate knowledge, no explicit 

mechanism for cladding failure is included in the TPA code. To capture the potential effect of cladding 

degradation, however, a fraction of the rods inside a WP may be specified to have failed at the time of WP 

failure. In the basecase, cladding failure is specified at 100 percent of the fuel rods, indicating no cladding 

protection for the SF (see Table 3-4). 

3.1.4.2 SF Dissolution and Mobilization 

SF dissolution is modeled by defining rate equations for the SF exposed after WP failure and 

cladding degradation. The rate equation is based on laboratory data in the presence of calcium (Ca) and 

silicon (Si). The data follow an Arrhenius-type trend that uses the time-varying temperature as the 

independent parameter. The dissolution rate is calculated from a mass balance on the water flowing into the 

WP. Because the flow rate is subarea-dependent, the dissolution rate varies from subarea to subarea. 

The average temperature of the WP surface, calculated in the drift-scale thermohydrology model, 

is used in the dissolution rate equation. This assumption that the temperature of the WP surface is close to 

the temperature at the interior of the WP is justified because by the time the WP fails from corrosion (the 

dominant failure mechanism) at around 17,000 yr, the thermal effects have subsided. The surface area of the 

SF available for dissolution is about 746 m2 (8000 ft2) based on the SF particle size, grain density, and the 

SF wetted fraction. 

As with SF dissolution, the mobilization of the SF also depends on the initial inventory 

instantaneously released from the gap between SF and cladding into the contacting water as soon as the WP 

fails. Radionuclide gap fractions are presented in Table 3-7.

3-11
Analysis of Total-system Behavior

Table 3-4. Parameters used in determining radionuclide releases from the engineered barrier system

MP~n

0.00 

1.73 x 10-1 

4.47 x 10-2 

5.0 x 10-1 

0.00 yr 

5.05 x 10-3

fi+Ahtrhutinn

Lognormal; 0.01, 3.0 

Lognormal; 0.01, 0.2 

Uniform; 0.0, 1.0 

Uniform; 1.0 x 10-4, 1.0 X 10-2

Parameter 

Flow model flag (0 = bathtub, 

1 = flow through) 

Flow convergence/divergence factor 

Flow multiplication factor 

Subarea wet fraction 

Initial failure time 

Defective fraction of waste packages 

per cell 

Number of SEISMO waste package 

failure intervals 

Beginning of seismic waste package 

failure intervals 

Waste package internal volume 

Flow onset temperature 

Spent fuel density 

Surface area model 

Spent fuel dissolution model 

Oxygen partial pressure 

Negative log 10 carbonate concentration 

User leach rate 

Initial radius of spent fuel particle 

Radius of spent fuel grain 

Cladding correction factor 

Subgrain fragment radius of U0 2 

particle after transgranular fracture 

Thickness of cladding 

Spent fuel 14

C inventory of spent fuel 

Clad 14

C inventory of spent fuel 

Zirconium oxide and crud '

4C inventory 

of spent fuel 

Gap and grain boundary inventory of 

spent fuel 

Spent fuel wetted fraction for all 

failure types 

Invert bypass (0 = use ebsfilt, 

1 = bypass ebsfilt) 

Invert rock porosity 

Invert thickness 

Invert diffusion coefficient 

Invert matrix permeability 

Unsaturated zone minimum velocity 

change factor (fraction)

0, 2000, 5000, 10,000 yr 

4.83 m3 

9.99 x 102 OC 

1.06 x 104 kg/i 3 

1.00 

2.00 

2.10 x 10- atm 

3.71 mol/L 

2.50 x 10-6 kg/yr/m2 

1.85 X 10-3 i 

1.25 x 10-' 

1.0 

1.25 x 10-6 m 

6.1 x 10-4 m 

7.2 x 10-4 Ci/kg 

4.89 x 10-4 Ci/kg

Normal; 7.0 x 10-4 , 3.0 x 10-3 

Normal; 5.0 x 10-7, 2.0 x 10-6

2.48 x 10- 'Ci/kg 

6.2 x 10-6 Ciikg

5.0 x 10-1 Uniform; 0.0, 1.0

0 

3.0 x 10

7.5 x 10-'m 

4.4 x 10-'m 2 /yr 

2.0 × 10-17m 2

Lognormal; 2.0 x 10-"8 , 2.0 x 10-16

4.0 x 10-1

3-12

4.00

Mean
Analysis of Total-system Behavior

Table 3-4. Parameters used in determining radionuclide releases from the engineered barrier system 

(cont'd)

Parameter 

Invert RD 

2 4 1

AjU 

14

c 36c1 

245Cm 

1291 

2 3 7

Np 

2 3 9

pu 

7 9

Se 

"

99

Tc 2 3

OTb 

234U

MAs

3.00 x 103 

6.10 x 101 

1.00 

6.00 x 103 

7.00 

1.20 x 103 

3.00 x 103 

1.00 

1.00 

3.00 x 103 

6.01 x 102

Table 3-5. Distributions of solubility limits

Radionuclide Mean Value (kg/rm) Distribution (k/m 3

) Am 1.20 x 10 Uniform; 2.4 x 10-8, 2.4 x 10

14c 1.40 x 10' -

36

C1 3.60 x 101 2 4 5

Cm 2.40 x 10-4 

129I 1.29 x 102 

237

Np 2.14 x 10-2 Log triangular; 1.2 x 10-3, 3.4 x 10-2, 2.4 x 10-1 

•29pu 1.21 x 10-4 Uniform; 2.4 x 10-6, 2.4 x 10-4 

79Se 7.90 x 101 

9Tc 9.93 x 10' 

23°Th 2.30 x 10-4 

234U 7.60 x 10-3 

Table 3-6. Radionuclide decay chains 

Chain Chain 

Number 

1 2 4 5

Cm -* 241,Am - 237Np 

2 "29pu 

3 234U -+ 23 0

Th 

4 1291 

5 9 TC 

6 14C 

7 79

Se 

8 36

C1

3-13

I|ietrihntinn
Analysis of Total-system Behavior

Table 3-7. Initial inventory, gap inventory, and half-life of radionuclides in spent nuclear fuel for 

groundwater release

Inventory at 10 yr Gap 

from Reactor Inventory Half-life 

Radionuclide (Ci/WP) (%) (yr) 

2411.60 x 104 0 4.32 x 102 

14c 1.30 x 101 10 5.73 x 10' 

36C1 1.14 x 10-1 12 3.01 x 105 

245Cm 1.22 0 8.50 x 103 

1291 2.88 x 10-' 6 1.57 x 10' 

237

Np 2.80 0 2.14 x 106 23 9

pu 3.01 x 103 0 2.41 x 104 

79Se 3.71 6 6.50 x 104 

9Tc 1.20 x 102 1 2.13 x 10' 

23°Th 1.26 x 10-3 0 7.70 x 10 4 

234 U 1.10 x 101 0 2.45 x 10' 

3.1.4.3 Transport in the EBS 

The TPA code models advective transport out of the WP and advective and diffusive transport 

through the invert below the WP. Two different flow rates are used in these transport calculations. The 

volumetric flow rate of water into the WP is calculated by scaling the seepage flux into the drift with the 

surface area of the pits. The volumetric flux through the invert is based on the volume of water entering the 

drift rather than the volume of water entering the WP. 

Inside the WP, high solubility nuclides released from the solid matrix are carried out of the WP. 

However, low-solubility nuclides precipitate out of solution if released from the solid matrix at a 

concentration exceeding the carrying capacity of water (or solubility limit of a particular nuclide). The 

volume of water available for dissolution of waste is the amount of water in the failed WP and the difference 

between the volume of water flowing in and out of the failed WP. Table 3-5 provides solubility limits of the 

radio-elements evaluated in the TPA Version 3.2 code. 

In the invert, advective and diffusive transport is modeled through 0.75 m (2.5 ft) of concrete having 

a 30-percent porosity. The determination of whether flow through the invert occurs in the matrix or fractures 

is based on the invert matrix permeability and the average flow rate of water through the invert. Radionuclide 

sorption is modeled in the concrete invert, and the mean values of the Rds are presented in Table 3-4, together 

with values for other parameters used to compute transport in the EBS. Colloidal transport of radionuclides 

is not considered in this calculation. 

3.1.5 UZ Transport 

In UZ transport calculations, the NEFTRAN II code (Olague, et al., 1991) models 1 -D advection and 

retardation of radionuclides with chain decay. Inputs to the UZ transport model are the release rates of 

radionuclides from the EB S, the time-varying flow results from the UZ shown in Figure 3-1, and the chemical 

and physical properties of the hydrostratigraphic units between the repository and the water table 

(see Figure 3-9 and Table 3-8).

3-14
o 0 o o 04

(W) sseuJp'IAnalysis of Total-system Behavior

m0

I

,t (

0,

C C C

4

Co Li 

= 

4

Ct 

04 U, 

Ct 

I

Ct 

U, 

C 

U, 

U, oJ 

Li 

-c 

H 

I3-15

C00I

00 

4-0 0) 

> N 

,9 0 0 0& 0 0

0 

C 

t

C 

C 

on
Table 3-8. Mean values and sampled distributions of sorption coefficient, Kd (m3/kg), parameters. (Other parameters for UZ radionuclide 

transport are also included. The dash in the last column indicates a constant value for the parameter distribution.) 

Bull Frog Calico Hills Calico Hills Prow Pass Topopah Spring Upper Crater 

Element welded unit nonvitric unit nonzeolitic unit welded unit welded unit Flat unit 

Ai 3.89 x 103 1.25 x 104 1.15 x 104 9.09 x 10' 3.99 x 10' 9.54 x 10' 

(Lognormal; (Lognormal; (Lognormal; (Lognormal; (Lognormal; (Lognornal; 4.1, 3.7 x 106) 1.3 x 10', 1.2 102) 1.2 x 101,. L x 10) 9.5, 8.7 x 106) 4.2 x 101,3.8 x 106) 1.0 x 01, 9.1 x 106) C 0.00 0.00 0.00 0.00 0.00 0.00 

Cl 0.00 0.00 0.00 0.00 0.00 0.00

0.00 

0.00 

5.61 X 10 .4 

(Lognormal, 

1.5 x 10-6, 2.1 x 10-1) 

6.95 x 10 ' 

(Lognormal; 

2.3 x 10 -2, 2.1 x 10') 

9.49 x 10-5 

(Lognormal; 

3.0 x 10"', 3.0 x 10-2) 

0.00 

3.36 x 10-' 

(Lognormal; 

4.7 x 10-', 2.4 x 103) 

2.02 x 10-5 

(Lognormal, 

1.0x 10"_2_6)

0.00 

0.00 

1.78 x 10.' 

(Lognormal; 

4.8 x 10.6, 6.6 x 10") 

2.18 

(Lognormal; 

7.1 x 10-2, 6.7 x 10') 

6.32 x 10 5 

(Lognormal; 

2.0 x 10"-' 2.0 x 10"-) 

0.00 

1.07 

(Lognormal; 

1.5 x 10-4, 7.6 x 103) 

6.55 x 10 ' 

(Lognormal, 

1.3 x 109. 3.3)

0.00 

0.00 

1.62 x 10.' 

(Lognormal; 

4.4 x 10-6, 6.0 x 10-1) 

1.99 

(Lognormal; 

6.5 x 10- ,6.1 x 10') 

4.74 x 10-5 

(Lognormal; 

1.5 x 10-", 1.5 x 10.2) 

0.00 

9.47 x 10' 

(Lognormal; 

1.3 x 10"4, 6.9 x 103) 

6.00 x 10-5 

(Lognormal; 

1.2 x 10"9. 3.0)

0.00 

0.00 

1.34 x 10.3 

(Lognormal; 

3.6 x 10.6, 5.0 x 10-') 

1.63 

(Lognormal; 

5.3 x 10"-, 5.0 x 10') 

9.49 x 10-5 

(Lognormal; 

3.0 x 10"-, 3.0 x -10-2) 

0.00 

7.92x 10"' 

(Lognormal; 

1.1 X 10-4, 5.7 x 103) 

4.90 x 10 2 

(Lognormal, 

9.6 x 10"`0, 2.5)

0.00 

0.00 

5.93 x 10-4 

(Lognormal; 

1.6 x 10.6, 2.2 x 10-1) 

7.11x10"' 

(Lognornal; 

2.3 x 10.2, 2.2 x 10') 

9.49 x 10-5 

(Lognormal; 

3.0 x 10"', 3.0 x 10.2) 

0.00 

3.46 x 10"' 

(Lognonnal; 

4.8 x 10-, 2.5 x 103) 

2.15 x 10"

(Lognormal; 

4.2 x 10"I, 1.1)

4.2 1010.11) 1.0 x 10-' 2 6)

0.00 

0.00 

1.40 x 10' 

(Lognormal; 

3.8× 10-6 5.2 x 10-1) 

1.71 

(Lognormal; 

5.6 x 10-', 5.2 xA010) 

9.49 x 10-5 

(Lognormal; 

3.0 x 10"-, 3.0 x 10.2) 

0.00 

8.06 x 10"' 

(Lognormal; 

1.1×X 10-4 , 5.7 x 103) 

5.10 x 10-5 

(Lognormal;

CIl1 

I 

Np

kON

Pu 

Se 

Tc 

Th 

U

.f • € ... .. .... t IO 1. x 10 -9 3.0- ... . 26)~v
Table 3-8. Mean values and sampled distributions of sorption coefficient, Kd (m3/kg), parameters. (Other parameters for UZ radionuclide 

transport are also included. (cont'd)

rarameter .. ,, ......

Matrix Permeability 

Topopah Springs-welded 

Calico Hills-nonwelded vitric 

Calico Hills-nonwelded zeolitic 

Prow Pass-welded 

Upper Crater Flat 

Bull Frog-welded 

Unsaturated Fracture Zone 

Matrix Porosity 

Topopah Springs-welded 

Calico Hills-nonwelded vitric 

Calico Hills-nonwelded zeolitic 

Prow Pass-welded 

Upper Crater Flat 

Bull Frog-welded 

Unsaturated Fracture Zone 

Matrix Beta 

Topopah Springs-welded 

Calico Hills-nonwelded vitric 

Calico Hills-nonwelded zeolitic 

Prow Pass-welded 

Upper Crater Flat 

Bull Frog-welded 

Unsaturated Fracture Zone 

Matrix Grain Density 

Topopah Springs-welded 

Calico Hills-nonwelded vitric 

Calico Hills-nonwelded zeolitic 

Prow Pass-welded

2.00 , 10'9 m 2 

2.00 , 10"14 m2 

5.00 - 10' m2 

1.00. 10-7 m 2 

3.00 x 10 18n m2 

2.00 x 10"19 m2 

1.94 x 10"17 m2

Lognormal; 2.0 x 10.20, 2.0 x 10.`8 

Lognormal; 2.0 x 10-"1, 2.0 x 10" 

Lognormal; 5.0 x 10"19, 5.0 x 1017 

Lognormal; 1.0 x 10-18, 1.0 x 10-16 

Lognormal; 3.0 x 10"19, 3.0 x 10"17 

Lognormal; 2.0 x 10-20, 2.0 x 10-18 

Lognormal; 1.8 x 1018, 2.1 x 10.16

1.20 x 10-1 

3.30 , 10.1 

3.20 x 10-1 

2.80 x 10-1 

2.80 x 10.1 

1.20 x 10"' 

1.20 x 10

1.50 

1.30 

2.30 

1.50 

1.40 

1.70 

2.30 

2.46 x 10' kg/m3 

2.26 x 10 3 kg/m3 

2.40 - 10' kg/mr 

2.54 x 10 3 kg/m3

S..... akA• ILVII,,. I IINIrl IIHi:ll•ln

I 

.-..I
Table 3-8. Mean values and sampled distributions of sorption coefficient, Kd (m3

/kg), parameters. (Other parameters for UZ radionuclide 

transport are also included. (cont'd)

Parameter 

Matrix Grain Density 

Upper Crater Flat 

Bull Frog-welded 

Unsaturated Fracture Zone 

Fracture Permeability 

Topopah Springs-welded 

Calico Hills-nonwelded vitric 

Calico Hills-nonwelded zeolitic 

Prow Pass-welded 

Upper Crater Flat 

Bull Frog-welded 

Unsaturated Fracture Zone 

Fracture porosity for all units 

Fracture beta for all units 

Matrix and fracture longitudinal dispersivity as a 

fraction of unit

Mean

2.42 - 10 3 kg/m3 

2.57 x 103 kg/m3 

2.63 x 10' kg/m3 

8.00 x 10-13 m2 

8.00 - 10"-13 m2 

6.00 10-13 m2 

6.00, 10- 13 m2 

6.00 x 10-13 m 2 

3.00 x 10-13 M2 

1.00. 10- 12 m2 

3.16 , 10-3 

3.00

Distribution

Lognormal; 8.0 x 1015, 8.0 - 1011 

Lognormal; 8.0 x 10-15, 8.0 x 10"11 

Lognormal; 6.0 x 10-15, 6.0 x 10-11 

Lognormal; 6.0 x 10-15, 6.0 10"11 

Lognormal; 6.0 x 10-15, 6.0 x 10-11 

Lognormal; 3.0 x 10-15, 3.0 - 1011 

Lognormal; 1.0 10-13, 1.0 X 10-' 

Lognormal; 1.0 x 10, 1.0 - 10-2

1.O0x 10.1

0 

0 

0

00O
Analysis of Total-system Behavior

The water table elevation remains constant in the TPA calculations. Thus, the thickness of the UZ 

does not change with time even during the pluvial climate. Sorption in fractures is neglected because of the 

fast travel times, whereas sorption in the matrix is modeled using the sorption coefficients presented in 

Table 3-8. The effects of matrix diffusion on transport in the UZ are not modeled. 

Figure 3-10 shows the release rate for 36

C1. Because 36

C1 moves unretarded, comparison of the times 

of the release rates in this figure indirectly illustrate the UZ and SZ travel times. The EBS and UZ release 

rates are nearly the same, indicating that the UZ does not significantly delay groundwater transport. 

3.1.6 SZ Flow and Transport 

For each subarea, radionuclide transport out of the EBS and into the UZ and the SZ can be 

conceptualized as occurring in a single streamtube that originates in the repository, extends to the water table, 

and continues to the receptor location. In the SZ, streamtubes begin at the water table directly below the 

repository and continue to the receptor location. Each subarea in the repository is assigned to the nearest 

streamtube. Subareas 1 and 2 are mapped to streamtube D, subareas 3 and 4 are mapped to streamtube, B and 

subareas 5, 6, and 7 are mapped to streamtube A. Figure 3-11 shows the subareas and streamtubes used for 

the SZ transport model, and Table 3-9 provides the length of the SZ flow path by subarea. The groundwater 

travel times (GWTT) from the point where the radionuclides enter the SZ to the receptor location are 6000 yr 

for subareas 1 and 2 (streamtube D); 2700 yr for subareas 3 and 4 (streamtube B); and 2800 yr for 

subareas 5, 6, and 7 (streamtube A). Large variations in the GWTT are primarily the result of variations in 

the streamtube length, width, and flow rates. There are no subareas mapped to streamtube C, consequently, 

streamtube C, which contains 26 percent of the total SZ flow, serves to dilute the concentration of 

radionuclides in the groundwater. The total SZ flow rate in all the streamtubes is 2.56 x 101 m3

/yr 

(9.04 x 106 ft3

/yr). The relative contributions of streamtubes A, B, and D to the total SZ flow are 27, 29, and 

18 percent. 

The release rate at the outlet of the streamtubes is determined using the sum of the release rates from 

all the streamtubes and is dependent on the time-varying concentration at the inlet. Figure 3-10 shows the 

SZ release rates for 3 6C1, which is not retarded in the SZ. When compared with the time of peak UZ release 

rate, this figure also indicates the GWTT through the SZ is on the order of a few thousand years. 

The source term for the SZ transport model is the time-varying radionuclide release rate from the 

UZ calculations. Other inputs to the SZ transport model include the physical and chemical properties of the 

tuff and alluvium and the streamtube flow rates, widths, and lengths. The mean values for the SZ input 

parameters are presented in Table 3-9. 

3.1.7 Dose to the Receptor Group 

The receptor location for the basecase data set is 20 km (12.4 mi) from the repository. At 20 km 

(12.4 mi), the mean value for the pumping rate is 1.21 X 107 m3/yr (4.3 x 108 ft3/yr), which is sufficient to 

capture the entire contaminant plume. Because the TPA code assumes the volume of water pumped is 

constant throughout the TPI, values for the concentration of the well water exhibit the same behavior as the 

SZ release rates. For example, to convert from 36

C1 release rates in Figure 3-10 to concentration, the release 

rates are divided by the well pumping rate to compute the well-water concentrations.

3-19
Analysis of Total-system Behavior

100 1 

0 -2 S 10. 

104-4 

Z "-6 10 IM 

-8 10 

N All Subarea EBS 

E 10. ---- All Subarea UZ 

o0- All Subarea SZ Z 

10 "12 I I I Ii I I 

0 20000 40000 60000 80000 100000 

Time (yr) 

Figure 3-10. 36C1 normalized release rates from the EBS, UZ, and SZ for the mean value data set. 

The groundwater dose is determined by multiplying the concentration of the nuclides in the pumped 

water with the DCF. The mass of radionuclides captured by pumping is diluted in the volume of water 

extracted from the pumping well and converted from a groundwater concentration to a dose using DCFs. The 

dose to an individual of the receptor group originates from drinking and irrigation water used by an average 

adult living in Amargosa Valley. The groundwater pathway DCFs for the 11 radionuclides used in the 

basecase mean value data set are summarized in Table 3-10. 

3.2 RESULTS FROM THE MEAN VALUE DATA SET 

This section illustrates the behavior of the total system with the mean value of parameters and how 

the individual dose is influenced by the various subsystem models and parameters. Time history plots of key 

system parameters for both doses and release rates at various subsystem boundaries are presented in this 

section for the mean value single-realization case.

3-20
Streamtube

Streamtubes

Figure 3-11. SZ streanitubes assigned to each subarea.

3-21

Analysis of Total-system Behavior

I- Subarea

1 

2 

3 

4 

5 

6 

7

D
Analysis of Total-system Behavior

Table 3-9. Parameter values used for SZ flow and radionuclide transport in TPA

Mean 

1.00 x 10-2 

1.00 x 10-2 

1.00 X 10-1 

3.16 x 10-' 

1.25 x 10-1 

1.80 x 104 

1.00 X 10-2 

0.00 

1.00 

1.00 X 101 yr 

1.00 x 10' yr

Distribution

Log-uniform; 1.0 x 10-', 1.0 x 10-2 

Uniform; 1.0 x 10-1, 1.5 x 10-1 

Not used because matrix diffusion = 0

Parameter 

Mixing zone dispersion fraction 

Tuff dispersion fraction 

Alluvium dispersion fraction 

Tuff fracture porosity 

Alluvium matrix porosity 

Immobile Rd for tuff for 2 4 1

AMn 

Immobile porosity for tuff 

Diffusion rate for tuff 

Fracture Rd for tuff for all nuclides 

Min residence time for tuff 

Min residence time for alluvium 

Well pumping rate at receptor group 

at 20 km 

Mixing zone thickness at 20 km 

Alluvium Matrix Rd 241AMn 

14C 

36

C1 

24 5

Cm 

1291 

237

Np 

239pu 

79

Se 

99Tc 

230Th 

234u 

Streamtube Flow Properties 

Subarea 1 

Subarea 2 

Subarea 3 

Subarea 4 

Subarea 5 

Subarea 6 

Subarea 7

7.14 x 107 

1.00 

1.00 

7.50 x 104 

2.00 

6.24 x 10' 

1.28 x 104 

2.24 x 101 

5.48 

9.25 x 10' 

1.38 x 102 

Length (m) 

29,200 

28,600 

25,200 

24,600 

23,400 

23,000 

22,500

Lognormal; 7.5 x 104, 6.8 x 101° 

Log-uniform; 1.0, 4.0 

Lognormal; 1.0, 3.9 x 10' 

Lognormal; 4.2 x 102, 3.9 x 105 

Log-uniform; 1.0, 500.0 

Log-uniform; 1.0, 30.0 

Lognormal; 1.9, 4.5 x 107 

Lognormal; 1.0, 1.9 x 104

Streamtube 

D 

D 

B 

B 

A 

A 

A

3-22

8.75 x 106 gal/day 

1.25 x 102 m
Analysis of Total-system Behavior

Table 3-10. Biosphere dose conversion factors for groundwater at the 20-km receptor location 

Nonpluvial DCF Pluvial DCF 

Radionuclide (rem/year)/(Ci/m 3

) (rem/year)/(Ci/m3) 

241Am 6.11 x 106 4.31 x 106 

14C 1.35 x 104 8.60 x 10' 

36C1 4.52 x 104 3.02 x 104 

245Cm 6.32 x 106 4.51 x 106 

1291 1.27 x 106 7.90 x 105 

27Np 9.01 x 106 6.43 x 106 

239

pu 6.00 x 106 4.30 x 106 79

Se 2.51 x 104 1.68 x 104 

99Tc 4.74 x 103 3.29 x 103 

230

Th 9.32 x 105 6.61 x 105 

234U 5.06 x 105 3.66 x 10' 

The dose to an average individual residing 20 km (12.4 mi) downgradient of the repository is 

presented in Figure 3-12 for radionuclides with doses greater than 10-1 mSv/yr (10-6 mrem/yr). The results 

are presented for the first 10,000 and 100,000 yr, respectively. The period of 100,000 yr is chosen so that the 

effects of one cycle of the pluvial climate and the effects of WP corrosion, which occur after the 

10,000-yr TPI, can be studied. 

A peak total dose of about 2 x 108 Sv/yr (0.002 mrem/yr) was calculated during the 10,000-yr TPI. 

The dose is dominated in the 10,000-yr TPI by 1291 and 36

C1, which are nonsorbing nuclides with relatively 

long half-lives. For the 100,000-yr TPI, a peak total dose of 3 x 10-6 Sv/yr (0.3 mrem/yr) occurred at 

23,000 yr, and the dose was dominated by the nuclides 129I, 9Tc, and "

6

C1. A discussion of the TPA results 

from the 10,000- and 100,000-yr TPIs, with and without the faulting and igneous activity disruptive events, 

follows in the next two sections. 

3.2.1 10,000-Year Releases and Dose 

As evident from Figure 3-8 and explained in Section 3.1.3, all basecase releases in 10,000 yr would 

arise from initially defective WP failures. Although initially defective failure takes place at the zero year, 

releases do not occur until approximately 3400 yr later. Before 3400 yr, refluxing water enters and fills the 

failed WP. Once the WP fills, water overflows from the WP, and radionuclides leave the failed WP. 

The time histories of radionuclide releases at the downgradient boundaries of the EBS, the UZ, and 

the SZ are provided in Figure 3-13. In general, the release rates from the EBS in Figure 3-13(a) for the 

soluble radionuclides drop within a few years after the peak release, because of radioactive decay and 

because the removal of radionuclides from the WP decreases the inventory available for release. Other 

radionuclides, such as 2

-U, 237

Np, 2

13 pu, and 2

-1'fM, which are less soluble, and have relatively longer half

lives, exhibit increasing release rates in the 10,000-yr TPI. The radionuclide 241

Am also has a low solubility; 

however, with a relatively short half-life of 432 yr, the release rate decreases to match the release rate of its 

parent 245

Cm and establishes secular equilibrium. 

There is no initial increase in the EBS release rates observed from the instantaneous release of the 

gap fraction inventory. Moreover, climatic change from current to pluvial conditions could be a key event

3-23
Analysis of Total-system Behavior

E 

E 

0 

a

E 

.0E 

0 

0

100 

10-1 

10-2 

10-1 

10O-6 

10 0 

lO& 

I 0

0 -2 

0 -3

ITS 

10

Figure 3-12.

Time (yr)

0 20000 40000 60000 80000 100000 

Time (yr) 

Groundwater dose to an average individual as a function of time at the receptor location 

20 km (12.4 mi) downgradient of the repository, for the mean value data set in the: 

(a) 10,000-yr, and (b) 100,000-yr, time periods of interest.

3-24
Analysis of Total-system Behavior

5000 6000 7000 

Time (yr)

8000 9000 101

10"1 

102 

• 10, 

10o 

M S 10, 

S o10

000 4000 5000 6000 7000 8000 9000 100

Time (yr)

10-7 - , 

3000

S 24 5Cm 

- 241

Am 

237 Np 

- 2 39 pu 

-V-- 234U 

I' 0 Th 

I @ . 1291 

------- 9 Tc 

- 7 9

Se 

- 36cl 

I00

10"1 

10-2 

S10

* -6 * 10, 

34 

101 

10-2 

10-3 

C.) 

*10, 0"S 

•. 10-

10000

Figure 3-13. Release rates in the 10,000-yr time period of interest from the: (a) EBS (b) UZ; and 

(c) SZ for the mean value data set.

3-25

EB72 Egg (a)• 

F

246Cm 

- - 241

Am 

239

pu 

-- 234u 

-O2 Th 

S

-M 99

Tc 

$ 79

Se 

- - 3

GC

10-7 

30

241Cm 

-- 241

Am 

- --- Np 

•---*-- "SPu 

-v 23 4

U 

14 ?"Th ---- -- 129I 

-~---- 99

Tc 

- 79Se 

- - ci

O00 4000
Analysis of Total-system Behavior

that affects performance. The increase in infiltration rate over the 10,000-yr TPI shown in Figure 3-1 does 

not result in increased release rates from the EB S for the highly soluble radionuclides, although an effect is 

evident for the less soluble radionuclides, as discussed previously. 

The similarity between EBS and UZ releases shown in Figures 3-13(a) and (b) indicates the UZ as 

modeled does not significantly influence the releases into the SZ. One might expect the UZ to delay the 

transport of radionuclides, because the radionuclides must be transported 300 m (984 ft) from the repository 

to the water table. 

The GWTT through the UZ is only 20 yr (i.e., fracture flow) for all subareas except subareas 5 and 6, 

which have a travel time of about 1400 yr (i.e., matrix flow). Consequently, for subareas 1 through 4 and 

subarea 7, which encompass almost 80 percent of the SF inventory, the UZ does not delay radionuclide 

transport subsequent to release from the EBS. For the remaining 20 percent of the SF inventory, the 

1400-yr GWTT is relatively small compared with the 1 0,000-yr TPI. 

The SZ illustrated in Figure 3-13(c) reveals releases of only 99Tc, 1291, and 36

C1 in the 10,000-yr TPI. 

As provided in Table 3-9, these radionuclides have the weakest sorbing properties in the SZ alluvium. The 

SZ release rates presented in Figure 3-13(c) can also be compared with Figure 3-13(b) to evaluate the effects 

of flow and transport in the SZ. The GWTT computed using the streamtube flow rates and lengths in the SZ 

is about 3700 yr. However, sorption in the alluvium significantly increases the travel time for most of 

the radionuclides. 

As illustrated in Figure 3-12(a), the groundwater pathway dose at 10,000 yr is dominated by 1291 and 36C1. These nuclides contribute the most to dose because of no or little retardation during transport, a large 

initial inventory, long half-lives compared to the 10,000-yr time frame of interest, relatively large DCFs, and 

high solubilities. Tables 3-5 and 3-7 through 3-10 provide a summary of the mean values for these 

parameters. To obtain a perspective of the magnitude of the dose, a total dose of 10-11 Sv/yr (1 nanorem/yr) 

does not appear until 4500 yr in the time evolution of dose curve in Figure 3-12(a). Furthermore, the SZ 

release rate for 129I corresponding to 74,0000 Bq/yr (2 ýtCi/yr) does not occur until 6,500 yr, at which time 

the dose from 129I is 1/10th of a jtrem/yr. The only nuclides that contribute more than 10-"m Sv/yr 

(1 nanorem/yr ) to dose in 10,000 yr are 1291 and 36C1, which exhibit the peak doses at the end of the 

10,000-yr-TPI. 

The dose histories for a particular faulting event and a particular igneous event are presented in 

Figures 3-14(a) and (b). It must be made very clear that the purpose of the following discussion is not to 

compare the incremental risk posed by the faulting crust or the igneous event, but rather to illustrate the 

behavior of the underlying model abstractions for faulting and igneous activity. To determine the risk, one 

would need to multiply the additional doses caused by faulting and igneous activity by their respective annual 

probabilities of occurrence (5 x 10-6 and 1 x 10-7). For the mean value data set, there are no faulting events 

because the mean value of the threshold displacement is greater than the mean value of the credible 

displacement along a fault. However, if the threshold is made smaller than the mean value of the credible 

displacement, the faulting event occurs at about 4900 yr and causes the failure of 162 WPs. Figure 3-14(a) 

shows that the groundwater dose from the forced faulting event is approximately twice the dose without a 

faulting event at 10,000 yr. The difference between the results arises solely from the release of SF from WPs 

failed by faulting.

3-26
Analysis of Total-system Behavior

Basecase - -- Basecase with Faulting

(a) I I I I I S I I I I I

Lr

104 

102 

100 

10-2 

10-4

I I

2000 4000

Time (yr)

6000 8000 10(

2000 4000 6000 8000 

Time (yr)

00

10000

Figure 3-14. Groundwater dose in 10,000-yr time period of interest with and without: (a) faulting; 

and (b) igneous-activity disruptive events, for the mean value data set, without 

probability weighting. (The ground-surface dose is shown for releases caused by 

extrusive igneous activity.)

3-27

-u 

-i 

-I

0-4 

E 

0) 0

UlO 

0

E 

E 

C) 

0 

O

10? 

102 

100 

10-2 

10-4 

10-

0

I I I I
Analysis of Total-system Behavior

The groundwater dose from igneous activity in Figure 3-14(b) behaves similarly to the dose from 

faulting events. The increase in groundwater dose from igneous activity is smaller than that for faulting 

events because only 31 WPs are failed by the intrusive igneous activity compared with 162 WPs failed by 

the faulting event in the mean value single-realization case. Extrusive igneous events also result in a peak 

ground-surface dose of about 0.01 Sv/yr (1,000 mrem/yr) at 4900 yr, which is the time of the volcanic event, 

and the dose exponentially decreases thereafter. 

The following section presents a discussion of the TPA results from the 100,000-yr TPI for dose, 

release rates, and other intermediate values such as corrosion failure time. The results for the 1 00,000-yr TPI 

are different from the results for the 10,000-yr TPI, partly because all WPs fail from corrosion before 

17,000 yr. 

3.2.2 100,000-Year Releases and Dose 

Figure 3-8 provides the performance of the EBS showing the number of failed WPs during the 

100,000-yr TPI. Initially defective failures in all subareas account for 31 WPs, whereas of those remaining, 

928 WPs in subareas 5 and 7 fail from corrosion at 16,300 yr; and 5468 WPs in subareas 1, 2, 3, 4, and 6 fail 

from corrosion at 17,000 yr. Thus, all 6427 WPs in the repository fail by 17,000 yr. Table 3-3 provides a 

summary of the TPA input parameters that determine the WP failure time. 

The release rate histories for all 11 radionuclides at the three boundaries (i.e., EBS, UZ, and SZ 

presented in Figure 3-15) reflect the time required for the initially defective WPs to fill with water (3400 yr) 

and release radionuclides, together with the corrosion failure time of 17,000 yr. The WPs failed by corrosion 

fill relatively faster and release radionuclides relatively faster compared with initially defective failures, 

because the thermal reflux period has passed and the pluvial period has taken effect. The first peak releases 

begin at about 4000 yr, and the second peak occurs before 20,000 yr. Just as with the 10,000-yr TPI in 

Figure 3-13, release rates for radionuclides are impacted by sorption coefficients, half-lives, initial 

inventories, solubilities, and DCFs. Values for these parameters are presented in Tables 3-5 and 3-7 

through 3-10. 

When water starts to leave the WP after it has filled with water, the releases of 99Tc, 1291, and the 

other highly soluble radionuclides represent the accumulation of the radionuclides in water that occurs as 

the WP fills. The peak releases for these highly soluble radionuclides occur after the WP fills with water at 

3400 yr. As seen in Figure 3-15 for the less soluble radionuclides such as 237Np, the release rate peaks at the 

end of the 10,000-yr TPI. This implies that the solubility limit is controlling the release rate. Because 237Np 

leaves the WP at the solubility limit, the release rate from the WP is proportional to the rate of water flow 

through the WP. With a half-life of 2.14 x 106 yr, the 237

Np inventory is available for release throughout the 

simulation period. This effect is observable in Figure 3-15(a), from 3400 yr to the corrosion failure time at 

17,000 yr. After 17,000 yr, radionuclide releases decrease (i.e., not solubility-limited) following the peak 

releases at approximately 17,000 yr. The decrease in release rates for the radionuclides with low solubilities 

can be attributed to high flow rates during the pluvial period. 239pu is another actinide that is solubility

limited in ambient YM pore waters. Therefore, release rates from the EBS should be similar to 237Np as 

shown in Figure 3-15(a). 

The plot in Figure 3-15(b) represents the release rates from the seven subareas summed over all 

nuclides at the water table. Comparison of the EBS and UZ release rates in Figures 3-15(a) and (b) shows 

that the UZ has little delaying effect, not only on the transport of 9Tc, a nonsorbing nuclide, but also on the

3-28
Analysis of Total-system Behavior

EBS ''''(a) MGMc 

o - - 241

Am 

- •- 2 39 pu 

"102 C)u _____________________24U 

S (UU U lo-9 

0 In 

lo l 90 ',ýc 

(• -A Tc 

10 14 

0 20000 40000 60000 80000 100000 

Time (yr) 

1 0!UZ III( )2C 

Sto' 2aNAm 

a 237 

(2U 

6214 4 T 

S10" to' 

C 7Se 

0 20000 40000 60000 80000 100000 

Time (yr) 

1o z - 24sc 

E3 • 241Am 

6 217l 

o10. & 

2asPu 

4) U o104- CTI -'3dT 

10-4 

0 20000 40000 60000 80000 100000 

Time (yr) 

Figure 3-15. Release rates in 100,000 yr from the: (a) EBS; (b) UZ; and (c) SZ for the mean value 

data set. 

3-29 

coz
Analysis of Total-system Behavior

transport of the other 10 radionuclides. As discussed in the previous section, the UZ does not significantly 

affect the release rates because flow mainly occurs in fractures with no retardation. 

Figure 3-15(c) illustrates the performance of the SZ in the 100,000-yr TPI. The figure shows the SZ 

release rates at a distance of 20 km (12.4 mi) from the repository. In the SZ, sorption significantly affects the 

release rates. The only radionuclides that arrive at the receptor location with a release rate greater than 

3 7 Bq/yr (10 -6 Ci/yr) are 99

Tc, 79

Se, 1291, and 36C1. Retardation of the remaining seven radionuclides in the 

alluvium delays their time of arrival past the 100,000-yr TPI. The SZ alluvium sorption coefficients for all 

radionuclides are provided in Table 3-9. 

The radionuclides contributing to the 100,000-yr dose are completely different than those dominating 

the 10,000-yr dose. For the 100,000-yr TPI, the dose provided in Figure 3-12(b) is dominated by 99Tc and 

1291, with smaller contributions from 36C1 and 79Se. The radionuclide contributing the most to the peak dose 

at 23,000 yr is 1291, with minor contributions from 99

Tc and 136

C1. Although 1

3 6

C1 has a relatively long half-life 

at 3.01 x 10' yr, the chloride inventory is small (see Table 3-7). Thus, although contributing significantly to 

peak dose at 23,000 yr, 36

C1 rapidly becomes an insignificant contributor to dose. Figure 3-12(b) also 

illustrates the impact of retardation in the alluvium on the arrival of radionuclides at the 20-km (12.4-mi) 

receptor location. Radionuclides with lower retardation factors arrive earlier than those with higher values. 

The retardation factors for 36C1, 1291, 99

Tc, and 79 Se are 1, 2, 5.5, and 22.4, respectively. The reasons 99

Tc and 1291 dominate the dose in Figure 3-12(b) are: (i) high solubility in the water contacting the SF; (ii) almost no 

retardation; (iii) large initial inventory; (iv) long half-lives; and (v) relatively large DCFs. Tables 3-5 and 3-7 

through 3-10 provide summaries of the values for these parameters. 

Figures 3-16 and 3-17 present 99Tc and 237

Np release rates and 99

Tc dose, respectively, by subarea 

and for the repository. The EBS release rates for 99

Tc and 237

Np in Figure 3-16(a) exhibit similar behavior 

with the subareas having the largest inventory contributing the most to the total release. The number of WPs 

in each subarea, which are directly related to the inventory, are 1663; 1767; 855; 472; 654; 73 8; and 278, for 

subareas 1 through 7, respectively. Subareas 1 and 2 are the largest subareas and show the highest release 

rates, whereas subarea 7 contains the fewest WVPs and has the lowest release rates. 

The plots of the UZ releases in Figure 3-16(b) indicate that the 99Tc and 237

Np release rates are the 

same as the EBS releases in Figure 3-16(a) in all subareas except 5 and 6. Only subareas 5 and 6 have the 

Calico Hills nonvitric unit (Figure 3-9), which has relatively high matrix permeability compared with other 

units. At the infiltration rate corresponding to the mean value data set, only matrix flow can occur in this unit. 

Flow occurs in the fractures for subareas 1, 2, 3, 4, and 7, with GWTTs of about 20 yr and no retardation. 

However, for subareas 5 and 6, the transport of 237

Np is retarded in the matrix and the effects of the 

time-varying UZ flow change the 99

Tc and 237

Np release rates. As evident in Figure 3-16(b), retardation in 

the matrix produces a greater effect on the 237

Np UZ release rates than the release rates for 99Tc, which is not 

retarded in the UZ matrix. 

The SZ release rates for 99

Tc in Figure 3-16(c) exhibit a delay when compared with the 99

Tc UZ 

release rates in Figure 3-16(b). However, the general characteristics of the engineered barrier and UZ releases 

are preserved insofar as the peak releases arising from initially defective failures and corrosion failures are 

apparent in the plot. The variability by subarea is also consistent for the 99

Tc release rates. There is no 2'37Np 

release from the SZ because of retardation in the SZ alluvium.

3-30
Analysis of Total-system Behavior

S~101 19 To 37 Np(a) 

10 BS 10 2 EBS 

2 1010-o 

Sio/ 

S -- Total -v Subarea 4 1 -- Total - - Subarea 4 

S io• -E0 Subarea 1 -------- -2--- E Subarea 1 -10- Subarea 2- Subarea 6 4 l0 -C- Subarea 2- Subarea 

-Subarea 3- Subarea 7 X Subarea 3 - Subarea 7 

0 20000 40000 60000 80000 100000 0 20000 40000 60000 80000 100000 

Time (yr) Time (yr) 

100 

S-10 

Total 9 Subarea 4 04 Total V Subarea 4 S10 4 ED Subarea I' l -• - 1E Subarea-- I ~e 

8e--- Subarea 2---- Subaa 5 i 10 - Subarea 2 a Subarea 

-E- Subarea 3- Subarea 7 10-X Subarea 3 Subarea 7 10 , I l•o 10 2 006o o , 0. I o 

0 20000 40000 60000 00000 100000 0 20000 40000 80000 80000 100000 

Time (yr) Time (yr) 

be9Tc 

V- SZ i -zl 0*2 SZ 

1021 (NO RELEASE) 

Total - Subarea 4 -- 4 Total V Subarea 4 

- Subare- 3 0- Subarea 2 Ie . 6 

-4 -- Subareaal 3 - Subar, 7 -0E----- Subarea 3- Subarea 7 

0 20000 40000 60000 80000 100000 0 20000 40000 60000 80000 100000 

Time (yr) Time (yr) 

Figure 3-16. "a7Np and 99

Tc total release and releases by subarea in 100,000 yr from the: (a) EBS; 

(b) UZ; and (c) SZ for the mean value data set. 

3-31 

003
S

Analysis of Totalsystem Behavior

20000 40000 60000 

Time (yr)

I

E 

E 

0 

0"

Figure 3-17. "Tc groundwater doses, total and by subarea, in 100,000 yr, for the mean value data set.

The groundwater doses for 99

"'Tc by subarea are shown in Figure 3-17. The general characteristics of 

this plot match the SZ release rates for e"Tc in Figure 3-16(c). For 100,000 yr, the subareas with the largest "9

•Tc release rates and dose in Figure 3-17 contain the greatest amount of SF (ie., the subareas listed from 

the largest to the smallest amount of SF are subareas 2, 1,3, 6, 5, 4, and 7). The effects of GWTT on dose 

at the receptor location is evident in Figure 3118 with the peak dose from subareas I and 2 arriving at about 

20,000 yr after peak doses from subareas 3 through 7. The SZ travel times vary by subarea because subareas 

use different streamtubes. Subareas 3 and 4 are assigned to streamtube B and exhibit the shortest SZ travel 

times, whereas subareas 5, 6, and 7 are assigned to streamtube A, and subareas I and 2 use streamtube D. 

The longest travel times are found in streamtube D (see Table 3-9 for streamtube lengths).

Thedose history for faulting events and igneous activity2 over 100,000 yris presented inFigure 3-19. 

As with the results for the 10,000-yr TPI, using the mean value data set results show no faulting events 

because the mean value of the threshold displacement is greater than the mean value of the credible 

displacement along a fault. However, if the threshold is made smaller than the credible displacement, the 

faulting event occurs at about 4900 yr and causes the failure of 162 WPs. Figure 3-19(a) shows that the 

groundwater dose from the faulting event is approximately twice the dose without a faulting event from about 

10,000 to 17,000 yr. After 17,000 yr. the releases from WPs failed by corrosion dominate the groundwater

6

These results are presented only to show the process-level trends and must be used in proper context, because these are not weighted by appropriate probabilities. The annual probability for the faulting event is 5 x W0 and for the igneous event is 

I x 10"' yr'.

3-32

cOLý

10"1

-- Subarea 7 

80000

10,

10o

10o7

10,

0 100000
Analysis of Total-system Behavior

100 = 

(a): 

-1 Total Dose 

10-1 - Subarea 1 

-- Subarea 2 

X Subarea 3 

ia- - Subarea 4 - Subarea 5 

A- Subarea s 

E ® 10-3 -V-- Subarea 7 

E 

u• 1 0 "4 

0 

10s 

0 2000 4000 6000 0000 10000 

Time (yr) 

100 

I = 

10-1 

•,1- -. •142 to 

E Total Dose 

-R Subarea I 

) 04 

Subarea 2 

0 X Subarea 3 

o -+---- Subarea 4 

1 Subarea5 

z4" "Subarea 

-Q• Subarea 7 

10 .61 II t I I I II 

0 20000 40000 60000 80000 100000 

Time (yr) 

Figure 3-18. Groundwater dose, total and by subarea, in: (a) 10,000, and (b) 100,000 yr, for the mean 

value data set. 

3-33

C05
Analysis of Total-system Behavior

40000 60000 

Time (yr)

20000 40000 60000 

Time (yr)

Figure 3-19. Groundwater dose in 100,000 yr with and without: (a) faulting, and (b) igneous activity 

disruptive events for the mean value data set, without probability weighting. (The 

ground-surface dose is shown for releases caused by extrusive igneous activity.)

3-34

10 4 

102 

100 

10-2

-' I ' , , I ' I I , I la _____ (a)~ 

Basecase 

Basecase with Faulting

E 

0 

0

10"

106 

0 20000 80000 100000

E. 

E 

4) 

0 

0

10 4 

102 

10 0 

10"2 

10 4 

10 6

-- Basecase 

--0-- with IA - GW 

----X-- with IA - GS 

-E-- with IA - GW & GS

IA = Igneous Activity 

GW = Groundwater 

GS = Ground Surface

0 80000 100000
Analysis of Total-system Behavior

dose, and the results plotted in Figure 3-19(a) of the groundwater dose with and without faulting events are 

not distinguishably different. 

The groundwater dose from igneous activity over the 100,000-yr TPI in Figure 3-19(b) behaves 

similarly to the dose from faulting events. As with the results for the 10,000-yr TPI, the increase in 

groundwater dose from igneous activity for 100,000 yr is smaller than that for faulting events because only 

31 WPs are failed by the intrusive igneous activity, compared with 162 WPs failed by the faulting event. 

Extrusive igneous events also result in a ground-surface dose that peaks at about 10 mSv/yr (1000 mrem/yr) 

when the volcanic events occur at 4900 yr and exponentially decreases thereafter. At about 12,000 yr, the 

groundwater and ground-surface contributions to dose are equal. From 17,000 yr, when all the WPs have 

failed by corrosion, through 100,000 yr, groundwater dose dominates the receptor dose. The doses presented 

in Figure 3-19 are not probability-weighted. 

3.3 MULTIPLE-REALIZATION ANALYSIS 

The performance of the YM repository is evaluated with a probabilistic approach that comprises 

results from simulations performed with multiple realizations. This approach uses the probabilistic sampling 

of input data to compute dose at a receptor location 20 km (12.4 mi) from the repository during time periods 

of 10,000 and 100,000 yr. Although the deterministic approach (previous section) was presented to illustrate 

in detail how the behavior of the various components or processes influences other components or dose, the 

probabilistic approach provides a range of results that shows the variation in the output resulting from the 

combined effects of the variability in the input data. Also, trends not evident in the results from the 

deterministic data may become evident in the probabilistic results. 

Probabilistic sampling is conducted using Latin Hypercube Sampling (LHS) (Iman, et al., 1980) for 

the 250 realizations, which is sufficiently large to obtain convergence in results while maintaining 

computational efficiency. Each realization uses a set of values generated from probability distribution 

functions specified in the TPA input file. The probability distribution functions are constructed for the input 

parametersthought to contain uncertainty and variability, using available data and interpretation. Uncertainty 

arises from a lack of complete information, whereas variability is the natural or inherent variance in the value 

of a parameter. 

The previous section presents TPA results computed with mean values forthe distributions specified 

in the basecase data set. The basecase data set comprises the best available information of the TPA input 

parameters. In the basecase data set, of the 838 parameters, 592 parameters are defined as constants, and 

246 parameters are specified with probability distribution functions. The basis for assigning a constant value 

or a probability distribution to the parameter depends on various factors. For example, constant values are 

assigned to parameters that are either well-characterized or have negligible variability. Probability 

distribution functions are assigned to parameters with either a natural variability or uncertainty that has been 

observed in data. Expert elicitation also provides a valid basis to assign a constant value or a probability 

distribution function to a parameter. The selection of the particular distribution type, such as normal, 

uniform, or beta, depends on the information available for the parameter and may involve either the best fit 

of data to a distribution or a reasonable assumption of the distribution type. Specification of a probability 

distribution function in the TPA code consists of a distribution type and limits (e.g., uniform with a minimum 

of 0 and a maximum of 100, or log-triangular, with a minimum of 1.0 x 10-1, maximum of 1.0 x 10-', and 

a peak of 1.0 x 10-'). The impact of assuming a particular distribution for a parameter is evaluated in 

sensitivity analyses.

3-35
Analysis of Total-system Behavior

When the TPA code is executed for a realization of the parameter vector, dose to the receptor is 

calculated for realization. The results from all Monte Carlo realizations using the LHS sampler are plotted 

to evaluate the repository performance. For example, dose to the receptor is presented in a scatterplot of peak 

dose versus time of peak dose, a time history of average and expected dose for all realizations, and a CCDF 

of peak dose. The expected dose is computed by averaging the doses at an instant of time from all 

realizations. The resulting curve is a time-dependent dose curve that represents the expected dose. The peak 

expected dose is the largest expected dose obtained from the expected dose curve versus time. For example, 

groundwater dose from a single realization using the mean value data set is shown in Figure 3-18, and the 

expected dose from multiple realizations is presented in Figure 3-20, which also provides dose from 

individual realizations. Additionally, the relationship between dose and intermediate results, such as WP 

failure time, flow of water onto a WP, and radionuclide release rates, is presented for all realizations. 

This section provides results from simulations conducted with the TPA Version 3.2 code, using the 

basecase data set with 250 realizations. For the major components of the TPA code, results are summarized 

and trends presented. The values and distributions of the TPA parameters in the basecase data set used to 

generate the multiple-realization results are provided in Tables 3-1 through 3-10, and the correlated 

parameters with associated correlation coefficients are presented in Table 3-11. 

3.3.1 UZ Flow 

The variation in the mean, minimum, and maximum infiltration rates is illustrated in Figure 3-21. 

For the mean infiltration rates, a present-day climate exists from 0 to about 3000 yr, and 89,000 to 

100,000 yr, with the pluvial climate occurring between 3000 and 89,000 yr. Figure 3-21 shows that the range 

from the minimum to the maximum infiltration rates is approximately 1 order of magnitude. This range is 

related to the TPA input parameter for the initial infiltration rate, which has a uniform distribution from 1 

to 10 mm/yr (0.0394 to 0.394 inches/year). 

Subarea 3 exhibits the largest infiltration rates, because of higher infiltration at the ground surface 

above subarea 3 attributable to near-surface processes such as elevation and soil depth, whereas subareas 1, 

2, and 4 have the lowest infiltration rates. In any single realization, the largest difference among the subarea 

infiltration rates is approximately 10 percent. The minimum and maximum pluvial infiltration rates, which 

occur between about 3000 and 89,000 yr, vary from about 10 to 280 mm/yr (0.394 to 11.02 in/yr) for all 

realizations and subareas. 

In realizations with higher flow rates, there are generally more radionuclides released from the EB S 

because of a greater amount of water available to dissolve radionuclides. This effect is illustrated in 

Figure 3-22, which provides scatterplots of the cumulative releases of 99

Tc and 237

Np in 100,000 yr versus 

the maximum flow rate into the repository for each realization. The variability in the maximum flow rate is 

slightly more than 1 order of magnitude, whereas the cumulative release varies over 3 orders of magnitude. 

Although these releases are solubility limited, there is not a one-to-one relationship with the flow rate 

because of other parameters such as flow factors and the subarea wet fraction that affect the EBS release rate. 

Figure 3-23 shows the trend of higher peak groundwater dose for maximum flow rate in both the 

10,000- and 100,000-yr TPIs. Higher flow rates in the UZ transport a larger mass of radionuclides from the 

EBS and result in higher groundwater dose. Although the peak flow rate varies about 1 order of magnitude, 

the variability in the peak groundwater dose spans 5 orders of magnitude.

3-36
Analysis of Total-system Behavior

102 

100 

loe 

102 

loe 1le

Time (yr) _

I I I _______

Expected Dose 

\ -- -- :.-7=-, -: ••

*6' - - - - -- 1

'-.7-

V 

ii'

20000 40000 60000 80000 100000

Time (yr)

Figure 3-20. Groundwater dose in: (a) 10,000, and (b) 100,000 yr, including the average dose, for 

250 realizations.

3-37

E 

0 a 

01

10000

102 

100 

102 

lOe 

1078

V 

0 

a

0

I I I I I I i I I i i ,

L

• I . . . i
Analysis of Total-system Behavior

Table 3-11. Correlated parameters and correlation coefficients for the multiple realizations

Correlated Parameter 1 

SubAreaWetFraction A 

SubAreaWetFraction M 

FowFactor A 

FowFactor M 

FowFactor S 

AlluviumMafrbkRDSAV_AAm 

AlluviumMatrixRDSAVAm 

AlluviumMatrixRDSAVAm 

AlluviumMatrixRDSAV Am 

AlluviumMatrixRDSAVPu 

AlluviumMatrixRDSAVPu 

AlluviumMatrixRDSAVPu 

AlluviumMatfixRDSAV_Np 

AlluviumMatrixRDSAV_Np 

AlluviumiMatrixRD SAV Th

E 

E 

cc 

C 

0 o 

L.. 

4.' 

ii300 

250 

200 

150 

100

50

20000 40000 60000 80000 

Time (yr)

Figure 3-21. Mean, maximum, and minimum infiltration rates in the UZ for each 

subarea mean infiltration rate is averaged over all 250 realizations.)

subarea. (The

3-38

0 100000

Correlated Parameter 2 

realAverageMeanAnnuallnfiltrationAtStartn[mm/yr] 

atrixPermeabilityTSw_[m2] 

realAverageMeanAnnuallnfiltrationAtStart[mm/yr] 

atrixPermeabilityTSw_[m2] 

ubAreaWetFraction 

Alluv iumMatrixRDSAVPu 

Alluv iumMatrixRDSAV_U 

Alluv iumMatfixRDSAV_Np 

Alluv iumMatrixRDSAVTh 

Alluv iumMatrixRD SAV U 

Alluv iumMatrixRDSAVNp 

Alluv iumMatrixRDSAVTh 

Alluv iumMatrixRDSAVTh 

Alluv iumMatrixRDSAVU 

Alluv iumMatrixRD SAV U

Correlation 

0.631 

0.623 

0.224 

0.13 

0.366 

0.964 

0.346 

0.837 

0.112 

0.489 

0.881 

0.109 

0.260 

0.610 

0.165
Analysis of Total-system Behavior

106 

_10s 

c 104 

"102 

10 

100 

S10i 

0 

( 104 

C 101 

"106 

0 10 

10o

(a) 

* 0

: 9Tc 

- . 0. 4 

- .0 

0

IOe

I I I I I INp-237 

I I I I I

105

Maximum Flow Rate (m3/yr)

* .0 

0

* 0

(b) 

I I I 1 I I I

Maximum Flow Rate (m3lyr)

Figure 3-22. Cumulative release rates of 99

Tc and 237Np from the EBS plotted with the maximum flow 

rate of water into the repository, for 250 realizations.

3-39

• o

10

10
100 

L. E 10 

S102 

*0 

0 

0 

10-10

2xl 0'

1x10s 

Maximum Flow Rate (m31yr)

4x10' 6x105 

Maximum Flow Rate (m3

/yr)

1.5x105 2x

8x10' lx

10,000 yr (a): 

* t *p=,-. .. **. *' '. ". 

ee*e 

S•* 

al** 

Fe 

? ;,**•[,*w ,

10, 

106

Figure 3-23. Peak groundwater dose in: (a) 10,000, and (b) 100,000 yr, plotted with the maximum 

flow rate of water into the repository, for 250 realizations.

3-40

Analysis of Total-system Behavior

0 5x1 e

10 3 

101 

10-1 

10 

10 

10 7

E1 

E 

0 

V~ 

0 

IL

- ,O ''y I ' I I ' ' I ' I ' -= 10,00 yr(b) 

- -- U-': . 

: fb4%t2..: ~

r- "1 

II , , I , , , I , I, ,

0
Analysis of Total-system Behavior

3.3.2 Near-Field Environment 

The time history of average WP temperature is provided in Figure 3-24(a), for each subarea. The 

subarea variability in the WP temperature from 10,000 and 100,000 yr is small compared with the difference 

in temperatures exhibited over about 100-10,000yr, with a maximum difference in average WP temperature 

about 10 °C (50 -F) at 1,000 yr. In the 100-10,000-yr TPI, the greatest amount of heat is generated from the 

radioactive decay of SF. 

Figure 3-24(b) shows the average, minimum, and maximum WP temperatures for subarea 1. The 

range between the minimum and maximum temperatures is about 10 'C (50 'F) at 100-1000 yr. 

Subareas 2-7 exhibit the same general variability in the average, minimum, and maximum WP temperatures 

as subarea 1. Inasmuch as the variation from the average temperature among the subareas is less than 

5 percent in Figure 3-24, the parameters sampled in the basecase data set do not have a large influence on 

the range of computed WP temperatures. This small difference could affect corrosion calculations because 

the corrosion rate is sensitive to the WP temperature. 

3.3.3 WP Degradation 

In the basecase data set, the outer and inner overpack materials for the WP are specified as carbon 

steel and Alloy C-22, respectively, consistent with the DOE TSPA-VA design (U.S. Department of Energy, 

1998). Figure 3-25 presents results from all realizations and the expected failure curve of WPs failed by 

corrosion for the probabilistic case. The WP failure times by corrosion range from about 11,000 to 46,000 yr, 

with an average corrosion failure time, for 250 realizations, of approximately 20,000 yr. There are no WPs 

failing from corrosion before 10,000 yr. It should be noted that effects of welds and closures, which could 

substantially decrease WP failure time, have not been considered in this calculation. 

The relationsl~p between average WP failure time and both the peak groundwater dose and the time 

of the peak groundwater dose is presented in Figure 3-26. The variability in the peak groundwater dose in 

Figure 3-26(a) ranges over 5 orders of magnitude, whereas the average WP failure time is 11,000-46,000 yr. 

An overall trend of decreasing peak groundwater dose with increasing average WP failure time is observable 

in this figure. When the WP failure time is delayed, more of the SF inventory decays and the transport time 

through the UZ and SZ is delayed. Thus, the peak groundwater dose is generally expected to be lower for 

larger WP failure times. 

The average WP failure time and time of peak groundwater dose are provided as a scatterplot in 

Figure 3-26(b). In all instances, the peak groundwater dose occurs after the average WP failure time for 

100,000-yr analyses. However, for approximately one-half the realizations, the peak groundwater dose occurs 

at times greater than 90,000 yr. 

3.3.4 WP Release 

Water transports radionuclides out of the WP and into the UZ and SZ to the receptor location. Thus, 

the flow rate of water in the UZ should be positively correlated with the release from the EBS. The 

relationships between the flow of water into the WP and the release of 9Tc and 237

Np are illustrated in 

Figure 3-22. Furthermore, higher release rates contribute to greater peak groundwater doses, as shown in 

Figure 3-27, for 9Tc and 2

13Np, in subarea 1. The subarea 1 release rates presented in these figures are 

representative of release rates from subareas 2 through 7. The 9Tc and 23 7

Np peak release rates and time of

3-41
Analysis of Total-system Behavior

250 ' ' 1'' "' Ili -"- (a): 

2 200 

I..

a_ 

.. 150 E 

io,100 

0 • Subarea I - Subarea 5 

CL 50 - -- Subarea 2 Sarea a 55 

- - Subarea 3 - Subarea 7 

cc X Subarea 4 Average all subareas 

0 r ,I f i l I II l 1 1 1 1 i .l l 1 1 1 1 1 l 1 1 , 1 1 1 i I 100 101 102 103 4 

Time (yr) 

2 5 0 . . . . . . .. I . . . . . .. I . . . . . ... I .. . .. . & (b): 0 

4) m 200 

cc 

4) 

CL 150 

E 

I0C 100 

C, Subarea 1 d) 50 5- Subarea 1 minimum 

0 Subarea 1 maximum 

0 

10° 101 102 103 10 4 10 

Time (yr) 

Figure 3-24. WP surface temperature: (a) averaged over the repository and for each subarea and 

(b) in subarea 1; the average, minimum, and maximum values, for 250 realizations.

3-42
Analysis of Total-system Behavior

Average 

"O.8 

U

S0.6 

0 

S0.4 

S.. 

u. 0.2 

0 20000 40000 60000 80000 100000 

Time (yr) 

Figure 3-25. Fraction of Wps failed by corrosion for each of the 250 realizations, and the average 

fraction of failed WPs. 

the peak release rates are presented in Figure 3-28. This figure shows that nearly all the 9Tc and 237

Np peak 

releases occur between 11,000 and 46,000 yr, when WPs fail by corrosion. The variability in the peak release 

rates is slightly less than that for the groundwater dose. The peak release rates of 99Tc and 237

Np vary over 

3 to 4 orders of magnitude, whereas the peak groundwater dose exhibits over 5 orders of magnitude 

variability. Factors that influence the radionuclide transport from the EBS to the receptor location, such as 

well pumping rate and retardation, cause a greater variability in the groundwater dose than the release rate 

from the EBS. 

Figure 3-29 provides the release rate of 99

Tc from subarea 1 for 10,000 and 100,000 yr. The results 

in this figure demonstrate that the variability in the EBS release rates is greater in the first 10,000 yr than in 

the period between 10,000 and 100,000 yr. It appears that the variability can be attributed to factors such as 

lower flow rates at times less than 10,000 yr, initially defective failures, and time to fill up the WP. Releases 

before to 10,000 yr are from initially defective and seismic failures, whereas the peak releases observed after 

10,000 yr result mainly from corrosion failures. The magnitude of the releases extends over 4 to 5 orders of 

magnitude and arises partly from the variability in the flow rate into the EBS. 

The cumulative release ofradionuclides from the EBS is plotted in Figure 3-30, along with the initial 

inventory and the UZ and SZ releases. This graph reveals that more radionuclides are released relatively 

early, with most of the releases occurring during the first 50,000 yr. Radionuclides with a combination of 

the higher solubility, half-life, and initial inventory, such as 9Tc, exhibit the largest release rates. Source 

depletion and radioactive decay result in lower releases toward the end of the 100,000-yr TPI.

3-43
Analysis of Total-system Behavior

10 2 

101 

10"0 

10.1 

102 

10 -4 

10 4

0'' (a)~ * 1 0l 

*, *'o. Oo 

• 0• o 

00 0

E 

Z1 0 

"CD 

0 

0 

0 

ED l-o 

0. 

0. 

I@

o 

CA

Average Waste Package Failure Time (yr)

10

Average Waste Package Failure Time (yr)

Figure 3-26. Average WP failure time by corrosion plotted with: (a) peak groundwater dose; and 

(b) time of the peak groundwater dose, for 250 realizations.

3-44'

* 0 

.0

10 5

10 5 

10 

4

10 4
Analysis of Total-system Behavior

102 

101 

100 

10-1 

102 

10.3 

10-4

10-4 10 -3

I I I 111111 I

I I |u .Il| 0 0 00:.0" 

0L 0O*

0

* 0 0 * 0 

0 

0

. a)

IQ-) 

E 

C 

0) I0

- I 1 11111I1l 

9TC 

Subarea I 

0 

I I I . . . I . . . I ... ... 2I

10.2 10

Peak Release Rate (Cilyr)

100

U I I IIEh1

2 7 Np 

Subarea I

n i , * ' , I

S 0 

S 0 

0 

0

0 * 0 

.0 0

* • 0 . * *• O° 

*O qq 

oO 0.'• 

• ,.* 

0* 

0•ee 

g*

0

, I .

10 4

I , , , , , , , , I

10 

Peak Release Rate (Ci/yr)

1021

*,

I I I ,1II

10"1

Figure 3-27. Peak groundwater dose, and the: (a) 9Tc, and (b) 3

7Np, peak release rates from 

subarea 1, for 250 realizations.

3-45

,

0 * 0

101

102 101 

-100 

a,0 

0 

10 

0-2 

C 102 

0 

L. _ 

010, 

cc 

am

10- 1 

10-5

(a) i•

I I I I I ~~~ II ~~I I I I . . .. . . . i

I
Analysis of Total-system Behavior

I I ] I 

-,0

101 

10 0 > 100 

I•10-1 a) 

S10

S10, 

7,. 

10.

0 20000

O 0 

u

ITS I

* 4

0 A

' I ' I ' •Tc (a) 

EBS 

Subarea I 

I 

00 

I. 

0 

I II I I I i I I

40000 60000 

Time of Peak Release (yr)

80000 100000

'j I I ' 

23"7 Np (b) 

EBS 

Subarea I r .*:d! 

• ,"*1* ;- 0 ~ 

01 0. 

e% •

* 0 

0o • 0 

0O1

I I

20000 40000 60000 

Time of Peak Release (yr)

80000

Figure 3-28. Peak release rates from the EBS and time of the peak release for: (a) 99 Tc, and (b) 27Np, 

in 250 realizations.

3-46

r@0 *0e So * jE 

* i.e * - 0 

0 

0 0 

I I I I

0-% 

2 

10-1 

0 cc 

_ 10-4 

M () 

C0

100000

S. . . . 1 I I r

, i i , I I I I II I I

I I

0
2000 4000 6000 8000 

Time (yr)

Ave.ige II

+,

10,

it ~ ~ 2 -

1 0L 

0 20000 40000 60000 

Time (yr)

80000 100000

Figure 3-29. " Tc release rates from the EBS over: (a) 10,000, and (b) 100,000 yr, including the 

average release rate, in subarea 1, for 250 realizations.

3-47

Analysis of Total-system Behavior

10 1 

10-1 

10, 

10,

cc 

W"

10,

0

10 1

" "TC

10000

(b) 

4) 

Z 

M)

-l

I

10 -7
Analysis of Total-system Behavior

3.3.5 UZ Transport 

Figure 3-31 presents 9Tc, 237

Np, and 239

Pu average release rates for the basecase data set. In the first 

10,000 yr, releases are from initial WP failures. The failure of WPs from corrosion begins after 10,000 yr 

and an increase in the release rates is evident in Figure 3-31, from 10,000 to 20,000 yr, with the peak average 

release rate for 250 realizations occurring at approximately 20,000 yr. 

The results in Figure 3-30 indicate that the UZ releases are only slightly less than the EBS releases 

and suggest that the effects of the hydrostratigraphic units beneath the repository on the radionuclide release 

rates are not significant. 

Figure 3-32 provides the 9Tc release rate from the UZ, for subarea 1, from 10,000 and 100,000 yr. 

When compared with the EBS release rates in Figure 3-29, these results demonstrate that the movement of 

"

99

Tc through the UZ is not significantly different. As with the EBS, releases from the UZ before 10,000 yr 

are from initially defective and seismic failures, whereas the peak releases observed after 10,000 yr result 

mainly from corrosion failures. The magnitude of the releases extends over 4 to 5 orders of magnitude and 

arises partly from the variability in the flow rate into the EBS. 

The conclusion that the UZ has a small effect on the EBS release rates is further supported by the 

results for the relatively short UZ GWTTs shown in Figure 3-33. The average UZ travel time is about 530 yr 

with a range 200-1200 yr, which is small, compared with the 10,000- and 100,000-yr TPIs. Differences in 

the travel times arise from distributions specified in the basecase data set for the porosities of the 

hydrostratigraphic units below the repository and for the climate conditions used to determine the UZ 

flow rates. 

3.3.6 SZ Flow and Transport 

Release rates from the SZ are presented in Figure 3-34 for 9Tc, 237

Np, and 239

pu. The 99Tc, 237

Np, and 

239pu UZ and SZ release rates can be significantly different because of the flow path length and retardation 

in the SZ alluvium. The path length thickness in the SZ alluvium ranges from 8000 to 12,000 m, whereas the 

UZ path length is about 3 00 m (984 ft). Saturated zone retardation occurs in the alluvium. For UZ retardation 

to occur, flow needs to be in the matrix. Because UZ flow is mainly in fractures, UZ retardation has little 

effect on delaying radionuclide transport. Additionally, the average retardation factors for Tc, Np, and Pu 

are 1, 9, and 10,000 in the UZ matrix; and 5, 62, and 13,000 in the SZ alluvium, respectively. Consequently, 

the longer flow path, combined with greater retardation, has a larger effect on the SZ release rates than on 

the UZ release rates. These effects are apparent in the UZ and SZ release rates plotted in Figures 3-31 

and 3-34. Compared with the releases from the UZ, 9Tc and 237

Np releases are smaller from the SZ and, 

because of a larger retardation factor, there is no Pu released from the SZ in 100,000 yr. 

The effect of retardation and of the flow path length, on the 9Tc SZ release rates for subarea 1, from 

10,000 and 100,000 yr, is evident, when comparing Figure 3-35 with the UZ release rates in Figure 3-32. 

Higher retardation factors increase the SZ travel time and shift the release rate to the right (i.e., later time). 

The average GWTT in the SZ is approximately 3680 yr, compared with about 500 yr for the UZ (see 

Figure 3-3 3). For each subarea, the minimum travel times vary from 2130 to 473 0 yr, whereas the maximum 

travel times range from 3320 to 7240 yr. Table 3-12 provides a summary of the average, minimum, and

3-48
Analysis of Total-system Behavior

109 

) 1,7 

"• 101 

E 10'

10 -3 

Figure 3-30. 

10°

0 20000 

Cumulative releases from 

inventory in the repository.

40000 60000 80000 100000 

Time (yr) 

the EBS, the UZ, and the SZ, together with the initial

IV0 

102 

le. 

10, 

I 08

0 20000 40000 60000 80000 

Time (yr)

100000

Figure 3-31. UZ average release rates of "Tc, "

7Np, and "gPu, for 250 realizations.

3-49

c

4) 

N 

M. 

!',
2000 4000 6000 8000 

Time (vr)

A "verage I

20000 40000

Time (yr)

60000 80000

10000

(b)

100000

Figure 3-32. UZ release rates of 9Tc over: (a) 10,000, and (b) 100,000 yr, including the average release 

rate, in subarea 1, for 250 realizations.

3-50

Analysis of Total-system Behavior

101 

"I- 10"1 

0 

U) 6 10

10 7 

10 9

0

101

99Tc 

10.1 

10 

S 10"'

10 "7 

10" -9 

0
Analysis of Total-system Behavior

100 

x 10 

0) 

i 10103. 

lJ 

Figue-33

Time (yr) 

CCDF function of UZ groundwater travel times, for 250 realizations.

I._. 

cc 

4) 

0 

0)

100 

101 l-3 

10s 

101 

lOe 

O-0

0 20000 40000 60000 80000 

Time (yr) 

Figure 3-34. SZ average release rates of 9Tc, "7

Np, and 23Pu, for 250 realizations.

3-51

100000
Analysis of Total-system Behavior

10"1 "Tc 1a, 

I 

"-3 

10 

10 

10 

0 2000 4000 6000 8000 10000 

Time (yr) 

10"1 AveAver 

-13 10 0a 

-5z 

S 10.3;", ••' 

-7 10 t4II 

o 2000 4000 Time 6000 8000 10000 (yr) 

10gre-15 SZrlasertso T vr a 000 n b 0,0 r nldn hveragereas 

rae 

00* -z' / ' 

;r . /(f 

m/ /0 // 

.2IP : / ' * I , .. t ' : ' .... I~ 

10 " _ -• ._. :...- . ! 

0 20000 40000 60000 80000 100000 

Time (yr) 

Figure 3-35. SZ release rates of 9Tc over: (a) 10,000; and (b) 100,000 yr, including the average release 

rate, in subarea 1, for 250 realizations.

3-52
Analysis of Total-system Behavior

Table 3-12. Average, maximum, and minimum SZ groundwater travel times, by subarea and 

average, for all subareas, from 250 realizations 

SZ Travel Time (yr) 

Subarea Minimum Maximum Average 

1 4730 7240 5990 

2 4730 7240 5980 

3 2130 3330 2730 

4 2130 3320 2720 

5 2180 3380 2720 

6 2180 3380 2780 

7 2180 3370 2770 

Average (all subareas) 2890 4460 3680 

maximum SZ GWTTs for the repository and for each subarea. The average for each subarea is obtained using 

equal weighting of GWTTs from each realization. Similarly, the repository average for all subareas is the 

mean of subarea averages. 

The variability in the SZ travel times is approximately the same order of magnitude as for the UZ. 

The repository averaged SZ GWTTs range from about 2700 to 6000 yr; for the UZ, GWTTs vary from 200 

to 1200 yr. A CCDF of the SZ GWTTs for all 250 realizations is presented in Figure 3-36. For comparison, 

a CCDF of the UZ travel times can be found in Figure 3-33. 

3.4 COMPARISON OF DOSES FROM MEAN VALUE DATA SET AND 

MULTIPLE-REALIZATION CASES 

To illustrate the difference between results from a mean value data set and results from multiple 

realizations, the peak expected dose is computed as a function of time from the multiple realizations. The 

peak dose from the mean-value data set is 2 x 10-5 mSv/yr (0.002 mrem/yr), whereas the peak expected dose 

from the multiple-realization case is 3 x 10i' mSv/yr (0.003 mrem/yr) for the 10,000-yr TPI. For the 

100,000-yr TPI, the peak dose from the mean value data set is 3 x 10-' mSv/yr (0.3 mrem/yr) compared with 

4 x 10-2 mSv/yr (4 mrem/yr) peak expected dose for the multiple-realization case. For comparison purposes, 

the primary nuclides contributing to peak dose are presented in Table 3-13. 

The major contributors to the peak dose from table 3-13 in the mean value data set for 10,000 yr are 

1291 and 36C1; for the multiple-realization case, they are 27Np, 1291, 9Tc, and 234

U. For the 100,000-yr TPI, the 

major contributors to the peak dose in the mean value data set are 9Tc, 1291, and 79Se, compared with 237

Np, 234

U, and 'Tc, for the multiple-realization case. Thus, some radionuclides that are major contributors to peak 

dose could not be accounted for by the use of the mean value data set. This clearly indicates the inadequacy 

of the analysis using the mean value data set. However, as indicated before, the mean value data set provides 

a convenient means for observing deterministic trends in the intermediate outputs. 

The variability in dose within realizations is shown in Figure 3-20, for 10,000 and 100,000 yr, 

together with the average dose. The minimum and maximum peak doses vary over 5 orders of magnitude,

3-53
Analysis of Total-system Behavior

100

40 

X 10"

"U (U 

0 

10

Time (yr)

Figure 3-36. CCDF of UZ GWTTs, for 250 realizations. 

Table 3-13. Primary radionuclides contributing to peak expected dose

10,000 yr 100,000 yr 

Mean Value Multiple-Realization Mean Value Multiple-Realization 

Radionuclide Data Set Data Set Data Set Data Set 

237Np 0 0.389 0 0.924 

1291 0.95 0.349 0.38 0.015 

99

Tc 0.0002 0.138 0.59 0.022 

234u 0 0.1 0 0.035 

36CI 0.05 0.014 0.004 0 

79Se 0 0.010 0.03 0

3-54

10 4
Analysis of Total-system Behavior

from about 4 x 10-' to 0.003 mSv/yr (4 x 10- to 0.3 mrem/yr), for 10,000 yr, and 2 x 10-6 to 0.5 mSv/yr 

(2 x 10' to 50 mrem/yr), for 100,000 yr. The doses occurring before 10,000 yr are from initially defective 

and seismic failures of WPs. From 11,000 to 46,000 yr, corrosion failures occur and contribute to increased 

dose. At about 85,000 yr, a slight increase in dose is observed, attributable to the arrival of 237

Np, and 

switching from DCFs, associated with the pluvial climate, to a present-day climate. 

Figure 3-37 shows the variation in peak dose and the arrival time of the peak dose at the pumping 

well, for 9Tc and 237

Np. For more than one-half the realizations, the 9Tc peak dose does not arrive until after 

90,000 yr, whereas the 237

Np peak dose does not occur for most realizations until the end of the 100,000-yr 

TPI. The difference in results arises because 9Tc retardation factors are less than those for 237

Np. Although 

the peak dose is not captured in all realizations, a maximum simulation time of 100,000 yr is long enough 

to evaluate the peak dose for the 10,000-yr TPI and a significant time period thereafter. 

The groundwater dose expressed as a percent of total dose for the radionuclides 245

Cm, 241

Am , 237

Np, 23 9 Pu, 234 U, 23 0T1, 1291, 99Tc, 14C, 79

Se, and 36

C1 is illustrated in Figure 3-38, for all 250 realizations. The 

radionuclides 23 7

Np, 234 U, 2 30

Th, 1291, 99Tc, 79Se, and 36

C1 contribute at least 1 percent to the groundwater dose 

for any single realization. The radionuclides with the greatest consistency in contributing to peak dose in all 

realizations are 237

Np, followed by 1291 and 9Tc. The results plotted in Figure 3-39, of the expected dose for 

each nuclide, show similar behavior over the 10,000- and 100,000-yr TPI, as does Figure 3-38, with the same 

nuclides having the largest contribution to the groundwater dose. 

The volume of well water pumped, which is used as the dilution volume for the 20-km receptor group 

location, is assigned a uniform distribution ranging from 6.2 x 106 to 1.8 x 10' m3

/yr (2.2 x 10' to 

6.3 x 108 ft3/yr. Figure 3-40 illustrates the relationship between the peak groundwater dose to the receptor 

in 100,000 yr and the dilution volume for 25 0 realizations. The scatterplot reveals a slight trend of decreasing 

peak groundwater dose with dilution volume. The mass release rates from the SZ are converted into a 

groundwater dose by dividing the mass release rate by the dilution volume and multiplying by the DCF. 

Consequently, higher dilution volumes should be associated with lower groundwater dose. 

3.5 ALTERNATIVE CONCEPTUAL MODELS 

This section compares repository performance, as measured by dose, for the mean value data set, 

with doses computed from mean values for alternative conceptual models described in Section 2.3. The 

alternative models include different conceptualizations for fuel dissolution, fuel wetting, and transport. Only 

the general trends in the groundwater dose of the alternative models relative to the basecase are described 

in this section. Discussion of the sensitivity of TPA output to a conceptual model, using multiple realizations, 

is provided in Section 4.4. 

Sensitivity of repository performance to the basecase model abstractions was evaluated by 

performing TPA simulations using alternative conceptual models. Conceptual models can either be activated 

with flags in the TPA input file, or a conceptual model may be evaluated by modifying TPA input 

parameters. Both approaches are used in this section to specify a conceptual model and to analyze the 

influences of the conceptual model on groundwater dose. Conceptual models activated with flags in the TPA 

input file include the four dissolution rate models, the bathtub and flowthrough models, bypassing invert 

transport, and the particle and grain surface-area models. Parameter values in the TPA input file are modified 

to evaluate conceptual models for focused flow, matrix diffusion, no retardation, and cladding protection.

3-55
Analysis of Total-system Behavior 

100 Z I I I I I I 

•Tc (a) 

0%0 

10is * 

1010. ' , 

10,0 

10

0 .00 o0 8 0 1 

0 3 

10- Np0 • 

1 -2 

m 10, 

E0' 

0 20000 40000 60000 80000 100000 Peak Time (yr) 

100 [ 27 Np 3 .**() I 

102 

6 0 -4 

S104 

10 

0 12 

• 10"l 

10"16 

10"20 r= , I , , , I , I 

0 20000 40000 60000 80000 100000 

Peak Time (yr) 

Figure 3-37. Peak groundwater dose of: (a) 99

Tc; and (b) 237Np; and time of the peak dose, for 

250 realizations.

3-56
Analysis of Total-system Behavior

I -- I I ' I ' [ -

90 

• j_8 0 

0 0 

0

2

'Cm "

4 Am "

7 Np 'Pu 14U °Th

1 I I 

I, 1EL

1291 9Tc 14

C 79Se 36CI

Figure 3-38. Percent each radionuclide contributes to the peak groundwater dose, for 

250 realizations. 

3-57

100% 

80%

W 

,4), 0 

940 

'I0 4.) 4) 

CL

60% 

40% 

20% 

0% i i [ 1 1 1 I I I I I I I I I I I I 1 I I
Analysis of Total-system Behavior

10 0 Total 237 Np 0 230

Th 14C 

B 2 45~ 239p a 1291 3 79e 

~ 4 Cm PU Pu 

10-2 24 :o 99Tc - - Cl S24Am _ T 

-4 'V 101 

0 

V -6 

4) 10 

0 

6~c 101= 

0. 

LUJ 

10-10 

0 2000 4000 6000 8000 10000 

Time (yr) 

100 

E10-2 0 

M-6 

tt-,Total 237 250 1 

jf 18 E 245C * 239 1291 V 79

S 

Am 9 Tc 

0 20000 40000 60000 80000 100000 

Time (yr) 

Figure 3-39. Average groundwater dose in: (a) 10,000, and (b) 100,000 yr, for each nuclide, including 

the total dose, for 250 realizations.

3-58
Analysis of Total-system Behavior

' I 

-0@ 0 0

• *0 *4

I I I I

OS 0. 0 

JO a

'* 0 

*0 

w 0 @0 *

0*• 

00 

0

0 0 4

I I I I

6o 8xi 0 lx107 1.2x10 7 1.4x107 

Dilution Volume (m3/yr)

1.6xl 0 1.8x1 0

Figure 3-40. Peak groundwater dose and the volume of well water pumped, for 250 realizations. (The 

well water dilutes the plume of radionuclides traveling in the SZ.) 

3-59

102

L

E 

0 

C3 

4) 

M.

101 

100 

101 

10

10 -3

l1e4 6x1( !I I I ! I I I I I . I I It I I I I I ' , '

W'
Analysis of Total-system Behavior

Figures 3-41 through 3-43 present groundwater dose in 10,000 and 100,000 yr for the basecase mean 

value data set, together with groundwater doses from the TPA alternative conceptual models. For the 

conceptual models evaluated using the mean value data set, repository performance spans almost 7 orders 

of magnitude for the 100,000-yr TPI and encompasses the basecase dose. The general trend in groundwater 

dose exhibited in Figures 3-41 through 3-43 indicates a wide range in the sensitivity of groundwater dose to 

the conceptual model. The alternative models with the most deviation from the basecase dose are the no 

retardation case, which is more than 2 orders of magnitude greater than the basecase, and the Schoepite and 

Clad-Mi cases, which are 3 to 4 orders of magnitude less than the basecase dose, through most of the 

100,000-yr TPI. The following sections discuss the alternative conceptual models grouped by fuel 

dissolution, fuel wetting, and transport assumptions, and compare the groundwater dose with the basecase 

groundwater dose, computed with mean values. The TPA Version 3.2 code "User's Guide" (Mohanty and 

McCartin, 1998) presents a description of these models. 

3.5.1 Fuel-Dissolution Models 

Results from TPA simulations, using three different fuel-dissolution models, are evaluated by 

comparing the groundwater dose from each of the models with the basecase groundwater doses. The 

groundwater doses from the basecase, and from the fuel-dissolution, three-alternative conceptual models, 

are presented in Figure 3-41. 

3.5.1.1 Fuel-Dissolution Model 1 

The groundwater doses in Figure 3-41 (labeled as Modell) indicate an earlier release andhigher dose 

through about 60,000 yrs. From 60,000 to 100,000 years, the basecase dose is greater than that calculated 

with fuel-dissolution model 1. At the end of the 100,000-yr TPI, the dose from the first fuel-dissolution-rate 

model is more than two orders of magnitude less than the basecase dose (Model 2 used). Dissolution Model 1 

is characterized by a higher release rate resulting from faster dissolution, compared with Model 2. But faster 

dissolution (congruent) results in faster source depletion from the WP for the dissolution-limited 

radionuclides. Consequently, the release rate for Model 1 becomes less than that for Model 2 at longer times. 

The dose for this conceptual model follows a sinusoidal pattern, after 20,000 yr, attributable to variations 

in the transport of nuclides to the receptor location not only by nuclide but by subarea. This effect is not 

evident in the basecase dose, and further studies are underway to explain this behavior. 

3.5.1.2 Fuel-Dissolution Model 3 (Natural Analog) 

The groundwater doses in Figure 3-41 (labeled as Natan), which are the same as the results from the 

schoepite dissolution model, show a slightly later release, with lower doses, throughout the 100,000-yr TPI, 

than the basecase dose, indicating a slower dissolution rate. Just as with the first fuel-dissolution-rate model, 

which exhibits a release rate that peaks and drops quickly, the dose for this conceptual model follows a 

sinusoidal pattern after 20,000 yr, attributable to differences in the transport of nuclides to the receptor 

location not only by nuclide, but by subarea. The variations in dose for this dissolution model are smaller 

compared with the first model, but greater, compared with Model 2. Further studies are under way to explain 

this behavior.

3-60
Analysis of Total-system Behavior

3.5.1.3 Fuel-Dissolution Model 4 (Schoepite Dissolution) 

The groundwater doses in Figure 3-41 (labeled as Schoepite) indicate a slightly later release with 

lower doses throughout the 100,000-yr TPI. Just as with the first and natural analog fuel-dissolution-rate 

models, the dose for this conceptual model follows a similar sinusoidal pattern after 20,000 yr, attributable 

to differences in the transport of nuclides to the receptor location not only by nuclide, but by subarea. 

However, the variations in dose are similar for this dissolution model and the first model, although the 

groundwater dose at 100,000 yr is more than 3 orders of magnitude less than the basecase dose. Justification 

for the trend in the curve is similar to that of the natural analog model. Further studies are under way to 

explain the trend. 

3.5.2 Fuel-Wetting Assumptions 

The amount of water contacting a WP affects the EBS release rate and the time of the release. This 

section presents results that investigate the assumptions for fuel wetting with five alternative conceptual 

models. The groundwater doses computed using these models and the basecase results are provided 

in Figure 3-42. 

3.5.2.1 Flowthrough Model with Fuel-Dissolution Model 2 

The groundwater doses in Figure 3-42 (labeled as Flwthru-2) have an earlier release and higher dose 

than the basecase dose from the beginning of the simulation, through about 20,000 yr. An earlier dose is 

expected because in the flowthrough model, release from the WP occurs instantaneously (i.e., no time to fill 

WP). From about 20,000 to 40,000 yr, the basecase dose is greater than the dose computed with this 

conceptual model. Beyond 40,000 yr, the groundwater doses are almost equal. One of the reasons these two 

doses are almost equal is that at high flow rates into the WP, the flowthrough model behaves like the bathtub 

model once the bathtub is full. 

3.5.2.2 Flowthrough Model with Fuel-Dissolution Model 1 

Groundwater doses in Figure 3-42 (labeled as Flwthru-1) indicate an earlier release and higher dose 

from the beginning of the simulation through about 60,000 yr, while from about 60,000 to 100,000 yr, the 

basecase dose is greater than the dose computed with the flowthrough model. This behavior is consistent with 

the faster dissolution rate and source depletion associated with Model 1. At 100,000 yr, the basecase dose 

is about 3 orders of magnitude greater than the flowthrough model dose. The greatest difference between 

these plots is the behavior of the doses over time. The basecase dose exhibits a smoother behavior than the 

flowthrough model dose, which shows a sinusoidal pattern caused by the arrival of different nuclides and 

releases from different subareas at the receptor location. 

3.5.2.3 Focused Flow 

As presented in Figure 3-42, the groundwater doses (labeled as Focflow) computed using a focused 

flow of water onto the WP are greater than the basecase dose, before about 7000 yr, indicating an earlier 

release. The groundwater doses are approximately 1 order of magnitude less than the basecase dose, from 

about 7000 to 100,000 yr. These results are consistent with solubility limited releases associated with higher 

flows at earlier times and lower doses thereafter, attributable to fewer wet WPs.

3-61
Analysis of Total-system Behavior

3.5.2.4 Cladding Credit with Model 1 

The groundwater doses in Figure 3-42 (labeled as Clad-M 1) calculated for this conceptual model are 

less than the groundwater doses for the basecase, from about 5000 yr, to the end of the 100,000-yr TPI. 

Before 5000 yr, the dose with cladding protection is greater than the basecase dose. During the 

5000-100,000-yr period, the general trends in the dose computed with cladding protection follow a 

sinusoidal pattern that is attributable to subarea and nuclide variability. The groundwater dose for this 

alternative conceptual model is about 6 orders of magnitude less than the basecase dose, at 100,000 yr. 

3.5.2.5 Grain-Size Model with Fuel Dissolution Model 1 

Groundwater doses in Figure 3-42 (labeled as Grainl) are characterized by an earlier release and 

higher dose than the basecase dose, from the beginning of the simulation through about 60,000 yr. The high 

dose results from a high dissolution rate, the result of a larger surface area associated with the grain-base 

model, in which grain size as opposed to the particle size is used for determining the surface area over which 

water contacts SF. From about 60,000 to 100,000 yr, the source becomes depleted and the basecase dose is 

greater than the dose computed using the grain-based surface area model. At the end of the 100,000-yr TPI, 

the dose is more than 3 orders of magnitude less than the basecase dose. The sinusoidal behavior of the dose 

is attributable to the arrival of different nuclides and releases from different subareas at the receptor location. 

3.5.3 Transport Alternatives 

The three alternative conceptual models that investigate assumptions of transport in the EBS, UZ, 

and SZ are assessed in this section. Figure 3-43 presents the groundwater doses for these conceptual models 

and the basecase dose. 

3.5.3.1 No Retardation of Pu, Am, and Th 

As presented in Figure 3-43, the groundwater doses (labeled as NoRet) calculated assuming no 

retardation in the UZ and SZ are greater than the basecase dose for the entire 100,000-yr TPI. Moreover, the 

general characteristics of the groundwater doses are consistent with the dose with no retardation, and 

approximately 2 orders of magnitude greater than the basecase dose. 

3.5.3.2 No-Invert Model 

Using the basecase mean value data set, flow through the invert is greater than the concrete 

permeability, and fracture flow does occur. Thus, the invert does not affect the radionuclide release rates 

from the EBS. Consequently, the basecase doses and the doses computedwhen bypassing the invert transport 

computations using the TPA input file flag are the same. 

3.5.3.3 Matrix Diffusion 

The groundwater doses presented in Figure 3-43 (labeled Matdif) with matrix diffusion are less than 

the basecase doses, from the beginning of the simulation time to about 25,000 yr, because of the retention 

of radionuclides in the matrix lateral to the fracture transport path. From approximately 25,000 to 60,000 yr, 

the dose exhibits a sinusoidal behavior that appears to be attributable to subarea variations in the arrival time

3-62
Analysis of Total-system Behavior

of nuclides, at the receptor location, that are not present in the basecase groundwater dose. Further 

investigation is underway to explain this behavior. After 60,000 yr, the groundwater dose computed with 

matrix diffusion increases, and at 100,000 yr, is almost 1 order of magnitude greater than the basecase 

groundwater dose. The increase in dose is caused by the increase in the release rate presumably resulting 

from the reversal in the diffusion (matrix to fracture). The increasing doses from the matrix diffusion case 

are nonintuitive, and may be caused by the way the NEFTRAN flow legs are specified in the basecase and 

alternative models. For the basecase model, the saturated flow pathway is specified as a "composite" flow 

leg, for which a single equivalent medium represents several hydrogeologic media in series. NEFTRAN does 

not allow this feature when the matrix diffusion option is stipulated. Although average travel times are the 

same for both fhodels, the treatment of dispersion is different. 

3.6 DISRUPTIVE EVENTS 

The TPA results from faulting and igneous activity are presented in this section for single and 

multiple realizations. The groundwater doses for the disruptive events and the ground-surface doses from 

igneous activity are compared with doses computed using the basecase data set. 

3.6.1 Single-Realization Analysis of Disruptive Events 

To determine the number of WPs ruptured by seismically induced rockfalls, which is part of the 

basecase, the time evolution of seismicity that includes the number, time, and magnitude of seismic events 

is obtained using the seismic hazard curve presented in Figure 3-44. The vertical extent ofrockfall associated 

with different categories of seismic events (Figure 3-45), and the joint spacing information (Figure 3-46) for 

computing the rockfall area, are used in determining the rockfall volume. The rockfall volume is then used 

in computing impact stress which, when inducing a plastic strain on the WP at the contact of impact 

exceeding 2 percent, will fail the WP. Other associated information is presented in Table 3-14 

and Figure 3-47. 

To determine the number of WPs failed by a faulting disruptive event, the TPA code uses the time 

of the faulting event and the fault length and width information summarized in Table 3-15. Faults modeled 

in the TPA code are hidden faults (i.e., either unknown and unmapped faults or underestimated faults), and 

thus the TPA calculations recognize that the WPs will be emplaced with an appropriate setback distance from 

known faults. The conditional probability for a faulting event is 1.69 x 10- 4

/yr (Mohanty and McCartin, 

1998). 

Igneous activity contributes to WP failure for both extrusive and intrusive events. As modeled, 

extrusive events result in the direct release of radionuclides to the ground surface, whereas intrusive events 

contribute to groundwater releases. The igneous event occurs between 100- and 10,000-yr postclosure, with 

a recurrent probability of 1 0-7 /yr. The parameters corresponding to the determination of the timing of future 

igneous events, subsurface areas affected by a volcanic event, and the number of WPs affected by intrusions 

extending laterally from the volcanic conduit, are presented in Table 3-16. 

After the volcanic event penetrates the repository and exhumes SF, areal density from deposition of 

ash and radionuclides is computed at the compliance point. Input parameters, such as eruption height, wind 

velocity, and parameters that determine the transport and deposition of radionuclides in ash, are presented 

in Table 3-16. The radionuclides modeled for extrusive releases, in addition to those evaluated for 

groundwater transport, are listed in Table 3-17 with corresponding initial inventories and half-lives.

3-63
Analysis of Total-system Behavior

101- -A Natan 

-U--- Shoepite 

a

E 10'

E 

0 -3 10 

0 

10-5 

10-7 . . . 

0 2000 4000 6000 8000 10000 

Time (yr) 

Fuel-Dissolution Models (b) 

Base 

101 - Modell 

Natan 

S- -Shoepite 

10-1 

0 

S10, coO 

0 

10

10 -7 • 

0 20000 40000 60000 80000 100000 

Time (yr) 

Figure 3-41. Groundwater dose from the basecase and the fuel-dissolution alternative conceptual 

models for: (a) 10,000, and (b) 100,000 yr, using the mean value data set.

3-64
Analysis of Total-system Behavior

10 Flwthru 1 0 1 rR F o c fl o w -l 

S--- --- Clad-M1 

E 101 

a) 1'1 .E 100, 0 

0 2000 4000 6000 8000 10000 

Time (yr) 

Fuel Wetting Assumptions Base (b --E3t- Flwthru-2 

10 N Focflow Flwthru-1 

: i Clad-g 1 Sr 6 Grain1 

E 10"' a) 

~101 

0 

101 

1 0 

0 20000 40000 60000 80000 100000 

Time (yr) 

Figure 3-42. Groundwater dose from the basecase and the fuel-wetting alternative conceptual 

models, for: (a) 10,000; and (b) 100,000 yr, using the mean value data set.

3-65
Analysis of Total-system Behavior

101 

..10-1 

10 0 

10 

Base 

F3 NoRet 

-*-MatDif 10 -7 , , I ,, I , , , I 

0 20000 40000 60000 80000 100000 

Time (yr) 

Transport Alte'rnatives' P B 

101 

E 

01 0-3 

0 

0 

10 

-1 

Base 

-2- NoRet 

-7 MatDif if 

0 20000 40000 60000 80000 100000 

Time (yr) 

Figure 3-43. Groundwater dose from the basecase and the transport alternative conceptual models 

for: (a) 10,000; and (b) 100,000 yr, using the mean value data set.

3-66
10000 20000 30000 40000 

Recurrence Time (yr)

Figure 3-44. Seismic hazard curve comprises ground accelerations 

determine the time of seismic events.

and recurrence times used to

8

7

E 

0 cc 

C) 

0 

0) 

C 

LU 

4-

6

5

4

3

2

1

a

5 6 

Event Type

Figure 3-45. Vertical extent of rockfall associated with the 5 rock types and 10 seismic events defined 

by the seismic hazard curve.

3-67

CO(P

0

0.1

Analysis of Total-system Behavior

0.2

0.3

C 

0 

C 

0) 

(U

0.4

0.5

0.6

0 50000
Analysis of Total-system Behavior

0.7

S0.6 

0.5 

.

0 0.3 

U) . 0.2 

o 0.1

0

3

Rock Type

4

Figure 3-46. Joint spacing of the 5 rock types and 10 seismic events.

0.6

C 

0 

'r, 

o 0.5 

C 

n0.4 

0 

0 0.3 

0.2 

C 

0 

S0.1 

0 

U0

1 2 3 4 5 6 7 8 9 10

Event Type

Figure 3-47. Fraction of the area with ground motion for each of the 10 seismic events defined by the

seismic hazard curve.

3-68

c07

1 

0.8 

0 

0.6 o. 

0.4 

0.2 

0 

o -;1 5

SI I I I I I 

I I I I. I [ I ' I
Analysis of Total-system Behavior

Table 3-14. Parameters used in determining seismic failure of WPs

Parameter 

WP stiffness for SEISMO 

WP modulus of elasticity for SEISMO 

Rock modulus of elasticity for SEISMO 

WP Poisson ratio for SEISMO 

Rock Poisson ratio for SEISMO 

Rock falling distance for SEISMO 

WP falling distance for SEISMO 

WP number of support pair for SEISMO 

WP support stiffness for SEISMO 

WP ultimate strength 

Grain density for Topopah Spring - welded 

for SEISMO 

WP yield point 

WP elastic elonaation

Mean Value 

1.21 x 1010 Pam 

2.07 x 1011 Pa 

3.45 x 1010 Pa 

2.00 x 10-1 

2.00 x 10-1 

2.00 m 

3.00 x 10-1 m 

2.00 

5.50 x 109Pam 

4.50 x 108 N/m2

Distribution 

Normal; 2.76 x 1010, 4.14 x 1010 

Normal; 0.15, 0.25

2.55 g/cm3 

2.00 x 10-3 

2.00 x 10 2

Table 3-15. Faulting disruptive event parameters

Parameter 

Time of next faulting event in region 

of interest 

Threshold displacement for fault disruption 

of waste package 

X coordinate of faulting event in region 

of interest 

Y coordinate of faulting event in region 

of interest 

Probability for NW orientation of faults 

Random number to determine fault 

orientation 

NW fault strike orientation measured from 

North - clockwise 

NE fault strike orientation measured from 

North - clockwise 

NW fault trace length 

NE fault trace length 

NW fault zone width 

NE fault zone width 

NW amount of largest credible displacement 

NE amount of largest credible displacement 

NW cumulative displacement rate 

NE cumulative disnlacement rate

Mean Value 

4.89 x 103 yr 

2.00 x 10-1 m 

5.48 x 105 m 

4.08 x 106 m 

5.00 x 10-2 

5.00 x 10-1

Distribution 

Finite exponential; 

100.0, 10000.0, 2.0 x 10-5 

User distribution; 

4 values: 0.1, 0.2, 0.3, 0.4 

Uniform; 547400.0, 548600.0 

Uniform; 4076200.0, 

4079040.0 

Uniform; 0.0, 1.0

-32.50

100 

4.00 x 10 3 m 

4.00 x 10 3 m 

2.16 x 101 m 

2.85 x 101 m 

1.34 x 10-1 m 

1.34 x 10-1 m 

5.00 x 10-' mm/yr 

5.00 x 10- mm/yr

Beta; 0.5, 275.0, 1.25, 15.0 

Beta; 0.5, 365.0, 1.25, 15.0

3-69

I it 

Table 3-15. Faulting disruptive event parameters
Analysis of Total-system Behavior

Table 3-16. Igneous activity parameters

Parameter 

Time of next volcanic event in region of interest 

X location in region of interest 

Y location in region of interest 

Random number to determine if extrusive or 

intrusive volcanic event 

Fraction of time volcanic event is extrusive 

Angle of volcanic dike measured from 

north-clockwise 

Length of volcanic dike 

Width of volcanic dike 

Diameter of volcanic cone 

Density of air at standard pressure 

Viscosity of air at standard pressure 

Constant relating fall time to eddy diffusivity 

Maximum particle diameter for particle transport 

Minimum fuel particulate size 

Mode fuel particulate size 

Maximum fuel particulate size 

Minimum ash density for variation with size 

Maximum ash density for variation with size 

Minimum ash log-diameter for density variation 

Maximum ash log-diameter for density variation 

Particle shape parameter 

Incorporation ratio 

Wind direction 

Wind speed 

Volcanic event duration 

Volcanic event power 

Volcanic column constant beta 

Ash mean particle log-diameter 

Ash particle size distribution standard deviation 

Relative rate of blanket removal 

Fraction of precipitation lost 

to evapotranspiration 

Fraction of irrigation lost to evapotranspiration 

Annual precipitation 

Annual irrigation 

Fraction of year soil is saturated 

from precipitation 

Fraction of year soil is saturated from irrigation

3-70

Mean Value 

5.05 x 10' yr 

5.48 x 105 m 

4.08 x 106 m 

5.00 x 10-' 

9.99 x 10-1 

7.500 

6.50 x 10 m 

5.50 m 

5.13 x 10' m 

1.29 x 10-3 g/cm 3 

1.80 x 10 -4 g/cm-s 

4.00 x 102 

cm2/sec5 P

2 

1.00 x 10, cm 

1.00 x 10-4 cm 

1.00 x 10-' cm 

1.00 x 10-2 cm 

1.20 g/cm 3 

2.00 g/cm3 

-2.00 

-1.00 

5.00 x 10-1 

3.00 x 10' 

-900 

1.20 x 10' cm/sec 

6.66 x 105 sec 

3.02 x 1010 W 

1.00 X 101 

1.00 x 10' cm 

1.00 

1.00 x 10-3/yr 

6.80 x 10-1 

5.00 x 10-1 

8.50 x 10-2 m/yr 

1.52 m/yr 

5.40 x 10-3 

2.00 x 10-1

Distribution 

Finite exponential; 

100.0, 10000.0, 1.0 X 10-7 

Uniform; 0.0, 1.0 

Uniform; 0.0, 15.0 

Uniform; 2000.0, 11000.0 

Uniform; 1.0, 10.0 

Uniform; 24.6, 77.9 

Exponential; 8.3 x 104 

Log-uniform; 6.13 x 104, 

7.24 x 106 

Log-uniform; 2.57 x 10', 

3.55 x 1011 

Log triangular; 0.01, 0.1, 1.0
Analysis of Total-system Behavior

Table 3-16. Igneous activity parameters (cont'd) 

Parameter Mean Value Distribution 

Ash bulk density 1.40 g/cm3 

Ash volumetric moisture fraction at saturation 4.00 x 10-1 

Depth of the rooting zone 1.50 x 10-1 m 

Table 3-17. Initial inventory and half-life of additional radionuclides considered for ground-surface 

release, but not for groundwater release

Radionuclide 

227Ac 

lOSmAg 

242roAm 

243 Am 

243Cm 

244CM 

246CM 

"135

Cs 

137Cs 

9 3

Mo 

94 Nb 

59

Ni 63 Ni 

231

Pa 

210pb 

241pu 

242pu 

238pu 

2 6

Ra 

"

1

51SM 

1

26

Sn 

121mSn 

9OSr 

2 2 9 Th 

23

2U 

233U 

235U 

236U 

23

SU 

9 3

Zr

3-71

Inventory at 10 yr 

from Reactor (Ci/WP) 

5.07 x 10-. 

1.17 x 10-1 

7.31 x 101 

1.50 x 102 

1.49 x 102 

1.12 x 104 

2.50 x 10-1 

3.43 

7.46 x 101 

9.86 x 10-2 

4.92 

2.40 x 101 

2.98 x 103 

1.90 x 10-4 

4.61 x 10-7 

1.02 

4.96 x 103 

7.26 x 101 

1.56 x 101 

2.06 x 104 

3.58 x 10-6 

3.10 x 103 

6.99 

7.78 

5.18 x 10' 

1.36 x 10-6 

2.42 x 10-1 

2.34 x 10-4 

1.65 x 10-1 

2.34 

3.11 

1.81 x 101

Half-life 

(yr) 

2.18 x 101 

1.27 x 102 

1.52 x 102 

7.38 x 103 

2.85 x 101 

1.81 x 101 

4.73 x 103 

2.30 x 106 

3.00 x 101 

3.50 x 103 

2.03 x 104 

8.00 x 104 

9.20 x 101 

3.28 x 104 

2.23 x 101 

6.50 x 106 

6.54 x 103 

1.44 x 101 

3.87 x 10' 

8.77 x 101 

1.60 x 10i 

9.00 x 101 

1.00 x 101 

5.00 x 101 

2.91 x 101 

7.34 x 103 

7.20 x 101 

1.59 x 105 

7.04 x 108 

2.34 x 107 

4.47 x 109 

1.53 x 106
Analysis of Total-system Behavior

Parameters associated with surface erosion ofradionuclides from the ash blanket deposited after an extrusive 

igneous event are presented in Table 3-18. For the ground-surface pathway, the areal densities calculated for 

each radionuclide, computed with the ASHPLUME (Jarzemba et al., 1997) ash transport model, are used in 

determining the dose TEDEs, by using the DCFs presented in Table 3-19. 

3.6.2 Multiple-Realization Analysis of Disruptive Events 

The variability in the average dose arising from faulting events and igneous activity for the 

multiple-realization simulations is presented in this section. The dose history for faulting events for the 

100,000-yr TPI without probability weighting is presented in Figure 3-48(a). The average groundwater dose 

from the faulting events is approximately 20 percent greater than the dose without a faulting event at 

10,000 yr. However, after 10,000 yr, the releases from WPs failed by corrosion dominate the dose; the 

groundwater dose with faulting and the basecase in the 1 00,000-yr TPI are not distinguishable. 

The probability-weighted expected dose from igneous activity is presented in Figure 3-48(b) together 

with the groundwater dose computed using the basecase data set. In the 10,000-yr TPI, the 

probability-weighted dose from igneous activity is about 2 to 4 orders of magnitude greater than the basecase 

groundwater dose. The next section presents the methodology used to determine the risk arising from faulting 

and igneous disruptive events. 

3.7 CALCULATION OF RISK 

Risk is defined in this section as the probability-weighted dose. Doses are calculated from three 

scenario classes: (i) basecase with seismicity; (ii) faulting; and (iii) igneous activity. The probability of the 

three scenario classes is assumed to sum to unity. This implies that other scenario classes are either too 

improbable, or have consequences too small, to affect the overall risk materially. 

The average risk to a receptor can be computed by summing contributions to dose from each Monte 

Carlo simulation, weighted by the scenario probability and the conditional probability of each realization 

within the scenario. The methodology for computing conditional risk (i.e., assuming that the scenario has 

a probability of one) from scenarios other than extrusive igneous activity is presented in Section 3.7.1. The 

methodology used to determine the conditional risk from scenarios with extrusive igneous activity is 

described in Section 3.7.2. The methodology for combining the conditional risks to an overall risk is 

presented in Section 3.7.3. 

3.7.1 Scenarios Other Than Extrusive Igneous Activity 

The risk or effective dose equivalent is the product of the consequence (i.e., dose) and the probability 

that the dose has occurred. Estimates of dose are uncertain because the models and their input parameters 

are uncertain, as are the times of occurrence of the disruptive events such as faulting and intrusive igneous 

activity. Monte Carlo analysis is used to account for the uncertainty in parameters and events. The Monte 

Carlo analysis propagates the uncertainty in model inputs through the conceptual models. A Monte Carlo 

simulation evaluates a model repeatedly, using input values that have been randomly selected from the 

probability distributions for the input variables. The output of the Monte Carlo analysis is a set of results 

such as dose versus time, for each of the randomly chosen input sets of values. Generally, each Monte Carlo 

output result has equal probability. Thus, each dose curve from the Monte Carlo analysis has a probability 

of occurrence equal to 1/N, where Nis the number of Monte Carlo samples. The analysis in this section does

3-72
Analysis of Total-system Behavior

102 

101 

'•100 

0I

S10" 

E 

4) 

U) 102 

w10• 

0 

0 

d) 

C, -4 *10 

U10. 

10, 

10 2

2000 4000 6000 8000 10000 

Time (yr) 

Groundwater dose in 10,000 and 100,000 yr with and without: (a) faulting, and 

(b) igneous activity, in 10,000 yr, for 250 realizations. (Only the ground-surface dose for 

releases caused by extrusive igneous activity in (b) is probability-weighted. The basecase 

and faulting doses are not probability-weighted.)

3-73

40000 

Time (yr)

"IE E 

0 

0. 

x 

u.

101 

100 

10-1 

102 

10 3 

10

10.6

0 

L.

10" 

Figure 3-48

t
Analysis of Total-system Behavior

Table 3-18. Parameters used in computing ash and radionuclide removal from the ground surface

Element 

Ac 

Am 

C 

Cs 

Cl 

Cm 

I 

Pb 

Mo 

Np 

Ni 

Nb 

Pd 

Pu 

Pa 

Ra 

Sm 

Se 

Au 

Sr 

Tc 

Th 

Sb 

U 

Zr

Other parameters 

Parameter Mean Value Distribution 

Distance cutoff for dose conversion 

duality in DCAGS module 2.00 x 101 km 

Airborne mass load for igneous activity 

dose calculation 1.00 x 10-3 g/m3 Log-uniform; 1.0 x 10-4, 1.0 x 10-2 

Occupancy factor for igneous activity dose 

calculation 2.40 x 10-1 

Depth of resuspendable layer 3.00 x 10-1 cm -

3-74

Kd in Volcanic Ash 

(cm3la) 

4.50 x 102 

1.90 x 103 

5.00 

2.80 x 102 

0.00 

4.00 x 103 

1.00 

2.70 x 102 

1.00 x 101 

5.00 

4.00 x 102 

1.60 x 102 

5.50 x 101 

5.50 x 102 

5.50 x 102 

5.00 x 102 

2.45 x 102 

1.50 x 102 

5.50 x 101 

1.50 x 101 

1.00 x 10-1 

3.20 x 103 

1.30 x 102 

3.50 x 101 

6.00 x 102

Solubility in Volcanic Ash 

(mol/L) 

1.00 X 10-6 

1.00 x 10-6 

1.00 

1.00 

1.00 

1.00 x 10-6 

1.00 

3.20 x 10-' 

1.00 

1.00 x 10-4 

2.00 x 10-' 

1.00 X 10-8 

9.50 x 10 4 

5.00 x 10-6 

3.20 x 10-' 

1.00 x 10-7 

5.00 X 10-6 

1.00 

1.00 

1.30 x 10-4 

1.00 

3.20 x 10-9 

5.00 x 10-8 

4.50 x 10-5 

3.20 x 10-1'
Analysis of Total-system Behavior

Table 3-19. Biosphere dose conversion factors of all 43 nuclides for ground surface at the 

20-km receptor location 

Nonpluvial and Pluvial Dose Conversion Factor (DCF) 

Ingestion of Animal 

Radionuclide Direct Exposure Inhalation Products Ingestion of Crops (rem/yr)/(Ci/m2) (rem/yr)/(Ci/m 3) (rem/yr)/(Ci/m2) (remlyr)l(Cilm 2) 

W Ac 3.80 7.02 x 101" 2.13 x 102 4.73 x 104 

1°smAg 6.20 x 10W 2.97 x 109 3.70 2.40 x 102 

241Am 6.70 x 102 4.66 x 1012 1.50 x 10' 9.80 x 103 

2 4 2 mjli 7.30 x 10' 4.46 x 1012 1.41 x 10! 9.53 x 10' 

243

Am 1.30 x 103 4.62 x 1012 1.50 x 101 9.81 x 10' 

14C 3.90 x 10- 2.19 x 107 0.00 1.70 x 10' 

36

C1 1.70 x 10' 2.30 x 10W 1.70 x 10W 3.90 x 104 

24 3

Cm 3.10 x 103 3.22 x 1012 2.80 x 10, 6.80 x 103 

2

44Cm 2.20 x 10' 2.60 x 1012 2.30 X 10' 5.40 x 103 

245

Cm 2.10 x 103 4.77 x 1012 4.20 x 10' 1.00 x 104 

2

4Cm 1.90 x 101 4.73 x 1012 4.20 x 10' 1.00 x 104 

"135Cs 8.30 x 10-' 4.77 x 107 1.00 x 102 5.50 x 10' 

"137Cs 1.30 x 104 3.35 x 108 6.90 X 102 3.80 x 102 

1291 6.20 x 102 1.82 x 109 2.20 X 103 1.60 x 103 

93

Mo 1.30 x 102 2.99 x 108 1.10 x 10, 1.90 x 102 

gNb 3.70 x 104 4.35 x 109 2.70 x 10-3 4.40 x 10' 

5

9

Ni 0.00 2.83 x 107 4.30 1.90 

63

Ni 0.00 6.60 x 107 1.20 x 10' 5.20 

237Np 7.30 x 102 5.67 x 1012 6.50 x 102 2.50 x 104 

231pa 9.80 x 102 1.35 x 1013 3.80 x 10' 3.30 x 104 

210pb 6.20 x 101 1.42 x 10l 1.09 x 103 1.96 x 104 

1°7pd 0.00 1.34 x 108 1.70 4.70 

238u 8.30 4.11 x 1012 4.43 8.60 x 103 

239pU 8.80 4.50 x 1012 4.90 9.50 x 103 

240

pu 2.00 x 101 4.50 x 1012 4.90 9.50 x 103 

2411U 1.30 x 10-' 8.65 x 1010 9.51 x 10-2 1.84 x 102 

242pU 1.70 x 101 4.31 x 1012 4.70 9.00 x 103 

226Ra 1.60 x 102 9.00 x 1010 1.20 x 103 3.60 x 103 

79Se 5.10 x 10-' 1.03 x 108 3.60 x 101 6.20 x 10' 

"151Sm 1.20 x 10-1 3.14 x 10' 1.70 x 10-' 1.70 

121mSn 1.20 x 102 1.21 x 10W 1.90 x 10' 1.88 X 10' 

1

26

Sn 1.30 x 103 1.05 x 109 1.69 x 102 1.68 x 102 

9°Sr 6.70 1.36 x 10'0 2.49 x 103 6.92 x 103 

9rc 1.90 8.73 x 107 1.10 x 102 2.30 x 103 

2 2 9

Th 2.10 x 103 2.25 x 1013 8.53 x 10' 1.02 x 104 

23°T 1.80 x 10' 3.42 x 1012 1.80 1.50 x 103 

232U 2.50 x 101 6.91 x 1012 3.82 x 102 4.54 x 10' 

233u 1.80 x 10' 1.42 x 1012 8.50 x 101 9.90 X 102 

234U 1.80 X 10' 1.39 x 1012 8.30 x 10' 9.80 x 102 

235U 3.60 x 103 1.29 x 1012 7.82 x 10' 9.14 x 102 

236U 1.60 x 101 1.32 x 1012 7.90 x 10' 9.20 x 102 

2 3 8

U 1.30 x 101 1.24 x 1012 7.53 x 10' 9.02 x 102 

93

Zr 0.00 3.38 x 10W 1.86 x 10-3 4.75

3-75
Analysis of Total-system Behavior

not explicitly include conceptual model uncertainty, other than that captured by changes in the input 

parameters. Alternative conceptual models are covered in Sections 2.3 and 3.5. 

The expected dose-versus-time relationship for scenarioj (e.g., intrusive volcanic scenario) can be 

developed by summing, over all realizations, the probability-weighted contributions from the family of dose 

relationships produced by the N Monte Carlo samples. The mathematical representation of this calculation is: 

N 

Dj(t) = LpiCijt) (3-1) 

where 

D3 (t) - average annual dose to the receptor individual as a function of time for the jth 

scenario; 

Ci. - dose as a function of time for the ith realization of thejth scenario; 

pi probability assigned to the dose curve for the ith realization. For Monte Carlo 

sampling, p, = (I/N); and 

N number of model simulations that compose the family of dose curves (i.e., N Monte 

Carlo samples of the model inputs are used to generate N model outputs in the form 

of dose curves). 

The index indicates that the event can occur at any time between [O,t]. 

3.7.2 Extrusive Igneous-Activity Scenario 

For the igneous-activity scenario, dose consequences are largest for events that occur soon after 

repository closure, while the relatively short-lived but high-activity radionuclides such as 241

Am are still 

present in significant quantities. Radionuclides can reach the affected population in short times (hours to 

days), but persist in the environment and also cause lower levels of exposure long after the event (hundreds 

to thousands of years). The time of occurrence of the event is extremely important to the dose consequences, 

and is, therefore, included in the probabilistic analysis as one of the sampled parameters. The fact that there 

are short-term, relatively high consequences and long-term, lower consequences from igneous events 

complicates the probabilistic analysis by requiring a large number of Monte Carlo samples to resolve the 

overall expected dose on both the short- and long-term time scales. To get a reasonably converged mean 

value, hundreds of realizations must be performed at each potential occurrence time, which may be 

impractical with the present models run in the usual Monte Carlo fashion. 

Because the expected dose-versus-time curve is anticipated to be smooth, a much more efficient 

convolution approach to generating the curve is to develop the expected dose for igneous events at a few, 

discrete event times and then use linear interpolation between the discrete event times. The procedure for 

developing the expected dose curve involves the following steps:

3-76
Analysis of Total-system Behavior

Conduct Event-Time-Specific Probabilistic Analyses 

Specific occurrences of igneous activity are selected for the evaluation rather than randomly 

selecting occurrence times in a Monte Carlo approach. A separate probabilistic analysis, based 

on the parameter uncertainty, is conducted for each specific occurrence time. In the present 

model, the event times were 100; 500; and 1000 to 10,000 yr, in 1000-yr steps. 

" Generate Conditional Expected Dose Curves for Specific Event Times 

Each of the separate probabilistic analyses described previously is used to develop a separate 

conditional expected dose curve for the specified occurrence times, using Eq. (3-1). 

" Generate Probability-Weighted Dose Curve for Specific Event Times 

The probability-weighted dose D, for the specific event times, is generated by multiplying the 

conditional dose curves by the probability in a given year that an igneous event occurred 

(annual probability can be used provided it is constant over time). Figure 3-49 presents the 

series of probability-weighted dose curves calculated in this analysis. 

Generate an Overall Expected Dose Curve 

The expected dose at any given time t is the sum of conditional expected dose 91 ; overall, the 

expected dose curve from igneous activity occurring over the TPI is determined by cumulating 

probability-weighted dose over time, using the probability-weighted dose curves at the 

12 specified event times. Equation (3-2) describes how the expected annual dose to the receptor 

individual is estimated in this approach: 

E 

I= (A) t) (3-2) 

n=1 

where 

W(t) - expected annual dose to the receptor individual as a function of time; 

Dn (t) - probability-weighted mean dose as a function of time for specific event time n; 

(At) n - increment of time associated with event time n (if events are evaluated on a per year 

basis, this would be lyr); and 

E - number of specific event times used to represent variation in event uncertainty 

(interpolation between events can be used to generate dose curves for each year). 

The probability-weighted dose curve calculated with this more efficient approach is presented in 

Figure 3-50. As expected, the consequences of an igneous event are highest at early times. The probability 

weighted dose curve goes through a maximum at around 500 yr. This results from the accumulation of dose 

from potential earlier events.

3-77
Analysis of Total-system Behavior

3.7.3 Combining Conditional Risks into an Overall Risk 

The overall risk, D(t), is calculated by summing the scenario mean doses weighted by the scenario 

probability Pj The mathematical representation of this calculation is: 

M 

j=l 

where 

Dj (t) - dose rate from scenarioj, averaged over the Monte Carlo realizations; 

M - number of scenario classes; and 

P - annual probability of scenarioj. J

3-78
Analysis of Total-system Behavior

5000 

Time (yr)

Figure 3-49.

E 

"0 a 

V 

LU 0. 

x wl

0.6 

0.5 

0.4 

0.3 

0.2 

0.1

Mean dose arising from extrusive igneous-activity shown 

volcanic event in 400 realizations.

with various times for the

0

0 2000 4000 6000 8000 

Time (yr)

10000

Figure 3-50. Contribution of extrusive igneous-activity to the total dose, weighted by an annual 

probability for the volcanic event of 10-.

3-79

50 

40 

. 30 

0 

a 

M 0 20 

C 

0 

10 

0
4 SYSTEM-LEVEL SENSITIVITY STUDIES 

This chapter describes the sensitivity and uncertainty analysis techniques used in conjunction with results 

of the TPA Version 3.2 code system-level calculations. In general, a sensitive parameter is defined as one 

that provides a relatively large change in the output variable for a unit change in an input parameter. The goal 

of the sensitivity analyses presented in this report is to determine the parameters to which peak dose or the 

TPI shows the most sensitivity. The goal of the uncertainty analyses is to determine the parameters that are 

driving uncertainty (i.e., variation) in peak dose output. The analyses were conducted primarily for the 

basecase and to a limited extent for the igneous activity and faulting disruptive events. The analyses 

conducted herein rely on the models and assumptions used in the TPA Version 3.2 code.7 For a more detailed 

description of these models and assumptions, the reader is referred to the TPA Version 3.2 code "User's 

Guide" (Mohanty and McCartin, 1998). Conclusions based on these analyses may be updated as the models 

or assumptions are updated, and certain parameters or processes may become more or less influential. 

The sensitivity analyses in this report use peak dose as the output variable for each realization because this 

result is most likely to demonstrate sensitivity relationships among the independent and dependent variables. 

The performance measure in the draft version of the YM implementing regulation 10 CFR Part 63 

(Nuclear Regulatory Commission, 1999a) is stipulated to be the peak of the average dose history within the 

10,000-yr TPI. Although there is an important distinction between these two measures of performance, the 

use of the peak dose for each realization would not significantly alter the sensitivity analysis conclusions 

since approximately 90 percent of the realizations have their peak dose at 10,000 yr, and for those 

realizations with earlier peak doses, the peak dose does not significantly differ from the dose at 10,000 yr. 

4.1 SENSITIVITY ANALYSIS TECHNIQUES 

Most techniques used herein rely on the Monte Carlo method for probabilistically determining 

system performance. As mentioned in the previous chapters, the performance measure of the system in the 

NRC YM repository PA exercises is the peak dose in the TPI to an average member of a receptor group 

located 20 km (12.4 mi) from the repository. Many of the input parameters are not precisely known and are 

spatially variable, so their values are described by probability distributions (Figure 4-1). The Monte Carlo 

technique makes repeated calculations (called realizations) of the possible states for the system, choosing 

values for the input parameters from their probability distributions. Although 246 input parameters' are 

sampled in the TPA Version 3.2 code, only a few of these parameters contribute significantly to the 

uncertainty in peak dose, because of the great sensitivity of peak dose to the parameters, the large variability 

of the parameters, or both. 

This section describes the techniques used to determine which input parameters in the 

TPA Version 3.2 code most influence the results. It is noted that not all techniques described were applied 

to all cases. For generalization purposes, the output from the system is denoted as y. In general, y is a 

7

The specific version of the TPA code used in this Chapter is 3.2. whereas Version 3.2.3 was used in developing Chapter 3. 

Results from Version 3.2.3 do not affect the peak dose calculation, compared with Version 3.2, which is the performance measure 

used in this chapter. 

sThe actual number of parameters contributing to the variability in peak dose is fewer than 246, depending on which group 

of conceptual models is used in the calculation. The LHS module in the TPA Version 3.2 code samples all parameters that are not 

constant, regardless of their use in a specific run. 

4-1
p(xi)

X2-mean 

-..P' 0 2 1'-

tQ

P(xn)

Stochastic EN -._ "Sampling

Stochastic,,.0.X2 

iSampling 

Stochastic ._ .X 

"Sampling

Xn-low Xn-high 

Probability 

Distributions 

of Input 

Parameters

Realization

Specific 

Input 

Parameters

Conceptual Models

Performance Measure 

or Output

Figure 4-1. A diagram illustrating the use of the Monte Carlo method in performance assessment.

X1-10w Xi-high

-- W-Y(X ,""ý.. Xn)
System-level Sensitivity Studies

function of random parameters, xi; deterministic parameters, dk; and model assumptions, a,,. The system 

output, y, is such that 

y = f(xljX 2 ,j,..., xl,j ,dk,am) (4-1) 

wherej represents thejth realization and I is the total number of sampled parameters in the model. It is 

assumed that the behavior of the system is simulated by appropriately sampling the random parameters and 

then computing the system output, y, for each realization of parameter vector (see Figure 4-1). For the 

purposes of this section, which are to outline a method for analyzing simulation output, to identify important 

random parameters, and to develop understanding of their relationship to the output, it is assumed that the 

decisions about appropriate model assumptions and deterministic parameters have been made a priori. As 

a result, we do not consider the dependence of y on deterministic parameters and model assumptions any 

further, and focus on the dependence ofy on the xis only. 

4.1.1 Regression Analyses Methods 

4.1.1.1 Scatter Plot/Single Linear Regression on One Variable 

To understand the nature and strength of relationships between input and output variables of a model, 

it is often useful to examine scatter plots in which the output variable is plotted against one input variable 

at a time. As shown in Figure 4-2, results of scatter plots give an initial visual indication of nonlinear effects, 

thresholds, and variables likely to be important to further sensitivity and uncertainty analyses. Single linear 

regression (i.e., regression with only the first power of one input variable and an intercept) of the output 

variable, with respect to each of the input parameters, can give a quantitative measure of the correlation 

through the coefficient of determination, R2. This figure can be misleading, however, in cases where the 

dependencies are not purely of the first order with respect to the input variable. It is noted that linear here 

and throughout this chapter refers to the functional form of the regression and not the order to which the 

fitting parameters appear (although the regressions are also linear in the fitting parameters). Even when the 

output variable is linearly dependent on the input variable being studied, univariate linear regression of 

Monte Carlo results may fail to show unambiguous correlation because other sampled parameters that affect 

the output are varying at the same time, and the model is clearly underspecified (i.e., the results depend on 

more than one variable). 

The coefficient of determination, R2, is small for most variables in the current analyses, and is not 

necessarily a good indicator of the importance of the variables. A better indication of influence is to 

determine the probability that the slope of the linear regression line is significantly different from zero. This 

is done with a t-test or t-statistic as described in succeeding sections. 

Use of the t-Statistic to Determine Significance of Regression Parameters 

The t-statistic is generally used to estimate with a specified confidence level that an estimated 

parameter value differs from another value. A parameter, xi, is deemed influential if there is a specified 

(e.g., 95 percent) confidence that the slope of its regression curve, (mi), is different from zero (Benjamin and 

Cornell, 1970).

4-3
System-level Sensitivity Studies

- ~ II I I I~I I I I 

-4 • 

0-6 

00 R .111 

-10 

-21. -1. -1. -1.2 -1-- -0.8 -0. 

• pt Variable 

Fiue42Eapeo a scte p ot/inl liea rereson.Y MO M* 

o -8 -•• 

•MO -4.9354 

-9 M1 0.81129 

.1° R 0.1 91 19 

-2 -1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 

Input Variable 

Figure 4-2. Example of a scatter plot/single linear regression. 

The t-statistic of the slope of a single-variable regression line is defined as 

M. n•j E2 (4-2) 

S 2 

where 

t. 6 t-statistic for regression coefficient i; 

m, 6 estimated value of regression coefficient i (i.e., slope of the best-fit line for dose 

versus the independent variable, xi ); 

S 6 estimated standard deviation of dose; 

S, 6 estimated standard deviation of independent variable, xi; and 

n 6 number of samples.

4-4
System-level Sensitivity Studies

For the analyses conducted herein, the number of realizations is greater than 250, which provides 

essentially an infinite number of degrees of freedom for the t-statistic. The critical value to ensure 95-percent 

confidence that m, differs from zero under these conditions is 1.96 (Mason, et al., 1989). Equation (4-2) is 

used, therefore, to determine if the absolute value of the t-statistic for each independent variable is greater 

than 1.96. If not, then the hypothesis that the independent variable was significant is rejected. 

The t-statistic was used for the single variable regressions and multiple linear regressions as 

described in Eq. (4-5). 

4.1.1.2 Variable Transformations and Their Attributes 

The correlation between input and output variables can be enhanced by transforming the variables. 

This section describes variable transformations used in this study. In general, variable transformations are 

used to: (i) eliminate dimensionality of the variables; (ii) reduce the role of points at the tails of the 

distributions; and (iii) properly scale the resulting sensitivities to the variability of the input variables. 

Although transformations generally increase the goodness of the fit analyses, they distort the meaning of the 

results. For example, transformations such as rank, logarithmic, and power law frequently give unfair weight 

to small doses, which do not affect the mean results as much as the higher doses. Because the proposed 

regulations are based on mean doses, regression results based on transformed variables should be used 

cautiously. 

Normalization 

In normalization, the input variable, x,, is transformed by dividing it by its mean value (or another 

baseline value such as the median, 90' percentile, and such): 

Xi =- (4-3) 

Xi 

Normalized variables are dimensionless and are scalar multiples of their baseline values. Dimensionless 

variables allow the comparison of sensitivities to other independent variables with different dimensions. 

Other types of normalization can also be used and will be shown later in this chapter. 

Sensitivity measures based on normalized variables describe only the relative change in the 

dependent variable (peak dose) to changes in the independent variables. Although this is a useful measure 

of sensitivity, it does not consider the ranges of the variability of the independent and dependent variables 

(see standardization, following). 

Rank Transformation 

If the distributions of input and output are far from a normal distribution, particularly if they have 

one or two long tails, they are liable to distortions from the effect of outliers. One way to avoid such effects 

is to arrange the output values according to the rank order, or the samples of each input parameter (Morgan 

and Henrion, 1990). Rank transformation, a dimensionless transform, replaces the value of a variable by its 

rank (i.e., the position in a list that has been sorted from largest to smallest values) (Iman and

4-5
System-level Sensitivity Studies

Conover, 1979). Analyses with ranks tend to show a greater sensitivity than results with untransformed 

variables. If the distribution of doses is skewed toward the low end, which is usually the case, rank 

transformation gives unfair weights to lower doses. 

Logarithmic Transformation 

For situations in which input and output variables range over many orders of magnitude, it may be 

advantageous or even necessary to perform analyses on the logarithm of the variables instead of the variable 

values themselves. The log transformation is also valuable for creating regression equations, where the 

subprocesses of the model multiply each other to form the output variable, such as in a transfer function 

approach. For the present situation in which the dose calculation results from radionuclide releases from the 

waste form, transport through the geosphere, and uptake by humans, the processes are indeed largely 

multiplicative rather than additive. Log transforms, therefore, tend to give better fits to the Monte Carlo 

results than untransformed variables, but at the expense of unfair weighting of the smaller doses. The log 

transformation may be used in conjunction with normalization. 

Scaled-Power Transformation 

The scaled power transformation is similar to the logarithmic transformation, but often allows a 

closer approach to normality. For a variable, v, and power, p (p not equal to 0), the scaled power 

transformation is (Cook and Weisberg, 1994): 

v(P) = (VP - )(4-4) P 

For p = 0, it can be demonstrated that the scaled power transformation reduces to the 

logarithmic transformation. 

The algorithm steps through a range of values of the exponent, p, in small increments and compares 

the shape of the resultant scaled distribution to the shape of a normal distribution. The staff employed the 

Lilliefors test for normality (Bowen and Bennett, 1988). The exponent yielding the best fit to the normal 

distribution is then chosen to scale the variable under consideration. This procedure is used for the 

independent variables and the dependent variable (peak dose). 

The scaled power transformation can be shown graphically for an example of the peak dose for 

10,000 yr. Figure 4-3 shows a normal probability plot of dose for 10,000 yr in the 1000-vector basecase, 

demonstrating that it is highly skewed. Using Eq. (4-4) with an exponent, p = 0.1, transforms the data to a 

close fit to the normal distribution, as shown in Figure 4-4. As with the logarithmic transformation, the 

improved fit is at the expense of an overemphasis on the smaller dose.

4-6
0 

cc

a

F4

1000 Vector 

10,000 yr TPI 

Normalized wvith 

respect to the mean

z 

-2 0 2 

Quantiles of Standard Normal 

Figure 4-3. Normal probability plot of dose for 10,000 yr in the 1000-vector basecase.

0 0) 0 

E 

0 

N 

0 

0 

0

(0

Pr

1000 Vector 

10,000 yr TPI 

Normalized with 

respect to the mean

-2 0 2 

Quantiles of Standard Normal 

Figure 4-4. Figure showing a close fit to normal distribution after using p = 0.1 transforms. 

4-7

0 

0 

M 

0

Vvetam-701yal Ra"CifillifI7 V21"fiav
System-level Sensitivity Studies

Standardization 

The independent and dependent variables can be standardized by subtracting the mean and dividing 

by the standard deviation 

. xi- x (4-5) 

Sensitivity measures based on standardized variables (standardized sensitivities) have the advantage 

of taking into iccount the uncertainty (in the standard deviation) of the independent variable. Furthermore, 

the standardized sensitivities preserve the absolute values of peak dose because the derivatives are divided 

by the standard deviation for the entire set of calculations, rather than the mean peak dose at the evaluation 

point. Therefore, the absolute value of changes in mean peak dose is preserved with 

standardized sensitivities. 

Standardized variables can be greater or less than zero, hence they cannot be used directly in the 

regression analyses using the log-transformed variables. Instead, the standardized sensitivities can be derived 

from sensitivities based on logs of the normalized variables: 

•. xt Y(4-6) Cx'(•Y 

where y* and x* are the standardized dependent and independent variables as defined by Eq. (4-5). The 

quantity in parentheses is the sensitivity derived from regression analysis with the logs of the normalized 

variables. Note that since Eq. (4-6) requires the normalized sensitivities, it necessarily suffers from some of 

the same disadvantages as normalized sensitivities. Direct linear regression with standardized variables gives 

the proper weight to all doses. 

A modified form of the standardized sensitivities approach was also used in the differential analysis 

described in Section 4.1.2. In this case, only seven points were defined for the parameter space, so the 

independent variables were standardized by the same standard deviations used in the regression analyses 

(i.e., the standard deviation based on 250 samples generated in the Monte Carlo analyses). Peak dose did not 

need to be standardized to show the relative sensitivities to the standardized independent variable. Therefore, 

those sensitivities have units of dose. 

4.1.1.3 Stepwise Multiple Linear Regression 

Stepwise multiple linear regression (stepwise regression) determines the most influential input 

parameters according to how much each input parameter reduces the residual sum of squares (RSS) 

(Helton, 1991). The form of the regression equation is

4-8
System-level Sensitivity Studies

y = hx 1 + m 2x 2,+...+mnxn+b (4-7) 

where 

y - dependent variable; 

x, - independent variables; 

mi - regression coefficients (also known as partial correlation coefficients); and 

b - intercept. 

The regression coefficients, mr, are measures of linear sensitivity ofy to input x, (Draper and Smith, 

1981). The variables may be the raw variables, transformed variables, or ranks. The stepwise algorithm 

calculates the reduction in RSS for the independent variables in the order that gives the greatest reduction 

first. In the implementation of the procedure, a multiple linear regression model is fitted to the data in an 

iterative fashion. The procedure starts with the variable, x,, which explains most of the variations in the 

model output, y. Then it adds additional variables (one at a time) to maximize the improvement in fit of the 

model according to the R2 value. In the regression model, R2, the coefficient of determination indicates the 

fraction of variability in the data explained by all the variability in the model. The sequence in which the 

inputs are selected is a useful measure of their uncertainty importance, as is the increment inR2 they produce. 

Iman and Conover (1979) also suggested the use of partial correlation coefficients, which are measures of 

the contribution of each uncertain input to the output uncertainty, after removing the effects attributable to 

other inputs. These coefficients are useful when there are significant correlations between the inputs 

(Morgan and Henrion, 1990). 

The regression coefficients, m• ,are the partial derivatives of the dependent variable with respect to 

each of the independent variables. The correlation coefficient reflects the fractions of the variability 

explained by the individual variables (Zimmerman, et al., 1991). The form of the linear regression equation 

that gave the best fit used the log of the normalized peak dose and the log of the normalized independent 

variables, xn: 

log = b + mn 1 log + 10 9og2+...+m! logL+...+m, logX-- (4-8) 

(4Y) Xl X2 Xi Xn 

where 

b - intercept; and 

mi - coefficient of the regression 

and the overbars denote the value of the quantities used for normalization (generally the mean value). 

When the antilog of both sides of Eq. (4-8) is taken, then the resulting equation becomes 

=Y =101il xr- x (4-9) 

y- ( ixiir X "'"7

4-9
System-level Sensitivity Studies

After taking the partial derivative of both sides of Eq. (4-9) with respect to the independent variables and 

rearranging, it reduces to 

x. dy - mi (4-10) y odx, 

Therefore, the normalized sensitivities are exactly the coefficients of the regression equation using the logs 

of the normalized peak dose and independent variables. The form of the sensitivities given by Eq. (4-10) is 

the same measure calculated by the differential method of Eq. (4-12) in Section 4.1.2. 

4.1.1.4 Application of the Kolmogorov-Smirnov and Sign Tests for Determining 

Important Parameters 

The K-S and Sign tests differ from regression in that they are nonparametric; that is, these tests do 

not require fitting the data to prespecified functional forms. 

The Kolmogorov-Smirnov Test 

The K-S test determines if a set of samples was drawn from a given distribution (Bowen and Bennett, 

1988). It is used to determine if an independent variable is influential by comparing the distribution of a 

subset of the independent variables composed of the values from the highest 10 percent of the peak dose 

realizations to the theoretical distribution of that variable. If the two distributions are equivalent, then peak 

dose is not sensitive to the variable in question. Conversely, if the distributions are different, then the variable 

in question does have an effect on peak dose. For the present study, there are 1000 vectors in the entire set, 

and the subset consists of the 100 vectors corresponding to the top 10 percent of the peak doses. The 

distribution of the variable in the 1000-vector set is taken as the theoretical distribution, although it would 

also be possible to get the theoretical distribution directly from the generating function specified in the 

LHS routine. The significance of the K-S test was determined at the 95-percent confidence level. 

The Sign Test 

The Sign test is another nonparametric test used to determine if a set of data corresponds to a given 

theoretical distribution (Bowen and Bennett, 1988). It is used in a manner similar to the K-S test. In the Sign 

test, each observation of the input variable is represented by either a plus sign (+) or a minus sign (-), 

depending on if it is greater than or less than the median value estimated by the theoretical distribution. The 

subset of the input parameter values corresponds to the highest 10 percent of the calculated peak doses. The 

subset is compared with the theoretical distribution, which, in this case, is assumed represented by the entire 

set of 1000 vectors. The significance of the Sign test was determined at the 90 percent confidence level. 

4.1.2 Differential Analysis Technique 

Regression analysis on the Monte Carlo results can only determine the most influential parameters 

when those parameters also have large enough correlation coefficients that they are distinguishable from the 

confounding effects of the simultaneous sampling of all other independent variables. Differential analysis 

determines sensitivity unambiguously because it deals with changes in only one independent variable at a 

time. Differential analysis determines sensitivity of parameters only at local points in parameter space and

4-10
System-level Sensitivity Studies

does not consider the wide range of parameter variations, as does the Monte Carlo method. This section 

describes the results of a differential analysis conducted to determine the most influential parameters with 

respect to peak dose. 

Differential analysis tests were conducted through multiple deterministic runs in which a single input 

parameter was changed by a known amount compared to its initial baseline value, and all other input 

parameters were held at a baseline value. The baseline value for the purposes of this report is a sampled value 

for the input parameter. The sensitivity of a performance measure (in this case peak dose for the TPI) to a 

parameter is estimated as the first derivative of the performance measure with respect to that parameter 

.5Y y(xi + Ax,)- y(x,) (4-11) 

&x1 Axi 

Usually Ax, is relatively small (e.g., 10 percent of the parameter value). These estimates of sensitivity are 

local (i.e., the value of the derivative may change at different points in the sample space). To partially 

alleviate this concern, the derivative may be evaluated at several points in the sample space. In the analyses 

presented herein, the derivative is transformed in one of two ways to allow for comparison of sensitivity 

coefficients between parameters whose units may differ. The first transformation is described by 

i=Y Xi (4-12) &i y 

where S, is the dimensionless normalized sensitivity coefficient. These normalized sensitivity coefficients 

are in the same form as the sensitivities defined by the regression analyses with the log of the normalized 

variables. Because S, does not account for the range of the input parameter, a second transformation of the 

derivative is also performed where the derivative is multiplied by the standard deviation of the input 

parameter distribution. This transformation is described by 

S a a-x, (4-13) 

Baseline cases were run with input parameter values set at seven random points within each parameter 

distribution range selected using the LHS technique. Seven points may not cover the whole space, but this 

limitation was imposed for expediency purposes.

4-11
System-level Sensitivity Studies

4.1.3 Morris Method Technique 

The Morris method (Morris, 1991) considers 0y/f)x, 9 as a random variable and uses the mean and 

standard deviation of the random variable to determine the sensitivity of y to x,. A large value of mean of 

Dyfi)x1 implies that x, has a large overall influence on y. A large value of standard deviation implies that 

either x, has significant interactions with other input parameters (i.e., xk, k = 1, 2, ..., I, k 9i) or its influence 

is highly nonlinear. Therefore, both the mean and standard deviations of )y/lZx, are used to rank the 

influence of input parameters. 

In the Morris method, the random variable, Dy/l)x, , is evaluated using the current and the previous 

values of y: 

oyy(x1 + Axl, IX2 +- AX2, ... , Xi "45 Z•i..., 5X1) 

oai Ax, 

_y(x 1 +AXI, x 2 + AX22,... ,xi,...,xI) (4-14) 

Ax, 

This is in contrast to the differential analysis method in which dy/1)x, is evaluated using the current and 

baseline values of y, as presented in Eq. (4-11). 

To compute ay/axi , a design matrix is constructed using input variables as shown: 

X1 X2 ... Xi_1 Xi Xi+1 ' X1 I 

... ... ... ... ... ... ... ... 

Xl+A 1 X2 +A 2 ... Xi- 1 + A,- 1 Xi X+1 ... Xl i 

X1 +A 1 X2 +A 2 *** Xi_1 + Ai_1 Xi + Ai Xj+1 ... Xl i+1 

Xl+A I X2 +A 2 . x. + AI- 1 xi +Ai Xi+. 11 +A, A1 .. i+2 

... ... ... ... ... ... ... ... 

_X1 A1 X2 +A 2 "x_ 1 -A_,-I+-i x +A xj 1 -A+1 "A" x,+A, A 

where A = Ax, . To construct this matrix, the range of each variable is subdivided into (p-l) intervals using 

(p-i) equally spaced points. Then x, values are randomly sampled from thesep intervals. It should be noted 

that each interval represents the left-most value in the original distribution. The increment A is now 

represented by A, = p/2(p - 1) . 

9

Strictly speaking, ay/ax, should be denoted as Ay / Axi because Ax, is not necessarily a small value, as in the case 

of differential analysis. Here the notation is maintained to simplify the comparison with the differential analysis method.

4-12
System-level Sensitivity Studies

To implement the Morris method, the input variables are first normalized using the following 

transformation such that the transformed input parameters, x* , range from 0 to 1. 

* xi - m , 1,2, i...,x1 (4-15) 

Ximax - Ximin 

To minimize the influence of the baseline sampling on the parameter sensitivity, seven samples are collected 

for each random variable qdY/dx . The steps necessary to obtain the design matrix, which includes these 

samples, are presented in Appendix A. This was accomplished by sampling seven baseline realizations, using 

LHS, from which seven different design matrices were constructed. 

4.1.4 Fourier Amplitude Sensitivity Test Method 

Both the differential analysis and the Morris method handle one input parameter at a time. For a 

nonlinear computational model, input parameters are likely to have strong interactions. It would be desirable 

therefore to have a sensitivity analysis method that would investigate the influence of all input parameters 

at the same time. The Fourier Amplitude Sensitivity Test (FAST) method (Cukier, et al., 1973) does this. It 

first applies trigonometric transforms to the input parameters: 

Xi gi (sin Ois), i = 1,2,..., I (4-16) 

The trigonometric transforms relate each input parameter, x1, to a unique integer frequency, w,. All 

transforms have a common parameter s, where 0:< s • 21r. As s varies from 0 to 2z, all the input parameters 

vary through their ranges simultaneously at different rates controlled by the integer frequencies assigned to 

them through Eq. (4-16). Equally spaced values of s between 0 and 2n are chosen to generate values of x, in 

Eq. (4-16). Because trigonometric transforms and integer frequencies are used in Eq. (4-16), the output, y, 

becomes periodic in s, and the discrete Fourier analysis can be used to obtain the Fourier coefficients ofy 

with respect to each integer frequency (Appendix B). The sensitivity ofy to x, is measured by the magnitudes 

of the Fourier coefficients with respect to C0 , and y is considered sensitive to the input parameters with 

larger magnitudes of Fourier coefficients. 

The use of integer frequencies causes some errors because of aliasing among Fourier coefficients. 

The integer frequencies in Eq. (4-16) were chosen to minimize interactions among Fourier coefficients to 

ensure, as much as possible, that the particular coefficient, A, (Appendix B), through the particular integer 

frequency, w,, represents only the influence of the corresponding input parameter, x,. Appendix B explains 

how the integer frequencies are selected and how the FAST method is implemented. Assuming 0•< x, _< 1, 

the trigonometric transformation functions used here were 

1 1 

xi =- +- arcsin[sin(aos + r)j,i = 1,2,...,I (4-17) 2 ;r 

where r,, and i = 1, 2, ..., I are random numbers. If the range of variation of a parameter is different from 

[0, 1], Eq. (4-17) can be modified easily.

4-13
System-level Sensitivity Studies

Currently, implementation of the FAST method is limited to 50 input parameters. According to 

Cukier, et al., (1975), as many as 43,606 realizations are needed to perform a satisfactory analysis on 

50 input parameters, to avoid aliasing among any four Fourier amplitudes. 

4.1.5 Parameter Tree Method 

The parameter tree method examines total system output relative sensitivity and correlations of 

output to subgroups of input parameters. The parameter trees appear similar to event trees but are different 

because no specific initiating event is associated with parameter trees. In this technique, the Monte Carlo 

(or LHS) method is used to examine the possible outcomes of a combination of parameter sets. Bins of 

realizations are examined where the bins are determined by a commonality of their input parameter states 

(e.g., all sampled input parameters above their median value). 

To analyze the outputs, yj, in Eq. (4-1), to determine the sensitivity and correlations of output, y, to 

subgroups of the input parameters, xi, n = 1, 2, ..., N, where N<I, a tree structure is developed. The parameter 

tree partitions input parameter space into bins, each bin forming a branch of the tree based on a partitioning 

(or branching) criterion, as done in an event tree. The simplest branching criterion is a classification based 

on parameter magnitude, which treats sampled input values as either a + or a - depending on whether the 

sampled value is greater or less than the branching criterion value. The event tree analogy is appropriate if 

a + is considered a parameter failure and a - is considered a parameter success, or vice-versa. Figure 4-5 

depicts a general parameter tree. To explain Figure 4-5 using a system model, a number of realizations are 

generated for a given scenario class. Next, the realizations are partitioned into two subsets determined by 

whether the first influential parameter, x,, is greater than or less than a specified level. Realizations with a 

high value are all treated as a + and low as a-, regardless of their position within the subset. Let the number 

of realizations associated with the two branches be N,+ and N,.- Next, the output variable, - 1, is examined 

for realization associated with each branch of the tree. The number of realizations with y greater than a 

criterion (e.g., mean) are counted for both the branches. Let these numbers be L1+ (L1+•_N,+) and LI_ 

(L. •--N1 _). The difference between LI+ / N1+ and Lj_ / N, is a measure of sensitivity ofy to x,. The procedure 

is repeated in each of these two subsets with the next influential parameter to be considered and so on until 

each of the influential parameters is considered. This procedure determines 2M bins of realizations where M 

is the number of influential parameters. Note that not every sampled parameter in the system model need be 

considered if a subset of the sampled parameters satisfactorily explains system behavior of interest. 

Sensitivity measures similar to those over explained for one parameter are developed for a set of parameters. 

Another measure ofinfluence of a subset of parameters may be defined through the contribution that 

realizations in a bin make to specific statistics of the output. For example, one can compute the expected 

value of y for realizations associated with each branch of the tree and compare these means to the overall 

mean ofy. Statistics other than the mean can be used or probability distributions can be developed for each 

branch and compared with the overall probability distribution of y. If, for example, the probability of y 

exceeding a certain limiting value (perhaps specified by regulations) is of interest, one could find the value 

of such exceedance probability for each branch and estimate (in a relative sense) the contribution that each 

parameter set makes to such a probability. Formally then, if T is a statistic (e.g., mean, mode, median, 

exceedance probability) of interest, for the second level of the tree, the ratios of T,2,., T2, ,÷,, T,2. to T or 

y as a whole provide measures of relative sensitivity.

4-14
2N subsets of

input parameter 

value 

for realization 

greater 

than cutoff (+)

input parameter 

value 

for realization 

less 

than cutoff (-)

nos

output variable

.- .• 

output variable 

output variable

Figure 4-5. General parameter tree.

scena

I 

t•
System-level Sensitivity Studies

The branching criterion can be something other than the magnitude of a parameter. One of the more 

useful possibilities is to assume the system is made up of several components in series such that the output 

from one component becomes an input to the second and so on. With this conceptualization, the branching 

criterion can be stated as the magnitude of the output of a component. In this case, each branch of the tree 

would represent the contribution of a component or a set of components to overall system performance. 

Relative sensitivity measures could then be defined in exactly the same manner as explained previously. 

4.2 ANALYSIS OF SENSITIVITY FROM MONTE CARLO RUNS 

This section presents the sensitivity and uncertainty analyses results generated using methods 

described in the previous section. Statistical results of the 1000-vector Monte Carlo runs, treated separately 

from the differential analysis, Morris method, and FAST method will be covered first in this section. 

Comparison of the results among methods will be presented in subsequent sections. 

4.2.1 Procedure for Screening Monte Carlo Sensitivity Results 

The Monte Carlo simulation results were screened to estimate which variables were likely to be 

significantly influential and provide an estimate of the sensitivity coefficients. The sequence by which these 

procedures were employed is described next. 

Preliminary screening analyses-This stage of the analyses used a variety of techniques to determine 

in gross terms whether an independent variable was possibly related to dose. All variables that passed any 

of the screening tests are included in the subsequent analyses. For all analyses, zero values of dose were 

eliminated from the data sets because these were inadmissible for logarithmic and power law transformations. 

For each TPI (10,000 or 50,000 yr), the following procedures were employed: 

"* Visual inspection of scatter plots 

" t-statistic test for single linear regression of dose versus each variable 

- Normalized variables 

- Log of normalized variables 

Stepwise linear regression 

- Normalized variables 

- Log of normalized variables 

- Scaled-power transformed variables 

- Ranks of variables 

Nonparametric tests 

- K-S test 

- Sign test 

Linear models-For each TPI, the list of independent variables from any of the preliminary screening 

analyses was used to construct a linear model, to be fitted by regression to the data, using Eq. (4-7). This was 

also performed on the logarithmically transformed variables.

4-16
System-level Sensitivity Studies

Refined screening-The regression coefficients resulting from the linear models were then screened 

for significance using the t-test. The hypothesis that an independent variable is significant was rejected if the 

absolute value of t was less than 1.96, corresponding to a 95" percentile confidence limit, for either the 

normalized or logarithmically transformed variables. Note that the t-test performed on the single-variable 

regressions in the first step frequently accepted variables that were later screened by the refined analysis. 

Transform sensitivity of the variables resulting from refined screening to standardized form-Use 

Eq. (4-5) to transform the normalized sensitivities resulting from regression of the logarithmically 

transformed variables to the standardized form. 

4.2.1.1 Sensitivity Results from Monte Carlo Analysis 

This section presents the sensitivity analyses based on the statistical analysis of a 1000-vector 

Monte Carlo analysis of the basecase for 10,000- and 50,000-yr TPI.1° The screening and regression analyses 

are summarized in Tables 4-1 and 4-2 forthe 10,000- and 50,000-yr TPIs, respectively. The column headings 

in Tables 4-1 and 4-2 have the following explanations: 

" Variable Name-The abbreviated name of the independent variable appearing potentially 

sensitive in any of the screening analyses. There is a complete list of the variable names in 

Appendix D. 

" Step Norm-Variables that appeared to be influential from stepwise regression of the 

normalized variables. 

" Step Lnorm-Variables that appeared to be significant for stepwise regression of the log of the 

normalized variables. 

" Step Rank-Variables that appeared to be significant from stepwise regression of the ranks of 

the variables. 

" Step Lilli-Variables that appeared to be significant from stepwise regression of the power-law 

transformed variables. 

KS + Sign--Variables that passed both the K-S and Sign tests. 

" t-Norm-Variables for which the t-value of a single-variable regression of the normalized 

variables is greater than 1.96 (95-percent confidence level). 

" t-Lnorm-Variables for which the t-value of a single-variable regression of the log of the 

normalized variables is greater than 1.96. 

" t-Lilli-Variables for which the t-value of a single-variable regression of the power-law 

transformed variables is greater than 1.96. 

01The time period of interest of 100,000 yr used in presenting the basecase results is different from that used in the 

sensitivity analyses (10,000 and 50,000 yr) primarily because the basecase results were also used in reviewing the U.S. Department 

of Energy Total System Performance Assessment-Viability Assessment results, which extended to 100,000 yr and beyond.

4-17
Table 4-1. Summary of regression and screening for basecase, 10,000-yr time period of interest 

Step Step Step Step KS + t- t- t- In LM t-stat t-stat 

Variable Name Norm Lnorm Rank Lilli Sign Norm Lnorm Lilli Model Norm Lognorm Sens ? 

AAMAI@S - X X X X X X X X 2.86 8.03 X 

MAPM@GM - X X - X X X X X 1.61 3.16 X 

MATI@GM - - - X - X X X X 2.13 1.06 X 

FOC-R - X X - X - X X X 1.36 0.10 

FOCTR-R - - - X - - - X .- 

InnOvrEI -... X ....... 

SSMO-RPR X .. . ........ 

SSMOV201 ... . X ....... 

SSMOV501 X . . . . X - - X 1.96 0.15 X 

Fow* X X X X X X X X X 4.10 14.60 X 

Fmult* X X X X X X X X X 3.01 7.65 X 

SbArWt% X X X X X X X X X 32.40 15.37 X 

WP-Def% X X X X X X X X X 4.34 12.66 X 

InitRSFP X X X X - X X X X 0.09 2.27 X 

SFWt%I1 ... . X ...- -. 

SFWt%13 X - - - X X - - X 2.28 0.91 X 

SFWt%S46 X - - - X X - - X 2.43 0.37 X 

MKDPPwAm - .X - - -.. 

MKDCHzNp -... X -... .... 

MKDCHzNp - - - - X -. .. 

MKDUFZNp - - - - X -. .. 

MKDCHzU - - - - X -. .. 

MKDCHvPb - - - - X -. .. 

MKDBFwPb - - - - X .- 

MKDBFwSe X - - - - X- X 2.19 0.78 X 

MPrmTSw . - - X X X - X 0.54 0.35 -
Table 4-1. Summary of regression and screening for basecase, 10,000-yr time period of interest (cont'd) 

Step Step Step Step KS + t- t- t- In LM t-stat t-stat 

Variable Name Norm Lnorm Rank Lilli Sign Norm Luorm Lilli Model Norm Lognorm Sens ? 

FPrmCHv 

- x 

FPrmBFw X - - - X - - X 2.28 - X 

ARDSAVAm - X X 0.75 0.49 

ARDSAVNp - X X - X - X - X 1.43 2.91 X 

ARDSAVI - X X X - - X X X 0.32 4.86 X 

ARDSAVTc X X X X X X - X X 2.90 5.04 X 

ARDSAVU - - X X - X X X 0.22 1.40 

ARDSAVPu - -

APrsSAV X - X X - X 0.09 1.95 X 

WPRRG@20 X X X X X X X X - 2.90 4.72 X 

N W FZnW .... X .... 

NELCDAmt - X -
Table 4-2. Summary of regression and screening for basecase, 50,000-yr time period of interest

Step

Variable Name Norm

AAMAI@S 

MATI@GM 

H2OFThK 

AA_2_1 

O0-CofLC 

SSMO-RE 

SSMO-RPR 

SSMO-JS5 

SSMOV206 

SSMOV408 

Fow* 

Fmult* 

SbArWt% 

InitRSFP 

SbGFRATF 

SFWt%C1 

SFWtC2 

SFWt%C3 

SFWt%C5 

SFWt%C6 

SFWt%C7 

MIKDPPwAm 

MKDCHvNp 

MPrmTSw 

MPrm UFZ

x 

x 

x 

x 

x 

x 

x 

x

Step Step KS + t

Rank Lilli Sign Norm 

- y Y

Step 

Lnorm 

x 

x 

x 

x 

x 

x 

x 

x 

x

x 

x 

x 

x 

x 

x 

x 

x 

x 

x

x 

x 

x 

x 

x 

x

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x

x 

x 

x 

x 

x 

x

x 

x

t- t" In LM t-stat t-stat

Lnorm Lilli 

x x 

x x 

x x 

x x 

x x 

x

-- x 

-- x 

x x 

x x

.r. 

t'J 

0

Model Lognorm

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x

Norm 

1.67 

3.33 

-2.22 

0.55 

1.81 

-0.51 

2.46 

-2.18 

-1.79 

0.88 

1.69 

1.13 

0.22 

0.28 

-0.7

-31 

9.30 

0.04 

2.00 

0.66 

-2.14 

35.20 

4.20 

-2.92 

3.96 

3.57 

4.20 

2.13 

3.53 

-2.11

Sens ? 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x

x 

x 

x
Table 4-2. Summary of regression and screening for basecase, 50,000-yr time period of interest (cont'd) 

Step Step Step Step KS + t- t- t- In LM t-stat t-stat 

Variable Name Norm Lnorm Rank Lilli Sign Norm Lnorm Lilli Model Norm Lognorm Sens? 

FPrsPPw X .. . . . . 

ARDSAVAm X - - X X X . .. 

ARDSAVNp X X X X X X X X X -4.16 24.40 X 

ARDSAVI - X X X - - X X X -0.71 -3.16 X 

ARDSAVTc - X X X - - X X X 0.08 -4.6 X 

ARDSAVU - - - X X X X X X -1.12 -2.57 X 

ARDSAVTh - - - X - X X X -0.82 1.20 

APrs SAV - X - x - - X X X -1.02 -3.29 X 

WPRRG@20 X X X X X X X X X -2.2 -9.2 X 

.r• 

t'3
System-level Sensitivity Studies

"• Include in LM Model-Variables included in linear models for multiple linear regression. 

"* t-stat Norm-The t-statistic for the variable in the linear model for normalized variables. 

" t-stat Lognorm-The t-statistic for the variable in the linear model for log of 

normalized variables. 

" Sens ?-The variable had a t-statistic in either the normalized or lognormalized multiple linear 

regression analysis that exceeded 1.96 (95 percent confidence). 

Tables 4-3 and 4-4 summarize the sensitive parameters, resulting from linear regression, for the 

10,000- and 50,000-yr TPIs, with using standardized variables that give a truer indication of parameter 

sensitivity by taking into account the standard deviations of the independent variables sampled in the Monte 

Carlo analyses. Figures 4-6 and 4-7 present sensitive parameters, obtained from step-wise regression 

analyses, using standardized input variables for 10,000 and 50,000 yr, respectively. The ranks of the 

standardized variables are compared with the ranks from the other sensitivity measures in Section 4.3. In 

these tables, x and y represent the mean of the input and output variables. Variables o,,.and a,•,in Tables 4-3 

and 4-4 represent the standard deviations of normalized input and output variables (indicated by x*, andy*,). 

The headings m-norm and m-lognorm represent coefficients from regression equations using normalized 

variables and lognormalized. 

4.2.1.2 Parameter Sensitivity at High End of Peak Doses 

Doses at the high end of the calculated range, and their associated parameter sensitivities, may be 

of more interest than low doses. To develop this idea further, vectors from the basecase were segregated into 

those with doses higher than a threshold of 0.1 mSv (10 millirem/yr), and those below for the 50,000-yr TPI. 

The higher category contained 51 vectors and the lower category contained the balance of 949 vectors. 

A t-test was then conducted on means of the independent variables to determine if the means of the 

two populations are statistically the same at the 95-percent confidence limit. For each independent variable 

x1 from the high-dose category and x2 from the low-dose category, calculate the sample means [tj, and 2., 

together with the variances a1 and 0,. At the 95-percent significance level, accept the hypothesis if 

tI= 19 1 - ]U21 < 1.96 (4-18) 

where m, and m_, are the number of samples in sets 1 and 2. The results of this screening are listed in 

Table 4-5. 

Note there were several parameters left off the list because they were probably spurious and cannot 

have had an effect on the results. For example, the water use parameter at 10 km was sampled but not used. 

Several of the significant parameters were associated with properties of Am and Pu, although neither 2

-

41

Am 

nor 2 gPu have any doses at all. The effects of the parameters in the models are due in large part to the 

deliberate correlations of several of the radionuclide retardation parameters, and it is likely that these factors

4-22
System-level Sensitivity Studies

0 20 40 60 80

Number of Parameters Included in Fit 

Plot of the residual sum of squares versus number of parameters included in the fit for 

the basecase with a time period of interest of 10,000 yr.

I I

10 20 30 40 

Number of Parameters Included in Fit

5O 60

Plot of the residual sum of squares versus number of parameters included in the fit for 

the basecase, with a time period of interest of 50,000 yr.

4-23

0

0 

E 

CO 

.'0 

CD 0r

§

Figure 4-6.

. SbArWt%/6 

Fow* 

WP-Def/o 

Fmult* 

* AAMAI@S 

* ARDSAVTc 

.ARDSAV_I 

* MAPM@GM 

FOC-R 

. *. *. *********•***oeeo*ossoe**o *******o**eo*o*.. ***.o.

(a 

0" 

(0 

E 

Cr)

0.

I 

0

Figure 4-7.
System-level Sensitivity Studies

Table 4-3. Standardized sensitivities for basecase, 10,000-yr time period of interest

Variable Name 

AAMAI@s 

MAPM@GM 

MATI@GM 

SSMOV501 

Fow* 

Fmult* 

SbArWt% 

WP-DEF% 

InitRSFP 

SFWtI1 

SFWtS46 

MTKDBFwSe 

FPrmBFw 

ARDSAVNp 

ARDSAV I 

ARDSAVTc 

APrsSAV 

WPRRGn(.20

Table 4-4. Standardized sensitivities for basecase, 50,000-yr time period of interest 

UY ay_ ay 

Variable Name m-norm (norm) m-lognorm (lognorm) 

AAMAI@s 0.9314 0.134 0.101 0.8856 0.089 

SSMO-RPR 0.0154 0.0292 -0.067 -0.0154 -0.0004 

SSMO-JS5 0.4284 0.0389 0.0170 0.5603 0.0.022 

SSMOV206 0.5560 0.0989 0.0550 0.0700 0.0007 

Fmult* -0.0837 0.1840 -0.015 -0.135 -0.025 

SbArWt% 1.0020 0.2087 0.2090 1.0810 0.2260 

InitRSFP -0.9080 0.0726 -0.066 -0.6052 -0.044 

SbGFRATF -0.7740 0.0700 -0.0540 -0.4374 -0.031 

SFWtC1 0.1448 0.2090 0.0300 0.1210 0.0250 

SFWt%C2 0.2445 0.2090 0.0510 0.1080 0.0230 

SFWtC3 0.1631 0.2090 0.0340 0.1284 0.0270 

SFWt%C6 0.0319 0.2090 0.0070 0.0706 0.0150 

SFWt%C7 0.0403 0.2090 0.0080 0.1083 0.0290

4-24

cry x,

m-norm 

0.659 

1.208 

1.208 

0.485 

0.401 

0.64 

0.612 

0.847 

0.0492 

0.429 

-0.462 

0.11 

0.104 

-0.0807 

-0.0872 

-0.349 

-0.0845 

-1.125

ay * 

(norm) 

0.088 

0.051 

-0.067 

0.066 

0.131 

0.093 

0.099 

0.139 

0.003 

0.072 

-0.078 

0.07 

0.071 

-0.046 

-0.010 

-0.092 

0.003 

0.092

0.134 

0.042 

-0.05586 

0.136 

0.326 

0.1456 

0.161 

0.164 

0.0586 

0.1684 

0.168 

0.636 

0.686 

0.567 

.1149 

0.264 

0.0335 

0.0818

m-lognorm 

0.934 

1.463 

0.367 

-0.0174 

1.08 

1.075 

1.054 

1.079 

-0.726 

0.062 

-0.025 

0.016 

0.013 

-0.148 

-0.827 

-0.35 

-1.141 

-1.08

axy* 

(lognorm) 

0.125 

0.061 

-0.021 

-0.002 

0.353 

0.157 

0.17 

0.177 

-0.043 

0.01 

-0.004 

-0.01 

0.049 

-0.084 

-0.095 

-0.092 

-0.038 

-0.088
System-level Sensitivity Studies

Table 4-4. Standardized sensitivities for basecase, 50,000-yr time period of interest (cont'd) 

1X.1 Y_ y 2 

Gay. ax,. 

Variable Name m-norm (norm) m-lognorm (lognorm) 

MKDCHvNp -0.0164 1.2900 -0.021 -0.0338 -0.044 

ARDSAVNp -0.2 0.6930 -0.069 -0.72 -0.499 

ARDSAV_1 -0.151 0.1420 -0.008 -0.242 -0.034 

ARDSAVTc -0.0083 0.3270 0.0030 -4.6 -0.047 

ARDSAV_U -0.0407 0.9280 -0.038 -0.0623 -0.058 

APrsSAV -0.7362 0.0417 -0.031 -0.8617 -0.036 

WPRRG(&20 -0.6631 0.1010 0.0670 -0.945 0.0040 

Table 4-5. t-test on means of high- and low-dose categories for 50,000-yr time period of interest 

Variable Name t value 

AAMAI@s 3.79 

OOCofLC 3.89 

SSMO-RPR 3.13 

SSMOV203 2 

SbArWt% 7.7 

WP-Def/o 2.11 

SFWS37 2.15 

MKDUFZAm 4.16 

MKDUCFNp 3.23 

MKDCHvU 2.88 

MKDCHzU 2.82 

MKDUCFU 2.78 

M4]KDUFZU 2.57 

MKDTSwTh 2.93 

MKDCHvTh 2.93 

MKDUCFTh 2.4 

MKDBFwTh 3.42 

MlPrmTSw 6.14 

MPrmUFz 1.97 

FPrsCHz 2.68 

FPrsPPw 2.12 

ARDSAVAm 6.72 

ARDSAVNp 15.8 

ARDSAVTh 3.98

4-25
System-level Sensitivity Studies

show up because of the large contribution to peak dose of 237

Np. In the case of 241

Am, some dose also may 

be indirectly attributed to 241

Am decaying to 23

.Np. Dependence of several of the parameters, particularly 

MKDUFZAm, MKDUFZU, and MPrm UFZ, are suspicious, since these parameters were sampled but not 

used. It is likely that these results, and possibly others, are spurious because of the relatively small sample 

size of 51 samples in the high-dose category. The same also is likely to be true for U, since the contribution 

of 234

U to dose is small. 

Inspection of the terms that passed this screening and of their respective t statistics indicates strong 

relationships between some of the parameters and relatively high doses, in particular the subarea wet fraction 

(SbArWt%), matrix permeability of the Topopah Springs welded tuff (MPrm_TSw), and retardation factors 

for Am Np, U, and Th. 

4.3 ANALYSIS OF SENSITIVITY FROM NONSTATISTICAL METHODS 

4.3.1 Results from Differential Analyses 

Differential analyses were performed using TPA Version 3.2 code with the basecase. Cases where 

faulting and igneous activity were activated in the TPA code were modeled separately. A total of 223 input 

parameter values were perturbed for each series. The input parameters perturbed are defined by a distribution 

in the basecase tpa.inp input file. The parameters sampled in the tpa.inp file are the ones where a significant 

amount of uncertainty remains in their value or they have been shown potentially significant to estimating 

peak dose in the process-level sensitivity analyses. 

Seven random sets of input parameters were evaluated. Perturbations to the parameters in these 

random sets were selected so that the parameter values were maintained in their respectively defined ranges; 

the first, second, fourth, fifth, and seventh random sets of input parameters were perturbed by +1 percent, 

whereas the third and sixth random sets of input parameters were perturbed by- 1 percent. The selection of 

random values yields calculations similar to one realization of a probabilistic TPA code run. The percent 

perturbations are with respect to the baseline (i.e., local) parameter value. 

In the TPA Version 3.2 code, transport through the UZ stratigraphic units is neglected for those units 

where groundwater residence time is less than 10 yr, or 10 percent of the residence time for the entire UZ 

below the repository (Mohanty and McCartin, 1998). Differential analyses, in which UZ transport 

calculations are omitted because of this assumption, will result in peak dose showing no sensitivity to 

parameters that describe UZ properties in those stratigraphic units excluded from the transport calculations. 

For example, when all parameters were set at their mean values, the UZ portion of NEFTRAN was skipped 

for a majority of the subareas. Thus, sampled UZ flow and transport (UZFT) parameters did not show any 

sensitivity in these calculations. However, when the transport time in the UZ is short, it is unlikely that any 

of the UZ parameters would have a substantial effect on the peak dose, so this should not have a significant 

effect on the results of the differential analysis. 

For all sets of the random parameters, the WPs did not fail from either seismicity or corrosion in the 

10,000-yr TPI, but did fail from corrosion within the 50,000-yr TPI. The baseline dose values in these cases 

are solely from initially defective WPs.

4-26
System-level Sensitivity Studies

Each set of base values was used in a TPA code run, to determine the reference value of peak dose 

necessary to calculate several sensitivity measures. The baseline value peak doses can be found in Appendix E. 

The results of the differential analysis are shown in the following tables for TPIs of 10,000 and 

50,000 yr in Appendix E: Tables E-1 and E-2 for the basecase, Tables E-3 and E-4 for the basecase plus 

faulting, and table E-5 for the basecase plus igneous activity. The basecase plus igneous activity was not run 

for the 50,000-yr TPI because the results are not expected to change after the 10,000-yr TPI when 

groundwater dose dominates and the primary contributors to ground-surface dose have decayed. Variables 

tested but indicating zero sensitivity at all baseline values are not shown in the tables for the basecase. 

Tables E-1 through E-5 of Appendix E show the sensitivities calculated using four 

different measures: 

(1) The geometric mean of the absolute value of the sensitivity coefficientS, [see Eq. (4-12)] was 

calculated for the seven base values. The geometric mean is useful for emphasizing parameters 

that are sensitive over the entire range of base values. In cases where the sensitivity coefficient 

was zero (i.e., smaller than the least significant digit in code output) at a base value, the 

geometric mean is an upper estimate for that parameter. 

(2) The arithmetic mean of the absolute values of S, was calculated for the seven base values. 

(3) The highest sensitivity of S, is calculated at any of the seven points. This sensitivity measure 

is useful to determine if the parameter is sensitive at any of the seven points. 

(4) An arithmetic mean of the derivative is weighted by the standard deviation of the input 

parameter. This sensitivity measures the response of peak dose to each of the independent 

variables, weighted by their standard deviation. The standard deviations are determined by the 

parameter range and distribution used in the Monte Carlo analyses. This measure takes into 

account the magnitude of the change in peak dose and the uncertainty in the .independent 

variables. For comparison, the normalized sensitivity measure, S,, is a relative sensitivitywhere 

the slope is scaled by the local values of dose and the independent variable. Therefore S, does 

not depend on whether the baseline dose is small or large, but only on the change in dose 

relative to the change in the independent variable. 

Measure (4) was used to sort the input parameters in descending order because it reflects both the 

absolute value of peak dose and the uncertainty in the independent variables. The other three sensitivity 

measures are also given in the tables provided in Appendix E. The lists of influential parameters are 

generated based on the top 10 parameters for the basecase (i.e., at 10,000- and 50,000-yr TPIs). 

The tables in Appendix E provide a list of the parameters that showed nonzero sensitivity at any of 

the seven baseline values about which the derivatives were evaluated. Some of the sensitivities shown, 

however, were exceedingly small. To focus attention on the parameters to which peak dose showed the 

largest sensitivity for the current models on which this report is based, Tables 4-6 and 4-7 list the influential 

parameters for the basecase [i.e., the top 10 parameters based on the mean of S0 as in Eq. (4-13)] for the 

two TPIs. Table 4-8 lists the influential parameters for the disruptive scenarios for the two TPIs. The 

influential parameters for the disruptive scenarios were determined by including any parameter whose 

sensitivity was within 1 order of magnitude of the most influential parameter from the basecase, using

4-27
System-level Sensitivity Studies

measure (4). For the igneous activity scenario, all sampled parameters are influential, and for the faulting 

scenario, three sampled parameters are influential for the 1 0,000-yr TPI, but no sampled parameters are 

influential for the 50,000-yr TPI. The reason for this difference is that the only impact of faulting on the 

repository is failure of the additional WPs. In the longer TPI, all the WPs fail by corrosion, and the peak dose 

is dominated by the WPs failed by corrosion. 

4.3.2 Results from the Morris Method 

The Morris method was applied to the TPA Version 3.2 code with the basecase parameter set. A total 

of 246 input parameters was investigated. A 1729 x 246 matrix was generated and used in sampling input 

parameters to the TPA code for the 1729 realizations. The 1729 realizations [(246 +1)x 7] produced 

seven samples for each Dy/axj , which were used to calculate mean and standard deviation for each D)y/)xj . 

Seven samples were chosen to be consistent with the differential analysis method. 

Figures 4-8 and 4-9 show graphs for the values of mean (abscissa) and standard deviation (ordinate) 

of )y/f)xj values for the 10,000- and 50,000-yr TPIs. As described earlier, the greater the distance 

d'y/Dxi for parameter xi is from zero, the more influential the parameter xi is. Physically, apoint with 

large values of both mean and standard deviation suggests that the corresponding input parameter has not 

only a strong nonlinear effect itself, but also strong interactive effects with other parameters on the output. 

The top 10 most influential input parameters identified by the Morris method are listed in Table 4-6 

for the 10,000-yr TPI and Table 4-7 for the 50,000-yr TPI, where each parameter was standardized according 

to Eq. (4-3). For the 10,000-yr TPI, the listed parameters are either related to thermal reflux or transport 

properties in alluvium. But for the 50,000-yr TPI, no thermal reflux-related parameters make the top 10 list 

of influential parameters. The parameter, WPRRG @ 20 [well pumping rate for farming receptor group 

located at or beyond 20 km (12.4 mi) from YM], appears in both 10,000- and 50,000-yr TPIs, as well as some 

parameters related to transport properties in alluvium. Several SF wet-fraction-related parameters for 

corrosion failure appear in Table 4-7, for the 50,000-yr TPI, but not in Table 4-6, for the 10,000-yr TPI. 

The ranking of parameters using the Morris method was also examined using normalized Eq. (4-13) 

and log of normalized parameters. For the top 10 most influential parameters list, the normalization scheme 

replaced SbArWt% (subarea wet fraction) with APrs__SAV (alluvium matrix porosity) for the 10,000-yr TPI, 

and the list of influential parameters did not change for the 50,000-yr TPI. However, ranking among the top 

10 parameters changed for several parameters for both TPIs. The log of normalized parameters replaced 

radionuclide parameters ARDSAV_I (AlluviumMatrixRDSAV_I) and ARDSAV_U 

(AlluviumMatfixRD)_SAVU) with MAPM@GM (mean average precipitation multiplier at glacial 

maximum) and SbWt% (subarea wet fraction for the 10,000-yr TPI. For the 50,000-yr TPI, parameters 

AA_21 (a parameter representing the corrosion rate); SFWtC4 (SF wet fraction for corrosion failures in 

subarea 4); and SFWt%C5 (SF wet fraction for corrosion failures in subarea 5) replaced ARDSAV_U 

(AlluviumMarixRDSAVU); ARDSAVTc (AlluviumMatrixRD_SAV_Tc); and MKD_CHvU (matrix Kd 

of U for Calico Hills). The logarithmic transformation also changed the ranking for both TPIs.

4-28
Table 4-6. Top 10 influential parameters (standardized) from statistical and nonstatistical analyses, for 10,000-yr time period of interest 

Normalized Log-Normalized Differential Morris Method FAST Method 

Rank Variables Variables Analysis 

I VvT-Defl/o Fow* ARDSAVTc FOCTR-R WPRRG@20 

2 Fow* WP-Defl/b FOCTR-R FOC-R ARDSAV-1 

3 SbArWtO/o SbArWt% Fow* FOCTR AAMAI@S 

4 Fmult* Fmult* ARDSAV -I WPRRG@20 Fow* 

5 ARDSAVTc AAMAI@S SFWtI3 AAMAI@S FmuIt* 

6 WPRRG@20 ARDSAV-I WP-DeP/o ARDSAV-U NIKDBFwSe 

7 AAMAI@S ARDSAVTc ARDSAVSe Fow* SbArWt/o 

8 SFWtS46 WPRRG@20 SbArWt% WP-Def'O/o ARDSAVNp 

9 SFWtO/oIl ARDSAVNp Fmult* ARDSAV-1 SFWt%13. 

10 FPrm-BFw MAPM@GM FOC-R SbArWt% MATI@GM

4ý. 

t!j 110

Abbreviation Description 

SbArWto/o SubAreaWetFraction

Description 

FraultFactor

Abbreviation 

Fmult*

Description 

ArealAwrageMeanArmualInfilt 

rationAtStart[nini/yr] 

AlluviumMatrixRD-SAV-I 

AlluviuniMatrixRDSAV-Np 

AlluviumMatrixRD-SAV-Se 

AlluviumMatrixRDý_SAYTC 

AlluviurnMatrixRIý_SAV__U

Abbreviat 

AAMAI g(S 

ARDSAV-I 

ARDSAVNp 

ARDSAVSe 

ARDSAVTc 

ARDSAV-U

SFWettedFraction-Initial-I FOC-R FractionOfCondensateRemoved[ 

1/yr] 

FOCTR FractionOfCondensateToward 

Repository[ I/yr] 

FOCIR-R FractionOfCondensateToward 

RepositoryRemoved[l/yr] 

Fow* FowFactor 

FPrtn-BFw Fractureftrrneability.ýFwlm2j 

MATI@GM MeanAverageTemperaturelncreas 

eA&GlaciaIMaximutn[degC1 

MAPM@GM MeanAveragePrecipitationMultip 

lierAtGlacialMaximum 

MYDBFwSE MatrixYJD-BFw-Se[m3/kg]

SFWto/oll

SFWtO/ol3 SFWettedFraction-Initial-3 

SFWtO/oS46 SFWettedFraction-SEISM04-6

DefectiveftactionOfWskell 

WeliPumpingRateAtReceptorGroup 

20km [gal/day]

WP-DefO/o 

WPRRC".,c20
Rank 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10

WPRRG@20 

AA-2-1 

ARDSAV-I 

Froult* 

SbArWt% 

SFWt'/oC3 

SFWtCl 

ARDSAV-U 

SFWtO/oC5 

SFWtO/oC6

-PI

Abbreviation 

SFWe/oC2 

SFWtO/oC3 

SFWtO/oC5 

SFWtO/oC6 

SSMOpRPR 

SSMOV206 

WP-DeP/o

Description 

SFWeftedFraction-Corrosion-2 

SFWeftedFraction-Corrosion-3 

SFWettedFraction-Corrosion-5 

SFWettedFraction-Coffosion-6 

RockPoissonRafioforSEISMO0 

VerficaIExtentOfRockFaII2-6[mj 

Defectivel7ractionOWl's/cell

Abbreviation 

Fow* 

InitRSFP 

MAPM@GM 

A41KD-CHnv 

OO-CofLC 

SbArWtO/o 

SbGFRATF

Description 

FowFactor 

InifialRadiusOfWarticle[m] 

MeanAveragePrecipitation 

MulfiplierAtGlaciafflaximum 

MatrixKD-CHnv[m3/kgj 

CoeffiorLocCorrOfOuter 

Overpack 

SubAreaWetFraction 

SubGrainFraginentRadiusAfter 

TransFrac[m] 

SFWettedFraction-Corrosion-I

Abbreviation Description 

AA 2 1 AA - 2 - I[C/m2/yr) 

AAIýd@S ArealAverageMeanAnnuallnfiltrat 

ionAtStart[mrn/yr] 

APrs-SAV AlluviumMatrixPorositySAV 

ARDSAV - I AlluviumMatrixRD-SAV-I 

ARDSAVNp AIIuviurnMatrixRD-SAVNp 

ARDSAVTc AJIuviurnMatrixRD-SAV-Tc 

ARDSAV-U AlluviumMatrixRD-SAV-U

WPRRG@20 WelIPumpingRateAtReceptorGroup2Okm 

[gal/day]

Fmult* FraultFactor SFWtCl

Table 4-7. Top 10 influential parameters from statistical and nonstatistical analyses, for 50,000-yr time period of interest

ARDSAVNp 

WPRRG@20 

APrs-SAV 

MYCID-ClIvU 

SbArWtO/o 

InitRSFP 

ARDSAV-U 

SFWtO/oC3 

ARDSAVTc 

SFWtC6

Differential Analysis C")

ARDSAVNp 

Fow* 

00-CofLC 

AA-2-1 

SbArWt% 

ARDSAVTc 

Fmult* 

WPRRG@20 

APrs-SAV 

ARDSAV I

Normalized Variables Morri% Method FAST Method

SbArWt% 

AAMAI@S 

WPRRG@20 

ARDSAVNp 

SSMO-RPR 

InitRSFP 

SSMOV206 

SbGFRATF 

SFWtC2 

ARDSAV U

LogNormalized Variables 

Fow* 

VvT-Defl/o 

SbArWt% 

Fmult* 

AAMAI@S 

ARDSAV I 

ARDSAVTc 

WPRRG@20 

ARDSAVNp 

MAPM(q)GM
System-level Sensitivity Studies

Table 4-8. Most influential parameters from differential analysis for disruptive event scenarios 

10,000-yr Time Period of Interest 50,000-yr Time Period of Interest 

Igneous Activity Parameters 

VE-Power VE-Power 

ABMLFVDC ABMLFVDC 

VE-Dur VE-Dur 

VEROI-Tn VEROI-Tn 

VC-Dia VC-Dia 

WindSpd WindSpd 

AshMnPLD AshMnPLD 

Faulting Parameters 

FERIO-Tn None' 

SFWtFO 

NEFZnW 

'No sensitivities greater than zero 

4.3.3 Results from the FAST Method 

Conducting sensitivity analyses for all 246 sampled parameters in the TPA code using the FAST 

method is impractical because it would take more than 40,000 realizations for the FAST method to conduct 

a sensitivity analysis on 50 input parameters. Such a large number of realizations is needed to avoid aliasing 

among Fourier coefficients (Cukier, et al., 1975). Therefore, preliminary screening was necessary to reduce 

the number of parameters evaluated with the FAST method. In this report, the FAST method is applied to 

the 18 parameters identified by the statistical screening method presented in the last column of Table 4-1 for 

the 10,000-yr TPI, and the 20 parameters in the last column of Table 4-2 for the 50,000-yr TPI. These 

parameters were selected on the basis of t-statistic of the normalized or lognormalized multiple linear 

regression analysisthat exceeded 1.96 (95-percent confidence). Forthe 18 parameters, only 33 10 realizations 

are needed to avoid aliasing among any four Fourier amplitudes (Appendix B). For the 20 parameters, the 

number of realizations increases to 4174.To account for the range of an input parameter, each Fourier 

amplitude was multiplied by the standard deviation of the corresponding input parameter, as defined by 

Eq. (4-13). The ranking for the top 10 parameters using the FAST method is listed in Tables 4-6 and 4-7 for 

the 10,000- and 50,000-yr TPIs. 

It should be noted that the analysis presented here is limited by the initial selection of 20 parameters 

from the regression analysis. Thus, some influential parameters may be identified by other nonstatistical 

methods, but not by the FAST method. 

4.4 RESULTS FROM THE PARAMETER TREE METHOD 

Several trees are presented, each using different branching criteria such as median, mean, and 

percentiles, for the important input parameters. A stepwise implementation of the approach is also presented. 

As described previously, the method used for examining system sensitivity to combinations of parameters

4-31
1.4x10-5 

1.2x10"'

-4x10.6 -2x106 0 

Mean of aylaxi

2x10'

Figure 4-8. Results from the Morris method from the basecase, with a time period of interest of 10,000 yr.

O I ' II 

0 FOCTR-R 

* FOCR-R 

FOCTR * 

WPRRG@200 

0 ARDSAVU AAMAI@S. 

Fow* 0 

ARDSAVJ*I * APrs_SAV 0 WPDef%

x 

0 

C 

'U

lx10-5 F

8x1A0'-

6x1O' I

4x1~0 

2x10• 

0

4x10'

IL 

5,

-P, 

k!o 

t-j

r
1 xi 0-1 , I , 

ARDSAVNp 

X- 8x10-4 WPRRG@20 

% '\ APrs _SAV 

0 

C 

0 

: 6x10" 

> 0 MKDCHvU 

0 

I,-• 

40- ARDSAV -U S-D . SbArWt% 9 

0 InitRSFP 0 SFWt%C3 

ARDSAVrC e 

0 SFWt%C6 

2x10- 0 

2A 0

00 

a. 

I . 

-0.0004 -0.0002 0 0.0002 0.0004 

Mean of DylDx, 

Figure 4-9. Results from the Morris method from the basecase, with a time period of interest of 50,000 yr. (Arrows indicate that the 

associated points lie outside the graph.)
System-level Sensitivity Studies

found to be most important is to treat each realization of a parameter value as either a + or a - depending on 

whether the realized value is greater than or less than a specified value. This is similar to the procedure 

followed in a Sign Test (Bowen and Bennet, 1988) as described in Section 4.1.1.4. Next, the realizations are 

sorted based on the commonality of their input parameters being either a + or a-. For example, realizations 

with all five important input parameters sampled above the median would be placed in the same bin. 

Similarly, all realizations where the first four parameters are a + and the last one is a - would be placed in 

another bin and so on. 

Figure 4-10 shows the parameter tree based on median values as the branching criterion. A set of 

4000 realizations of the TPA Version 3.2 code was used, and 244 input parameters were sampled for the 

basecase." Table 4-9 shows some statistical information for the most influential parameters identified by the 

multiple regression analysis for use in the median-based parametertree method and the statistics of the output 

variable. The table presents the median, the mean and the 90' percentile values of the parameter distribution 

for the identified influential input parameters and the output variable (i.e., peak dose in 10,000 yr). 

In Figure 4-10, Column A is the number of realizations of peak dose above the overall median value (i.e., of 

the 4000 realizations) in that bin. For example, row one in Column A shows that 129 out of 4,000 realizations 

had all 5 of the important parameters with values above the median. Of these 129 realizations, 128 had peak 

doses above the median value for all 4000 realizations (1.84 x 10' rem/yr, table 4-9). Column B shows that 

for these 129 realizations, the mean value of peak dose was 1.20 x 10-4 rem/yr (1.2 x 10-6 Sv/yr), and 

Column C shows these 129 realizations accounted for 21.07 percent of the population mean of peak doses. 

This analysis reinforces the notion that these are indeed influential parameters because slightly less than 

3 percent of the realizations account for over 21 percent of the mean from all realizations. 

Column D shows an "importance factor R" which is determined as the ratio of the contribution to the overall 

mean from realizations in that bin to the average contribution of the same number of realizations to the 

overall mean, that is, 

R fractional contribution to the overall mean dose (Column C) (number of realizations in bin' 

total number of realizations ) (4-19) 

mean peak dose in bin (Column B) 

mean peak dose over all realizations 

All of the data in Columns A-D serve as figures of merit for characterizing the group of realizations 

in a bin. Two other interesting observations can be made about Figure 4-10. First, the realizations where none 

or one of the input parameters is a - account for 67 percent of the mean from all realizations (includes 798 

out of 4000 realizations). Second, only 8 out of 32 bins have importance factors above unity, indicating that 

the output variable distribution is skewed (the 8 bins include 999 out of 4000 realizations). Column 2 of 

Table 4-10 presents the sensitivity coefficients for the influential parameters in the median-value-based 

parameter tree. Symbols x, to x5 for this column correspond to the five influential parameters shown in 

Figure 4-10. It is emphasized that these sensitivity coefficients provide only the relative sensitivities. For 

example, from Table 4-10, Column 2, one can infer that the system is 1.8 times (0.351/0.192) more sensitive 

to parameter x, than it is to parameter x,. In the lower portion of Table 4-10, the system sensitivities to joint 

sets of parameters (see Appendix C) are presented. As can be seen in the table, the system shows relatively 

" The data used in the parameter tree analyses are slightly different from the latest data used in implementing other methods; 

however, the differences do not contribute to significant changes to the output.

4-34
AAMAI@S Fow* WPT-Def/o Fmult* SbArWt%

Parameter value 

for realization 

greater 

than median (+) 

4,000 

Realizations 

Parameter value 

for realization 

less 

than median (-)

A B C D

128/129 1.20E-04 96/97 6.11E-05 

135/140 6.64E-05 

57/68 2.27E-05 

130/141 4.68E-05 

53/70 1.52E-05 

104/133 2.19E-05 

49/87 9.63E-06 

179/224 4.04E-05 

49/58 1.78E-05 

128/216 9.78E-06 

20/59 3.73E-06 

135/223 1.05E-05 

20/62 4.19E-06 

62/230 3.19E-06 

6/63 1.05E-06 

59/67 4.34E-05 

125/226 1.72E-05 

35/53 1.79E-05 

85/230 5.86E-06 

42/60 1.18E-05 

91/227 6.11E-06 

29/54 1.29E-05 

39/218 2.19E-06 

37/73 8.52E-06 

35/125 4.OOE-06 

22/87 1.90E-06 

12/148 7.60E-07 

21/96 2.23E-06 

11/122 1.03E-06 

3/74 6.33E-07 

3/140 4.47E-07

Figure 4-10. Median-based parameter tree describing the technique for examining system sensitivity to groups of parameters.

0.2107 0.0803 

0.1261 

0.0209 

0.0894 

0.0114 

0.0395 

0.0114 

0.1226 

0.0140 

0.0286 

0.0030 

0.0317 

0.0035 

0.0099 

0.0009 

0.0395 

0.0528 

0.0129 

0.0186 

0.0096 

0.0188 

0.0094 

0.0065 

0.0084 

0.0068 

0.0022 

0.0015 

0.0029 

0.0017 

0.0006 

0.0008

6.52 3.32 

3.61 

1.23 

2.54 

0.83 

1.19 

0.52 

2.20 

0.97 

0.53 

0.20 

0.57 

0.23 

0.17 

0.06 

2.36 

0.93 

0.97 

0.33 

0.64 

0.33 

0.70 

0.12 

0.46 

0.22 

0.10 

0.04 

0.12 

0.06 

0.03 

0.02

4• !
System-level Sensitivity Studies

Table 4-9. Statistical information about the 4000 realizations

Distribution Type; 

Minimum, Maximum 

Parameter Median Value Mean Value 9 01h Percentile Values 

AAMAI@S 5.5 5.5 9.1 Uniform; 1,10 

Fow* 0.173 0.264 0.566 Lognormal; 0.1, 3.0 

WP-Deff 0.00505 0.00505 0.00901 Uniform; 0.0001,0.01 

Fmult* 0.0447 0.0503 0.0833 Lognormal; 0.01,0.2 

SbArWt% 0.5 0.5 0.9 Uniform; 0.0,1.0 

Peak dose (rem/yr) 2.82 x 10-6 1.84 x 10-i 4.97 x 10-5 

greater sensitivity to parameter sets of increasing size. Again, consider that such results are necessarily 

dependent on conceptual models embodied in the simulation model as well as on the many fixed value 

(deterministic) parameters in the TPA code. Other columns of Table 4-10 pertain to the parameter trees using 

other branching schemes presented in the following sections. 

4.4.1 Parameter Trees Using Different Branching 

Different branching criteria may be used to determine a + or a - value for a given parameter or 

the output variable as shown in Figures 4-11 and 4-12. The most influential parameters identified by multiple 

regression analysis are used in constructing the parameter tree. Figure 4-11 shows a tree where both the input 

parameters and the output variable have been partitioned based on their mean values. Again, the bins toward 

above its mean value (see Column A, Row 1, in Figure 4-11). The realizations where none or one of the input 

parameters is a - account for 55 percent of the mean from all realizations (includes 528 out of 

4000 realizations), which is a greater fraction on a per-realizations basis than the example presented in 

Figure 4-10. Column 3 of Table 4-10 shows the ranking of the parameters according to sensitivity is slightly 

different with the mean than with the branching criterion; in this case, x, is the most influential parameter. 

In Figure 4-12, the input parameters are partitioned based on their median values, and the output 

variable is partitioned based on its 90t' percentile. Columns B, C, and D of this figure contain numeric entries 

identical to those in Figure 4-10. Row 1 of Column A, however, shows that if all five of the important 

parameters are sampled above their median values (129 out of 4000 realizations), the output variable is above 

its 90' percentile 4.97 x 10-' Sv/yr (4.97 x 10-' rem/yr) in 103 of these realizations. That is, only 

79.8 percent of the output above its 90' percentile is provided by the set of five parameters taking on values 

greater than their median. Comparing to corresponding values for Cases 1 and 2, it is clear that a significant 

number of extreme values (i.e., above 90' percentile) of the output are produced by combinations of 

Although these cases use parameter statistics as the branching criteria, other quantities could also 

be used. For example, total system failure could be defined as a peak dose to the hypothetical receptor greater 

than a predetermined limit defined by the regulation (U.S. Nuclear Regulatory Commission, 1999a). 

Similarly, input parameters could be partitioned based on a value that has some physical significance. For 

example, in the TPA Version 3.2 code, flow in fractures in the UZ begins when the infiltration exceeds the 

saturated matrix conductivity, currently estimated at about 3 mm/yr (0.12 inches/yr). This cutoff is important 

to performance of this subsystem because flow in fractures occurs more rapidly and dissolved contaminants 

experience much less chemical retardation than flow in the rock matrix. Hence, initiation of fracture flow 

in the UZ could be thought of as a transition from one performance regime to another for the UZ.

4-36
I I I I

AAMAI@S Fow* WP-Def Fmult* SbArWt% A B C D 

+mean +mean 62/62 1.48E-04 0.1244 8.04 

+mean +mean 42/52 8.3 IE-05 0.0586 4.52 

-mean 85196 9.94E-05 0.1294 5.40 

Parameter value +mean 34/53 3.66E-05 0.0263 1.99 

for realization 48/61 4.94E-05 0.0408 2.68 

greater -meea +mean 13/35 1.86E-05 0.0088 1.01 

than meante -mean +mean 55/94 3.29E-05 0.0420 1.79 

17/78 1.21E-05 0.0128 0.66 

+mean +mean 128/229 5.42E-05 0.1683 2.95 

+mean L -mean 41/72 2.31E-05 0.0226 1.26 

+mean 82/322 1.51E-05 0.0659 0.82 

mean 12/105 7.50E-06 0.0107 0.41 

+mean +mean 66/220 1.95E-05 0.0581 1.06 

mean -mean 8/73 6.11E-06 0.0060 0.33 

a +mean 35/352 6.20E-06 0.0296 0.34 

-leao 0/96 1.95E-06 0.0025 0.11 

4,000 +m n +mean 23/28 6.30E-05 0.0239 3.42 

R 47/138 2.14E-05 0.0401 1.16 

-mean +mean 17/39 2.44E-05 0.0129 1.33 

+mean + 20/185 8.05E-06 0.0202 0.44 

+ma +L mean 7/27 1.45E-05 0.0053 0.79 

men -mean + n 14/120 7.58E-06 0.0123 0.41 

-mea. -mean 10/41 1.73E-05 0.0096 0.94 

9/185 3.35E-06 0.0084 0.18 

+mean 25/90 1.77E-05 0.0217 0.96 

Paaee vlue-men 18/157 6.69E-06 0.0142 0.36 for realizatione -mean mean 1/123 2.71E-06 0.0045 0.15 

less mean 3/249 1.52E-06 0.0051 0.08 

than mean ()+mean mean 7/96 4.34E-06 0.0056 0.24 

- 5/159 2.30E-06 0.0050 0.13 

-meanen +mean 2/120 1.23E-06 0.0020 0.07 

1/243 6.47E-07 0.0021 0.04

Figure 4-11. Mean-based parameter tree describing the technique for examining system sensitivity to groups of parameters.
AAMAI@S Fow* I WP-DeP/o I Fmult* ISbArWt%

+

Parameter value 

for realization 

greater 

than median (+) 

4,000 

Realizations 

Parameter value 

for realization 

less 

than median (-)

+

A B C D 

103/129 1.20E-04' 0.2107 6.52 

31/97 6.1 IE-05 0.0803 3.32 

65/140 6.64E-05 0.1261 3.61 

11/68 2.27E-05 0.0209 1.23 

44/141 4.68E-05 0.0894 2.54 

4/70 1.52E-05 0.0114 0.83 

16/133 2.19E-05 0.0395 1.19 

3/87 9.63E-06 0.0114 0.52 

41/224 4.04E-05 0.1226 2.20 

4/58 1.78E-05 0.0140 0.97 

6/216 9.78E-06 0.0286 0.53 

0/59 3.73E-06 0.0030 0.20 

6/223 1.05E-05 0.0317 0.57 

0/62 4.19E-06 0.0035 0.23 

0/230 3.19E-06 0.0099 0.17 

0/63 1.05E-06 0.0009 0.06 

21/67 4.34E-05 0.0395 2.36 

25/226 1.72E-05 0.0528 0.93 

5/53 1.79E-05 0.0129 0.97 

3/230 5.86E-06 0.0186 0.33 

1/60 1.18E-05 0.0096 0.64 

2/227 6.11E-06 0.0188 0.33 

5/54 1.29E-05 0.0094 0.70 

0/218 2.19E-06 0.0065 0.12 

3/73 8.52E-06 0.0084 0.46 

1/125 4.OOE-06 0.0068 0.22 

0/87 1.90E-06 0.0022 0.10 

0/148 7.60E-07 0.0015 0.04 

0/96 2.23E-06 0.0029 0.12 

0/122 1.03E-06 0.0017 0.06 

0/74 6.33E-07 0.0006 0.03 

0/140 4.47E-07 0.0008 0.02

Figure 4-12. Mean-percentile-based parameter tree describing the technique for examining system sensitivity to groups of 

parameters; input parameters divided based on their median values, and output variable divided based on its 90t 

percentile value, from all 4000 realizations.

00
System-level Sensitivity Studies

Table 4-10. Sensitivity coefficients calculated for various parameter trees

Case 1 Case 2 Case 3

Coefficient (Figure 4-10) (Figure 4-11) (Figure 4-12) (Figure 4-13) 

Unconditional Sxý 0.351 0.26 0.134 0.351 

Sensitivities of 

Individual Sx2 0.31 0.28 0.16 0.31 

Parameters 

SX3 0.202 0.173 0.119 0.202 

Sx4 0.204 0.178 0.084 0.204 

SX5 0.192 0.15 0.102 0.081 

Joint Sensitivities 0.541 0.351 0.155 0.541 

of Parameter IPH - PLI 2.37 1.63 0.462 2.37 

Groups 1--PH -PLI 6.75 4.68 0.938 6.75 

(see Appendix C) -JL 26 9.42 1.46 26 

33.5 249 3.95 26.8 

4.4.2 Stepwise Implementation of the Technique 

The parameter tree technique was implemented in a stepwise fashion with the importance factor 

(Column D of Figures 4-10 through 4-12) as the figure of merit for determining maximum polarity of the bins 

and the median value as the branching criterion. First, a one-parameter-depth tree was drawn for each 

sampled parameter. The parameter that yielded the greatest importance factor for one of the two branches 

was then used as the first-level parameter for the following iteration in the stepwise implementation. Next, 

for all remaining sampled parameters, a two-parameter-depth tree was drawn where the first-level parameter 

was determined as from the previous iteration. In this second iteration, the parameter that yielded the greatest 

importance factor on any branch of the tree was used as the second-level parameter for the third iteration. 

The procedure was repeated until the number of realizations in any bin dropped below 50, with the results 

of that iteration being discarded. This procedure resulted in a tree that was five parameters deep, as shown 

in Figure 4-13. The influential parameters identified by this method are compared with results from other 

methods in Chapter 5. It may be noted that the first four parameters appear in the same order as in the 

stepwise regression conducted separately; however, the fifth parameter is the well-pumping rate at the 

receptor location 20 km (12.4 mi) down gradient (WPRRG@20) instead of the subarea wet fraction 

(SbArWt%). This result is important because it shows that these parameters comprise the most important 

five-parameter set, which differs from the five individually most important parameters as determined by 

traditional methods. Also, note that WPRRG@20 is negatively correlated with the output variable (because 

in the TPA Version 3.2 code model, increased pumping merely increases the dilution volume and not the 

interception fraction of the contaminant plume by the well) and the procedure for assigning + and - was not 

reversed so the + + + + - bin represents the most pessimistic case in this example (i.e., the bin with the 

largest peak doses). In Figure 4-13, note that this group of five parameters together produces a higher value 

of importance factor (7.06) for one of the branches (second branch from top of the tree) as compared to that

4-39

Case 4
AAMAI@S Fow* WT-Def I Fmult* WPRRG@20 A B

Parameter value 

for realization 

greater 

than median (+)

Parameter value 

for realization 

less 

than median (-)

* I

C D

124/124 6.59E-05 

100/102 1,30E-04 

82/90 4.31E-05 

110/118 5.90E-05 

84/102 2.81E-05 

99/109 4.39E-05 

74/109 1.44E-05 

79/111 1.96E-05 

102/137 1.86E-05 

126/145 5.19E-05 

66/134 5.51E-06 

82/141 1.13E-05 

66/135 6.78E-06 

89/150 1.12E-05 

23/145 1.71E-06 

45/148 3.73E-06 

84/153 1.55E-05 

100/140 3.17E-05 

57/145 6.93E-06 

63/138 9.55E-06 

54/133 5.69E-06 

79/154 8.67E-06 

29/148 2.97E-06 

39/124 5.92E-06 

30/95 4.1IE-06 

42/103 7.10E-06 

17/115 1.23E-06 

17/120 1.13E-06 

17/111 1.53E-06 

15/107 1.60E-06 

2/124 3.23E-07 

4/90 7.70E-07

0.1109 

0.1801 

0.0526 

0.0944 

0,0389 

0.0649 

0.0213 

0.0295 

0.0345 

0.1021 

0.0100 

0.0216 

0.0124 

0.0228 

0.0034 

0.0075 

0.0321 

0.0601 

0.0136 

0.0179 

0,0103 

0.0181 

0.0060 

0.0100 

0.0053 

0.0099 

0.0019 

0.0018 

0.0023 

0.0023 

0.0005 

0.0009

Figure 4-13. Tree developed using a stepwise implementation of the technique, based on the importance factor.

3.58 

7.06 

2.37 

3.20 

1.53 

2.38 

0.78 

1.06 

1.01 

2.82 

0.30 

0.61 

0.37 

0.61 

0.09 

0.20 

0.84 

1.72 

0.38 

0.52 

0.31 

0.47 

0.16 

0.32 

0.22 

0.39 

0.67 

0.06 

0.08 

0.09 

0.02 

0.04

0

4,000 Realizations MM

CI
System-level Sensitivity Studies

in Figure 4-10 (6.52 for the topmost branch). In contrast, the sensitivity measures in Table 4-10 for Case 4 

show that the combination of these five parameters (i.e., the last row) have a joint relative sensitivity less 

than that of Case 1 (26.8 versus 33.5). Thus, the nature of information provided by each sensitivity measure 

is somewhat different. In other words, if it had been decided to implement the stepwise procedure using the 

joint relative sensitivity measure, the five parameters would match exactly those of Case 1. 

For all sensitivity analysis methods presented in this chapter, it should be noted that changes to 

the sampling ranges of the influential parameters (either expansion or contraction) should be made with 

greater caution than for other parameters because peak dose for the TPI shows the largest change per unit 

deviation in these parameters. 

4.5 ALTERNATIVE CONCEPTUAL MODELS AND SCENARIO CASES 

STUDIED AT THE SYSTEM LEVEL 

The system-level sensitivity studies cover alternative conceptual models and scenario cases. The 

analyses in this chapter include the full ranges of parameter variations for all modules. Two sets of results 

are presented. The first set of results reflects model runs that compare the basecase with alternative 

conceptual models. First, the basecase was evaluated with a 250-vector run. Alternative conceptual model 

tests were conducted with 250-vector runs, and the results were compared with the basecase. The alternative 

conceptual models were selected to evaluate: (i) the effect on repository performance of several repository 

design features currently being considered by DOE; (ii) the effect on repository performance of plausible 

alternate thermo-hydrologic conditions in the repository near field; and (iii) bounding engineered or natural 

system behavior. The second set of results reflects the effects of disruptive scenarios, including igneous 

activity and major faulting. Seismicity is considered part of the basecase. • 

For both sets of analyses, the runs were limited to 10,000 and 50,000 yr. The number of 

realizations was limited to 250, to keep computer resources within reasonable limits. Runs up to 50,000 yr 

with 4000 realizations are included in the sensitivity analyses in the previous sections of this chapter. 

Section 2.3.2 outlines the alternative conceptual models evaluated in this chapter. 

For each alternative conceptual model, only the noted changes as described in Section 2.3.2 to 

the TPA input file were made, with all other input parameters set to the values used in the basecase. Results 

are presented as the peak of the mean dose. 

Figure 4-14 shows the results for the 10,000-yr TPI, whereas Figure 4-15 is for the 50,000 yr 

results. The results for the NoInvert alternative were not plotted because they could not be distinguished from 

the basecase results. 

Various observations can be made based on the calculational results shown in this chapter. 

" Except for NoRet the relative effects of the alternative conceptual models (based on the 

peak of the mean dose) changed substantially between the 10,000- and 50,000-yr TPIs. 

" The largest mean doses resulted from the NoRet assumption, demonstrating the 

importance of retardation in the alluvium of Pu, Am, and Th. 

" The Flwthru- 1 conceptual model led to a larger release in the 10,000-yr TPI, but was much 

less important for the 50,000-yr TPI. This probably can be attributed to the lack of a delay

4-41
System-level Sensitivity Studies

time caused by the necessity to fill the WP in the bathtub model. This effect is less 

important for the 50,000-yr TPI. 

"Fast dissolution in the case of the dissolution (Model 1) and grain-size (Grain 1) 

alternatives led to an increased peak dose at 10,000-yr TPI, but it was not proportional 

simply to the increased rate of dissolution. In some cases, the high rate of dissolution did 

not contribute to an overall increase of dose for the 50,000-yr TPI. This is probably an 

indication that the high dissolution rate of the fuel led to near-total depletion of the SF. 

" Alternatives based on natural analog data (Natan) and assumptions about the behavior of 

radionuclides in secondary uranium minerals (Schoepite) led to much smaller peak doses. 

Protection of the fuel by cladding (Clad-Mi) leads to a large reduction in peak doses. 

Matrix diffusion (Matdif) would reduce the peak of the mean dose for both the 10,000

and 50,000-yr TPI. Note, however, that the results from a single calculation, such as the 

mean value estimates in Chapter 3, indicate that matrix diffusion might occasionally cause 

an increase in dose at later times.

4-42
System-level Sensitivity Studies

NoRet 

Flwthru-1 

GrainI 

Modell 

Flwthru-2 

Focflow 

Base 

Matdif 

Clad-MI 

Schoepite 

Natan 

0 0.01 0.02 0.03 0.04 0.05 

Peak Mean Dose (mrem/yr) 

Figure 4-14. Bar chart showing the effects of alternative conceptual models at 10,000 yr. 

NoRet 

Modell 

Grain1 

Flwthru-1 

Base 

Focflow 

Flwthru-2 

Matdif 

Natan 

Clad-Mi 

Schoepite 

20 40 6o 80 1;0 

Peak Mean Dose (mrem/yr) 

Figure 4-15. Bar chart showing the effects of alternative conceptual models at 50,000 yr.

4-43

I
5 SYNTHESIS OF SENSITIVITY RESULTS AND LINKAGE OF 

SENSITIVE PARAMETERS TO INTEGRATED SUBISSUES 

This chapter attempts to identify influential parameters using the analyses presented in Chapters 3 and 4. 

Chapter 4 presented the sensitivity analyses and their results, as well as results from alternative conceptual 

models. This chapter focuses on identifying the parameters and alternative models that significantly 

influence performance. 

5.1 SELECTION OF INFLUENTIAL PARAMETERS 

In the previous chapter, seven different sensitivity analyses methods (i.e., regression with normalized 

variables, regression with log-normalized variables, differential analysis, Morris method, FAST method, 

t-test on means, and parameter tree method) were used to determine the most influential parameters. The first 

five methods are scaled (i.e., standardized) so that the sensitivity results reflect the variability of the inputs. 

The last two are not scaled because their results are based on ranking the input variables using a set of 

predetermined criteria. Only six of the methods were used at a time for either the 10,000- or 50,000-yr TPI. 

The parameter tree method was used only for 10,000 yr and the t-test on means was used only for 50,000 yr. 

The seven methods have different approaches to determining sensitivity. For example, regression with log

transformed variables places greater emphasis on smaller doses than regression with untransformed variables. 

Also, the t-test on means was conducted to determine sensitive parameters relating only to relatively high 

doses. It is not clear that any one method is superior to another for this determination of sensitivity (or 

influence) and, consequently, no method can be fully relied on to provide a unique ranking of parameters. 

Therefore, the final list of parameters was selected on the basis of frequency of occurrence among 

various methods. 

The selected parameters are presented in Tables 5-1 and 5-2. The score in these tables specifies the 

number of methods that selected a particular parameter among the top 10. For example, a score of 6/6 for 

the subarea wet fraction parameter (SbArWt%) implies that the parameter ranked among the top 10 (five for 

the parameter tree method) in all six methods. Also note that, among the seven methods, there are 

two statistical methods (regression with normalized variables, and regression with log-normalized variables) 

and three nonstatistical methods (differential analysis, Morris method, and FAST method). It should be noted 

that the FAST method selected the most influential parameters only out of the top 20 listed in Tables 4-1 

and 4-2. The parameters that did not make the final list include those selected as influential by only one of 

the seven methods, those selected by only two statistical methods, and those selected by only two out of three 

nonstatistical methods. This resulted in only eight parameters being selected for 10,000- and 50,000-yr TPIs. 

Comparison of scores between these two TPIs also indicates that the influential parameters are common to 

most methods forthe 10,000-yr TPI, whereas significant variation exists forthe 50,000-yr TPI. Also note that 

for the 10,000-yr TPI, all parameters that ranked as the top five in the parameter tree method also were 

picked by other sensitivity analyses methods.

5-1
Synthesis of Sensitivity Results and Linkage of Sensitive Parameters to Integrated Subissues

Table 5-1. Influential parameters for 10,000-yr time period of interest, from sensitivity 

analysis studies 

Parameter abbreviation Parameter Name Score 

Fow* Flow focusing factor 6/6 

WP-Defb/o Initially defective fraction of WPs 5/6 

Fmult* Fmult factor for flow entering a WP 5/6 

AAMAI@S Areal average mean annual infiltration at start 5/6 

WPRRG@20 Well-pumping rate at 20 km receptor group 5/5 

ARDSAV-I Alluvium Rd for 1291 5/6 

SbArWt% Subarea wet fraction 5/5 

ARDSAV-Tc Alluvium Rd for 99

Tc 3/5* 

"**Parameter Tree method selected only the top 5 parameters of which ARDSAV-Tc is one. Hence, the 

score is 3/5 and not 3/6. 

Table 5-2. Influential parameters for 50,000-yr time period of interest, from sensitivity 

analysis studies 

Parameter Abbreviation Parameter Name Score 

SbArWt0 /o Subarea wet fraction 6/6 

WPRRG@20 Well-pumping rate at 20-km receptor group 5/6 

ARDSAV-Np Alluvium Rd for 237

Np 4/6 

ARDSAV-Tc Alluvium Rd for 9Tc 3/6 

Fmult* Fmult factor for flow entering a WP 3/6 

ARDSAV-I Alluvium Rd for 1291 3/6 

ARDSAV-U Alluvium Rd for 234U 3/6 

AAMAI@S Areal average mean annual infiltration at start 3/6 

For both TPIs several parameters were found most influential for the basecase (the basecase is 

defined as the undisturbed scenario along with the effects of rockfall because of seismicity). The 

parameters include: 

* Areal fraction of the repository wetted by water infiltrating into the repository (SbArWt%); 

* Well-pumping rate at 20-km receptor group (WPRRG@20); 

• Areal average mean annual infiltration at start (AAMAI@S); 

* Alluvium Rd for 9Tc (ARDSAV-Tc); 

* Alluvium Rd for 1291 (ARDSAV-I); and 

. The fraction of water infiltrating to the repository from the UZ above the repository that will 

enter the WP and contribute to the release of radionuclides (Fmult*).

5-2
Synthesis of Sensitivity Results and Linkage of Sensitive Parameters to Integrated Subissues

In addition, the parameters influential for the 10,000-yr TPI, but not for the 50,000-yr, are: 

"* A flow-focusing factor that expresses the flow potentially reaching a wetted WP (Fow*); and 

"* Initially defective fraction of WPs (WP-Def%). 

Two parameters influential for the 50,000-yr TPI, but not for the 1 0,000-yr, are: 

"* Alluvium R& for 237

Np (ARDSAV Np); and 

"* Alluvium Rd for 234U (ARDSAVU). 

5.2 COMPARING INFLUENTIAL PARAMETERS WITH 

INTEGRATED SUBISSUES 

The influential parameters identified previously were crosswalked to the NRC integrated subissues 

[previously specified as key elements of subsystem abstraction in the Revision 1, "TSPA&I Methodology 

KTI Issue Resolution Status Report" (U.S. Nuclear Regulatory Commission, 1998)]. The crosswalking of 

these parameters for the basecase results and for the igneous activity disruptive events is presented in 

Table 5-3. The alternative conceptual models investigated in this report are also cross-referenced to 

integrated subissues in Table 5-3. The influential parameters corresponding to the disruptive events were 

determined from only differential analysis. 

The influential parameters identified in Tables 5-1 to 5-3 must be viewed in the proper context. The 

following are key points to consider when examining these tabulated results: 

" All analysis results are based on the models and reference input values used in the 

TPA Version 3.2 code. Chapter 2 of this report gives a description of the conceptual models. 

TPA Version 3.2 code "User's Guide" (Mohanty and McCartin, 1998) lays out the key 

assumptions for the conceptual models. Chapter 3 lists the reference input values. 

"• No consideration is given to corrosion or the defects of welds. 

* No credit is given to retardation in fractures or matrix diffusion in the UZ. 

Fracture-only flow occurs in the UZ if the flux exceeds the saturated hydraulic conductivity of 

a stratigraphic unit. 

The DCFs are kept as constants in all the analyses performed, which implies that the DCFs are 

known with certainty. 

The receptor group is located 20 km (12.4 mi) from the repository and uses partially 

contaminated groundwater for drinking and farming. 

* All WPs in a subarea fail from corrosion when the representative WP fails. 

* No consideration is given to the effect of dripping of chloride-rich water on WP corrosion.

5-3
Synthesis of Sensitivity Results and Linkage of Sensitive Parameters to Integrated Subissues

Table 5-3. A crosswalk between the integrated subissues, alternative conceptual models, and the 

influential parameters

Integrated Subissues 

WP degradation (temperature, 

humidity, and chemistry) 

Mechanical disruption of WPs 

(seismicity, faulting, rockfall, and 

dike intrusion)

Alternative Models 

Investigated 

Not evaluated

Not evaluated

Influential Parameters 

-Initially defective fraction of waste 

packages (10,000-yr) 

-Time of next faulting event in the 

region of interest* 

-Spent fuel wetted fraction for 

faulting event* 

-North-East fault-zone width*

Quantity and chemistry of water Clad-Ml -Fmult factor for flow entering into 

contacting WPs and waste forms Flwthru-1 a WP (10,000-yr, 50,000-yr) 

Flwthru-2 -Subarea wet fraction (10,000-yr, 

Focflow 50,000-yr) 

Grain 1 -Flow-focusing factor (10,000-yr) 

Radionuclide release rates and Modell 

solubility limits Flwthru-1 

Flwthru-2 

Natan 

Schoepite 

Spatial and temporal distributions Focflow -Areal average mean annual 

of flow infiltration at start (10,000-yr, 

50,000-yr) 

Distribution of mass flux between 

fracture and matrix in unsaturated 

zone 

Retardation in fractures in the Not evaluated (No retardation or matrix diffusion 

unsaturated zone in the unsaturated zone) 

Flow rates in water Not evaluated 

production zones 

Retardation in water production NoRet Matdif -Alluvium matrix Rd for 1291 

zones and alluvium (10,000-yr, 50,000-yr) 

-Alluvium matrix Rd for 237

Np 

(50,000-yr) 

-Alluvium matrix Rd for 9Tc 

(10,000-yr, 50,000-yr) 

-Alluvium matrix Rd for 234U 

(50,000-yr)

5-4
Synthesis of Sensitivity Results and Linkage of Sensitive Parameters to Integrated Subissues

Table 5-3. A crosswalk between the integrated subissues, alternative conceptual models, and the 

influential parameters (cont'd)

Integrated Subissues 

Volcanic disruption of WPs

Alternative Models 

Investigated 

Evaluated as a 

special case

Influential Parameters 

-Diameter of volcanic cone 

(10,000-yr, 50,000-yr) * 

-Volcanic event power (10,000-yr, 

50,000-yr)* 

-Volcanic event duration 

(10,000-yr, 50,000-yr)* 

-Time of next volcanic event in 

region of interest (1 0,000-yr, 

50,000-yr)*

Airborne transport of Evaluated as a -Airborne mass load for igneous 

radionuclides special case activity dose calculation 

(10,000-yr, 50,000-yr)* 

-Ash mean particle log diameter 

(10,000-yr, 50,000-yr) 

-Wind Speed (10,000-yr, 

50,000-yr)* 

Dilution of radionuclides in Not evaluated -Well pumping rate at receptor 

groundwater through well group at 20 km (10,000-yr, 

pumping 50,000-yr) 

Dilution of radionuclides in soil Not evaluated 

through surface processes 

Critical group lifestyle Not evaluated (DCFs were set as constants) 

*Sensitive parameters obtained directly from disruptive event scenario calculations without any 

consideration of event probability 

The following conclusions, drawn solely on the basis of the sensitivity analyses, provide an 

indication of which integrated subissues may deserve more attention relative to others. Because the model 

abstractions are preliminary and data are continuously updated, results shown in this report provide a 

snapshot of the current relative importance and should not be used alone to determine the significance of any 

of the integrated subissues. 

5.2.1 Key Integrated Subissues for 10,000-yr TPI 

For the 10,000-yr TPI, the basecase results have shown that total system performance is most 

sensitive to the following integrated subissues: 

* WP degradation; 

* Quantity and chemistry of water contacting WPs and waste forms; 

* Spatial and temporal distribution of flow;

5-5
Synthesis of Sensitivity Results and Linkage of Sensitive Parameters to Integrated Subissues

* Retardation in water-production zone and alluvium; and 

* Dilution of radionuclides in groundwater because of well pumping. 

When disruptive events are included, the following two integrated subissues are the most important: 

* Volcanic disruption of Wps; and 

* Airborne transport of radionuclides. 

The predominance of the integrated subissues identified previously is the result of several processes 

and model abstractions that may merit further examination. These include: (i) thermal period delays the onset 

of flow into the repository; (ii) bathtub fill-up could take several hundreds to thousands of years, thus 

delaying releases; and (iii) corrosion-resistant material significantly increases the life of the container, thus 

pushing the release time to late times or even beyond 10,000 yr. Consequently, the results are extremely 

sensitive to the initially defective failures and igneous activity disruptive event. 

Based on the sensitivity and alternative conceptual model analyses results, the following specific 

points can be made with regard to the integrated subissues for the 10,000-yr TPI: 

" Factors causing WPs to fail by mechanisms other than corrosion play a much more important 

role because of the long WP life. Total system performance is sensitive to the percent of initial 

defective WPs. Consistent with the deterministic analyses in Chapter 3, repository performance 

is not sensitive to seismic rockfall or instantaneous fault displacement on new or under

appreciated faults (Integrated subissue-mechanical disruption of WPs). 

" The number of WPs that are dripped on (immaterial before WP failure) and the amount of 

dripping water entering the WP are important to system performance (Integrated 

subissue-quantity and chemistry of water contacting WPs and waste forms). 

" The alternative conceptual model that assumes no retardation in the SZ produced a much higher 

peak expected dose than the basecase and illustrates the importance of evaluating retardation 

in the SZ. By comparison with retardation, matrix diffusion does not have nearly as pronounced 

an effect on the system performance (Integrated subissues-retardation in water production 

zones and alluvium; quantity and chemistry of water contacting WPs and waste forms). 

" Choice of the WP water retention model for release calculations (bathtub or flowthrough) has 

an effect on total system performance. The fuel dissolution rate also has an effect on total 

system performance (Integrated subissue-radionuclide release rates and solubility limits). 

" Retardation of 1291 and 9Tc in the alluvium is important to system performance (Integrated 

subissue-retardation in water-production zones and alluvium). 

" The alternative conceptual model that assumes partial cladding protection produced a much 

lower peak expected dose than the basecase, which illustrates the need to improve modeling 

capability and focus reviews in this area if the DOE decides to take credit for cladding 

(Integrated subissue-quantity and chemistry of water contacting WPs and waste forms).

5-6
Synthesis of Sensitivity Results and Linkage of Sensitive Parameters to Integrated Subissues

" The peak expected dose resulting from the igneous-activity scenario class is 2 orders of 

magnitude higher than the basecase after being weighted by its probability (Integrated 

subissues-volcanic disruption of WPs; airborne transport of radionuclides). 

" The well-pumping rate at the receptor group significantly influences the system performance. 

The well-pumping rate is used in determining the dilution of radionuclide concentration. Dose 

is directly proportional to the radionuclide concentration in water. (Integrated 

subissue-dilution of radionuclides in groundwater through well pumping). 

5.2.2 Key Integrated Subissues for 50,000-yr TPI 

For the 50,000-yr TPI, the results have shown that total system performance is most sensitive to the 

following integrated subissues (in the absence of igneous-activity disruptive event): 

"• Quantity and chemistry of water contacting WPs and waste forms; 

"• Radionuclide release rates and solubility limits; 

• Spatial and temporal distributions of flow; 

• Retardation in water production zones and alluvium; and 

• Dilution of radionuclides in groundwater through well pumping. 

The peak expected dose resulting from the igneous-activity scenario class was not computed for the 

50,000-yr TPI because the peak expected dose caused by igneous activity occurs during the first 1000 yr after 

closure (see Figure 3-50). The following specific points can be made with regard to the integrated subissues 

for the 10,000-yr TPI: 

" The number of WPs that are dripped on and the amount of water contacting the waste affect 

the system performance (Integrated subissue-spatial and temporal distribution of flow; 

quantity and chemistry of water contacting WPs and waste forms). 

" The choice of the release model (bathtub or flowthrough) has negligible effect on system 

performance. The fuel-dissolution rate has a relatively greater effect on the system 

performance. The grain/particle size has a relatively large effect on the system performance 

(Integrated subissue-radionuclide release rates and solubility limits). 

" As in the 10,000-yr case, partial cladding protection significantly reduced peak expected dose 

(Integrated subissue-quantity and chemistry of water contacting WPs and waste forms). 

" The alternative conceptual model that assumes no retardation in the SZ produced a much higher 

peak expected dose than the basecase, which illustrates the importance of evaluating 

radionuclide transport in the SZ. By comparison, matrix diffusion does not have a great effect 

on system performance (Integrated subissue-retardation in water-production zones and 

alluvium).

5-7
Synthesis of Sensitivity Results and Linkage of Sensitive Parameters to Integrated Subissues 

" Retardation of 237

Np, 1291, 9Tc, and 2U in the alluvium is important to system performance as 

indicated by sensitivity analysis (Integrated subissue-retardation in water production zones 

and alluvium). 

" Total system performance is sensitive to dilution introduced by well pumping (Integrated 

subissue-dilution of radionuclides in groundwater through well pumping).

5-8
6 CONCLUSIONS 

This report describes a series of computations performed for assessing the confidence in estimations of future 

repository performance in light ofthe uncertainty in conceptual models and the parameters of those models. 

These estimations allowed the staff to focus attention on what are likely to be the most important phenomena 

affecting repository performance and point out deficiencies in the current state of knowledge. The results of 

these analyses were also used to review the TSPA-VA and refine the issue resolution process, as described 

in Chapter 5, tying the parameter sensitivities and alternative conceptual model results to the integrated 

subissues identified in the "Total System Performance Assessment and Integration Methodology Issue 

Resolution Status Report." 

6.1 BASECASE RESULTS 

To gain insight into the basic functionality of the TPA code, the trend in results, and the influence 

of various code components on the overall results, TPA runs were analyzed using basecase data, scenario 

cases, and alternative conceptual model data sets. To explain the trend in the intermediate and final outputs, 

results from a single realization (using the mean value data set) were analyzed. Then the results from multiple 

realizations (250) using the basecase data set were presented to highlight the variability in dose as a function 

of variability in 246 sampled parameters. 

At 2 x 10-5 mSv/yr (0.002 mrem/yr), the peak dose from the mean value data set was found similar 

to a peak expected dose of 3 x 10-5 mSv/yr (0.003 mrem/yr) from multiple realizations for the 

10,000-yr TPI. But for 100,000-yr TPI, the peak dose from the mean value data set was 3 x 10- mSv/yr 

(0.3 mrem/yr) compared with the 4 x 10-2 mSv/yr (4-mrem/yr) peak expected dose from multiple realizations. 

The analysis indicated that, though the expected dose from these two cases (mean value versus multiple 

realization) are quite similar, analysis using the mean value data set can be misleading. For example, for the 

10,000-yr TPI, the major contributors to dose in the mean value data set case were 1291 and 36

C1; for multiple 

realizations, 237

Np, 1291, 9Tc, and 2341 were the major contributors. Forthe multiple realizations, the minimum 

and maximum of the peak dose varied over 5 orders of magnitude for both TPIs. Dose at early times is 

primarily caused by initially defective failures. A sharp rise in dose between 10,000 and 20,000 yr occurs 

predominantly because of corrosion failure. From 20,000 to 100,000 yr, the dose is generally constant except 

at about 85,000 yr, where the climatic conditions switch from pluvial back to nonpluvial. For the 10,000-yr 

TPI, the dose contributors were 237

Np, 1291, 99Tc, 234u, 36C1, and 79

Se. For the 100,000-yr TPI, the dose 

contributors were 237

Np, 234U, 99Tc, and 1291, with 92 percent of the contribution solely from "Np. When 

probability-weighted, faulting did not influence the peak expected dose for either TPI, whereas igneous 

activity increased the dose from 3 x I 0-5mSv/yr (0.003 mrem/yr) for the basecase, which includes the effects 

of rockfall caused by seismicity, to 0.006 mSv/yr (0.6 mrem/yr). 

6.2 ALTERNATIVE CONCEPTUAL MODELS 

Chapters 3 and 4 describe results of the basecase compared with alternative conceptual model cases. 

The analyses in these chapters used the TPA Version 3.2 code and a WP design using an Alloy C-22 inner 

corrosion-resistant layer. Other stipulations about the basecase model were no backfilling of the repository 

drifts, no matrix diffusion into the rock matrix, no credit for cladding protection of fuel, even distribution 

of infiltrating water to WPs, and the bathtub model for fuel wetting. These basecase analyses considered 

seismically induced rockfall, but not the effects of fault displacement or igneous activity on repository 

performance. Separate analyses were conducted for the faulting and igneous activity disruptive scenarios.

6-1
Conclusions

Alternative conceptual models considered in this study were: (i) matrix diffusion of radionuclides into the 

rock matrix in the SZ; (ii) a faster dissolution rate of exposed fuel, but offset by large credit for protection 

of fuel by cladding; (iii) focusing flow to a smaller number of WPs; (iv) flowthrough model with no pooling 

of water in WP; (v) flowthrough model, but with faster fuel dissolution; (vi) release rate based on a natural 

analog to SF; (vii) release based on the dissolution rate of schoepite; (viii) release based on fuel grain size 

rather than particle size; and (ix) no retardation of Pu, Th, and Am. 

The results of the analyses of alternative conceptual models highlight the importance of some of the 

assumptions made about the processes modeled in the TPA code. Note, however, that the relative effects of 

the alternative conceptual models change substantially between the 10,000- and 50,000-yr TPIs and are not 

always intuitive. For example, matrix diffusion for the mean value run reduces the peak dose for the 

10,000-yr TPI, but actually increases the peak dose for the 50,000-yr TPI. This result might be caused by a 

computational idiosyncracy of the code rather than a real phenomenon (see Section 3.5.3.3). Results from 

the Monte Carlo runs in Chapter 4 indicate that the peak mean dose is always decreased by matrix diffusion. 

Elimination of major barrier components such as retardation and cladding protection resulted in the 

largest dose increases. The largest peak expected doses resulted from the no-retardation assumption, 

demonstrating the importance of retardation of Pu, Am, and Th, especially if these radionuclides can travel 

as colloids unretarded through the geosphere. 

Switching to models for fast dissolution increased peak expected dose at 10,000-yr TPI, but not at 

a rate proportional to the increased rate of dissolution. In some cases, the high rate of dissolution did not 

contribute to an overall increase in dose for the 50,000-yr TPI, indicating near-total depletion of the SF 

inventory. Conversely, results using alternative release rate models for phenomena such as cladding 

protection and observations of uranium transport at natural analog sites could result in considerably smaller 

doses. Tying the release rate to the dissolution of the secondary mineral schoepite also showed a large 

decrease in dose, which warrants further investigation, to develop a better understanding of this geochemical 

process. 

6.3 SENSITIVITY ANALYSES 

The sensitivity analyses employed the TPA Version 3.2 code and applied a variety of statistical 

techniques to a large (>1000 vector) set of Monte Carlo runs and nonstatistical techniques (differential 

analysis, Morris method, and FAST method) to 250-4000 TPA realizations. Most of these analyses pertained 

to the basecase. Igneous activity and faulting were considered separately from the basecase, with their 

analyses limited to differential analysis. Statistical and nonstatistical analyses of the basecase were used to 

identify sensitive parameters for which a small input change can have a large effect on estimated repository 

performance. Other ranking techniques were applied to the Monte Carlo results to determine which 

parameters were important. The parameter tree method allowed the determination of combinations of 

variables that led to the highest doses. The Morris method and the FAST method were used in the current 

study to determine what further insights could be gained from techniques specifically designed for 

nonlinear models. 

Regression analyses were performed on a 1000-vector basecase run for 10,000- and 50,000-yr TPIs. 

Results from the regression analyses were based on both normalized and log-transforms of the normalized 

inputs. The normalized results weight each result equally, whereas the log-normalized results tend to 

overemphasize smaller doses. However, the log-transformed results generally provide a better fit for the

6-2
Conclusions

regression equations. Results of the regression analyses are standardized to account for the ranges of the 

input variables and allow a more accurate ranking of sensitivity coefficients. The results from differential 

analysis, and the Morris and FAST methods were also scaled by the standard deviation of the input variables 

so that the ranks of these variables could be compared with those from the statistical analyses. Tables 4-6 

and 4-7 summarize the results for the 10,000- and 50,000-yr TPIs from the regression, differential analysis, 

and the Morris and FAST methods. 

Several of the other sensitivity analyses could not be ranked directly for sensitivity and were, 

therefore, not included in Tables 4-6 and 4-7, but nevertheless supply insight to the sensitivity process. The 

parameter tree method fits into this category. Another is the statistical test in which the 1000 vectors for the 

50,000-yr TPI were sorted into two bins, depending on whether the dose was greater or less than 10 millirem. 

The means of the input variables in each bin were then compared statistically for significant differences 

between the two bins. 

To capture the information contained in all the sensitivity methods, Tables 5-1 and 5-2 list the 

influential parameters for the 10,000- and 50,000-yr TPIs that appear from the results of at least three out 

of the six sensitivity methods explored in this report. Some important conclusions that can be drawn by 

examining the lists of parameters in Tables 5-1, 5-2, and tables in Chapter 4, include: 

Numerous parameters affecting the flow of water onto and eventually into the failed WP 

(and onto SF) are important (e.g., Fow*, Fmult*, SF wetted fraction, and SbArWt%/o). There 

is no mechanistic basis for the input parameter ranges for these variables used in the 

TPA Version 3.2 code. 

Regression techniques were able to distinguish as many as 18 statistically significant 

variables (at the 9 5th percent confidence level) for the 10,000-yr TPI and 20 variables at the 

50,000-yr TPI. For the 10,000-yr TPI, 10 of the 18 significant variables were related to WP 

and fuel wetting, and five variables were related to retardation. For the 50,000-yr TPI, eight 

of the 20 significant variables were related to WP and fuel wetting, five to retardation, and 

three to seismically induced rockfall. 

In the analysis of the mean value of input variables leading to the highest doses, there were 

24 variables whose difference in means were determined statistically significant. Of these, 

four were associated with wetting, 13 with retardation, and four with UZ fracture and matrix 

flow. Thus, retardation factors take on added importance when considering the conditions 

that led to the largest doses. However, the dependence on UZ flow was for parameters that 

are not likely to have an effect on the results. It is likely that the sample size in the high-dose 

category (51 samples) was too small, and that some of these results are spurious. 

6.4 IMPORTANCE OF RADIONUCLIDES 

For a TPI of 10,000 yr, most of the peak mean dose came from the isotope 1291, with 9Tc and "

7Np 

(in descending order) accounting for most of the balance. For a TPI of 50,000 yr, most of the peak mean dose 

contribution came from 237

Np, with 1291, 99Tc, and 234

U (in descending order) accounting for most of the 

balance. For either the 10,000- or 50,000-yr TPIs, however, the largest peak doses from any realization came 

from 2

37Np.

6-3
Conclusions

6.5 INTEGRATED SUBISSUES REQUIRING FURTHER STUDIES 

The influential parameters, identified using various statistical and nonstatistical sensitivity analysis 

methods and screened further by comparing the outcomes of these methods, were crosswalked to the NRC 

integrated subissues. Nine of the 14 subissues were found to have at least one influential parameter 

(including the integrated subissues related to disruptive events). Because the staff has not yet developed an 

acceptable method for factoring event probability into sensitivity analysis, the influential parameters from 

the scenario events were crosswalked with the integrated subissues. Assuming an event probability of 1, the 

integrated subissues that deserve attention are summarized in Table 5-3. The integrated subissues for the 

10,000-yr TPI that deserve further examination are primarily because of the delay in radionuclide releases 

resulting from: (i) corrosion-resistant material of the inner overpack pushing the WP failure time beyond 

10,000 yr; (ii) thermal reflux delaying the onset of flow into the repository; (iii) bathtub filling time delaying 

the radionuclide release time by hundreds to thousands of years; and (iv) radionuclide sorption in the 

alluvium causing significant delay in the arrival time of radionuclides. 

Conclusions drawn from these analyses may change as the models and assumptions are updated, and 

certain parameters or processes may become more or less important. Also, the assumptions and limitations, 

as described in Chapter 2 of this report, should be considered when interpreting the results. NRC preparation 

to review the DOE TSPA products is an iterative process, of which this report represents one facet.

6-4
7 REFERENCES 

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7-3
APPENDIX A
DESIGN MATRIX FOR THE MORRIS METHOD 

This appendix explains the steps necessary to obtain the matrix used by the Total-system Performance 

Assessment (TPA) code as the input parameters. Let x,, i = 1, 2, ..., I, be the elements of x, where x is the 

input parameter vector with I elements. Assuming 0< x, •1 , the interval [0, 1] is now divided into p 

discrete levels. A randomly chosen base vector, x*, is then obtained by assigning each element ofx randomly 

from a set of discrete values: {0,1/ (p- 1),2/ (p- 1),...,1- A}, where A =p/2(p - 1). To obtain the matrix, first, 

a (I + 1)-by-I sampling matrix, B, with elements of 0's and l's is selected: 

0 0 0 ..- 0 

1 0 0 ... 0 

B= 1 1 0 ... 0 (A-i) 

1 1 1 -... 1 

Matrix B has an important property, namely, that any row differs from its immediate neighboring rows only 

in one column. For instance, the second row differs from the first row only in the first column and the third 

row in the second column. A matrix obtained by multiplying B with A can be used to produce I values of 

ody/odx1 , based on (I + 1) runs. But the elements of the matrix are not randomly selected. 

To randomize the matrix A B , the following operations are performed: 

B*= J( 1 + 1),I x*+(A/2)[(B-J(I + 1),I)D*+J (I+ 1),I] (A-2) 

where 

1 1 1 --. 1 

1 1 1 ..- 1 

Jl+),i 1 1 1 .-. 1 (A-3) 

.. . ... ... .. .... 

1 1 1 ... 1 (t+i),I 

D* is an I-dimensional diagonal matrix in which each diagonal element is either +1 or -1 with equal 

probability. The operations defined in Eq. (A-2) randomize the matrix AB. The matrix B* is called the 

design matrix.

A-1
Since the input variables are considered random, so is the output y(x). If a distribution of r samples is 

required for each oy/dx, , the previous process defined in Eq. (A-2) can be repeated r times to produce 

an r(I+1)-by-I design matrix X: 

Xr(i+l),I 2 (A-4) 

IB" 

Each row of X will next be used as input to the TPA code, to calculate y(x), and the matrix Xwill be used 

to produce rlnumber of dy/o3x1 , which, in turn, will produce I distributions for the input variables, each 

with r samples.

A-2
APPENDIX B
FORMALISM OF FOURIER AMPLITUDE 

SENSITIVITY TEST TECHNIQUE 

Consider again the nonlinear computational model of Eq. (3-1), which has only one output variable and I 

input variables. The I input variables through Itransformation functions can be represented as: 

xi= gi(sinow s),i = 1,2,...,1 (B-1) 

where g,, i = 1, ..., I, is a set of trigonometric transform functions and 0), i = 1, ..., I, a set of integer 

frequencies, with one frequency assigned arbitrarily to each x, of x (Cukier, 1973). Equation (B-I) is a 

parametric representation of an I-dimensional curve in the vector space of x. As s varies over the range 

0:• s _ 2;, xj, x2, ..., x, traverse the I-dimensional space simultaneously, with a relative rate of traversal in 

each direction proportional to the frequency assigned to the direction. 

After applying the transformation functions defined in Eq. (B- 1) to the input vectorx, the output variable y(x) 

becomes a periodic function of s: 

y(x) = y[g, (sin0o s),g2 (sin)2 s),...,g,(sino s)]= y(s) (B-2) 

andy can be expanded into a Fourier series: 

y(s) = I Asin(o is) = y(s + 2n) (B-3) 

i=1 

The Fourier amplitudes A,, i = 1, 2, ..., I, of the output variables corresponding to each frequency (0 i = 

1, ..., I, can be obtained as (Schaibly and Schuler, 1973): 

1 2n 

4= 'Jy(s)sin(o is)ds, i = 1, 2, ... , I (B-4) 

0 

The question now becomes whether the amplitudes Ai, i = 1, 2, ..., I, are strictly related to the input variable 

x1, i = 1, 2, ..., I, and x,, only. If it can be shown that the Fourier amplitudes A, i = 1, 2, ..., I, are affected by 

the it parameter x1, only, and not by any other parameters, then the Fourier amplitudes isolate, one by one, 

the sensitivity of the parameters x, i = 1, 2, ..., I, on the output. In other words, the magnitudes of the 

Fourier A,, i = 1, 2, ..., I, give the quantitative measurements of sensitivities of the input variables x,, i = 1, 

2, ..., L Because the measures are obtained by varying x,, i = 1, 2, ..., I, simultaneously, the FAST method 

simulates a more realistic situation than other sensitivity analysis methods that vary only one parameter at 

a time. 

The amplitudes A,, i = 1, 2, ..., I, calculated according to Eq. (B-4), are truly related to the input variable x,, 

i = 1, 2, ..., 1, only if a set of incommensurate frequencies is used in Eq. (B-I), where incommensurate means 

that there does not exist a common divisor among the frequencies. But this would require that the Eq. (B-4) 

be evaluated over an infinite period. Instead, a set of integer frequencies is used. By using integer

B-1
frequencies, the output variable becomes a periodic function with a period of 2p and the amplitudes A,, i = 

1, 2, ..., 1, can be obtained as: 

2 N 

A, = I y(s, )sin(o) ,sj) (B-5) 

N j=1 

The use of integer frequencies causes some problems. For instance, if (o4 = (oj + o)6 - o, then A(a)4) = A((o] 

+ o(, - 03), and A4 will not only reflect the sensitivity of x4, but also xj, x2, and x3. In the FAST method, the 

integer frequency set is chosen such that: 

Ei(O~i #• O, (B-6) 

i=1 

lrls M +1 (B-7) 

where M and r, i = 1, 2, ..., I, are integers. 

This set of frequencies is called approximately incommensurate to order M; it has the important property that 

no single frequency can be obtained by adding or subtracting any Mfrequencies. When the set of frequencies 

is used to determine the Fourier amplitudes A1, i = 1, 2, ..., I, the amplitudes segregate the sensitivity of the 

input variables on the output to the order M. For instance, if M = 4, then there is no mutual interference 

between any four Fourier amplitudes, but there might be among five amplitudes coefficients. Therefore, the 

larger the value of M, the greater the likelihood that the Fourier amplitude of each input frequency reflects 

solely the influence of the corresponding rate coefficient. On the other hand, the larger the M, the more 

difficult it is to select integer frequencies that satisfy both Eqs. (B-6) and (B-7). 

After selecting integer frequencies, N number of points are selected for s, which are used in Eq. (B-I) to 

generate x,, i = 1, 2, ..., 1, for numerical calculations: 

s=-21j-,j = 1,2,...,N (B-8) 

N 

But N cannot be an arbitrary integer. For instance, if t)i = mN - oJk , where m is an integer, then: 

y(O3 is) = y(mNs - 0) ks) = y(2n im- 0 kS) = Y(0 ks) (B-9) 

and the amplitude A, will not be distinguishable from A4. To avoid this problem, N is chosen such that:

B-2
I 

bioot # mN (B-10) 

i=1 

X bjj!ý M+J (B-11) 

i=1 

where bh, i = 1,2,..., , and Mare the same integers as in Eq. (B-7), in accordance with Eqs. (B-6) and (B-7). 

The particular trigonometric transformation functions used are 

11 ! o 

x,=2 + arcs sin(O) s+r] i = 1,2, (B-12) 

where r, i= 1, 2,..., 1, are random numbers. The Npoints of s are then used in Eq. (B-12)to obtain x,, i = 1, 

2, ..., I to calculate y(x) = y(s). The values of x, and y are then used in Eq. (B-5) to obtain the Fourier 

amplitudes A, i = 1, 2, ..... L 

REFERENCES 

Schaibly, J.H., and K.E. Schuler. "Study ofthe sensitivity of coupled reaction systems to uncertainties in rate 

coefficients. II: Applications." Journal of Chemical Physics 59(8): 3,879-3,888. 1973.

B-3
APPENDIX C
FORMALIZATION OF PARAMETER TREE 

SENSITIVITY ANALYSIS APPROACH 

The following is a formal explanation of the parameter tree sensitivity analysis approach presented in 

Section 4.1.5. Let • be the median value of xi , 5' the median value of y, and I the total number of 

sampled parameters. In this development, median values are used for partitioning criteria, but any other 

statistical or physical branching criterion could also be used. The first step is to partition all of the 

realizations into two bins: 

Xi+= [V realizations with x1j> - x1] (C-la) 

X-= [V realizations with x13j < X I(C-lb) 

where j represents a particular realization, assume that the two bins contain N,+ and N1 _ members, where 

Ni+ N1 _ = N is the total number of samples or realizations. Note that when the partitioning criterion 

is the median value, N+ = N1. = N12, but that will not be true for other branching criteria. 

Now consider the N1+ realizations ofy that are produced by the xi+ set. From these N,+ realizations, we 

select those that meet the following criterion: 

y = [V realizations with yj > S x1,3.E x1+] (C-2) 

Let the number of realizations satisfying this criteria be L . It follows that 

pi+ = P{y >-a YIXi >l- (C-3) 

The second branch of the tree is associated with the y," bin containing Lg_ members, where 

yi_ = [V realizations with y, > 9 Xl,j E X1- (C-4) 

In this case, similar to Eq. (C-3), 

P-P{YŽY > x 1 <X1j_-L (C-5) 

Ni

Equal values of p,+ and p,- would imply that whether x, takes values greater or smaller than its median, 

it does not affect the bin into which y values fall, thus indicating a lack of correlation or lack of sensitivity

C-1
of y to xj. Consequently, a measure of relative sensitivity of y with respect to x, can be constructed as 

pl., - Pr I. It is noted that the proposed measure provides only relative sensitivity because it does not 

provide a precise description of the change iny for a given change inx,, as a measure for absolute sensitivity 

would provide. However, the relative sensitivity measure is sufficient for ranking important parameters. In 

general, one can partition the xlj (and subsequent parameter realizations) into more than two bins, but such 

a generalization will lead to a complicated tree structure (i.e., with potentially large numbers of branches per 

level) and is not pursued further here. 

The branching strategy explained previously is now implemented for the second, third, and subsequent 

parameters until most of the output is sufficiently explained. For the second parameter, the procedure is as 

follows. Partition the bin x1+ containing NI+ realizations into two bins: 

X1-2- [V realizations with xij > x1 n"x2,j x2 (C-6a) 

and 

2 [V realizations with x . 1l" 2 > 2 ]. (C-6b) 

Similarly, the x bin can also be partitioned into two bins: 

x 2+ = [V realizations with xij < fl n x2, •2 (C-6c) 

and 

X1-2 = [V realizations with x <1 f< l x 2,j <2]- (C-6d) 

Let the number of members in each of the four bins be N 1+2+, N +2_, N 12+, and N 1-2. The output 

realizations associated with members of a bin are now scrutinized to count the number of realizations in 

which y > .5 . Thus, the four output bins associated with the four branches of the tree at the second 

parameter level are: 

Y1+2+ I yj> + X,j 1 X 2 ,j CX12+] (C-7a) 

Y1-2= [y x1,j, x 2,j r X1+2 -j (C-7b) 

Y1-

2_ yj +> ?Ix,j X2,j E Xr12+] (C-7c) 

12- [Yj + 1 1j , X2,j E X1- 2 -] (C-7d)

C-2
Let the number of realizations associated with the fourbins ofEq. (C-7) be L1+2+, LI+2-, L1 2+ , and L1 2 . 

Then at the second level of the tree, we can make the following probability statements: 

P1-2+ = Ply > y+xij> xi fX2,k > x2 N (C-8a) 

and with similar interpretations, 

=L+2- (C-8b) NI1+2

= L-2 (C-Sc) N1-2+ 

Pr2 L-2- (C-Sd) 

NP1-2--N _ 

If p = 1+2 , then the second parameter, x,, (given X1 , X1 ) has no influence on y. Thus, relative 

sensitivities of x, can be partially measured by -Pp+2+-/P1+2-I and I p1 _2+ - P1-2-I for the cases of 

X1 -- X^1 and X1 <X :

1 . The total relative sensitivity ofy to x, can be determined from: 

Sx2 Pl+2 - P12-1 P{XI l> I + 1 -2÷-P1-2- IP{x, <XdI (C-9) 

Also, P1+2+ equal to Pr-2- implies that whether the first two parameters together had high (greater than their 

medians) or low (smaller than their medians) values, there is an equal chance of producing a y lower or 

- ameasu oof relatve seti 

higher than its median value. We use the quantity 1- [pI+2+ - p-2 s a es 

ofy jointly to x, and x,. For this example, it is assumed that both x, and x, are positively correlated with y 

(i.e., large values of x, and x2 lead to large values of y and vice-versa). In general, this is not a valid 

assumption and input parameters can be positively or negatively correlated with the output variable. Hence, 

we now change our nomenclature for the joint relative sensitivity such that the coefficient is now defined 

as PH - PLI , wherePH andpL are the greatest and least values ofp among the bins. In this formulation, 

the numerator represents the "distance" of the output variable from perfect noncorrelation with the input 

parameter set (i.e., ify has no correlation with the input parameter set under study, thenp is the same in all

C-3
bins, and the numerator is zero). Similarly, the denominator represents the distance of the output variable 

from perfect correlation with the input parameter (i.e., ify shows perfect correlation with the input parameter 

set under study, p is unity in the highest bin and zero in the lowest bin, and the denominator is zero). With 

this formulation, the joint relative sensitivity is on the range [0,oo]. This formulation can be extended to any 

number of parameters.

C-4
APPENDIX D
DESCRIPTION OF ABBREVIATIONS USED FOR TPA VERSION 3.2 CODE INPUT 

PARAMETERS 

Short Name Full Name Description 

AA_2_1 AA_2_1 [C/m2/yr] A corrosion rate (passive current density) for the waste package 

(WP) inner overpack in EBSFAIL. 

AAMAI@S ArealAverageMeanAfnnualInfiltrationAtStart[mm/yr] Mean areal average infiltration into the subsurface at the start 

of a TPA Version 3.2 code run. 

ABMLFVDC AirbomeMassLoadForVolcanismDoseCalculation[g/m3] Mass load of ash/SF from volcanic event in the air available for 

inhalation by a receptor. 

APrsSAV AlluviumMatrixPorositySAV Amargosa Valley alluvium saturated zone (SZ) matrix porosity. 

,p AqThick5 AquiferThickness5km[m] Thickness of the aquifer at a location 5 km south of Yucca 

Mountain (YM). 

ARDSAVI AlluviumMatrixRDSAVI Matrix retardation for iodine (I) in the SZ of the Amargosa 

Valley alluvium. 

ARDSAVU AlluviumMatrixRDSAVU Matrix retardation for uranium (U) in the SZ of the Amargosa 

Valley alluvium. 

ARDSAVAm AlluviumMatrixRDSAVAm Matrix retardation for americium (Am) in the SZ of the 

Amargosa Valley alluvium.
DESCRIPTION OF ABBREVIATIONS USED FOR TPA VERSION 3.2 CODE INPUT 

PARAMETERS (cont'd)

Short Name 

ARDSAVCs 

ARDSAVNb 

ARDSAVNi 

ARDSAVNp 

k) 

ARDSAVPb 

ARDSAVPu 

ARDSAVRa 

ARDSAVSe 

ARDSAVTc

Full Name 

AlluviunmMatrixRDSAVCs 

AlluviumMatrixRDSAVNb 

AlluviumMatrixRDSAVNi 

AlluviumMatrixRDSAV_Np 

AlluviumMatrixRDSAVPb 

AlluviumMatrixRDSAVPu 

AlluviumMatrixRDSAVRa 

AlluviumMatrixRDSAVSe 

AlluviumMatrixRDSAV_Tc

Description 

Matrix retardation for cesium (Ce) in the SZ of the Amargosa 

Valley alluvium. 

Matrix retardation for niobium (Nb) in the SZ of the Amargosa 

Valley alluvium. 

Matrix retardation for nickel (NiI) in the SZ of the Amargosa 

Valley alluvium. 

Matrix retardation for neptunium (Np) in the SZ of the 

Amargosa Valley alluvium. 

Matrix retardation for lead (Pb) in the SZ of the Amargosa 

Valley alluvium. 

Matrix retardation for plutonium (Pu) in the SZ of the 

Amargosa Valley alluvium. 

Matrix retardation for radium (Ra) in the SZ of the Amargosa 

Valley alluvium. 

Matrix retardation for selenium (Se) in the SZ of the Amargosa 

Valley alluvium. 

Matrix retardation for technetium (Tc) in the SZ of the 

Amargosa Valley alluvium.
DESCRIPTION OF ABBREVIATIONS USED FOR TPA VERSION 3.2 CODE INPUT 

PARAMETERS (cont'd)

Short Name 

ARDSAVTh 

AshMnPLD 

*Chlorid 

SCladCorF 

CritRHAC 

FEROI-Tn 

FEROI-X 

FEROI-Y

Full Name 

AlluviumMatrixRDSAVTh 

AshMeanParticleLogDiameter[d-inScm] 

ChlorideMultFactor 

ClAddingCorrectionFactor 

CriticalRelativeHumidityAqueousCorrosion 

TimeOfNextFaultingEventinRegionOflnterest[yrI 

XlocationOfFaultingEventlnRegionOflnterest[m] 

YlocationOfFaultingEventhlRegionOflnterest[m]

Description 

Matrix retardation for thorium (Th) in the SZ of the Amargosa 

Valley alluvium. 

Relative size of ash/spent fuel (SF) particulates from a volcanic 

event. 

Factor by which chloride concentration in matrix is multiplied 

to compensate for dripping and drying that would lead to salt 

accumulation. 

A variable allowing for increased SF protection in a WP 

because of the presence of cladding on the SF. 

Critical relative humidity above which aqueous corrosion 

may initiate. 

Time of the next faulting event in the repository area (years 

from present). 

X location of the center of the faulting event within the 

repository area. 

Y location of the center of the faulting event within the 

repository area.
DESCRIPTION OF ABBREVIATIONS USED FOR TPA VERSION 3.2 CODE INPUT 

PARAMETERS (cont'd) 

Qhtý" Mama• IPuII 1%hame Description

Fmult* 

FO-Rn#Sd 

, FOC-R 

FOCTR 

FOCTR-R 

Fow* 

FPrmBFw 

FPrmCHv 

FPrmCHz 

FPrmPPw

FmultFactor 

RntoDetermineFaultOrientation 

FractionOfCondensateRemoved[ 1/yr] 

FractionOfCondensateTowardRepository[ 1/yr] 

FractionOfCondensateTowardRepositoryRemoved[l /yr] 

FowFactor 

FracturePermeabilityBFwm 2 ] 

FracturePermeability_CHnv[m 2] 

FracturePermeability CHnz[m2] 

FracturePermeabilityPPw [m2 ]

The fraction of water, infiltrating to the repository from the 

unsaturated zone above the repository, that will enter the WP 

and contribute to the release of radionuclides. Water dripping 

toward the drifts may be diverted around the drift because of 

capillary action, may be diverted down the side of the drift, or 

may not enter the WP for other reasons. 

Random number selected to determine the orientation of the 

fault within the repository area. 

Fraction of water condensate removed in each reflux3 time step. 

Fraction of water condensate moving toward the repository. 

Fraction of water condensate moving toward the repository but 

escaping before entering the repository. 

A flow focusing factor that expresses the flow potentially 

reaching a wetted WP (can be greater or less than 1.0). 

Bullfrog-welded fracture permeability unsaturated zone (UZ). 

Calico Hills-nonwelded vitric fracture permeability (UZ). 

Calico Hills-nonwelded zeolitic fracture permeability (UZ). 

Prow Pass-welded fracture permeability (UZ).
DESCRIPTION OF ABBREVIATIONS USED FOR TPA VERSION 3.2 CODE INPUT 

PARAMETERS (cont'd) 

Short Name Full Name Description

FPrmTSw 

FPrmUCF 

FPrmUFZ 

FPrsBFw 

FPrsCHv 

SFPrsCHz 

FPrsPPw 

FPrsSTF 

FPrsTSw 

FPrsUCF 

FPrsUFZ 

H20-FThk 

InitRSFP

FracturePermeability_TSw[mf2 ] 

FracturePermeabilityUCFm 2] 

FracturePermeabilityUFZ_[m2] 

FracturePorosity_BFw_ 

FracturePorosity_CHnv 

FracturePorosity_CHnz 

FracturePorosity_PPw_ 

FracturePorosity_STFF 

FracturePorosity_TSw_ 

FracturePorosityUCF_ 

FracturePorosityUFZ_ 

ThicknessOfWaterFilm[m] 

InitialRadiusOfSFParticle[m]

InnOvrEI InnerOverpackErpintercept

Topopah Spring-welded fracture permeability (UZ). 

Upper Crater Flat fracture permeability (UZ). 

UFZ fracture permeability (UZ). 

Bullfrog-welded fracture porosity (UZ). 

Calico Hills-nonwelded vitric fracture porosity (UZ). 

Calico Hills-nonwelded zeolitic fracture porosity (UZ). 

Prow Pass-welded fracture porosity (UZ). 

Fracture porosity of saturated tuff (SZ). 

Topopah Spring-welded fracture porosity (UZ). 

Upper Crater Flat fracture porosity (UZ). 

UFZ porosity (UZ). 

Thickness of water film on WP surface. 

Initial radius of spent fuel particle - affects SF alteration rate 

and transport out of a failed WP in EBSREL. 

Inner overpack EP intercept.
DESCRIPTION OF ABBREVIATIONS USED FOR TPA VERSION 3.2 CODE INPUT 

PARAMETERS (cont'd) 

Short Name Full Name Description

InvMPerm 

MAPM@GM 

MATI@GM 

MixZnT20 

MKDBFwU 

MKDCHvU 

MKDCHzU 

MKDPPwU 

MKDTSwU 

MKDUCFU 

MKDBFwAm 

MKDBFwCs

InvertMatrixPerneability[m^ 2] 

MeanAveragePrecipitationMultiplierAtGlacialMaximum 

MeanAverageTemperaturelncreaseAtGlacialMaximum[°C] 

MixingZoneThickness20km[m] 

MatrixKDBFwU[m3/kg] 

MatrixKDCHnvU[m3/kg] 

MatrixKDCHnzU[m3/kg] 

MatrixKDPPwU[m3/kg] 

MatrixKD_TSwU[m3/kg] 

MatrixKDUCFU[m3/kg] 

MatrixKDBFwAm[m3/kg] 

MatrixKDBFwCs[m3/kg]

Matrix permeability of the invert. 

Mean annual precipitation increase at glacial maximum

affects infiltration from the land surface in UZFLOW. 

Magnitude of mean annual temperature change at glacial 

maximum-affects infiltration from the land surface 

in UZFLOW. 

Mixing zone thickness in a well at a receptor group 20 km 

from YM. 

Bullfrog-welded matrix Kd for U. 

Calico Hills-nonwelded vitric matrix Kd for U. 

Calico Hills-nonwelded zeolitic matrix Kd for U. 

Prow Pass-welded matrix Kd for U. 

Topopah Spring-welded matrix Kd for U. 

Upper Crater Flat matrix Kd for U. 

Bullfrog-welded matrix Kd for Am. 

Bullfrog-welded matrix Kd for Cs.

C1~
DESCRIPTION OF ABBREVIATIONS USED FOR TPA VERSION 3.2 CODE INPUT 

PARAMETERS (cont'd) 

Short Name Full Name Description

MKDBFwNi 

MKDBFwNp 

MKDBFwPb 

MKDBFwPu 

MKDBFwRa 

SMKDBFwSe 

MKDBFwTh 

MKDCHvAm 

MKDCHvCs 

MKDCHvNi 

MKDCHvNp 

MKDCHvPb 

MKDCHvPu 

MKDCHvRa

MatrixKDBFwNi[m3/kg] 

MatrixKDBFwNpI[m3/kg] 

MatrixKDBFwPb[m3/kg] 

MatrixKDBFwPu[m3/kg] 

MatrixKDBFwRa[m3/kg] 

MatrixKDBFwSeI[m3/kg] 

MatrixKDBFwTh[m3/kg] 

MatrixKDCHnvAm[m3/kg] 

MatrixKDCHnvCsI[m3/kg] 

MatrixKDCHnvNi[m3/kg] 

MatrixKDCHnvNp[m3/kgl 

MatrixKDCHnvPb[m3/kg] 

MatrixKDCHnvPu[m3/kg] 

MatrixKDCHnvRa[m3/kg]

Bullfrog-welded matrix Kd for Ni. 

Bullfrog-welded matrix Kd for Np. 

Bullfrog-welded matrix Kd for Pb. 

Bullfrog-welded matrix Kd for Pu. 

Bullfrog-welded matrix Kd for Ra. 

Bullfrog-welded matrix Kd for Se. 

Bullfrog-welded matrix Kd for Th. 

Calico Hills-nonwelded vitric matrix Kd for Am. 

Calico Hills-nonwelded vitric matrix Kd for Cs. 

Calico Hills-nonwelded vitric matrix Kd for Ni. 

Calico Hills-nonwelded vitric matrix Kd for Np. 

Calico Hills-nonwelded vitric matrix Kd for Pb. 

Calico Hills-nonwelded vitric matrix Kd for Pu. 

Calico Hills-nonwelded vitric matrix Kd for Ra.
DESCRIPTION OF ABBREVIATIONS USED FOR TPA VERSION 3.2 CODE INPUT 

PARAMETERS (cont'd) 

Short Name Full Name Description

MKDCHvSe 

MKDCHvTh 

MKDCHzAm 

MKDCHzCs 

MKDCHzNi 

, MKDCHzNp 0o 

MKDCHzPb 

MKDCHzPu 

MKDCHzRa 

MKDCHzSe 

MKDCHzTh 

MKDPPwAm 

MKDPPwCs 

MKDPPwNi

MatrixKDCHnvSeI[m3/kg] 

MatrixKDCHnvTh[m3/kg] 

MatrixKDCHnzAm[m3/kg] 

MatrixKDCHnzCs[m3/kg] 

MatrixKDCHnzNi[m3ikg] 

MatrixKD_CHnzNp[m3/kg] 

MatrixKDCHnzPb[m3/kg] 

MatrixKDCHnzPu[m3/kg] 

MatrixKDCHnzRa[m3/kgl 

MatrixKDCHnzSe[m3/kg] 

MatrixKDCHnzTh[m3/kg] 

MatrixKDPPwAmI[m3/kg] 

MatrixKDPPwCs[m3/kg] 

MatrixKDPPwNi[m3/kg]

Calico Hills-nonwelded vitric matrix Kd for Se. 

Calico Hills-nonwelded vitric matrix Kd for Th. 

Calico Hills-nonwelded zeolitic matrix Kd for Am. 

Calico Hills-nonwelded zeolitic matrix Kd for Cs. 

Calico Hills-nonwelded zeolitic matrix Kd for Ni. 

Calico Hills-nonwelded zeolitic matrix Kd for Np. 

Calico Hills-nonwelded zeolitic matrix Kd for Pb. 

Calico Hills-nonwelded zeolitic matrix Kd for Pu. 

Calico Hills-nonwelded zeolitic matrix Kd for Ra. 

Calico Hills-nonwelded zeolitic matrix Kd for Se. 

Calico Hills-nonwelded zeolitic matrix Kd for Th. 

Prow Pass-welded matrix Kd for Am. 

Prow Pass-welded matrix Kd for Cs. 

Prow Pass-welded matrix Kd for Ni.
DESCRIPTION OF ABBREVIATIONS USED FOR TPA VERSION 3.2 CODE INPUT 

PARAMETERS (cont'd) 

Short Name Full Name Description

MKDPPwNp 

MKDPPwPb 

MKDPPwPu 

MKDPPwRa 

MKDPPwSe 

, MKDPPwTh 

MKDTSwAm 

MKDTSwCs 

MKDTSwNi 

MKDTSwNp 

MKDTSwPb 

MKDTSwPu 

MKDTSwRa 

MKDTSwSe

MatrixKDPPwNp[m3/kg] 

MatrixKDPPwPb[m3/kg] 

MatrixKDPPwPu[m3/kg] 

MatrixKDPPwRa[m3/kg] 

MatrixKDPPwSe[m3/kg] 

MatrixKDPPwTh[m3/kg] 

MatrixKDTSwAm[m3/kg] 

MatrixKDTSwCs[m3/kg] 

MatrixKDTSwNi[m3/kg] 

MatrixKDTSwNp[m3/kg] 

MatrixKDTSwPb[m3/kg] 

MatrixKDTSwPu[m3/kg] 

MatrixKDTSwRa[m3/kg] 

MatrixKDTSwSe[m3/kg]

Prow Pass-welded matrix Kd for Np. 

Prow Pass-welded matrix Kd for Pb. 

Prow Pass-welded matrix Kd for Pu. 

Prow Pass-welded matrix Kd for Ra. 

Prow Pass-welded matrix Kd for Se. 

Prow Pass-welded matrix Kd for Th. 

Topopah Spring-welded matrix Kd for Am. 

Topopah Spring-welded matrix Kd for Cs. 

Topopah Spring-welded matrix Kd for Ni. 

Topopah Spring-welded matrix Kd for Np. 

Topopah Spring-welded matrix Kd for Pb. 

Topopah Spring-welded matrix Kd for Pu. 

Topopah Spring-welded matrix Kd for Ra. 

Topopah Spring-welded matrix Kd for Se.
DESCRIPTION OF ABBREVIATIONS USED FOR TPA VERSION 3.2 CODE INPUT 

PARAMETERS (cont'd) 

Short Name Full Name Description

MKDTSwTh 

MKDUCFAm 

MKDUCFCs 

MKDUCFNi 

MKDUCFNp 

MKDUCFPb 

MKDUCFPu 

MKDUCFRa 

MKDUCFSe 

MKDUCFTh 

MKDUFZU 

MKDUFZAm 

MKDUFZCs 

MKDUFZNi

MatrixKDTSwTh[m3/kg] 

MatrixKDUCFAm[m3/kg 

MatrixKDUCFCs[m3/kg] 

MatrixKDUCFNi[m3/kgl 

MatrixKDUCFNpI[m3/kg] 

MatrixKDUCFPbI[m3/kg] 

MatrixKDUCFPu[m3/kg] 

MatrixKDUCFRa[m3/kg] 

MatrixKDUCFSe[m3/kg] 

MatrixKDUCFTh[m3/kg] 

MatrixKDUFZ U[m3/kg] 

MatrixKDUFZAmI[m3/kg] 

MatrixKDUFZCs[m3/kg] 

MatrixKDUFZNi[m3/kg]

Topopah Spring-welded matrix K4 for Th. 

Upper Crater Flat matrix Kd for Am. 

Upper Crater Flat matrix Kd for Cs. 

Upper Crater Flat matrix K4 for Ni. 

Upper Crater Flat matrix Kd for Np. 

Upper Crater Flat matrix Kd for Pb. 

Upper Crater Flat matrix Kd for Pu. 

Upper Crater Flat matrix Kd for Ra. 

Upper Crater Flat matrix Kd for Se. 

Upper Crater Flat matrix Kd for Th. 

UFZ matrix Kd for U. 

UFZ matrix Kd for Am. 

UFZ matrix Kd for Cs. 

UFZ matrix K. for Ni.

C
DESCRIPTION OF ABBREVIATIONS USED FOR TPA VERSION 3.2 CODE INPUT 

PARAMETERS (cont'd) 

Short Name Full Name Description

MKDUFZNp 

MKDUFZPb 

MKDUFZPu 

MKDUFZRa 

MKDUFZSe 

MKDUFZTh 

MprmBFw 

MPrmCHv 

MPrmCHz 

MPrmPPw 

MPrmTSw 

MPrmUCF 

MPrmUFZ 

NEFZnW

MatrixKD_UFZ_NpI[m3/kg] 

MatrixKDUFZPb[m3/kg] 

MatrixKDUFZPu[m3/kg] 

MatrixKDUFZRa[m3/kg] 

MatrixKDUFZSe[m3/kg] 

MatrixKDUFZThIm3/kg] 

MatrixPermeabilityBFwm2] 

MatrixPermeability_CHnv[m 2] 

MatrixPermeabilityHnz[m2 ] 

MatrixPermeabilityPPw_[m2] 

MatrixPermeabilityj Sw_[m2] 

MatrixPermeability_.UCF_[m2] 

MatrixPermeabilityUFZ_[m2] 

NEFaultZoneWidth[m]

UFZ matrix Kd for Np. 

UFZ matrix Kd for Pb. 

UFZ matrix Kd for Pu. 

UFZ matrix Kd for Ra. 

UFZ matrix Kd for Se. 

UFZ matrix Kd for Th. 

Bullfrog-welded matrix permeability. 

Calico Hills-nonwelded vitric matrix permeability. 

Calico Hills-nonwelded zeolitic matrix permeability. 

Prow Pass-welded matrix permeability. 

Topopah Spring-welded matrix permeability. 

Upper Crater Flat matrix permeability. 

UFZ matrix permeability. 

North-East fault zone width.

.m
DESCRIPTION OF ABBREVIATIONS USED FOR TPA VERSION 3.2 CODE INPUT 

PARAMETERS (cont'd) 

Short Name Full Name Description

NELCDAmt 

NWFZnW 

NWLCDAmt 

OO-CofLC 

PlumeTh5 

SbArWt% 

SbGFRATF 

SFWt%C1 

SFWt%C2 

SFWtC3 

SFWtC4 

SFWtC5 

SFWt%C6

NEAmountOfLargestCredibleDisplacement[m] 

NWFaultZoneWidth[m] 

NWAmountOfLargestCredibleDisplacement[m] 

CoefForLocCorrOfOuterOverpack 

PlumeThickness5km[m] 

SubAreaWetFraction 

SubGrainFragmentRadiusAfterTransFrac[m] 

SFWettedFractionCorrosion_1 

SFWettedFractionCorrosion_2 

SFWettedFractionCorrosion_3 

SFWettedFractionCorrosion_4 

SFWettedFractionCorrosion_5 

SFWettedFractionCorrosion_6

North-East largest credible displacement. 

North-West fault zone width. 

North-West largest credible displacement. 

Coefficient for localized corrosion rate of outer overpack. 

Plume thickness at 5 km. 

Subarea wet fraction. 

Subgrain fragment radius of UO2 particle after transgranular 

fracture; used only if fuel conversion takes place from U0 2 to 

U0 24 and U308 ; used only by the SF dissolution models that are 

dependent on exposed surface area. 

SF wet fraction for corrosion failures in subarea 1. 

SF wet fraction for corrosion failures in subarea 2. 

SF wet fraction for corrosion failures in subarea 3. 

SF wet fraction for corrosion failures in subarea 4. 

SF wet fraction for corrosion failures in subarea 5. 

SF wet fraction for corrosion failures in subarea 6.

to
DESCRIPTION OF ABBREVIATIONS USED FOR TPA VERSION 3.2 CODE INPUT 

PARAMETERS (cont'd) 

Short Name Full Name Description

SFWettedFractionCorrosion_7 

SFWettedFractionFAULTO 

SFWettedFractionInitial_1 

SFWettedFractionInitial_2 

SFWettedFractionInitial_3 

SFWettedFractionInitial_4 

SFWettedFraction Initial_5 

SFWettedFractionInitial_6 

SFWettedFractionInitial_7 

SFWettedFractionSEISMO1_1 

SFWettedFractionSEISMO1_2

SFWtS 13 SFWettedFractionSEISMO1_3

SFWtC7 

SFWtFO 

SFWt%I 1 

SFWtI2 

SFWtI3 

SFWtI4 

SFWt%15 

SFWtI6 

SFWt%17 

SFWt%S 11 

SFWt%So12

SF wet fraction for corrosion failures in subarea 7. 

SF wet fraction for faulting failures. 

SF wet fraction for initial failures in subarea 1. 

SF wet fraction for initial failures in subarea 2. 

SF wet fraction for initial failures in subarea 3. 

SF wet fraction for initial failures in subarea 4. 

SF wet fraction for initial failures in subarea 5. 

SF wet fraction for initial failures in subarea 6. 

SF wet fraction for initial failures in subarea 7. 

SF wet fraction for seismic failures for seismic interval 1 in 

subarea 1. 

SF wet fraction for seismic failures for seismic interval 1 in 

subarea 2. 

SF wet fraction for seismic failures for seismic interval 1 in 

subarea 3.
DESCRIPTION OF ABBREVIATIONS USED FOR TPA VERSION 3.2 CODE INPUT 

PARAMETERS (cont'd)

Short Name 

SFWtS14 

SFWt%S15 

SFWt%S16 

SFWt%S 17 

SFWtS21 

SFWt% S22 

SFWtS23 

SFWt%S24 

SFWtS25

4.

Full Name 

SFWettedFractionSEISMO1_4 

SFWettedFractionSEISMO1_5 

SFWettedFractionSEISMO1_6 

SFWettedFractionSEISMO1_7 

SFWettedFractionSEISMO2_1 

SFWettedFractionSEISMO2_2 

SFWettedFractionSEISMO2_3 

SFWettedFractionSEISMO2_4 

SFWettedFractionSEISMO2_5

Description 

SF wet fraction for seismic failures for seismic interval 1 in 

subarea 4. 

SF wet fraction for seismic failures for seismic interval 1 in 

subarea 5. 

SF wet fraction for seismic failures for seismic interval 1 in 

subarea 6. 

SF wet fraction for seismic failures for seismic interval 1 in 

subarea 7. 

SF wet fraction for seismic failures for seismic interval 2 in 

subarea 1. 

SF wet fraction for seismic failures for seismic interval 2 in 

subarea 2. 

SF wet fraction for seismic failures for seismic interval 2 in 

subarea 3. 

SF wet fraction for seismic failures for seismic interval 2 in 

subarea 4. 

SF wet fraction for seismic failures for seismic interval 2 in 

subarea 5.
DESCRIPTION OF ABBREVIATIONS USED FOR TPA VERSION 3.2 CODE INPUT 

PARAMETERS (cont'd)

Short Name 

SFWtS26 

SFWt%S27 

SFWt%S31 

SFWt%S32 

SFWt%S33 

SFWt%S34 

SFWt%S35 

SFWt%S36 

SFWt%S37

Full Name 

SFWettedFractionSEISMO2_6 

SFWettedFractionSEISMO2_7 

SFWettedFractionSEISMO3_I 

SFWettedFractionSEISMO3_2 

SFWettedFractionSEISMO3_3 

SFWettedFractionSEISMO3_4 

SFWettedFractionSEISMO3_5 

SFWettedFractionSEISMO3_6 

SFWettedFraction SEISMO3_7

Description 

SF wet fraction for seismic failures for seismic interval 2 in 

subarea 6. 

SF wet fraction for seismic failures for seismic interval 2 in 

subarea 7. 

SF wet fraction for seismic failures for seismic interval 3 in 

subarea 1. 

SF wet fraction for seismic failures for seismic interval 3 in 

subarea 2. 

SF wet fraction for seismic failures for seismic interval 3 in 

subarea 3. 

SF wet fraction for seismic failures for seismic interval 3 in 

subarea 4. 

SF wet fraction for seismic failures for seismic interval 3 in 

subarea 5. 

SF wet fraction for seismic failures for seismic interval 3 in 

subarea 6. 

SF wet fraction for seismic failures for seismic interval 3 in 

subarea 7.
DESCRIPTION OF ABBREVIATIONS USED FOR TPA VERSION 3.2 CODE INPUT 

PARAMETERS (cont'd)

Short Name 

SFWt%S41 

SFWt%S42 

SFWt%S43 

SFWt%S44 

SFWt% S45 

SFWt% S46 

SFWt% S47 

SFWtVO 

Solbl-Am 

Solbl-Np 

Solbl-Pu

e•

-N

Full Name 

SFWettedFractionSEISMO4_1 

SFWettedFractionSEISMO4_2 

SFWettedFractionSEISMO4_3 

SFWettedFractionSEISMO4_4 

SFWettedFractionSEISMO4_5 

SFWettedFractionSEISMO4_6 

SFWettedFractionSEISMO4_7 

SFWettedFractionVOLCANO 

SolubilityAm[kg/m3] 

SolubilityNp[kg/m3] 

SolubilityPu[kg/m3]

Description 

SF wet fraction for seismic failures for seismic interval 4 in 

subarea 1. 

SF wet fraction for seismic failures for seismic interval 4 in 

subarea 2. 

SF wet fraction for seismic failures for seismic interval 4 in 

subarea 3. 

SF wet fraction for seismic failures for seismic interval 4 in 

subarea 4. 

SF wet fraction for seismic failures for seismic interval 4 in 

subarea 5. 

SF wet fraction for seismic failures for seismic interval 4 in 

subarea 6. 

SF wet fraction for seismic failures for seismic interval 4 in 

subarea 7. 

SF wet fraction for volcanic failures. 

Solubility limit for Am. 

Solubility limit for Np. 

Solubility limit for Pu.
DESCRIPTION OF ABBREVIATIONS USED FOR TPA VERSION 3.2 CODE INPUT 

PARAMETERS (cont'd) 

S. . ,Description

SSMO-JS3 

SSMO-JS4 

SSMO-JS1 

SSMO-RE 

SSMO-JS2 

SSMO-JS5 

SSMO-RPR 

SSMOV201 

SSMOV202 

SSMOV203 

SSMOV204

SEISMOJointSpacing3 [m] 

SEISMOJointSpacing4[m] 

SEISMOJointSpacing I [m] 

RockModulusOfElasticityforSEISMO[Pa] 

SEISMOJointSpacing2[m] 

SEISMOJointSpacing5 [m] 

RockPoissonRatioforSEISMO] 

VerticalExtentOfRockFall2 _1 [m] 

VerticalExtentOfRockFall2_2[m] 

VerticalExtentOfRockFall2_3 [m] 

VerticalExtentOfRockFall2_4 [m]

Joint spacing (JS) for rock condition 3. Not all rocks falling 

from the roof of the emplacement will impact WPs. The 

effective size of the rock that impacts WPs will be controlled 

byJS. 

JS for rock condition 4. 

JS for rock condition 1. 

Rock modulus of elasticity. 

JS for rock condition 2. 

JS for rock condition 5. 

Rock poisson ratio. 

Vertical extent of rock fall for rock condition 2 and ground 

acceleration 0.05 g. The lower limit is approximately equivalent 

to the average rock joint spacing of rock condition 1. The upper 

limit is estimated from numerical results. 

Same as above except with ground acceleration 0.10g. 

Same as above except with ground acceleration 0.15g. 

Same as above except with ground acceleration 0.20g.

Y

Short Name
DESCRIPTION OF ABBREVIATIONS USED FOR TPA VERSION 3.2 CODE INPUT 

PARAMETERS (cont'd) 

Short Name Full Name Description

SSMOV205 

SSMOV206 

SSMOV207 

SSMOV208 

SSMOV209 

SSMOV210 

SSMOV301 

SSMOV302 

SSMOV303 

SSMOV304 

SSMOV305 

SSMOV306 

SSMOV307 

SSMOV308

VerticalExtentOfRockFall2_5 [m] 

VerticalExtentOfRockFall2_6[m] 

VerticalExtentOfRockFall2_7[m] 

VerticalExtentOfRockFall2_8[m] 

VerticalExtentOfRockFall2_9[m] 

VeiticalExtentOfRockFall2l 0[m] 

VerticalExtentOfRockFall3_ I [m] 

VerticalExtentOfRockFall3_2[m] 

VerticalExtentOfRockFall33 [nm] 

VerticalExtentOfRockFall3_4[m] 

VerticalExtentOfRockFall3_5 [m] 

VerticalExtentOfRockFall3_6[m] 

VerticalExtentOfRockFall3_7[m] 

VerticalExtentOfRockFall3_8[m]

Same as above except with ground acceleration 0.25g. 

Same as above except with ground acceleration 0.30g. 

Same as above except with ground acceleration 0.35g. 

Same as above except with ground acceleration 0.40g. 

Same as above except with ground acceleration 0.45g. 

Same as above except with ground acceleration 0.50g. 

Vertical extent of rock fall for rock condition 3 and ground 

acceleration 0.05 g. 

Same as above except with ground acceleration 0.10g. 

Same as above except with ground acceleration 0.15g. 

Same as above except with ground acceleration 0.20g. 

Same as above except with ground acceleration 0.25g. 

Same as above except with ground acceleration 0.30g. 

Same as above except with ground acceleration 0.35g. 

Same as above except with ground acceleration 0.40g.

&0
DESCRIPTION OF ABBREVIATIONS USED FOR TPA VERSION 3.2 CODE INPUT 

PARAMETERS (cont'd) 

Short Name Full Name Description

SSMOV309 

SSMOV310 

SSMOV401 

SSMOV402 

SSMOV403 

SSMOV404 

SSMOV405 

SSMOV406 

SSMOV407 

SSMOV408 

SSMOV409 

SSMOV410 

SSMOV501

VerticalExtentOfRockFall 3 _9[m] 

VerticalExtentOfRockFall3_ 0[m] 

VerticalExtentOfRockFaUl4_1 [m] 

VerticalExtentOfRockFall4_2[m] 

VerticalExtentOfRockFall4_3 [m] 

VerticalExtentOfRockFall 4 _4[m] 

VerticalExtentOfRockFaU4A5 [in] 

VerticalExtentOfRockFall4 _6[m] 

VerticalExtentOfRockFall4 _7 [m] 

VerticalExtentOfRockFallf4_ [m] 

VerticalExtentOfRockFall4 _

9 [m] 

VerticalExtentOfRockFall4_ 0[m] 

VerticalExtentOfRockFall5_I [m]

Same as above except with ground acceleration 0.45g. 

Same as above except with ground acceleration 0.50g. 

Vertical extent of rock fall for rock condition 4 and ground 

acceleration 0.05 g. 

Same as above except with ground acceleration 0.10g. 

Same as above except with ground acceleration 0.15g. 

Same as above except with ground acceleration 0.20g. 

Same as above except with ground acceleration 0.25g. 

Same as above except with ground acceleration 0.30g. 

Same as above except with ground acceleration 0.35g. 

Same as above except with ground acceleration 0.40g. 

Same as above except with ground acceleration 0.45g. 

Same as above except with ground acceleration 0.50g. 

Vertical extent of rock fall for rock condition 5 and ground 

acceleration 0.05 g.
DESCRIPTION OF ABBREVIATIONS USED FOR TPA VERSION 3.2 CODE INPUT 

PARAMETERS (cont'd) 

Short Name Full Name Description

SSMOV502 

SSMOV503 

SSMOV504 

SSMOV505 

SSMOV506 

SSMOV507 

SSMOV508 

SSMOV509 

SSMOV510 

TempGrBI 

VC-Dia 

VD-Angle 

VD-Width 

VD-Lengt

VerticalExtentOfRockFaU5_2 [m] 

VerticalExtentOfRockFall53 [im] 

VerticalExtentOfRockFall5_4[m] 

VerticalExtentOfRockFall5_ [m] 

VerticalExtentOfRockFall5_ 6 [m] 

VerticalExtentOfRockFall5_7 [m] 

VerticalExtentOfRockFall5_8 [m] 

VerticalExtentOfRockFall5_9[m] 

VerticalExtentOfRockFall5_l 0 [m] 

TemperatureGradientlnVicinityOfBoilinglsotherm[K/m] 

DiameterOfVolcanicCone[m] 

AngleOfVolcanicDikeMeasuredFromNorthClockwise[degrees] 

WidthOfVolcanicDike[m] 

LengthOfVolcanicDike[m]

Same as above except with ground acceleration 0.10g. 

Same as above except with ground acceleration 0.15g. 

Same as above except with ground acceleration 0.20g. 

Same as above except with ground acceleration 0.25g. 

Same as above except with ground acceleration 0.30g. 

Same as above except with ground acceleration 0.35g. 

Same as above except with ground acceleration 0.40g. 

Same as above except with ground acceleration 0.45g. 

Same as above except with ground acceleration 0.50g. 

Temperature gradient in the vicinity of the boiling isotherm. 

(Parameter specific to reflux3 model.) 

Cone diameter. 

Volcanic dike angle. 

Volcanic dike width. 

Volcanic dike length.

0O
DESCRIPTION OF ABBREVIATIONS USED FOR TPA VERSION 3.2 CODE INPUT 

PARAMETERS (cont'd) 

Short Name Full Name Description

VE-Power 

VE-Durat 

VEi/e-R# 

VEROI-Tn 

WindSpd 

WP-Def% 

WPFD-ThD 

WPRRG@10 

WPRRG@20

VolcanicEventPower[W] 

VolcanicEventDuration[s] 

RNtoDeterminelfExtrusiveOrlntrusiveVolcanicEvent 

TimeOfNextVolcanicEventinRegionOflnterestl[yr] 

WindSpeed[cm/s] 

DefectiveFractionOfWPs/cell 

ThresholdDisplacementforFaultDisruptionOfWP[m] 

WellPumpingRateAtReceptorGroup 1Okm[gal/day] 

WellPumpingRateAtReceptorGroup20km[gal/day]

YMR-TC ThermalConductivityofYMRock[W/(m-K)]

Volcanic event power. 

Volcanic event duration. 

Random number to determine volcanic event type. 

Time of next volcanic event. 

Wind speed. 

Fraction of total WPs in a subarea that fail at time t = 0. 

Threshold fault displacement for disruption. Data input order: 

number of fault displacement values to be provided followed by 

equiprobable displacement values. 

Well pumping rate for residential receptor group located less 

than 10 km from YM. 

Well-pumping rate for residential receptor group located less 

than 20 km from YM. 

Thermal conductivity of rock.
APPENDIX E
DETAILED RESULTS FROM DIFFERENTIAL ANALYSES 

The tables in this appendix present the results of the differential analysis. Tables E-1 and E-2 present the 

results for the basecase analysis for 10,000-yr and 50,000-yr Time Period of Regulatory Interest (TPI). 

Tables E-3 and E-4 present the results for the faulting scenario for 10,000-yr and 50,000-yr TPI. Table E-5 

presents the results for the volcanism scenario. The results for the 50,000-yr TPI are not expected to be 

different than the 10,000-yr results, because after the 10,000-yr TPI, when the groundwater dose dominates, 

the primary contributors to ground-surface dose have decreased (see Section 4.3.1). Therefore, only the table 

for the 10,000-yr TPI is shown. 

The tables are organized in the following manner. The first column lists an abbreviation of the parameter that 

was tested. Only those parameters that had a non-zero result in any of the seven runs are indluded on the 

table. The second column contains the arithmetic average of the sigma-weighted sensitivity coefficients of 

the seven runs. This value considers the uncertainty of the parameter as well as the magnitude of the dose 

for the given run in calculating the sensitivity of a parameter and is the result by which the parameters are 

sorted. The third column contains the arithmetic average of the scaled sensitivity coefficients, which show 

the absolute sensitivity that a parameter has on the results of the TPA code, without taldng the input range 

of the parameter into account. The fourth column shows the geometric average of the same value to weight 

more highly those parameters that show high sensitivity for all runs instead of just a high sensitivity for a 

couple of runs. The fifth column contains the highest value of the scaled sensitivity coefficients calculated 

in any of the runs. The remainder of the columns show the individual run results for both the sigma-weighted 

sensitivity coefficient and the scaled sensitivity coefficients.

E-1
Table E-1. Differential analysis results for the basecase for a time period of interest of 10,000 yr 

Arith. Mean 

Parameter Name- of Sigma 

10,000.-yr, Raked Weighted S - Arith. S - Geom. S -High R- R2- R3 - R4 - R5 - R6- R7

by Sigma Values Mean Mean Value Sigma Sigma- Simna Siona Sigma Sigma Sigma RI - S R2- S R3 - R4 - S R5 - S K6 -S R7- S 

Base Value Peak 

Total Effective Dose 

Equivalent (rem/vr) 3.85e-06 1,33f-07 1,44e-07 6.48e-06 4,0le-08 2.00e-06 4,02e-06 3.85e-06 1,33e-07 1,44e-07 6.48e-06 4,01%,08 2.00c-06 4.02e-06 

ARDSAVTc 1.138e-05 6.139e-01 4.766e-02 1.791e+00 l.lle-08 0.00e+00 1.86e-07 7.92e-05 2.31e-07 9.02e-09 0.00e+00 2.60e-03 7.5le-03 7.31e-01 1.76e+00 1.79e+00 5.00e-03 2.49e-03 

FOCTR-R 9.574e-06 9.796e-02 3.942e-02 2.753e-01 2.68e-08 7.02c-09 0.00e+00 5.77e-11 0.00e+00 6.70e-05 7.41e-l1 2.75e-01 1.95e-01 6.96e-03 2.62e-02 2.49e-03 4.50e-02 1.34e-01 

Fow* 3.822e-06 6.792e-01 4.682e-01 2.291e+00 2.09e-05 2.54e-07 4.54e-07 3.50e-06 7.90e-08 1.68e-07 1.44e-06 2.29e+00 4.66e-01 7.73e-OI 3.30c-01 4.81e-01 1.35e.01 2.79e-01 

ARDSAV_I 2.982e-06 2.137e+00 1.736e+00 4.264e+00 7.88e-06 7.80e-08 1.37e-07 3.85e-06 1.8le-08 8.31e-07 8.07e-06 2.82ei-00 9.54e-01 3.81e+00 8.60e-01 l.10e+O0 1.15e+00 4.26e+00 

SFWtI#3 2.618e-06 2.058e+00 5.144e-01 7.021e+00 6.78e-06 3.92e-08 5.63e-08 2.18e-06 0.00e+00 4.02e-07 8.86e-06 4.94e+00 7.06e-01 3.20e-01 8.06e-01 2.49e-03 6.05e-01 7.02e+OO 

WP-De%/o 2.167e-06 1.336e+00 1.212e+00 2.539e+00 1.05e-06 1.48e-07 4.57e-08 9.17e-06 3.29e-08 2.69e-06 2.03e-06 6.43e-01 1.38e+"0 8.96e-01 2.54e+00 1.87e+00 9.74e.01 1.04e+00 

ARDSAVSe 1.808e-06 5.714e-02 1.1lle-02 3.090e-01 1.l8e-05 0.00e+O0 O.00e+00 0.00-eO0 8.72e-07 0.00e+00 O.00e+00 6.75e-02 7.5le-03 6.96e-03 1.54e-03 3.09e-"1 5.00e-03 2.49e-03 

SbArWt% 1.681e-06 1.000e+00 1.000e+00 1.002e+00 1.27e-06 1.82e-06 1.32e-07 5.77e-06 5.23c-08 1.12e-06 1.61e-06 1.00e+00 9.99e-01 1.00e+00 1.000eO0 9.99e-01 1.00e+00 9.98e-01 

Fmult* 1.478e-06 6.823e-01 4.721e-01 2.290e+00 8.10e-06 2.lOe-08 3.20e-08 9.05e-07 1.82e-08 1.94e-07 1.07e-06 2.29e+00 4.81e-01 7.73e-01 3.33e-01 4.8le-01 1.35e-01 2.84e-01 

FOC-R 1.037e-06 4.578e-02 2.877e-02 9.347e-02 2.81e-08 1.84e-08 2.18e-13 1,08e-1O 2.28e-I0 7.21e-06 O.00e+O0 9.35L-02 2.25e-02 2.09e-02 6.64c-02 8.97e-02 2.50e-02 2.49e-03 

WPRRG@20 8.463e-07 9.956e-01 9.956e-01 1.010e+00 7.22e-07 4.57e-08 4.28e-08 2.74e-06 8.05c-09 7.29e-07 1.64e-06 9.89e-01 9.91e-01 l.Ole+O0 9.89e-01 9.89e-01 I.Ole+O0 9.91c-01 

SfWtI4 6.774e-07 3.365e-01 1.332e-01 1.468e+00 2.89e-07 5.28e-09 2.67e-08 4.20e-06 1.65e-08 5.48e-08 1.45e.07 3.37e-02 1.50e-02 2.51e-01 1.47e+00 3.84e-01 9.50e-02 1.10e-01 

APrsSAV 6.615e-07 2.522e+00 2.159e+00 4.780e+00 9.72e-07 2.25e-08 7.91e-08 1.37e-06 1.45e-08 2.08e-07 1.97e-06 2.OOe+OO 1.37e+00 4.78e+00 1.52e+00 3.28e+00 8.75e-01 3.83e+00 

AAMAI@S 4.890e-0 7 8.722e-01 4.354e-O1 2.446e+00 2.71e-06 6.07e-08 7.76e-08 3.18e-07 1.68e-08 7.36e-08 1.65e-07 2.45e+00 1.13e+00 1.43e+00 9.41e-02 S.12e-01 9.00e-02 1.10e-01 

SFWt%5 4.449e-07 5.342e-01 2.791e-01 1.672e+00 8.38e-08 4.86e-08 1.50e-08 1.07e-06 2.23e-07 2.68e-07 1.41e-06 6.75e-02 1.03e+00 2.37e-01 4.94e-02 l.67e+O0 2.00e-01 4.86e-01 

MAPM@GM 4.374e-07 l.116e+00 7.458e-01 3.323eQO0 1.79e-06 6.59e-09 2.29e-08 5.51e-07 6.07e-09 3.15e-08 6.52e-07 3.32e+00 4.13e-01 1.38e+00 4.89e-01 8.17e-01 1.35e-01 1.26e+00 

I'.) InitRSFP 4.032e-07 7.456e-01 7.433e-01 8.660e-01 5.68e-07 2.22e-08 2.20e-08 1.25e-06 7.15e-09 3.15e-07 6.40e-07 7.24e-01 7.44e-01 6.82e-01 8.66e-01 7.92e-01 7.00e-01 7.10e-01 

SFWtII 3.661e-07 2.806e-01 7.829e-02 1.119e+00 2.20e-06 7.06e-08 1.53e-08 1.32e-07 0.OOe+00 1.03e-0 7 4.13e-08 5.14e-01 1.12e+00 1.95e-01 5.40e-02 2.49c-03 6.00e-02 1.99e-02 

TempGrBI 3.256e-07 2.104e-01 1.041e-O1 4.80le-01 1.64e-06 1.04e-08 1.13e-09 1.30e-07 6.62e-09 3.69e-07 1.26e-07 2.91e-01 2.10e-01 6.96e-03 3.09e-02 4.Ole-O1 4.80e-01 5.23e-02 

SFWtI6 3.241e-07 1.500e-01 6.516e-02 3.551e-01 1.14e-07 1.29e-08 2.63e-09 9.99e.07 0.00e+O0 5.86e-07 5.53e-07 8.57e-02 1.50e-02 6.26e-02 2.58e-01 2.49e-03 3.55e-01 2.71e-01 

MPrm_CHv 2.681e-07 1.063e-01 1.048e-02 6.957c-01 1.83c-06 5.53e-09 O.OOe+00 0.00e400 0.00e+00 4.59e-08 0.OOe+O0 6.96e-01 1.50e-02 6.96e-03 1.54e-03 2.49e-03 2.00e-02 2.49c-03 

SFWtI7 2.057e-07 2.087e-01 6.076e-02 6.154e-01 9.49e-07 1.45e-09 6.36e-08 I.l1e-07 0.00e+00 1.30e-07 1.85e-07 6.15e-01 3.76e-02 5.71e-01 7.72e-03 2.49e-03 8.50e-02 1.42e-01 

YMR-TC 1.652e-07 1.285e+00 1.252e+00 1.692e+00 1.92e-07 1.20e-08 9.48e-09 4.89e-07 4.09e-09 1.86e-07 2.64e-07 8.39e-01 1.40e+O0 1.06e+00 l.32e+00 1.69e+00 1.61e+O0 1.07e+O0 

SFWtI2 1.537e-07 9.565e-02 3.249e-02 2.854e-01 0.O0e+00 5.29e-08 4.26e-08 5.31e-08 0.00e+00 2.60-08 9.O0e-07 2.60e-03 2.85e-01 2.09e-01 2.31e-02 2.49e-03 4.00e-02 1.07e-01 

FPrsSTF 1.359e-07 3.274e-02 3.021e-02 5.725e-02 2.31e-07 3.73e-09 6.83e-09 3.15e-07 2.13e-09 2.13e-08 3.71c-07 5.19e-02 2.25e-02 2.78e-02 2.47e-02 1.99e-02 2.50c-02 5.73e-02 

FOCTR 6.167e-08 1.745e-01 5.696e-02 5.456c-01 1.18e-08 1.65e-08 4.55e-09 1.67e-07 7.59e-09 1.99e-07 2.54e-08 7.79e-03 3.46e-01 1.39e-02 5.09e-02 5.46e-01 2.50e-01 7.47e-03 

MATI@GM 2.717e-08 1.245e-01 4.904e-02 5.580e-01 8.13e-08 1.47e-09 3.08e-I0 4.66e-08 3.86e-09 0.00e+O0 5.67e-08 1.14e-01 6.O0e-02 1.39e-02 2.78e-02 5.58e-01 5.00e-03 9.21e-02 

RFPm UCF 3,686c-09 4.094e-03 3.504e-03 7.507e-03 O.00e+O0 2,58e-08 0 00e+00 0.00e+O0 0.00e+00 0.0Oe+00 0 000O00 2.60e-03 7 51e"03 6.96e-03 1.54e-03 2,49e-03 5 OOe-03 2.49e-03
Table E-2. Differential analysis results for the basecase for a time period of interest of 50,000 yr

Arith. 

Mean of 

Parameter Name- Sigma S 

50,000-yr, Ranked Weighted S - Arith. Geometric S - High RI- R2 - R3- R4 - R5 - R6 - R7 

by Sigma Values Mean Mean Value Sigma Siema Si.w Sigma Sigma Sigma Sigma RI - S R2 - S R3 - S R4 - S R5 - S R6 - S R7 - S 

Base Value Peak 

Total Effective Dose 

Equivalent (rem/yr) 5.60e-04 1.90e-05 9,60e-05 4.40e-04 1.50e-04 5.40c-04 4.70e-04 5,60e-04 1.90e-05 9.60e-05 4.40e-04 1.50e-04 5.40e-04 4.70e-04 

ARDSAVNn 2.372e-03 1.205e+00 8.297e-03 8.4168+00 1.66e-02 0.00e+00 0.008+00 0.00e+00 0.00e+00 0.008+00 0.00e+00 8.42e+00 5.19e-03 1.04e-03 2.29e-03 6.53e-03 1.86e-03 2.14e-03

Fow* 

OO-CoMC 

AA_2_1 

SbArWt% 

ARDSAVTc 

Fmult* 

WPRRG@20 

APrsSAV 

ARDSAV I 

MAPM@GM 

AAMAI@S 

SFWtC6 

SFWt0

/oC3 

SFWt0

/oC2 

SFWtI/oC4 

SFWIC5 

SFWtO/oC1 

initRSFP 

ARDSAVSe 

MKDCHvNp 

SFWt0

/0C7 

MATI@GM 

YMR-TC 

Solbl-Np 

WP-Def/o 

FPrsSTF 

SFWtI/ol4 

ARDSAVNi 

SFWtI7 

SFWtI2 

SFWtI3 

SFWI%1o3 

TempGrBI 

SFWtI/o16 

SFWtI/ol5 

MPrmCHv 

MKDCHvSe 

FOCTR 

CritRHAC 

FOC-R 

FOCTR~-R

2.131e-04 

2.105e-04 

1.920e-04 

1.914e-04 

1.762e-04 

8,428e-05 

8.060e-05 

7.848e-05 

6.033e-05 

4.974e-05 

4.432e-05 

4.162e-05 

4,086e-05 

3.250e-05 

3.239e-05 

3.144e-05 

3.014e-05 

3.006e-05 

2.994e-05 

2.258e-05 

1.881e-05 

1.438e-05 

1.392e-05 

1.015e-05 

8.342e-06 

2.503e-06 

2.378e-06 

1. 150e-06 

1.023e-06 

7.838e-07 

7.633e-07 

6.962e-07 

6.230e-07 

5.317e-07 

4.526e-07 

3.056e-07 

1.783e-07 

1,686e-07 

1.548e-07 

1.115e-08 

3.63 le-09

6.92e-05 

9.12e-08 

2.38e-06 

8.79e-05 

9.19e-05 

4.91e-06 

2.86e-05 

6.85e-06 

4.26e-06 

6.0le-06 

2.88e-06 

8.79e-06 

1.27e-05 

1.98e-05 

4.47e-06 

7,04e-06 

1.56e-05 

2.00e-05 

1.92e-06 

0.00e+00

4.5le-04 

1.81e-04 

6.25e-05 

3.87e-04 

8.21e-04 

1.15e-04 

1. 84e-04 

2.23e-06 

8.37e-05 

1.15e-04 

1. 14e-04 

8.09e-05 

1. 15e-04 

1.37e-04 

5.16e-05 

7.72e-05 

8.54e-05 

3.34e-05 

0.00e+00 

0.00e+00

4.145e-01 

1.590e+00 

1.268e+00 

1.000e+00 

2.593e-01 

4.160e-01 

9.949e-01 

1.392e+00 

3.891e-01 

2.108e+00 

3.256e-01 

2.129e-01 

2.989e-01 

2.696e-01 

1.714e-01 

1.410e-01 

2.782e-01 

5.978e-01 

3.938e-03 

4.043e-02 

4.68le-02 

2.448e-01 

7.965e-01 

2.376e-02 

3.750e-02 

8.337e-03 

5.130e-03 

2.978e-03 

6.826e-03 

6.332e-03 

7.893e-03 

5.703e-03 

1.789e-02 

4.766e-03 

4.31 1e-03 

7.332e-03 

2.978e-03 

6.439e-03 

1.393e-01 

3.127e-03 

2.979e-03

3.11e-04 

1.43e-04 

7.93e-05 

2.Ole-04 

1.80e-04 

7.06e-05 

3.06e-05 

7.95e-06 

8.66e-06 

3.74e-05 

2.73e-05 

7.43e-06 

1.6ie-05 

2.88e-05 

6.57e-06 

1. 18e-05 

1.57e-05 

1.89e-05 

7.03e-05 

0.00e+00 

3.66e-06 

9.13e-06 

1.72e-05

2.794e-01 

7.834e-02 

2.346e-01 

1.000e+00 

1.349e-01 

2.785e-01 

9.949e-01 

4.233e-01 

2.02le-01 

9.541e-01 

2.190e-01 

1.365e-01 

1.644e-01 

1.330e-01 

1.478e-01 

1.071e-01 

1.902e-01 

5.170e-01 

3.538e-03 

5.060e-03 

3.565e-02 

1.404e-01 

6.034e-01 

4.655e-03 

7.792e-03 

6.352e-03 

3.833e-03 

2.480e-03 

3.687e-03 

5.027e-03 

6.537e-03 

4.41le-03 

4.422e-03 

4,034e-03 

3.448e-03 

4.140e-03 

2.480e-03 

3.617e-03 

6.050e-03 

2,738e-03 

2.481e-03

7.334e-01 

8.939e+00 

3.513e+00 

1.006e+00 

5.392e-01 

7.464e-01 

1.010e+00 

6.021e+00 

1.389e+00 

8.692e+00 

7.570e-01 

6.713e-01 

4.619e-01 

4.440e-01 

3.160e-01 

2,693e-01 

5.453e-01 

1.012e+00 

6,53le-03 

2.639e-01 

1.029e-01 

7.635e-01 

1.861e+00 

1.472e-01 

2.33le-01 

1.863e-02 

1.256e-02 

6.529e-03 

2.873e-02 

1.304e-02 

1.306e-02 

1.257e-02 

1,062e-01 

8.977e-03 

8.977e-03 

2.076e-02 

6.528e-03 

2.609e-02 

9.558e-01 

6.529e-03 

6.529e-03

1.66e-04 5.53e-05 

0.00e+00 .00e+00 

5.75e-04 1.53e-07 

1.83e-04 2.63e-04 

9.80e-05 6.14e-08 

6.52e-05 4.47e-06 

1.04e-04 6.6ie-06 

4.24e-04 6.14e-08 

7.25e-06 1.66e-06 

4.83e-05 2.01e-05 

2.93e-05 2.96e-06 

7.18e-05 1.65e-06 

1.24e-04 3.67e-06 

3.15e-05 5.42e-06 

1.22e-04 1.62e-06 

9.99e-05 1.39e-06 

2.24e-05 3.48e-06 

9.42e-05 9.89e-07 

1.36e-04 9.42e-07 

1.58e-04 0.00e+00 

7.1le-05 7.45e-07 

1.46e-05 6.23e-07 

5.58e-05 3.20e-07 

7.1 le-05 O,00e+00 

5.51e-05 6.40e-08 

6.94e-06 1.24e-07 

1.56e-05 0.O0e+00 

0.OOe+00 0.OOe+00 

6.41e-06 0.OOe+O0 

0.OOe+00 0.OOe+O0 

0.OOe+00 0.OOe+O0 

2.49e-06 0.OOe+O0 

1.46e-06 0.OOe+00 

1.73e-06 0.OOe+00 

1,61e-06 0.OOe+00 

0.OOe+00 1.1 le-06 

0.OOe+00 0.OOe+00 

3.95e-07 0.OOe+00 

0.OOe+00 0.OOe+O0 

7.81e-08 0.OOe+00 

253e-og O.OOe+O0

1.25e-06 4.38e-04 

1.14e-03 1.13e-05 

0.OOe+00 6.25e-04 

3.Ole-05 1.87e-04 

2. lOe-05 2.1 le-05 

1.36e-06 3.28e-04 

1.96e-05 1.90e-04 

5.39e-06 1.03e-04 

1.13e-05 3.05e-04 

3.85e-07 1.21e-04 

7.36e-07 1.33e-04 

5.53e-06 1.15e-04 

7.26e-06 7.40e-06 

5.40e-06 0.00e+00 

6.87e-07 4.Ole-05 

5.03e-06 1.78e-05 

5.30e-06 6.3 ie-05 

1.22e-05 3.08e-05 

4.17e-07 0.00e+00 

0.00e+00 0.00e+00 

2.77e-06 3.22e-05 

9.83e-08 5.46e-05 

1.61e-06 1.lOe-05 

0.00e+O 0.00e+00 

0.00e+00 9.72e-07 

4.27e-07 9.69e-06 

0.00e+00 9.88e-07 

0.008+00 0.008+00 

0.00e+00 3.24e-07 

2.27e-07 2. lOe-06 

1.72e-07 2.06e-06 

6.64e-08 1.26e-06 

2.19e-06 5.98e-07 

8.26e-08 1.52e-06 

6.70e-08 1.45e-06 

1.03e-06 0.008+00 

0.008+00 0.00e+00 

5.58e-07 0.00e+00 

1.08e-06 0.00e+00 

0.00e+00 0.00e+00 

0.00e+00 1.37e-10

1.26e-01 

1.80e-03 

3.15e+00 

1.00e+00 

1.58e-01 

1.27e-01 

9.89e-01 

6.02e+00 

1.80e-02 

6.19e-01 

1.83e-01 

5.57e-02 

2.41e-01 

1.47e-01 

3.16e-01 

2.69e-01 

1.97e-02 

8.31e-01 

5.39e-03 

2.64e-01 

1.62e-02 

1.42e-01 

1.68e+00 

1.47e-01 

2.33e-01 

1.08e-02 

1.26e-02 

1.80e-03 

2.87e-02 

1.80e-03 

1.80e-03 

1.26e-02 

1.80e-03 

8.98e-03 

8.98e-03 

1.80e-03 

1.80e-03 

1.80e-03 

1,80e-03 

1.80e-03 

1.80e-03

7.Ole-01 

5.19e-03 

4.15e-02 

9.96e-01 

5.19e-03 

7.06e-01 

9.91e-01 

2.59e-02 

1.40e-01 

8.69e+00 

3.79e-01 

2.75e-01 

4.62e-01 

4.41e-01 

1.25e-01 

4.15e-02 

4.15e-01 

2.28e-01 

5.19e-03 

5.19e-03 

6.23e-02 

1.76e-01 

2.60e-01 

5.19e-03 

4.15e-03 

5.19e-03 

5.19e-03 

5.19e-03 

5.19e-03 

5.19e-03 

5.19e-03 

5.19e-03 

5.19e-03 

5.19e-03 

5.19e-03 

2.08e-02 

5.19e-03 

5.19e-03 

5.19e-03 

5.19e-03 

5.19e-03

1.76e-01 

3.12e-03 

4.89e-02 

9.99e-01 

5.39e-01 

1.77e-01 

1.0le+00 

6.19e-0l 

1.77e-01 

5.41e-01 

7.91e-02 

9.58e-02 

3.53e-01 

3.62e-01 

1.5le-01 

5.73e-02 

2.60e-01 

9.27e-01 

4.16e-03 

1.04e-03 

7,29e-03 

9.79e-02 

5.26e-01 

1.04e-03 

8.12e-03 

2.08e-03 

1.04e-03 

1.04e-03 

1.04e-03 

4.16e-03 

1.15e-02 

1.04e-03 

1.04e-03 

2.08e-03 

1.04e-03 

1.04e-03 

1.04e-03 

1.04e-03 

1.04e-03 

2.08e-03 

1.04e-03

6.33e-01 6.26e-01 

6.28e-01 

9.99e-01 

2.70e-01 

6.30e-01 

9.90e-01 

3.67e-02 

2.77e-01 

1.51e4+00 

5.02e-01 

2.50e-01 

4.40e-01 

4.10e-O1 

1.67e-01 

1.53e-01 

5.45e-01 

3,44e-01 

2.29e-03 

2.29e-03 

4.58e-02 

1.79e-01 

3.4le-01 

2.29e-03 

7.10e-03 

2.29e-03 

2.29e-03 

2.29e-03 

2.29e-03 

1. 15e-02 

1. 15e-02 

2.29e-03 

2.29e-03 

2.29e-03 

2.29e-03 

2.29e-03 

2.29e-03 

2.29e-03 

2.29e-03 

2.29e-03 

2.29e.03

2.13e-06 1.91e-05 

1.45e-06 2.02e-05 

3.15e-06 8.52e-06 

0.008e+O 0.00e+00 

2.77e-07 1.73e-06 

3.42e-07 0.00e+00 

7.42e-08 0.008+00 

8.05e-06 0.00e+00 

7.75e-08 0.00e+00 

5.68e-07 1.77e-06 

6.02e-07 1.88e-06 

1.22e-07 4.18e-07 

1.13e-07 0.00e+00 

5.84e-08 0.00e+00 

4.41e-08 0.008+00 

0.00e+00 0.00e+00 

0.008+00 0.00e+00 

2.27e-07 0.00e+00 

0.00e+00 0.00e+00 

1.45e-11 0.008+00 

O.Oe+O000.00e+O00

0,00e+00 

2.62e-07 

0.00e+00 

0,00e+00 

0.00e+00 

3.48e-07 

8.26e-07 

6.24e-07 

5.16e-07 

0.00e+00 

3.29e-07 

0.00e+00 

0.00e+00 

1.25e-06 

0.00e+00 

0.00e+00 

0.00e+00 

0.00e+00

4.96e-01 

1.48e+00 

1.49e+00 

1.0le+00 

3.66e-01 

4.90e-01 

9.86e-01 

4.70e-01 

1.37e-01 

1.32e+00 

3.46e-01 

3.26e-02 

2.74e-01 

4.44e-01 

1.3le-O1 

1.83e-01 

3.20e-01 

5.49e-01 

6.53e-03 

6.53e-03 

3.92e-02 

3.46e-01 

1.86e+00 

6.53e-03 

3.92e-03 

6.53e-03 

6.53e-03 

6.53e-03 

6.53e-03 

6.53e-03 

1.31e-02 

6.53e-03 

6.53e-03 

6.53e-03 

6.53e-03 

6.53e-03 

6.53e-03 

6.53e-03 

6.53e-03 

6.53e-03 

6.53e-03

3.73e-02 7.33e-01 8.94e+00 7.51e-02 

1.86e-03 3.51e+00 

9.99e-01 1.00e+00 

4.34e-01 4.29e-02 

3.54e-02 7.46e-01 

1.01e+00 9.89e-01 

8,46e-01 1.73e+00 

5.85e-01 1.39e+00 

6.15e-02 2.Oie+00 

3,35e-02 7.57e-01 

1.10e-01 6.71e-01 

3.20e-01 2.14e-03 

8.01e-02 2.14e-03 

4.47e-02 2.66e-01 

2.46e-01 3.65e-02 

7.83e-02 3.09e-01 

1.Ole+00 2.94e-01 

1.86e-03 2.14e-03 

1.86e-03 2.14e-03 

5.40e-02 1.03e-01 

9.32e-03 7.63e-01 

5.20e-01 3.84e-01 

1.86e-03 2.14e-03 

1.86e-03 4.29e-03 

1.86e-02 1:29e-02 

1.86e-03 6.43e-03 

1.86e-03 2.14e-03 

1,86e-03 2.14e-03 

1.30e-02 2.14e-03 

3.73e-03 8.58e-03 

3.73e-03 8.58e-03 

1.06e-01 2.14e-03 

1.86e-03 6.43e-03 

L 86e-03 4.29e-03 

1.68e-02 2.14e-03 

1.86e-03 2.14e-03 

2.61e-02 2.14e-03 

9.56e-01 2.14e-03 

1.86e-03 2.14e-03 

1.86e-03 2.14e-03

FOCTR-R 2 53e-08 0 00e+00 0.00e+00 0.00000 2 29e-03
Table E-3. Differential analysis results for the faulting scenario for a time period of interest of 10,000 yr 

10,000-yr, Faulting, Random4 Values 

Increased by 1% dD/dx Sigma X bar Mean Dose dD/dx*sigma S 

SFWT/oFO 5.09e-04 2.89e-01 2.66e-01 4.34e-04 0.0001471003 0.3124591 

FEROI-Tn -1.16e-07 2.86e+03 7.140+03 4.34e-04 0.0003312564 1.9061315 

WPFD-ThD 0.00e+00 1.12e-01 1.00e-01 4.34e-04 0 0 

FEROI-X 0.00e+00 3.47e+03 5.48e+05 4.34e-04 0 0 

FEROI-Y 0.00e+00 8.20e+03 4.08e+06 4.34e-04 0 0 

FO-Rn#Sd 0.00e+00 2.89e-01 6.56e-01 4.34e-04 0 0 

NWFZnW 0.00e+00 1.74e+01 2.50e+01 4.34e-04 0 0 

NEFZnW -6.24e-07 2.32e+01 1.46e+01 4.34e-04 0.0000144944 0.0209178 

NWLCDAmt 0.00e+00 1.00e-01 2.03e-01 4.34e-04 0 0 

NELCDAmt 0.00e+00 1.00e-01 1.64e-01 4.34e-04 0 0
Table E-4. Differential analysis results for the faulting scenario for a time period of interest of 50,000 yr 

50,000-yr, Faulting, Random4 Values 

Increased by 1% dD/dx Sigma X bar Mean Dose dD/dx*sigma S 

NELCDAmt 0.00e+00 1.00e-01 1.64e-01 4.34e-04 0 0 

NEFZnW -6.87e-08 2.32e+01 1.46e+01 4.34e-04 0.0000015956 0.0023027 

NWLCDAmt 0.00e+00 1.00oe-01 2.03e-01 4.34e-04 0 0 

NWFZnW 0.00e+00 1.74e+01 2.50e+01 4.34e-04 0 0 

FO-Rn#Sd 0.00e+00 2.89e-01 6.56e-01 4.34e-04 0 0 

SFWtFO 1.50e-05 2.89e-01 2.66e-01 4.34e-04 0.0000043366 0.0092115 

WPFD-ThD 0.00e+00 1.12e-01 1.00e-01 4.34e-04 0 0 

FEROI-Tn 0.00e+00 2.86e+03 7.14e+03 4.34e-04 0 0 

FEROI-X 0.00e+00 3.47e+03 5.48e+05 4.34e-04 0 0 

FEROI-Y 0.00e+00 8.20e+03 4.08e+06 4.34e-04 0 0

ltt
Table E-5. Differential analysis results for the igneous activities scenario for a time period of interest of 10,000 yr 

Arith. Mean 

of Sigma 

Weighted S - Arith. S - Geom. S - High RI - R2- R3 - R4 - R5 - R6- R7 

Parameter Values Mean Mean Value Sioma Sigma Sinma Sitma Sigma Sigma Sima RI - S R2 - S R3 - S R4 -S R5-S R6 -S R7 - S 

Base Value Peak Total 

Effective Dose 2.35c-01 1.51e+00 1,89e+00 93"41O 5,90e-02 2,28C+00 2,12e+00 2.35e-o01 I.Se+00 1,89e+00 934c-01 5.90o-02 2.28e+00 2.12e+00 E e uv nt/rA w)* 

VE-Power 3.672e+00 8.051e-01 7.434e-01 1.328e+00 7.75e-02 1.55e+01 2.41e+00 1.23e+00 5.12e-02 2.30e000 4.15e+00 7.88e-01 3.05e-01 9.16e-01 9.13e-01 7.94e-01 5.92e-01 1.33e+00 

ABMLFVDC 2.835e+00 7.526e-01 5.856e-01 9.695e-01 6.02e-02 1.39e+01 2.22e+00 1.17e+00 7.37e-02 9.04e-01 1.53e+00 8.23e-01 8.36e-01 9.53e-01 9.70e-o01 8.99e-01 7.32e-01 5,65c-02 

VE-Durat 2.014e•OO 6.285e-01 2.945e-01 9.695e-01 5.70e-01 0.00e+00 7.50e+00 4.70e+00 1.45e-02 1.31e+00 8.16e-03 8.14e-01 6.63e-03 9.43e-01 9.70e-01 8.95e-01 7.10e-01 6.12e-02 

VEROI-Tn 1.300e+00 5.050e-01 4.627e-O0 8.700e-01 4.06o-02 2.29e+00 6.66e-O0 2.10e-01 1.32e-02 4.31e-01 5.45e+00 5.03e-O0 8.18e-01 3.32e-01 3.24e-01 3.24e-o01 3.64e-01 8.70e-01 

VC-Dia 7.689e-01 2.026e+00 2.026e+00 2.071e+00 1.02e-01 1.34e-O 1 .14e+00 8.29e-01 4.18e-02 9.63e-01 9.64e-01 2.00e+00 2.02e+00 2.07e+00 1.99e+00 2.04e+00 2.03e+00 2.03e+00 

WindSpd 6.267e-01 4.548e-01 2.324e-01 1.930e+00 3.11e-01 1.82e+00 3.90e-01 2.90e-01 6.95e-02 1.14e+00 3.66e-01 3.11e-01 1.93e+00 1.06e-01 1.17e-01 5.94e-02 4.9le-01 1.69e-O

AshMnPLD 2.306e-01 1.546e-01 1.137e-.01 4.841e-01 2.26e-02 5.83e-01 1.06e-01 4.59e-02 9.68e-03 3.02e-01 5.45e-01 1.15e-01 4.84e-01 6.89e-02 3.32e-02 9.84e-02 1.23e-01 1.60e-01 

VD-Angle 0.000e+00 4.007e-03 3.432e-03 6.632e-03 0.00e+00 0.00e+00 0.00e+00 0.00e+-OO 0.00e+00 0.00e+00 0.00e+00 4.26e-03 6.63e-03 5.30e-03 1.07o-03 1.70e-03 4.38e-03 4.71e-03 

VD-Lengt 0.000e+00 4.007e-03 3.432e-03 6.632e-03 0.00+000 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 4.26e-03 6.63e-03 5.30e-03 1.07e-03 1.70e-03 4.38e-03 4.71e-03 

SFWTVO 0.000e+00 4.007e-03 3.432e-03 6.632e-03 0.00e+00 0.00e+00 0.00e+00 0.00e+-OO 0.00e+00 0.00e+00 0.00e+00 4.26e-03 6.63e-03 5.30e-03 1.07e-03 1.70e-03 4.38e-03 4.7le-03 

VD-Width 0,000q+00 4.007o-03 3.432e-03 6,632e-03 0,00e+-00 0.00e+000 0.00e00 0.00•e+00 o.00e+00 0,ooe+00 0.00e+o0 4.26e-03 6,63c-03 5.30e-03 1,07e-03 1.70e-03 4,38e-03 4.71e-03 

*Conditional results not weighted by the scenario probability.

m &I
NRC FORM 335 U.S. NUCLEAR REGULATORY COMMISSION 1. REPORT NUMBER 

(2-89) (Assigned by NRC, Add Vol., Supp., Rev., 

NRCM 1102B and Addendum Numbers, if any.) 

3201, 3202 BIBLIOGRAPHIC DATA SHEET 

(See instructions on the reverse) 

2. TITLE AND SUBTITLE NUREG-1746 

System-Level Repository Sensitivity Analyses, Using TPA Version 3.2 Code 3. DATE REPORT PUBLUSHED 

MONTH YEAR 

August 2001 

4. FIN OR GRANT NUMBER 

5. AUTHOR(S) 6. TYPE OF REPORT 

R.B. Codell, M.R. Byrne, T.J. McCartin * Technical 

S. Mohanty, J. Weldy, M. Jarzemba, G.W. Wittmeyer** 

Y. Lu **- 7. PERIOD COVERED (Inclusive Dates) 

R.W. Rice 

8. PERFORMING ORGANIZATION - NAME AND ADDRESS (If NRC, provide Division, Office or Region, U.S. Nuclear Regulatory Commission, and mailing address; if contractor, 

provide name and mailing address) 

* Office of Nuclear Material Safety and Safeguards, U.S. Nuclear Regulatory Commission, Washington, DC 20555-0001 

Center for Nuclear Waste Regulatory Analyses, 6220 Culebra Road, San Antonio, Texas 78238-5166 

Office of Nuclear Waste Safety, Swedish Nuclear Power Inspectorate, S-106 58 Stockholm, Sweden 

Independent Consultant, 307 Quincy, El Paso, Texas 79922

9. SPONSORING ORGANIZATION - NAME AND ADDRESS (If NRC, type Same as above;" if contractor, provide NRC Division, Office or Region, U.S. Nuclear Regulatory Commission, 

and mailing address.)

Division of Waste Management 

Office of Nuclear Material Safety and Safeguards 

U.S. Nuclear Regulatory Commission 

Washington, DC 20555-0001

10. SUPPLEMENTARY NOTES

11. ABSTRACT (200 words or less) 

The total-system performance assessment (TPA) computer code was developed to assist the U.S. Nuclear Regulatory 

Commission (NRC) staff in evaluating the safety case for the proposed geologic repository at Yucca Mountain, Nevada. This report 

primarily presents: (i) the system- and component-level (intermediate) results using the U.S. Department of Energy (DOE) Viability 

Assessment data in TPA computer code Versions 3.2 and 3.2.3 to demonstrate trends and variabilities in outputs; 

(ii) the results of system-level sensitivity and uncertainty analyses using a variety of analysis techniques to determine the parameters 

that have the most influence on repository performance; and (iii) the relative importance of the integrated subissues in reviewing 

the DOE total-system performance assessment. An influential parameter is one that either drives uncertainty in performance, or 

one to which performance is sensitive. Results of system-level analyses are based on peak dose and peak expected dose to a 

receptor group. The influential parameters were compared to the current integrated subissues, which are used by NRC to focus 

work on items important to repository performance. In spite of simplifying assumptions, this study helped focus staff attention on 

phenomena most likely to be important relative to repository performance and point out deficiencies in the current state of 

knowledge.

12. KEY WORDS/DESCRIPTORS (List words or phrases that will assist researchers in locating the report.) 13. AVAILABILITY STATEMENT 

Computer code Waste Package unlimited 

Disruptive event Yucca Mountain, Nevada 14. SECURITY CLASSIFICATION 

Dose (This Page) 

Geologic repository unclassified 

Groundwater (This Report) 

High-level radioactive waste unclassified 

Performance assessment 

Probabilistic risk assessment 15. NUMBER OF PAGES 

Receptor group 

Scenario 16. PRICE 

Source term

NRC FORM 335 (2-89)
Federal Recycling Program
ISBN 0-16-050907-6 

90000 

9 780160 509070- ----------
UNITED STATES 

NUCLEAR REGULATORY COMMISSION 

WASHINGTON, DC 20555-0001 

OFFICIAL BUSINESS 

PENALTY FOR PRIVATE USE, $300