CONTENTS
CONTENTS
NOTATION xvii
ABSTRACT.............................................................................................................................. 1
1 INTRODUCTION ............................................................................................................. 1
2 HYDROGEOLOGICAL PARAMETERS 13
2.1 Soil Density 13
2.1.1 Definition 13
2.1.1.1 Soil Particle Density 14
2.1.1.2 Bulk (Dry) Density 15
2.1.1.3 Total (Wet) Density 16
2.1.2 Measurement Methodology 16
2.1.2.1 Soil Particle Density Measurement 18
2.1.2.2 Dry Density Measurement 20
2.1.3 Data Input Requirements 21
2.2 Total Porosity 22
2.2.1 Definition 22
2.2.2 Measurement Methodology 23
2.2.3 Data Input Requirements 25
2.3 Effective Porosity 25
2.3.1 Definition 25
2.3.2 Measurement Methodology 26
2.3.3 Data Input Requirements 27
2.4 Hydraulic Conductivity 28
2.4.1 Definition 28
2.4.2 Measurement Methodology 33
2.4.2.1 Laboratory Methods 40
2.4.2.2 Constant-Head Method 41
2.4.2.3 Falling-Head Method 41
2.4.2.4 Field Methods 42
2.4.3 Data Input Requirements 44
2.5 Soil-Specific Exponential b Parameter 46
2.5.1 Definition 46
2.5.2 Measurement Methodology 48
2.5.3 Data Input Requirements 48
2.6 Erosion Rate 49
2.6.1 Definition 49
2.6.2 Measurement Methodology 49
2.6.3 Data Input Requirements 50
CONTENTS (CONT.)
2.7 Hydraulic Gradient 52
2.7.1 Definition 52
2.7.2 Measurement Methodology 53
2.7.3 Data Input Requirements 53
2.8 Length of Contaminated Zone Parallel to the Aquifer Flow 54
2.8.1 Definition 54
2.8.2 Measurement Methodology 54
2.8.3 Data Input Requirements 55
2.9 Watershed Area for Nearby Stream or Pond 55
2.9.1 Definition 55
2.9.2 Measurement Methodology 56
2.9.3 Data Input Requirements 56
2.10 Water Table Drop Rate 56
2.10.1 Definition 56
2.10.2 Measurement Methodology 57
2.10.3 Data Input Requirements 57
2.11 WellPump Intake Depth 57
2.11.1 Definition 57
2.11.2 Data Input Requirements 57
2.12 Thickness of Uncontaminated Unsaturated Zone 58
2.12.1 Definition 58
2.12.2 Data Input Requirements 58
2.13 Distribution Coefficients 59
2.13.1 Definition 59
2.13.2 Measurement Methodology 60
2.13.2.1 Experimental Methods 60
2.13.2.2 Empirical Determination of the Distribution Coefficient 63
2.13.3 Summary of Literature Review 63
2.13.4 Data Input Requirements 64
2.14 Xxxxx Rate 64
2.14.1 Definition 64
2.14.2 Measurement Methodology 82
2.14.3 Data Input Requirements 84
2.15 Volumetric Water Content 85
2.15.1 Definition 85
2.15.2 Measurement Methodology 86
2.15.3 Data Input Requirements 89
2.16 Field Capacity 90
2.16.1 Definition 90
2.16.2 Measurement Methodology 90
2.16.3 Data Input Requirements 91
CONTENTS (CONT.)
3 METEOROLOGICAL PARAMETERS 92
3.1 Precipitation Rate 93
3.1.1 Definition 93
3.1.2 Measurement Methodology 95
3.1.3 Data Input Requirements 98
3.2 Runoff Coefficient 99
3.2.1 Definition 99
3.2.2 Estimation Methodology 100
3.2.3 Data Input Requirements 100
3.3 Evapotranspiration Coefficient 102
3.3.1 Definition 102
3.3.2 Measurement Methodology 104
3.3.3 Data Input Requirements 105
3.4 Irrigation Rate 106
3.4.1 Definition 106
3.4.2 Measurement Methodology 107
3.4.3 Data Input Requirements 108
3.5 Average Annual Wind Speed 109
3.5.1 Definition 109
3.5.2 Data Input Requirements 109
3.6 Mass Loading for Inhalation 111
3.6.1 Definition 111
3.6.2 Summary of Literature Review 111
3.6.3 Data Input Requirements 112
4 RADON EMANATION PARAMETERS 113
4.1 Effective Radon Diffusion Coefficient 113
4.1.1 Definition 113
4.1.2 Measurement Methodology 115
4.1.2.1 Laboratory Methods 115
4.1.2.2 Field Methods 117
4.1.3 Data Input Requirements 118
4.2 Radon Emanation Coefficient 119
4.2.1 Definition 119
4.2.2 Summary of Literature Data 122
4.2.3 Measurement Methodology 124
4.2.4 Data Input Requirements 132
4.3 Radon Vertical Dimension of Mixing 133
4.3.1 Definition 133
4.3.2 Data Input Requirements 133
CONTENTS (CONT.)
5 BUILDING CHARACTERISTIC PARAMETERS 135
5.1 | Average Building Air Exchange Rate..................................................................... | 135 |
5.1.1 Definition ................................................................................................... | 135 | |
5.1.2 Summary of Literature Data ...................................................................... | 135 | |
5.1.3 Measurement Methodology ....................................................................... | 137 | |
5.1.4 Data Input Requirements ........................................................................... | 138 | |
5.2 | Building Room Height ............................................................................................ | 138 |
5.2.1 Definition ................................................................................................... | 138 | |
5.2.2 Data Input Requirements ........................................................................... | 139 | |
5.3 | Building Indoor Area Factor ................................................................................... | 139 |
5.3.1 Definition ................................................................................................... | 139 | |
5.3.2 Data Input Requirements ........................................................................... | 139 | |
5.4 | Building Foundation Thickness .............................................................................. | 139 |
5.4.1 Definition ................................................................................................... | 139 | |
5.4.2 Summary of Literature Data ...................................................................... | 140 | |
5.4.3 Data Input Requirements ........................................................................... | 140 | |
5.5 | Foundation Depth Below Ground Surface.............................................................. | 141 |
5.5.1 Definition ................................................................................................... | 141 | |
5.5.2 Data Input Requirements ........................................................................... | 141 | |
5.6 | Filtration Factor for Inhalation Pathway................................................................. | 142 |
5.6.1 Definition ................................................................................................... | 142 | |
5.6.2 Summary of Literature Data ...................................................................... | 142 | |
5.6.3 Data Input Requirements ........................................................................... | 143 | |
5.7 | Shielding Factor for External Gamma Radiation.................................................... | 143 |
5.7.1 Definition ................................................................................................... | 143 | |
5.7.2 Summary of Literature Data ...................................................................... | 143 | |
5.7.3 Data Input Requirements ........................................................................... | 144 |
6 CROPS AND LIVESTOCK PARAMETERS 149
6.1 | Root | Depth .............................................................................................................. | 149 |
6.1.1 | Definition ................................................................................................... | 149 | |
6.1.2 | Summary of Literature Data ...................................................................... | 149 | |
6.1.3 | Data Input Requirements ........................................................................... | 150 | |
6.2 Livestock Water Intake Rate for Beef Cattle and Milk Cows 153 | |||
6.2.1 | Definition ................................................................................................... | 153 | |
6.2.2 | Data Input Requirements ........................................................................... | 153 | |
6.3 | Plant | Transfer Factors ............................................................................................. | 155 |
6.3.1 | Definition ................................................................................................... | 155 | |
6.3.2 | Discussion.................................................................................................. | 155 | |
6.3.3 | Data Input Requirements ........................................................................... | 158 | |
CONTENTS (CONT.)
6.4 | Meat | Transfer Factors ............................................................................................. | 171 |
6.4.1 | Definition ................................................................................................... | 171 | |
6.4.2 | Discussion.................................................................................................. | 171 | |
6.4.3 | Data Input Requirements ........................................................................... | 173 | |
6.5 | Milk | Transfer Factors ............................................................................................. | 176 |
6.5.1 | Definition ................................................................................................... | 176 | |
6.5.2 | Discussion.................................................................................................. | 176 | |
6.5.3 | Data Input Requirements ........................................................................... | 181 | |
6.6 | Bioaccumulation Factors for Aquatic Organisms................................................... | 185 | |
6.6.1 Definition ................................................................................................... | 185 | ||
6.6.2 Discussion.................................................................................................. | 185 | ||
6.6.3 Data Input Requirements ........................................................................... | 190 | ||
6.6.4 Fish Bioaccumulation Factors ................................................................... | 190 | ||
6.6.5 Crustacea and Mollusc Bioaccumulation Factors...................................... | 193 | ||
7 HUMAN INTAKE PARAMETERS 199
7.1 | DRINKING WATER INTAKE RATE .................................................................. | 199 |
7.1.1 Definition ................................................................................................... | 199 | |
7.1.2 Summary of Literature Review ................................................................. | 199 | |
7.1.3 Data Input Requirements ........................................................................... | 201 | |
7.2 | Inhalation Rate ........................................................................................................ | 201 |
7.2.1 Definition ................................................................................................... | 201 | |
7.2.2 Summary of Literature Review ................................................................. | 201 | |
7.2.3 Data Input Requirements ........................................................................... | 203 | |
7.3 | Soil and Dust Ingestion Rate................................................................................... | 207 |
7.3.1 Definition ................................................................................................... | 207 | |
7.3.2 Summary of Literature Review ................................................................. | 207 | |
7.3.3 Measurement Methodology ....................................................................... | 209 | |
7.3.4 Data Input Requirements ........................................................................... | 210 | |
7.4 | Seafood Consumption Rate..................................................................................... | 210 |
7.4.1 Definition ................................................................................................... | 210 | |
7.4.2 Summary of Literature Review ................................................................. | 211 | |
7.4.3 Data Input Requirements ........................................................................... | 216 | |
7.5 | Fruit, Vegetable, and Grain Consumption Rates .................................................... | 218 |
7.5.1 Definition ................................................................................................... | 218 | |
7.5.2 Summary of Literature Review ................................................................. | 218 | |
7.5.3 Data Input Requirements ........................................................................... | 222 | |
7.6 | Leafy Vegetable Consumption Rate ....................................................................... | 222 |
7.6.1 Definition ................................................................................................... | 222 | |
7.6.2 Summary of Literature Review ................................................................. | 224 | |
7.6.3 Data Input Requirements ........................................................................... | 225 |
CONTENTS (CONT.)
7.7 Meat And Poultry Consumption Rate 225
7.7.1 Definition 225
7.7.2 Summary of Literature Review 225
7.7.3 Data Input Requirements 227
7.8 Milk Consumption Rate 228
7.8.1 Definition 228
7.8.2 Summary of Literature Review 229
7.8.3 Data Input Requirements 231
8 SOURCE CHARACTERISTIC PARAMETERS 233
8.1 Area of Contaminated Zone 233
8.1.1 Definition 233
8.1.2 Data Input Requirements 233
8.2 Thickness of Contaminated Zone 233
8.2.1 | Definition ................................................................................................... | 233 | |
8.2.2 | Measurement Methodology ....................................................................... | 234 | |
8.2.3 | Data Input Requirements ........................................................................... | 235 | |
8.3 | Cover | Depth ............................................................................................................ | 236 |
8.3.1 | Definition ................................................................................................... | 236 | |
8.3.2 | Measurement Methodology ....................................................................... | 236 | |
8.3.3 | Data Input Requirements ........................................................................... | 237 | |
8.4 | Shape | Factor............................................................................................................ | 238 |
8.4.1 | Definition ................................................................................................... | 238 | |
8.4.2 | Data Input Requirements ........................................................................... | 238 |
9 MISCELLANEOUS PARAMETERS 239
9.1 | Radiation Dose Limit .............................................................................................. | 239 |
9.1.1 Definition ................................................................................................... | 239 | |
9.1.2 Data Input Requirements ........................................................................... | 239 | |
9.2 | Radionuclide Concentration in Groundwater ......................................................... | 239 |
9.2.1 Definition ................................................................................................... | 239 | |
9.2.2 Data Input Requirements ........................................................................... | 240 | |
9.3 | Elapsed Time of Waste Placement ......................................................................... | 240 |
9.3.1 Definition ................................................................................................... | 240 | |
9.3.2 Data Input Requirements ........................................................................... | 240 | |
9.4 | Initial Concentrations of Principal Radionuclides .................................................. | 241 |
9.4.1 Definition ................................................................................................... | 241 | |
9.4.2 Measurement Methodology ....................................................................... | 241 | |
9.4.3 Data Input Requirements ........................................................................... | 242 | |
9.5 | Fraction of Time Spent Indoors .............................................................................. | 242 |
9.5.1 Definition ................................................................................................... | 242 |
CONTENTS (CONT.)
9.5.2 Summary of Literature Review 242
9.5.3 Data Input Requirements 243
9.6 Fraction of Time Spent Outdoors 243
9.6.1 Definition 243
9.6.2 Summary of Literature Review 245
9.6.3 Data Input Requirements 246
10 REFERENCES 247
FIGURES
2.1.1 U.S. Department of Agriculture Method for Naming Soils Source: Xxxxx 1984 17
2.6.1 Erosion Rate on Cropland in the United States 52
3.1.1 Distribution of Average Annual Precipitation Rates over the
U.S. Continental Territory 97
3.3.1 Distribution of Average Annual Actual Evapotranspiration Rate over the
U.S. Continental Territory 104
3.5.1 Average of Annual Mean Wind Speeds 1979–2000 from NCDC Data Sets 110
4.2.1 Schematic Presentation of a Closed-Loop Approach to Radon Emanation
Coefficient Measurement 130
4.2.2 Schematic Presentation of a Flow-Through Approach to Radon Emanation
Coefficient Measurement 131
4.2.3 Schematic Presentation of a Gamma Spectrometry Method of Radon
Emanation Coefficient Measurement 131
8.2.1 Determining the Thickness of a Contaminated Zone with an Area Greater
Than 100 m2 235
8.2.2 Determining the Thickness of a Contaminated Zone with an Area Less
Than 100 m2 235
8.3.1 Determining the Cover Depth of a Contaminated Zone with an Area Greater
Than 100 m2 237
FIGURES (CONT.)
8.3.2 Determining the Cover Thickness of a Contaminated Zone with an Area Less
Than 100 m2 237
8.4.1 Example of Shape Factor Data 238
TABLES
1.1 Default Values, Lower Bounds, and Upper Bounds for RESRAD Input
Parameters ................................................................................................................ 3
1.2 Default Values, Lower Bounds, and Upper Bounds for RESRAD-OFFSITE
Input Parameters....................................................................................................... 7
2.1.1 Dry Bulk Density for Different Soil Types from Different Sourcesa 16
2.1.2 Standard Methods for Measuring Particle Density and Bulk Density in Soil
Materials at FUSRAP Sites 18
2.2.1 Range of Porosity Values 22
2.2.2 Representative Porosity Values 23
2.2.3 The Relationship between Physical Characteristics of Grains and Total
Porosity 24
2.3.1 Representative Values of Dry Bulk Density, Total Porosity, and Effective
Porosity for Common Aquifer Matrix Materials 27
2.4.1 Range of Saturated Hydraulic Conductivity of Various Soil Materials 29
2.4.2 Representative Values of Saturated Hydraulic Conductivity of Different Soil Textures 30
2.4.3 Estimated Saturated Hydraulic Conductivities for Fine-Grained Materials 30
2.4.4 Estimated Saturated Hydraulic Conductivities for Sands and Gravels
According to Degree of Sorting and Silt Contenta 31
2.4.5 Default Hydraulic Conductivity Values Used in RESRAD and
RESRAD-OFFSITE 32
TABLES (CONT.)
2.4.6 Standard Laboratory and Field Methods for Measuring Saturated Hydraulic Conductivity, K, in Soil Materials 35
2.5.1 Representative Values of Soil-Specific Exponential b Parameter 48
2.5.2 Default Soil-specific Exponential b Parameters Used in RESREAD and
RESRAD-OFFSITE 49
2.6.1 Default Erosion Rate Values Used in RESRAD 51
2.7.1 Default Hydraulic Gradient Values Used in RESRAD and RESRAD-OFFSITE 54
2.11.1 Default Well-pump Intake Depth Value Used in RESRAD 58
2.13.1 Kd Data for Each Element for Sand Soil Type 64
2.13.2 Kd Data for Each Element for Loam Soil Type 67
2.13.3 Kd Data for Each Element for Clay Soil Type 69
2.13.4 Kd Data for Each Element for Organic Soil Type 70
2.13.5 Kd Data for Each Element for Generic Soil Type 72
2.13.6 Correlations between Kd and Soil Main Properties for Selected Elements 73
2.13.7 Kd Values Grouped According to pH Values 75
2.13.8 Regression Equations for Kd Values for Some Nuclides 75
2.13.9 Summary of Geometric Mean Kd Values for Each Element by Soil Type 77
2.13.10 RESRAD Default Value and Distribution for the Kd Parameter for Different
Elements 80
2.14.1 Commonly Used Leaching Tests 83
2.15.1 Indirect Methods Used by Different Sensors for Measuring Water Content in
Soil 88
2.15.2 Characteristics of Some Types of Soil Water Sensors 89
2.16.1 Field Capacity and Plant Wilting Point for Different Soil Types 91
3.1.1 Default Precipitation Rates Used in RESRAD and RESRAD-OFFSITE 98
TABLES (CONT.)
3.2.1 Runoff Coefficient Values 100
3.5.1 Default Average Annual Wind Speed Used in RESRAD and
RESRAD-OFFSITE 110
4.1.1 Observed Effective Diffusion Coefficients for Radon in Unconsolidated Soil
Materials and Concretea 120
4.2.1 Summary of Radon-220 Emanation Coefficients for Various Source Materials 123
4.2.2 Summary of Radon-222 Emanation Coefficients for Various Source Materials 123
4.2.3 Radon-222 Emanation Coefficients for Various Types of Minerals 124
4.2.4 Radon-222 Emanation Coefficients for Various Types of Rocks 125
4.2.5 Radon-222 Emanation Coefficients for Various Types of Soil 126
4.2.6 Radon-222 Emanation Coefficients for Seven Common Types of Soil 128
4.2.7 Radon-222 Emanation Coefficients for Various Types of Uranium
Mill Tailings 129
4.2.8 Radon-222 Emanation Coefficients for Fly Ashes 130
5.1.1 Summary Statistics on Air Exchange Rates for Residential Buildings in
Different Regions 136
5.1.2 Air Exchange Rates for Different Types of Nonresidential Buildings 136
5.4.1 Characteristics of Different Housing Units 141
5.7.1 External Gamma Shielding Factors for Deposited Contamination 145
5.7.2 External Shielding Factors for Th-232 Series Radionuclides 145
5.7.3 Shield Protection Factors per Unit Thickness for Different Construction Materials 146
5.7.4 Average External Shielding Factors for Different Types of House Construction 147
6.1.1 Root Depths of Fruits and Nuts, Grains, and Nonleafy Vegetables from
Different Sources 151
6.1.2 Root Depths of Leafy Vegetables from Different Sources 152
TABLES (CONT.)
6.1.3 Root Depths of Forages from Different Sources 152
6.1.4 Root Depths of Grains from Different Sources 153
6.2.1 Variations in Total Daily Water Intake of Beef Cattle with Temperature 154
6.2.2 Water Consumption by Dairy Cattle 154
6.2.3 Water Consumption by Beef Cattle 154
6.3.1 Dry-to-Wet Weight Conversion Factors for Different Plant Types 156
6.3.2 Plant Transfer Factor Distribution Parameter Values from NCRP 159
6.3.3 PNNL-Recommended Plant Transfer Factor Values on Dry-Weight Basis for Different Plant Types 161
6.3.4 Plant Transfer Factors on Dry-Weight Basis for Grains in Temperate
Environment 163
6.3.5 Plant Transfer Factors on Dry-Weight Basis for Leafy Vegetables in
Temperate Environment 164
6.3.6 Plant Transfer Factors on Dry-Weight Basis for Root Crops and Tubers in
Temperate Environment 165
6.3.7 Plant Transfer Factors on Dry-Weight Basis for Nonleafy Vegetables and
Leguminous Vegetables in Temperate Environment 166
6.3.8 Plant Transfer Factors on Dry-Weight Basis for Stems and Shoots in Different
Plant Groups in Temperate Environment 167
6.3.9 Plant Transfer Factor Values on Dry-Weight Basis for Different Plant Types
from Naper et al 168
6.3.10 Comparison of RESRAD Default Plant Transfer Factors with Those from
Other References 169
6.4.1 Fractional Absorption for Different Elements in Ruminants 172
6.4.2 Comparison of RESRAD Meat Transfer Factors with Those from Other
References 174
6.4.3 Comparison of Meat Transfer Factors for Different Types of Meat 177
TABLES (CONT.)
6.4.4 Comparison of RESRAD Default Meat Transfer Factor Distributions with
Those from Other References 179
6.5.1 Comparison of RESRAD Default Milk Transfer Factors with Those from
Other References 183
6.5.2 Comparison of Milk Transfer Factors for Different Types of Milk 186
6.5.3 Comparison of RESRAD Default Milk Transfer Factor Distributions with
Those from Other References 187
6.6.1 Comparison of RESRAD Freshwater Fish Bioaccumulation Factors with
Those from Other References 191
6.6.2 Comparison of RESRAD Default Fish Transfer Factor Distributions with
Those Published by IAEA 194
6.6.3 Comparison of RESRAD Default Freshwater Crustacea Bioaccumulation
Factors with Those from Other References 196
7.1.1 Recommended Drinking Water Intake Rates 200
7.2.1 Summary of Human Inhalation Rates for Men, Women, and Children by
Activity Level 202
7.2.2 Reference Values for Inhalation Rates at Different Physical Activity Levels 203
7.2.3 Reference Values for Inhalation Rates and the Time Spent in Different
Physical Activities 204
7.2.4 Reference Values for Inhalation Rates of Sedentary and Heavy Workers 204
7.2.5 EPA-Recommended Inhalation Values for Long-Term Exposure 205
7.2.6 EPA-Recommended Inhalation Values for Short-Term Exposure 206
7.3.1 EPA Recommended Values for Daily Intake of Soil, Dust, and Soil + Dust 209
7.4.1 Best Fit Lognormal Distribution Parameters for Seafood Consumption from
NPD Research Survey 212
7.4.2 Per-capita Prepared-Seafood Consumption Rates 213
TABLES (CONT.)
7.4.3 Per-capita Uncooked-Seafood Consumption Rates 214
7.4.4 Consumers-Only Prepared-Seafood Consumption Rates 215
7.4.5 Consumers-Only Uncooked-Seafood Consumption Rates 216
7.4.6 Types of Seafood Consumed in the United States 217
7.4.7 Average Per-capita Consumption Rates in the United States for the Top 10
Seafood Species 219
7.4.8 EPA-Recommended Per-capita and Consumer-Only Mean Uncooked Seafood
Intake Values, g/kg-day 220
7.5.1 Vegetable and Fruit Intake Rates 221
7.5.2 Mean Vegetable, Fruit, and Grain Intake in Children of Different Age Groups 222
7.5.3 Average Intake of Different Vegetables in Children of Different Age Groups 223
7.5.4 Average Intake of Different Fruits in Children of Different Age Groups 223
7.5.5 Average Per-capita Intake of Total Fruits, Vegetables, and Grains 224
7.6.1 Average Per-capita Intake of Leafy Vegetables 225
7.7.1 Per-capita Intake of Total Meat 227
7.7.2 Per-capita Intake Rates for Red Meat and Poultry 228
7.8.1 Per-capita Intake of Total Dairy Products 230
7.8.2 Per-capita Intake Rates for Eggs, Dairy Products, and Milk 230
9.5.1 EPA-Recommended Average Time Fraction Spent in Different Environments 242
9.5.2 Fraction of Time Spent Indoors at a Residence 244
9.5.3 Fraction of Time Spent Working in a Main Job 244
9.6.1 Time Spent in Outdoor Recreational Activities 245
9.6.2 Fraction of Time Spent Outdoors 246
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NOTATION
The following is a list of acronyms, initialisms, and abbreviations (including units of measure) used in this document.
ACRONYMS, INITIALISMS, AND ABBREVIATIONS
AHS American Housing Survey
ANL Argonne National Laboratory
ASTM American Society for Testing and Materials
CSFII Continuing Survey of Food Intake by Individuals
CSSM Center for Survey Statistics and Methodology (Iowa State University)
DCF dose conversion factor
DOA U.S. Department of the Army
DOE U.S. Department of Energy
DOI U.S. Department of the Interior
DRF dose reduction factor
EPA U.S. Environmental Protection Agency FDR frequency domain reflectometer
FUSRAP Formerly Utilized Sites Remedial Action Program FW freshwater
IAEA International Atomic Energy Agency
ICRP International Commission on Radiological Protection
LLD lower limit of detection
L/S liquid-to-solid ratio
NAS National Academy of Sciences NCDC National Climate Data Center NCI National Cancer Institute
NCRP National Council on Radiation Protection and Measurements NHANES National Health and Nutrition Examination Survey
NMFS National Marine Fisheries Service NMM neutron moisture meter
NOAA National Oceanic and Atmospheric Administration NRC U.S. Nuclear Regulatory Commission
NRCS National Resources Conservation Service PNNL Pacific Northwest National Laboratory
RECS Residential Energy Consumption Survey REV representative elementary volume
SCS U.S. Soil Conservation Service
SW saltwater
TCDD tetrachlorodibenzo-p-dioxin TDR time domain reflectometer
USDA U.S. Department of Agriculture USLE Universal Soil Loss Equation
UNITS OF MEASURE
Bq xxxxxxxxx(s)
°C degree(s) Celsius
cm centimeter(s)
cm3 cubic centimeter(s)
d day(s)
ft2 square foot (feet)
g gram(s)
gal gallon(s)
h hour(s)
in. inch(es)
keV kiloelectron volt(s)
kg kilogram(s)
km2 square kilometer(s)
L liter(s)
l length
l2 length squared
l3 length cubed
lb pound(s)
M mass
m meter(s)
m2 square meter(s)
m3 cubic meter(s)
mi mile(s)
mi2 square mile(s)
mm millimeter(s)
mol mole(s)
mrem xxxxxxxx(s)
mSv millisievert(s)
pCi picocurie(s)
s second(s)
T time
V volume
yr year(s)
DATA COLLECTION HANDBOOK TO SUPPORT MODELING THE IMPACTS OF RADIOACTIVE MATERIAL IN SOIL AND BUILDING STRUCTURES
by
Xxxxxxx Xx, Xxxxxx Xxxxxx, Xxxxx Xxxx, and Xxxx-Xx Xxxxx
ABSTRACT
This handbook is an update of the 1993 version of the Data Collection Handbook and the Radionuclide Transfer Factors Report to support modeling the impact of radioactive material in soil. Many new parameters have been added to the RESRAD Family of Codes, and new measurement methodologies are available. A detailed review of available parameter databases was conducted in preparation of this new handbook. This handbook is a companion document to the user manuals when using the RESRAD (onsite) and RESRAD-OFFSITE code. It can also be used for RESRAD-BUILD code because some of the building-related parameters are included in this handbook. The RESRAD (onsite) has been developed for implementing U.S. Department of Energy Residual Radioactive Material Guidelines. Hydrogeological, meteorological, geochemical, geometrical (size, area, depth), crops and livestock, human intake, source characteristic, and building characteristic parameters are used in the RESRAD (onsite) code. The RESRAD-OFFSITE code is an extension of the RESRAD (onsite) code and can also model the transport of radionuclides to locations outside the footprint of the primary contamination. This handbook discusses parameter definitions, typical ranges, variations, and measurement methodologies. It also provides references for sources of additional information. Although this handbook was developed primarily to support the application of RESRAD Family of Codes, the discussions and values are valid for use of other pathway analysis models and codes.
1 INTRODUCTION
The RESRAD Family of Codes is a suite of software tools developed by Argonne National Laboratory (ANL) for the evaluation of radiologically contaminated sites
(Yu et al. 2013a; Yu 2007, 2006, Yu 1999). In 1993, a Data Collection Handbook (Xx et al. 1993) and a Radionuclide Transfer Factors Report (Xxxx et al. 1993) were published to support the use of RESRAD (onsite) code for modeling the impacts of radioactive materials in soil. The RESRAD (onsite) computer code evaluates the radiological dose and excess cancer risk to an individual who is exposed while residing and/or working in an area where soil is contaminated with radionuclides (Yu et al. 2001). RESRAD (onsite) code was developed by ANL in the 1980s (Xxxxxxx et al. 1989) in support of the U.S. Department of Energy (DOE) Order establishing
residual radioactive material guidelines (DOE Order 5400.5, now superseded by Order 458.1). The DOE and other agencies and their contractors have used the RESRAD (onsite) code and its manual to derive cleanup criteria and dose calculations. The DOE Office of Environment, Health, Safety and Security and the Office of Environmental Management provide periodic guidance regarding any significant changes to the code and manual. Since its first release in June 1989, many new features and pathways have been added to the RESRAD (onsite) code in response to feedback from users and sponsors. The RESRAD team has participated in many national and international model intercomparison studies in which both hypothetical and actual contaminated site-based scenarios were analyzed using the RESRAD (onsite) code. The development of the RESRAD-OFFSITE code started in the 1990s, and it was recently improved with a new source term model on the request of U.S. Nuclear Regulatory Commission
(Yu et al. 2013b). Because many new parameters have been added to the RESRAD codes and new measurement methodologies are available as well as parameter database are available now, it is time to update the 1993 Data Collection Handbook and Radionuclide Transfer Factors Report. Both RESRAD (onsite) and RESRAD-OFFSITE codes consider a building or house located on the contaminated soil. Therefore, many building-related parameters are discussed in this handbook. These building-related parameters are also used in the RESRAD-BUILD computer code, which is designed for the evaluation of radiologically contaminated buildings (Yu et al. 2003). Hence this handbook is useful when RESRAD-BUILD code is being applied to evaluate radiologically contaminated buildings and structures. Additional information on the parameters used in RESRAD-BUILD is documented in previous work (Xxxxxx et al. 2000,
Xx et al. 2000, and Biwer et al. 2002).
Fifty-six parameters are discussed in this handbook. The definition, typical range, default value used in RESRAD (onsite) and RESRAD-OFFSITE, relation to other parameters, and measurement methodology are given for most of the measurable parameters. Table 1.1 lists the default values and the lower and upper bounds set in the RESRAD (onsite) code for each parameter used in the code. Table 1.2 lists the default values and the lower and upper bounds set in the RESRAD-OFFSITE code for each parameter used in the code. The intent of this handbook is to provide users with a better understanding of each input parameter in terms of its typical range, variation, and use in the RESRAD (onsite) and RESRAD-OFFSITE codes.
The default parameter values listed in Tables 1.1 and 1.2 have been carefully selected, and use of these values, in most cases, will not result in significant underestimation of the dose or risk. Site-specific parameters should be used whenever possible, especially for sensitive parameters.
The topics discussed in each section of this handbook are as follows: Section 2, hydrogeological parameters; Section 3, meteorological parameters; Section 4, radon emanation parameters; Section 5, building characteristic parameters; Section 6, crop and livestock parameters; Section 7, human intake parameters; Section 8, source characteristic parameters; and Section 9, miscellaneous parameters to estimate derived concentration guideline levels.
References are given in Section 10.
TABLE 1.1 Default Values, Lower Bounds, and Upper Bounds for RESRAD (onsite) Input Parameters
Parameter | Unit | Default Value | Lowera Bound | Uppera Bound |
Soil bulk density | ||||
Cover material | g/cm3 | 1.5 | 0.001 | 22.5 |
Contaminated zone | g/cm3 | 1.5 | 0.001 | 22.5 |
Unsaturated zone | g/cm3 | 1.5 | 0.001 | 22.5 |
Saturated zone | g/cm3 | 1.5 | 0.001 | 22.5 |
Building foundation material | g/cm3 | 2.4 | 0.001 | 22.5 |
Total porosity Cover material | -b | 0.4 | 0.00001 | 1 |
Contaminated zone | - | 0.4 | 0.00001 | 1 |
Unsaturated zone | - | 0.4 | 0.00001 | 1 |
Saturated zone | - | 0.4 | 0.00001 | 1 |
Building foundation material | - | 0.1 | 0.00001 | 1 |
Effective porosity Saturated zone Unsaturated zone | - - | 0.2 0.2 | 1 × 10-34 1 × 10-34 | 1 1 |
Hydraulic conductivity Contaminated zone | m/yr | 10 | 0.001 | 1 × 1010 |
Unsaturated zone | m/yr | 10 | 0.001 | 1 × 1010 |
Saturated zone | m/yr | 100 | 0.001 | 1 × 1010 |
Volumetric water content | ||||
Cover material | - | 0.05 | 0 | 1 |
Building foundation material | - | 0.03 | 0 | 1 |
Effective radon diffusion coefficient Cover material | m2/s | 2 × 10-6 | -1c | 1 |
Contaminated zone | m2/s | 2 × 10-6 | -1c | 1 |
Building foundation material | m2/s | 3 × 10-7 | -1c | 1 |
Radon emanation coefficient (Radon-222/Radon-220) | - | 0.25/0.15 | 0.01 | 1 |
Precipitation rate | m/yr | 1 | 0 | 10 |
Runoff coefficient | - | 0.2 | 0 | 1 |
Irrigation rate | m/yr | 0.2 | 0 | 10 |
Evapotranspiration coefficient | - | 0.5 | 0 | 0.999 |
TABLE 1.1 (Cont.) | ||||
Parameter | Unit | Default Value | Lowera Bound | Uppera Bound |
Soil-specific b parameter Contaminated zone Unsaturated zone Saturated zone | - - - | 5.3 5.3 5.3 | 0 0 0 | 15 15 15 |
Erosion rate Cover material Contaminated zone | m/yr m/yr | 0.001 0.001 | 0 0 | 5 5 |
Hydraulic gradient | - | 0.02 | 1 × 10-10 | 10 |
Length of contaminated zone parallel to the aquifer flow | m | 100 | 0.0001 | 1 × 106 |
Watershed area for nearby stream or pond | m2 | 1 × 106 | 0.0001 | 1 × 1034 |
Water table drop rate | m/yr | 0.001 | 0 | 5 |
Well-pump intake depth | m | 10 | 0.00001 | 1,000 |
Radon vertical dimension of mixing | m | 2 | 0.001 | 1,000 |
Average annual wind speed | m/s | 2 | 0.0001 | 20 |
Average building air exchange rate | 1/h | 0.5 | 0 | 1,000 |
Building room height | m | 2.5 | 0.0001 | 100 |
Building indoor area factor | - | 0 | 0 | 100 |
Thickness of uncontaminated unsaturated zone | m | 4 | 0 | 10,000 |
Building foundation thickness | m | 0.15 | 0 | 10 |
Foundation depth below ground surface | m | -1c | -100 | 100 |
Fraction of time spent indoors on-site | - | 0.5 | 0 | 1 |
Fraction of time spent outdoors on-site | - | 0.25 | 0 | 1 |
Area of contaminated zone | m2 | 10,000 | 0.0001 | 1 × 1015 |
Cover depth | m | 0 | 0 | 100 |
TABLE 1.1 (Cont.)
Parameter | Unit | Default Value | Lowera Bound | Uppera Bound |
Distribution coefficient | cm3/g | d | 0 | ∝ |
Fraction of annular areas within contaminated area | - | 0 | 0 | 1 |
Radionuclide concentration in groundwater | pCi/L | 0 | 0 | ∝ |
Xxxxx rate | 1/yr | 0 | 0 | ∝ |
Livestock fodder intake Meat Milk | kg/d kg/d | 68 55 | 0 0 | 300 300 |
Mass loading for inhalation | g/m3 | 1 × 10-4 | 0 | 1 |
Milk consumption rate | L/yr | 92 | 0 | 1,000 |
Filtration factor for inhalation | - | 0.4 | 0 | 1 |
Depth of roots | m | 0.9 | 0 | 100 |
Soil ingestion rate | g/yr | 36.5 | 0 | 10,000 |
Thickness of contaminated zone | m | 2 | 1 × 10-5 | 1,000 |
Radiation dose limit | mrem/yr | 25 | 0 | ∝ |
Seafood consumption rate Fish Other seafood | kg/yr kg/yr | 5.4 0.9 | 0 0 | 1,000 100 |
Fruit, vegetable, and grain consumption rate | kg/yr | 160 | 0 | 1,000 |
Inhalation rate | m3/yr | 8,400 | 0 | 20,000 |
Leafy vegetable consumption rate | kg/yr | 14 | 0 | 100 |
Livestock water intake rate Meat Milk | L/d L/d | 50 160 | 0 0 | 500 500 |
Meat and poultry consumption rate | kg/yr | 63 | 0 | 300 |
Shielding factor for external gamma | - | 0.7 | 0 | 1 |
TABLE 1.1 (Cont.)
Parameter | Unit | Default Value | Lowera Bound | Uppera Bound |
Elapsed time of waste placement | yr | 0 | 0 | 100 |
Initial concentration of principal radionuclide | pCi/g | d | 0 | ∝ |
Drinking water intake rate | L/yr | 510 | 0 | 10,000 |
Fraction of drinking water from site | - | 1 | 0 | 1 |
Fraction of aquatic food from site | - | 0.5 | 0 | 1 |
Mass loading for foliar deposition | g/m3 | 1 × 10-4 | 0 | 1 |
Depth of soil mixing layer | m | 0.15 | 0 | 1 |
Fraction from groundwater | ||||
Drinking water | - | 1 | 0 | 1 |
Livestock water | - | 1 | 0 | 1 |
Irrigation water | - | 1 | 0 | 1 |
a The lower and upper bound values represent the lower and upper limit of an input value that can be entered to RESRAD (onsite) code. They do not represent the actual limit of the parameter value physically. For some secondary (derived) parameters (e.g., xxxxx rate), the upper and lower bounds are derived from other primary (basic) parameters (e.g., thickness of contaminated zone). b A hyphen indicates that the parameter is dimensionless. c A negative value of “-1” for this parameter serves as a flag in RESRAD (onsite) code. See the section in the handbook on the particular parameter for details. d The default value is radionuclide-dependent. | ||||
TABLE 1.2 Default Values, Lower Bounds, and Upper Bounds for RESRAD- OFFSITE Input Parameters
Parameter | Unit | Default Value | Lowera Bound | Uppera Bound |
Soil bulk density | ||||
Cover material | g/cm3 | 1.5 | 0.001 | 22.5 |
Contaminated zone | g/cm3 | 1.5 | 0.001 | 22.5 |
Unsaturated zone | g/cm3 | 1.5 | 0.001 | 22.5 |
Saturated zone | g/cm3 | 1.5 | 0.001 | 22.5 |
Building foundation material | g/cm3 | 2.4 | 0 | 22.5 |
Fruit, grain, nonleafy agriculture area | g/cm3 | 1.5 | 0.001 | 22.5 |
Leafy vegetable agriculture area | g/cm3 | 1.5 | 0.001 | 22.5 |
Pasture, silage growing area | g/cm3 | 1.5 | 0.001 | 22.5 |
Grain growing area | g/cm3 | 1.5 | 0.001 | 22.5 |
Offsite dwelling area | g/cm3 | 1.5 | 0.001 | 22.5 |
Total porosity Cover material | -b | 0.4 | 0 | 1 |
Contaminated zone | - | 0.4 | 0.00001 | 1 |
Unsaturated zone | - | 0.4 | 0.00001 | 1 |
Saturated zone | - | 0.4 | 0.00001 | 1 |
Building foundation material | - | 0.1 | 0.0001 | 1 |
Fruit, grain, nonleafy agriculture area | - | 0.4 | 0.00001 | 1 |
Leafy vegetable agriculture area | - | 0.4 | 0.00001 | 1 |
Pasture, silage growing area | - | 0.4 | 0.00001 | 1 |
Grain growing area | - | 0.4 | 0.00001 | 1 |
Offsite dwelling area | - | 0.4 | 0.0001 | 1 |
Effective porosity | ||||
Contaminated zone | - | 0.4 | 0.00001 | 1 |
Saturated zone | - | 0.2 | 0.00001 | 1 |
Unsaturated zone | - | 0.2 | 0.00001 | 1 |
Field capacity | ||||
Contaminated zone | - | 0.3 | 0.00001 | 1 |
Unsaturated zone | - | 0.3 | 0.00001 | 1 |
Hydraulic conductivity Contaminated zone | m/yr | 10 | 0.001 | 1 × 1010 |
Unsaturated zone | m/yr | 10 | 0.001 | 1 × 1010 |
Saturated zone | m/yr | 100 | 0.001 | 1 × 1010 |
Effective radon diffusion coefficient Cover material | m2/s | 2 × 10-6 | -1 | 1 |
Contaminated zone | m2/s | 2 × 10-6 | -1 | 1 |
Building foundation material | m2/s | 3 × 10-7 | -1 | 1 |
Fruit, grain, nonleafy agriculture area | m2/s | 2 × 10-6 | 0 | 1 |
Leafy vegetable agriculture area | m2/s | 2 × 10-6 | 0 | 1 |
Pasture, silage growing area | m2/s | 2 × 10-6 | 0 | 1 |
Grain growing area | m2/s | 2 × 10-6 | 0 | 1 |
Offsite dwelling area | m2/s | 2 × 10-6 | 0 | 1 |
TABLE 1.2 (Cont.) | ||||
Parameter | Unit | Default Value | Lowera Bound | Uppera Bound |
Radon emanation coefficient (Radon-222/Radon-220) | - | 0.25/0.15 | 0.01 | 1 |
Precipitation rate | m/yr | 1 | 0 | 10 |
Runoff coefficient (contaminated zone, agricultural areas, livestock feed growing areas, and offsite dwelling area) | - | 0.2 | 0 | 1 |
Irrigation rate (contaminated zone, agricultural areas, and livestock feed growing areas) | m/yr | 0.2 | 0 | 10 |
Evapotranspiration coefficient (contaminated zone, agricultural areas, and livestock feed growing areas) | - | 0.5 | 0 | 0.999 |
Soil-specific b parameter Contaminated zone Unsaturated zone | - - | 5.3 5.3 | 0 0 | 15 15 |
Hydraulic gradient of saturated zone to well and surface water body | - | 0.02 | 1 × 10-10 | 10 |
Length of contaminated zone parallel to the aquifer flow | m | 100 | 0.0001 | 1,000,000 |
Well-pump intake depthc | m | 10 | 0.00001 | 1,000 |
Surface water body intake depthc | m | 10 | 0 | 1,000 |
Radon vertical dimension of mixing | m | 2 | 0.001 | 1,000 |
Average annual wind speed | m/s | 2 | 0.001 | 20 |
Average building air exchange rate | 1/h | 0.5 | 0 | 1,000 |
Building room height | m | 2.5 | 0.001 | 100 |
Building indoor area factor | - | 0 | 0 | 100 |
Thickness of uncontaminated unsaturated zone | m | 4 | 0.01 | 10,000 |
Building foundation thickness | m | 0.15 | 0 | 10 |
Foundation depth below ground surface | m | -1 | -100 | 100 |
Fraction of time spent indoors on-site | - | 0 | 0 | 1 |
TABLE 1.2 (Cont.) | ||||
Parameter | Unit | Default Value | Lowera Bound | Uppera Bound |
Fraction of time spent outdoors on-site | - | 0 | 0 | 1 |
Fraction of time spent indoors in off-site dwelling | - | 0.5 | 0 | 1 |
Fraction of time spent outdoors off-site | - | 0.1 | 0 | 1 |
Fraction of time spent in fruit, grain, nonleafy fields | - | 0.1 | 0 | 1 |
Fraction of time spent in leafy vegetable fields | - | 0.1 | 0 | 1 |
Fraction of time spent in pasture and silage fields | - | 0.1 | 0 | 1 |
Fraction of time spent in livestock grain fields | - | 0.1 | 0 | 1 |
Area of primary contamination and other areas | m2 | d | e | e |
Cover depth | m | 0 | 0 | 100 |
Distribution coefficient | cm3/g | e | 0 | 1 × 1034 |
Shape of the primary contaminated areaf | - | polygon | - | - |
Radionuclide concentration in groundwaterg | pCi/L | NA | NA | XX |
Xxxxx rate | 1/yr | 0 | 0 | 1 × 1034 |
Mass loading for inhalation | g/m3 | 1 × 10-4 | 0 | 2 |
Milk consumption rate | L/yr | 92 | 0 | 1,000 |
Shielding factor for inhalation | - | 0.4 | 0 | 1 |
Soil ingestion rate | g/yr | 36.5 | 0 | 10,000 |
Thickness of contaminated zone | m | 2 | 1 × 10-5 | 1,000 |
Radiation dose limit | mrem/yr | 25 | - | - |
Seafood consumption rate Fish Other seafood | kg/yr kg/yr | 5.4 0.9 | 0 0 | 1,000 100 |
Fruit, vegetable, and grain consumption rate | kg/yr | 160 | 0 | 1,000 |
TABLE 1.2 (Cont.) | ||||
Parameter | Unit | Default Value | Lowera Bound | Uppera Bound |
Inhalation rate | m3/yr | 8,400 | 0 | 20,000 |
Leafy vegetable consumption rate | kg/yr | 14 | 0 | 100 |
Meat and poultry consumption rate | kg/yr | 63 | 0 | 300 |
Shielding factor for external gamma | - | 0.7 | 0 | 1 |
Initial concentration of principal radionuclide | pCi/g | d | 0 | 1 × 1020 |
Drinking water intake rate | L/yr | 510 | 0 | 1,000 |
Fraction of drinking water from site | - | 1 | 0 | 1 |
Fraction of aquatic food from site | - | 0.5 | 0 | 1 |
Livestock pasture and silage intake Meat Milk | kg/d kg/d | 14 44 | 0 0 | 300 300 |
Livestock grain intake Meat Milk | kg/d kg/d | 54 11 | 0 0 | 300 300 |
Livestock water intake rate Meat Milk | L/d L/d | 50 160 | 0 0 | 500 500 |
Livestock soil intake from pasture and silage Meat Milk | kg/d kg/d | 0.1 0.4 | 0 0 | 10 10 |
Livestock soil intake from grain Meat Milk | kg/d kg/d | 0.4 0.1 | 0 0 | 10 10 |
Mass loading for foliar deposition | g/m3 | 1 × 10-4 | 0 | 1 |
Depth of soil mixing layer | m | 0.15 | 0 | 1 |
Depth of roots Fruit, grain, nonleafy Leafy vegetables Pasture and silage Grain | m m m m | 1.2 0.9 0.9 1.2 | 0 0 0 0 | 10 3 3 10 |
TABLE 1.2 (Cont.) | ||||
Parameter | Unit | Default Value | Lowera Bound | Uppera Bound |
Fraction from groundwater Drinking water Household water Livestock water Irrigation water | - - - - | 1 1 1 1 | 0 0 0 0 | 1 1 1 1 |
a The lower and upper bound values represent the lower and upper limit of an input parameter that can be used in RESRAD-OFFSITE. For some secondary (derived) parameters (e.g., primary contaminated area), the upper and lower bounds are derived from other primary (basic) parameters (e.g., x and y coordinates). b A hyphen indicates that the parameter is dimensionless. c Defined as the depth of the aquifer contributing to the well or the surface water body. d The default value is calculated from other input parameters (x coordinates and y coordinates). e The default value is radionuclide dependent. f See the section in this handbook on the particular parameter for details. g Initially there is groundwater contamination. | ||||
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2 HYDROGEOLOGICAL PARAMETERS
The parameters discussed in this section include soil density, total porosity, effective porosity, hydraulic conductivity, soil-specific exponential b parameter, erosion rate, hydraulic gradient, length of contaminated zone parallel to the aquifer flow, watershed area for nearby stream or pond, water table drop rate, well-pump intake depth, thickness of uncontaminated unsaturated zone, distribution coefficient, and xxxxx rate.
2.1 SOIL DENSITY
Bulk density of dry soil (often referred to as dry density in the text) is used in RESRAD (onsite) and RESRAD-OFFSITE codes. Bulk density is related to the soil particle density and total porosity. This section provides descriptions of the techniques and procedures for measuring both types of densities (dry density and soil particle density) because both are required for calculating total porosity of the soil material.
2.1.1 Definition
Density, as applied to any kind of homogeneous monophasic material of mass M and volume V, is expressed as the ratio of M to V. Under specified conditions, this definition leads to unique values that represent a well-defined property of the material. For heterogeneous and multiphasic materials, such as porous media, however, application of this definition can lead to different results, depending on the exact way the mass and volume of the system are defined.
Soil is a typical heterogeneous multiphasic porous system which, in its general form, contains three natural phases: (1) the solid phase or the soil matrix (formed by mineral particles and solid organic materials); (2) the liquid phase, which is often represented by water and which could more properly be called the soil solution; and (3) the gaseous phase, which contains air and other gases. In this three-phase soil system, the concept of average density can be used to define the following densities: (1) density of solids or soil particle density, ρs; (2) bulk or dry density, ρb; and (3) total or wet density, ρt.
The masses and volumes associated with the three soil phases must be defined before the definitions of the different densities that characterize the soil system can be formalized. Thus, consider a representative elementary volume (REV) of soil that satisfies the following criteria (Bear 1972; Marsily 1986):
1. A sufficiently large volume of soil, containing a large number of pores, so that the concept of mean global properties is applicable, and
2. A sufficiently small volume of soil so that the variation of any parameter of the soil from one part of the domain to another can be approximated by a continuous function.
Within a REV, the masses of the phases composing the soil can be defined as follows:
Ms = the mass of solids,
Ml = the mass of liquids,
Mg = the mass of gases (negligible compared with the masses of the solid and liquid phases), and
Mt = Ms + Ml = the total mass.
Similarly, within the REV, the volumes associated with the soil phases can be defined as follows:
Vs = the volume of solids, Vl = the volume of liquids, Vg = the volume of gases,
Vp = Vl + Vg = the volume of pore space, and
Vt = Vs + Vl + Vg = the total volume.
These mass and volume definitions can be used to define the concepts of soil particle density, bulk (dry) soil density, and total (wet) soil density. The dimensional unit of soil density is mass per unit of cubic length (M1-3).
2.1.1.1 Soil Particle Density
The soil particle density, ρs, or the density of solids, represents the density of the soil (i.e., mineral) particles collectively and is expressed as the ratio of the solid phase mass to the volume of the solid phase of the soil. Soil particle density is defined as follows:
𝑠
𝜌 = 𝑀𝑠
𝑉𝑠
(2.1.1)
The soil particle density in soil minerals ranges from about 1.8 to 3.2 g/cm3 (United States Department of Agriculture [USDA] 2009). However, in most mineral soils, the soil particle density has a narrow range of 2.6–2.7 g/cm3 (Hillel 1980b). This density is close to that of quartz, which is usually the predominant constituent of xxxxx soils. A typical value of
2.65 g/cm3 has been suggested to characterize the soil particle density of a general mineral soil (Freeze and Xxxxxx 1979; USDA 2009). Aluminosilicate clay minerals have particle density variations in the same range. The presence of iron oxides and other heavy minerals increases the
value of the soil particle density. Goethite, a common iron oxyhydroxide soil mineral, has a particle density of 4.2 g/cm3 (USDA 2009). The presence of solid organic materials in the soil decreases the value.
2.1.1.2 Bulk (Dry) Density
The soil bulk or dry density, ρb, is the ratio of the mass of the solid phase of the soil (i.e., dried soil) to its total volume (solid and pore volumes together) and is defined as follows:
𝜌𝑏 = 𝑀𝑠 = 𝑀𝑠
(2.1.2)
𝑉𝑡 𝑉𝑠+Xx+𝑉𝑔
The bulk density, ρb, is related to the soil particle density, ρs, by the total soil porosity, pt, according to the following equation:
𝜌𝑏 = (1 − 𝑝𝑡)𝜌𝑠 , (2.1.3)
where (1-pt) is the ratio of the solid volume (Vs ) to the total volume (Vl + Vg + Vs ). Section 2.2 of this report discusses total porosity.
From the above definition, it should be obvious that the value of the dry density is always smaller than the value of the soil particle density. For example, if the volume of the pores
(Vl + Vg ) accounts for half of the total volume, the value of dry density is half the value of the soil particle density.
Typical values of dry density in different types of soils and in concrete are shown in Table 2.1.1. Dry density depends on the structure of the soil matrix (or its degree of compaction or looseness) and on the soil matrix’s swelling/shrinkage characteristics. Xxxxx soils, because of less pore space compared to silt or clay soils, have relatively high bulk density. Soils that are loose, porous, or rich in organic matter have lower bulk density (USDA Natural Resources Conservation Service [NRCS] 2008). High bulk density is an indicator of low soil porosity and soil compaction. It may cause restrictions to plant growth and poor movement of air and water through the soil (USDA NRCS 2008). Because of its high degree of aggregation (i.e., small total porosity), concrete has, in general, a higher dry density than soil.
To use Table 2.1.1 to estimate dry bulk density (or any other soil properties discussed in this handbook), the user needs to know the soil texture type. The common method used in the field to classify a soil is the “feel” method (Xxxxx 1984). This method consists of merely rubbing the soil between the thumb and fingers. Usually it is helpful to wet the sample to estimate plasticity more accurately. The way a wet soil “slicks out,” that is, develops a continuous ribbon when pressed between the thumb and fingers, gives a good idea of the amount of clay present.
The slicker the wet soil, the higher the clay content. The sand particles are gritty, and the silt has a floury or talcum-powder feel when dry and is only slightly plastic and sticky when wet.
Persistent cloddiness is generally the result of the presence of silt and clay. The accuracy of the feel method depends largely on experience. The laboratory method is more accurate but is time- consuming. The laboratory method to classify soil involves particle-size analysis, in which sieves are usually employed for coarser particles and the rate of settling in water for finer particles (Xxxxxxxx and Xxxxxx 1979). The USDA has developed a method for naming soils on the basis
of particle-size analysis. The relationship between such an analysis and soil class names is shown diagrammatically in Figure 2.1.1. The legend in the figure explains the use of this soil texture triangle.
TABLE 2.1.1 Dry Bulk Density (g/cm3) for Different Soil Types from Different Sourcesa
Soil Type | NUREG/CR-6697 (Xx et al. 2000) | Xxxxxxx et al. (1982); Poffijn (1988) |
Sand | 1.51 | 1.52 |
Loamy sand | 1.56 | NAb |
Xxxxx loam | 1.56 | 1.44 |
Xxxxx xxxx loam | 1.62 | NA |
Loam | 1.51 | 1.36 |
Silt loam | 1.46 | 1.28 |
Silt | 1.43 | NA |
Clay loam | 1.56 | 1.28 |
Silty clay loam | 1.51 | NA |
Xxxxx xxxx | 1.64 | NA |
Silty clay | 1.70 | NA |
Clay | 1.64 | 1.20 |
Generic soil type | 1.52 | NA |
Concrete | NA | 2.40 |
a The values are rounded to three significant digits. b NA = not applicable. | ||
2.1.1.3 Total (Wet) Density
The total, or wet, density of soil, ρt, is the ratio of the total mass of soil (with interstitial liquid) to its total volume and can be defined as follows:
𝜌𝑡 = 𝑀𝑡 = 𝑀𝑠+𝑀𝑙
(2.1.4)
𝑉𝑡 𝑉𝑠+Xx+𝑉𝑔
Total density differs from dry density in that it is strongly dependent on the moisture content of the soil. For a dry soil, total density approximates the value of dry density.
2.1.2 Measurement Methodology
For use in RESRAD (onsite), only the dry densities of five distinct materials (cover layer, contaminated zone, unsaturated and saturated zones, and building foundation material) are needed as input parameters. For the RESRAD-OFFSITE code, the dry densities of agricultural areas (fruit, grain, nonleafy, and leafy vegetables) and livestock field areas (pasture, silage, and grain) are also required. However, because information on both soil particle and bulk (i.e., dry)
density is required for calculating total porosity of the soil material, descriptions of the techniques and procedures for measuring both types of densities follow.
FIGURE 2.1.1 U.S. Department of Agriculture Method for Naming Soils (Note: Percentages of sand, silt, and clay in the major soil textural classes are shown. To use the diagram, locate the percentage of clay first and project inward as shown by the arrow. Do the same for the percentage of silt [or sand]. The point at which the two projections cross will identify the class name.) Source: Xxxxx 1984
The standard methods used on Formerly Utilized Sites Remedial Action Program (FUSRAP) sites for determining the particle density and the dry density in soil materials are those prepared by the American Society of Testing Materials (ASTM 2007; 2008a, b, c; 2009; 2010a, b, c) and the U.S. Department of the Army (DOA 1970), as listed in Table 2.1.2. A general discussion of these measurement methodologies is also provided by Xxxxx and
Xxxxxx (1986a,b).
TABLE 2.1.2 Standard Methods for Measuring Particle Density and Bulk (Dry) Density in Soil Materials at FUSRAP Sites
Parameter Measured | Type of Measurement | Standard Test Method | Reference |
Soil particle density | Soil sample testing | Appendix IV: Specific Gravity | DOA (1970) |
ASTM D 854–10: Standard Test Method for Specific Gravity of Soil Solids by Water Pycnometer | ASTM (2010a) | ||
Bulk (dry) soil density | Soil sample testing | Appendix II: Unit Weights, Void Ratio, Porosity, and Degree of Saturation | DOA (1970) |
ASTM D 7263–09: Standard Test Methods for Laboratory Determination of Density (Unit Weight) of Soil Specimens | ASTM (2009) | ||
In situ near- surface testing | ASTM D 1556–07: Standard Test Method for Density and Unit Weight of Soil in Place by the Sand-Cone Method | ASTM (2007) | |
ASTM D 2167–08: Standard Test Method for Density and Unit Weight of Soil in Place by the Rubber Balloon Method | ASTM (2008a) | ||
ASTM D 6938–10 : Standard Test Methods for In-Place Density and Water Content of Soil and Soil-Aggregate by Nuclear Methods (shallow depth) | ASTM (2010b) | ||
ASTM D 2937–10: Standard Test Method for Density of Soil in Place by the Drive-Cylinder Method | ASTM (2010c) | ||
ASTM D 4564–08e1: Standard Test Method for Density and Unit Weight of Soil in Place by the Sleeve Method | ASTM (2008b) | ||
In situ below- surface testing | ASTM D 5195–08: Standard Test Method for Density of Soil and Rock In-Place at Depths Below Surface by Nuclear Methods | ASTM (2008c) |
2.1.2.1 Soil Particle Density Measurement
The soil particle density of a soil sample is calculated on the basis of the measurement of two quantities: (1) Ms, the mass of the solid phase of the sample (dried mass), and (2) Vs, the volume of the solid phase (Xxxxx and Xxxxxx 1986b). Assuming that water is the only volatile in a soil sample, the mass (Ms) can be obtained by drying the sample (usually at 110 ± 5°C) until it reaches a constant weight, Ws. This method may not be valid for organic soils or soils with asphalt.
The solid phase volume, Vs, can be measured in different ways. One way is to measure the volume directly by observing the resulting increase in the volume of water as the sample of dried soil is introduced into a graduated flask that initially contains pure water (or another liquid). After making sure that the soil/water mixture is free from air bubbles, the observed expansion in volume (i.e., the replaced volume of water) should be equal to Vs, the solid phase volume. The problem with this approach is that the techniques used to eliminate air bubbles from the mixture (such as heating) can also disturb the total volume and thus introduce errors into the calculations.
Another way to measure the solid phase volume (Vs) is to evaluate the mass and density of water (or another fluid) displaced by the sample (after being oven-dried). This second approach has been used for quite some time and is simple, direct, and accurate if done carefully (Xxxxx and Xxxxxx 1986a). It is based on the fact that if Vdw, the volume of water displaced by the solids, is equal to Vs, then
𝑉𝑑𝑑𝑑 = 𝑀𝑑𝑑𝑑 = 𝑉𝑠 = 𝑀𝑠
(2.1.5)
and
where
𝜌𝑑𝑑
𝑀
𝜌𝑠 = 𝜌𝑑𝑑 𝑀𝑠
𝑑𝑑𝑑
𝜌𝑠
, (2.1.6)
Mdw =mass of the displaced water, and
ρw = water density.
Therefore, to obtain the soil particle density, it is necessary to evaluate the water density at the specific pressure and temperature conditions and to measure Ms and Mdw (DOA 1970, Appendix IV; ASTM 2010a).
The value of Mdw is obtained by using a graduated volumetric flask and taking the following measurements:
Mf = mass of the empty flask,
Mfs = mass of the flask plus the dried soil sample,
Mfsw = mass of the flask plus the soil after filling with water up to a fixed volume, Vf, and
Mfw = mass of the flask filled with pure water up to the fixed volume Vf. The mass of the displaced water, Mdw, can then be calculated as follows:
𝑀𝑑𝑑𝑑 = (𝑀𝑓𝑠 − 𝑀𝑓) − (𝑀𝑓𝑠𝑑𝑑 − 𝑀𝑓𝑑𝑑) (2.1.7) Substituting Mdw into the expression for soil particle density, ρs, yields
𝑠 𝑑𝑑
𝜌 = 𝜌 � 𝑀𝑠 � (2.1.8)
(𝑀𝑓𝑠−𝑀𝑓)−(𝑀𝑓𝑠𝑑𝑑−𝑀𝑓𝑑𝑑)
This method is very precise, but it requires careful measuring of volumes and masses and consideration of the effects of pressure and temperature conditions on the water density. Possible errors can result not only from determining the masses and volumes but from non-representative sampling.
2.1.2.2 Dry Density Measurement
The dry (bulk) density (ρb) of a soil sample is evaluated on the basis of two measured values: (1) Ms, the oven-dried mass of the sample, and (2) Vt, the field volume or the total volume of the sample. As stated previously, for the calculation of soil particle density (ρs), mass (Ms) is measured after drying the sample at 110 ± 5° C until a near constant weight is reached. This laboratory technique directly determines the dry density of a soil sample (DOA 1970, Appendix II). Possible direct methods of measuring the dry density include the core and excavation methods, which essentially consist of drying and weighing a known volume of soil.
Variations of these methods are related to different ways of collecting the soil sample and measuring volume. In the core method (Xxxxx and Xxxxxx 1986a; ASTM 2010c), a cylindrically shaped metal sampler is introduced into the soil, with care to avoid disturbing the sample. At the desired depth in the soil, a known field volume (Vt) of soil material is collected as it exists in situ. The sample is then oven-dried and weighed to obtain the mass. The value of the dry density is calculated by dividing the mass by the volume. Problems in using this technique include sampling difficulties, such as the presence of gravels in the soil, and the possibility of disturbing the structure of the soil during the sampling process when the sampler is introduced into the ground.
In the excavation method (Xxxxx and Xxxxxx 1986a), the dry density of the soil is determined by excavating a hole in the ground, oven-drying and weighing the amount of soil removed from the ground to determine the mass, and measuring the volume of the excavation. The volume (Vt) can be determined in different ways. One is to use the sand-funnel method (ASTM 2007), in which a selected type of sand with a known volume per unit mass is used to completely fill the hole. Then, by measuring the total mass of sand needed to fill the hole, the volume can be determined. Another possible way to measure the volume (Vt) is to use the rubber-balloon method (ASTM 2008a). In this technique, a balloon is placed within the hole and
filled with a liquid (water) up to the borders of the hole. The volume of the excavated soil sample is then equal to the volume of the liquid in the balloon.
An advantage of using the excavation method to measure dry densities of soils other than the core method is that it is more suitable for heterogeneous soils with gravels.
An indirect method of measuring soil density, applicable for in situ rather than laboratory determinations, is called the radiation method or gamma-ray attenuation densitometry (Xxxxx and Xxxxxx 1986a; ASTM 2010b; ASTM 2008c). This method is based on the principle that the amount of gamma radiation attenuated and scattered in the soil depends on the soil properties, including the combined densities of the solid/liquid components of the medium. By measuring the radiation that is transmitted through the medium or that is scattered by soil components and reaches a detector placed away from the source, and by using proper calibration, the wet density of the soil, ρt, can be determined. To determine the dry density, ρb, a correction of the result is needed to delete the contribution from the liquid phase of the soil.
The radiation method used for measuring soil density has several advantages over other related laboratory techniques: (1) it yields an in situ evaluation of soil density, (2) it causes minimum disturbance of the soil, (3) it requires a relatively short measurement time, (4) it is more applicable for deeper subsoil determinations because it requires minimal excavation, and
(5) it is a nondestructive technique because continuous or repeated measurements can be performed at the same spot. The radiation method also has some disadvantages compared with the other methods. Because it is a more sophisticated technique, it requires expensive equipment and highly trained operators who must be able to handle the frequent calibration procedures, the electronics, and the sampling equipment. The system operator must be trained in the radiation aspects and radiological protection procedures of the entire operation.
2.1.3 Data Input Requirements
In the RESRAD (onsite) code, one variable is assigned to represent the dry density, measured in units of grams per cubic centimeter, of each of the following five materials:
(1) cover material, (2) contaminated zone, (3) unsaturated zone, (4) saturated zone, and
(5) building foundation material (i.e., concrete). Density of soil in the contaminated zone, together with radionuclide concentrations, determines the total radioactive material inventory. For the RESRAD-OFFSITE code, the dry densities of agricultural areas (fruit, grain, nonleafy, and leafy vegetables) and livestock field areas (pasture, silage, and grain) are also required.
For different types of soil, a default value of 1.5 g/cm3 is assigned for the dry density, a value that is representative of a xxxxx soil. Although the building foundation material (i.e., concrete) has a solid phase density (i.e., particle density) similar to that of the soil, because of its small total porosity, concrete has, in general, a higher dry density than soils. In RESRAD (onsite) and RESRAD-OFFSITE, a default value of 2.4 g/cm3 is assigned for the dry density of the foundation building material. This default value is provided for generic use of the codes. For more accurate use of the codes, site-specific values for dry density should be experimentally determined by using one of the methods described in Section 2.1.2.2. If a site-specific value is not available, use knowledge of soil type to obtain a slightly more accurate estimate of dry density with data presented in Table 2.1.1. If neither site-specific value nor soil type is known, then use default value. For the probabilistic analysis, use the distributions developed for density of soil of different soil types in NUREG/CR-6697 (Yu et al. 2000).
2.2 TOTAL POROSITY
2.2.1 Definition
The total porosity of a porous medium is the ratio of the pore volume to the total volume of a representative sample of the medium. Assuming that the soil system comprises three phases— solid, liquid (water), and gas (air)—where Vs is the volume of the solid phase, Vl is the volume of the liquid phase, Vg is the volume of the gaseous phase, Vp = Vl + Vg is the volume of the pores, and Vt = Vs + Vl + Vg is the total volume of the sample, then the total porosity of the soil sample, pt, is defined as follows:
t
p = V p = V l +V g .
(2.2.1)
V t V s +V l +V g
Porosity is a dimensionless quantity and can be reported either as a decimal fraction or as a percentage. Table 2.2.1 lists representative total porosity ranges for various geologic materials. A more detailed list of representative porosity values (total and effective porosities) is provided in Table 2.2.2. In general, total porosity values for unconsolidated materials lie in the range of 0.25–0.7 (25%–70%). Coarse-textured soil materials such as gravel and sand tend to have a lower total porosity than fine-textured soils such as silts and clays. The total porosity in soils is not a constant quantity because the soil, particularly clayey soil, alternately swells, shrinks, compacts, and cracks. The porosity of a soil depends on several factors, such as (1) packing density, (2) the particle size distribution, (3) particle shape, and (4) cementing. Table 2.2.3 shows
TABLE 2.2.1 Range of Porosity Values
Soil Type | Porosity, pt |
Unconsolidated deposits | |
Gravel | 0.25–0.40 |
Sand | 0.25–0.50 |
Silt | 0.35–0.50 |
Clay | 0.40–0.70 |
Rocks | |
Fractured basalt | 0.05–0.50 |
Karst limestone | 0.05–0.50 |
Sandstone | 0.05–0.30 |
Limestone, dolomite | 0.00–0.20 |
Shale | 0.00–0.10 |
Fractured crystalline rock | 0.00–0.10 |
Dense crystalline rock | 0.00–0.05 |
Source: Freeze and Cherry (1979). |
TABLE 2.2.2 Representative Porosity Values
Total Porosity, pt | Effective Porosity,a pe | |||
Material | Range | Arithmetic Mean | Range | Arithmetic Mean |
Sedimentary material | ||||
Sandstone (fine) | 0.14–0.49 | 0.33 | 0.02–0.40 | 0.21 |
Sandstone (medium) | 0.30–0.44 | 0.37 | 0.12–0.41 | 0.27 |
Siltstone | 0.21–0.41 | 0.35 | 0.01–0.33 | 0.12 |
Sand (fine) | 0.25–0.53 | 0.43 | 0.01–0.46 | 0.33 |
Sand (medium) | 0.29–0.49 | 0.39 | 0.16–0.46 | 0.32 |
Sand (coarse) | 0.31–0.46 | 0.39 | 0.18–0.43 | 0.30 |
Gravel (fine) | 0.25–0.38 | 0.34 | 0.13–0.40 | 0.28 |
Gravel (medium) | 0.24–0.44 | 0.32 | 0.17–0.44 | 0.24 |
Gravel (coarse) | 0.24–0.36 | 0.28 | 0.13–0.25 | 0.21 |
Silt | 0.34–0.61 | 0.46 | 0.01–0.39 | 0.20 |
Clay | 0.34–0.57 | 0.42 | 0.01–0.18 | 0.06 |
Limestone | 0.07–0.56 | 0.30 | ~0–0.36 | 0.14 |
Wind-laid material | ||||
Loess | 0.44–0.57 | 0.49 | 0.14–0.22 | 0.18 |
Eolian sand | 0.40–0.51 | 0.45 | 0.32–0.47 | 0.38 |
Tuff | 0.07–0.55 | 0.41 | 0.02–0.47 | 0.21 |
Igneous rock | ||||
Weathered granite | 0.34–0.57 | 0.45 | -b | - |
Weathered gabbro | 0.42–0.45 | 0.43 | - | - |
Basalt | 0.03–0.35 | 0.17 | - | - |
Metamorphic rock | ||||
Schist | 0.04–0.49 | 0.38 | 0.22–0.33 | 0.26 |
a Effective porosity is discussed in Section 2.3 of this handbook. b A hyphen indicates that no data are available. Sources: Xxxxxx and Xxxxxxx (1967), McWorter and Xxxxxx (1977). | ||||
the relationship of total porosity to physical characteristics for the case of silica sand (Xxxx et al. 1984).
2.2.2 Measurement Methodology
A standard method approved by the U.S. Army Corps of Engineers for determining the total porosity of soil materials, and used on FUSRAP sites, is described in Appendix II of DOA (1970). Further discussion of this methodology is presented by Xxxxxxxxx and Xxxxxxxxxx (1986).
TABLE 2.2.3 The Relationship between Physical Characteristics of Grains and Total Porosity
Total Porosity | |||
Property | Low | High | Reason |
Size | NAa | NA | Grain size has no influence on porosity. |
Sorting | Poor | Good | Small grains fill in voids between large grains. |
Packing | Close | Loose | Close packing leads to fewer voids between grains. |
Shape | Spherical | Oblong | Spherical grains tend to pack more closely. |
Roundness | Rounded | Angular | Rounded grains tend to pack more closely. |
a NA = not applicable. Source: Xxxx et al. (1984). | |||
On the basis of the definition of total porosity, a soil sample could be evaluated for total porosity by directly measuring the pore volume (Vp) and the total volume (Vt). The total volume is easily obtained by measuring the total volume of the sample. The pore volume can, in principle, be evaluated directly by measuring the volume of water needed to completely saturate the sample. In practice, however, it is always difficult to saturate the soil sample exactly and completely and, therefore, the total porosity of the sample is rarely evaluated by a direct method. Usually, the total porosity is derived by using the following expression (DOA 1970, Appendix II; Xxxxxxxxx and Xxxxxxxxxx 1986):
⎛ V s ⎞ ⎛ ρb ⎞
pt = ⎜1 -
V
⎟ = ⎜1 - ρ ⎟ ,
(2.2.2)
⎝ t ⎠ ⎝ s ⎠
where
pt = a decimal fraction, Vs = soil particle volume, Vt = total volume,
ρs = solid phase (soil particle) density, and
ρb = dry bulk density of the sample.
Equation (2.2.2) can be obtained by rearranging Equation (2.1.3) in the soil density section of this handbook. Using this approach, the values of ρs and ρb are evaluated by laboratory or in situ measurements (Section 2 in the soil density section [2.1.2] of this handbook) and are then used to calculate the total porosity pt.
2.2.3 Data Input Requirements
To use the RESRAD (onsite) and RESRAD-OFFSITE codes, the user is required to define, or use the default values of, the total porosity of five distinct materials: (1) cover material,
(2) contaminated zone, (3) unsaturated zone, (4) saturated zone, and (5) building foundation material (i.e., concrete). For the RESRAD-OFFSITE code, the total porosity of soil materials in agricultural areas (fruit, grain, nonleafy, and leafy vegetables), livestock field areas (pasture, silage, and grain), and off-site dwelling areas are also required. In both codes, the total porosities are entered as decimal fractions rather than as percentages. RESRAD (onsite) and RESRAD- OFFSITE adopt the following values as defaults: pt = 0.4 for the four soil materials listed above and for agricultural and livestock field areas and dwelling areas in the RESRAD-OFFSITE code; a default value of pt = 0.1 for the building foundation (i.e., concrete) is used in both codes. These default values are listed in Table 1.1 and are provided for generic use of the codes. For more accurate use of the codes, site-specific data should be used. The total porosity is negatively correlated with bulk (dry) density, Equation (2.2.2). For the probabilistic analysis, use the distributions developed for porosity of different soil types in NUREG/CR-6697 (Yu et al. 2000).
Site-specific values for total porosity should be experimentally determined according to the method presented in Section 2.2.2. If a site-specific value is not available, use knowledge of soil type to obtain a slightly more accurate estimate of total porosity with data presented in Tables 2.2.1 and 2.2.2. If neither site-specific value nor soil type is known, then use default value.
2.3 EFFECTIVE POROSITY
2.3.1 Definition
The effective porosity, pe, also called the kinematic porosity, of a porous medium is defined as the ratio of the part of the pore volume where the water can circulate to the total volume of a representative sample of the medium. In naturally porous systems such as subsurface soil, where the flow of water is caused by the composition of capillary, molecular, and gravitational forces, the effective porosity can be approximated by the specific yield, or drainage porosity, which is defined as the ratio of the volume of water drained by gravity from a saturated representative sample of the soil to the total volume of the sample.
The definition of effective (kinematic) porosity is linked to the concept of pore fluid displacement rather than to the percentage of the volume occupied by the pore spaces. The pore volume occupied by the pore fluid that can circulate through the porous medium is smaller than the total pore space, and, consequently, the effective porosity is always smaller than the total porosity. In a saturated soil system composed of two phases (solid and liquid) where (1) Vs is the volume of the solid phase, (2) Vw = (Viw + Vmw) is the volume of the liquid phase, (3) Viw is the volume of immobile pores containing the water adsorbed onto the soil particle surfaces and the water in the dead-end pores, (4) Vmw is the volume of the mobile pores containing water that is free to move through the saturated system, and (5) Vt = (Vs + Viw + Vmw) is the total volume, the effective porosity can be defined as follows:
𝑃𝑒 = 𝑉𝑚𝑑𝑑 = 𝑉𝑚𝑑 𝑑
(2.3.1)
𝑉𝑡 𝑉𝑠+ 𝑉𝑚𝑑𝑑+ 𝑉𝑖𝑑𝑑
Another soil parameter related to the effective soil porosity is the field capacity, θr, also called specific retention, irreducible volumetric water content, or residual water content, which is defined as the ratio of the volume of water retained in the soil sample, after all downward gravity drainage has ceased, to the total volume of the sample. Considering the terms presented above for a saturated soil system, the total porosity pt and the field capacity θr can be expressed, respectively, as follows:
and
𝑃 = 𝑉𝑚𝑑𝑑+ 𝑉𝑖𝑑𝑑
𝑡
𝑉𝑡
𝑟
𝜃𝜃 = 𝑉𝑖𝑑𝑑
𝑉𝑡
(2.3.2)
(2.3.3)
Therefore, the effective porosity is related to the total porosity and the field capacity according to the following expression:
𝑃𝑒 = 𝑃𝑡 − 𝜃𝜃𝑟 (2.3.4)
Several aspects of the soil system influence the value of its effective porosity: (1) the adhesive water on minerals, (2) the absorbed water in the clay-mineral lattice, (3) the existence of unconnected pores, and (4) the existence of dead-end pores. The adhesive water in the soil is that part of the water present in the soil that is attached to the surface of the soil grains through the forces of molecular attraction (Marsily 1986). The sum of the volumes of the adhesive and absorbed water plus the water that fills the unconnected and dead-end pores constitutes the volume of the adsorbed water, Viw, that is unable to move through the system.
Table 2.3.1 lists the representative values of dry bulk density, total porosity, and effective porosity for common aquifer matrix materials. A detailed list of representative porosity values (total porosity and effective porosity) is also presented in Table 2.2.2 (see Section 2.2) in this handbook).
2.3.2 Measurement Methodology
Determination of the effective porosity, pe, of soils can be accomplished indirectly by measuring the total porosity, pt, and the field capacity, θr, and then calculating pe from Equation (2.3.4). The total porosity is obtained indirectly by measuring the soil densities
according to the method described in Section 2.1. To determine the field capacity of the soils, the soil sample is first saturated with water and is then allowed to drain completely under the action of gravity until it gets to its irreducible saturation. The value of θr can then be obtained according to the methods used for measuring volumetric water content (Section 2.15).
TABLE 2.3.1 Representative Values of Dry Bulk Density, Total Porosity, and Effective Porosity for Common Aquifer Matrix Materials
Aquifer Matrix | Dry Bulk Density Range (g/cm3) | Total Porosity Range | Effective Porosity Range |
Clay | 1.00–2.40 | 0.34–0.60 | 0.01–0.2 |
Peat | - | - | 0.3–0.5 |
Glacial sediments | 1.15–2.10 | - | 0.05–0.2 |
Xxxxx xxxx | - | - | 0.03–0.2 |
Silt | - | 0.34–0.61 | 0.01–0.3 |
Loess | 0.75–1.60 | - | 0.15–0.35 |
Fine sand | 1.37–1.81 | 0.26–0.53 | 0.1–0.3 |
Medium sand | 1.37–1.81 | - | 0.15–0.3 |
Coarse sand | 1.37–1.81 | 0.31–0.46 | 0.2 0.35 |
Gravely sand | 1.37–1.81 | - | 0.2–0.35 |
Fine gravel | 1.36–2.19 | 0.25–0.38 | 0.2–0.35 |
Medium gravel | 1.36–2.19 | - | 0.15–0.25 |
Coarse gravel | 1.36–2.19 | 0.24–0.36 | 0.1–0.25 |
Sandstone | 1.60–2.68 | 0.05–0.30 | 0.1–0.4 |
Siltstone | - | 0.21–0.41 | 0.01–0.35 |
Shale | 1.54–3.17 | 0.0–0.10 | - |
Limestone | 1.74–2.79 | 0.0–0.50 | 0.01–0.24 |
Granite | 2.24–2.46 | - | - |
Basalt | 2.00–2.70 | 0.03–0.35 | - |
Volcanic tuff | - | - | 0.02–0.35 |
Source: Xxxxxxxx and Xxxxxxxx 1990. | |||
2.3.3 Data Input Requirements
To use RESRAD (onsite) and RESRAD-OFFSITE, the user is required to define (or to use the default values of) the effective porosity of two distinct geologic materials: (1) saturated zone and (2) unsaturated zone. For the RESRAD-OFFSITE code, the effective porosity of the contaminated zone is also required. In both codes, the effective porosity values are entered as decimal fractions rather than as percentages. As a default value, the codes adopt the value of pe = 0.2 for all three geologic materials. These default values are listed in Tables 1.1 and 1.2,
respectively, for RESRAD (onsite) and RESRAD-OFFSITE and are provided for generic use of the codes. For more accurate use of the codes, site-specific data should be used. The effective porosity is positively correlated with the total porosity and negatively correlated with field capacity, Equation (2.3.4). For the probabilistic analysis, use the distributions developed for effective porosity of different soil types in NUREG/CR-6697 (Yu et al. 2000).
Site-specific values for effective porosity should be experimentally determined according to the method presented in Section 2.3.2. Effective porosity values should not be greater than total porosity values. If a site-specific value is not available, use knowledge of soil type to obtain a
slightly more accurate estimate of effective porosity with data presented in Table 2.2.2 (Section 2.2). If neither site specific value nor soil type is known, then use default value.
2.4 HYDRAULIC CONDUCTIVITY
2.4.1 Definition
The hydraulic conductivity of a soil is a measure of the soil’s ability to transmit water when subjected to a hydraulic gradient. Hydraulic conductivity is defined by Xxxxx’x law, which, for one-dimensional vertical flow, can be written as follows:
U = −K dh , (2.4.1)
dz
where U is Darcy’s velocity (or the average velocity of the soil fluid through a geometric cross- sectional area within the soil), h is the hydraulic head, and z is the vertical distance in the soil. The coefficient of proportionality, K, in Equation (2.4.1) is called the hydraulic conductivity. The term coefficient of permeability is also sometimes used as a synonym for hydraulic conductivity. On the basis of Equation (2.4.1), the hydraulic conductivity is defined as the ratio of Darcy’s velocity to the applied hydraulic gradient. The dimension of K is the same as that for velocity, that is, length per unit of time ( LT-1).
Hydraulic conductivity is one of the hydraulic properties of the soil; the other involves the soil’s fluid retention characteristics. These properties determine the behavior of the soil fluid within the soil system under specified conditions. More specifically, the hydraulic conductivity determines the ability of the soil fluid to flow through the soil matrix system under a specified hydraulic gradient; the soil fluid retention characteristics determine the ability of the soil system to retain the soil fluid under a specified pressure condition.
The hydraulic conductivity depends on the soil grain size, the structure of the soil matrix, the type of soil fluid, and the relative amount of soil fluid (saturation) present in the soil matrix. The important properties relevant to the solid matrix of the soil include pore size distribution, pore shape, tortuosity, specific surface, and porosity. In relation to the soil fluid, the important properties include fluid density, ρ, and fluid viscosity, μ. For a subsurface system saturated with the soil fluid, the hydraulic conductivity, K, can be expressed as follows (Bear 1972):
K = kpg , (2.4.2)
μ
where k, the intrinsic permeability of the soil, depends only on properties of the solid matrix, and ρg/μ, called the fluidity of the liquid, represents the properties of the percolating fluid. The hydraulic conductivity, K, is expressed in terms of length per unit of time (LT-1), the intrinsic permeability, k, is expressed in L2, and the fluidity, ρg/μ, in L-1T-1. By using Equation (2.4.2),
Xxxxx’x law can be rewritten explicitly in terms of its coefficient of proportionality (hydraulic conductivity K):
K = kpg =
μ
(2.4.3)
U
dh / dz
When the fluid properties of density and viscosity are known, Equation (2.4.3) can be used to experimentally determine the value of the intrinsic permeability, k, and the hydraulic conductivity, K, as will be shown in the following section.
The values of saturated hydraulic conductivity in soils vary within a wide range of several orders of magnitude, depending on the soil material. Table 2.4.1 lists the range of expected values of K for various unconsolidated and consolidated soil materials. The expected representative values of K for soil materials of different textures are presented in Table 2.4.2. A more detailed list of expected representative values of K based on the grain size distribution, degree of sorting, and silt content of several soil materials is presented in Table 2.4.3 and Table 2.4.4. The default hydraulic conductivity values are listed in Table 2.4.5. Xxxxxx et al. (1990) developed a hydrogeologic database from a technical survey of 400 sites across the United States and presented the box plot of hydraulic conductivity for 12 groups of hydrogeologic environments (see Figure 8 in Newell et al. [1990] for details.). Their research indicates that the hydraulic conductivity follows a lognormal distribution. The median of the national distribution of hydraulic conductivity is 0.005 cm/s (or 1.58 ×103 m/yr).
Because of the spatial variability usually found in the geological formation of soils, saturated hydraulic conductivity values also show variations throughout the space domain within a subsurface geological formation. Such a geological formation is said to be heterogeneous. If the properties of the geologic formation are invariable in space, the formation is homogeneous. A geological formation is said to be isotropic if at any point in the medium, the values of the saturated hydraulic conductivity (K) are independent of the direction of measurement. Again, because of the usually stratified nature of unconsolidated sedimentary soil materials, soils are usually anisotropic. Within an anisotropic geological formation, the vertical component of the saturated hydraulic conductivity is usually smaller (by one to two orders of magnitude) than the horizontal component.
TABLE 2.4.1 Range of Saturated Hydraulic Conductivity of Various Soil Materials
Soil Type | Saturated Hydraulic Conductivity, K (m/yr) |
Unconsolidated deposits | |
Gravel | 1 × 104–1 × 107 |
Clean sand | 1 × 102–1 × 105 |
Silty sand | 1 × 101–1 × 104 |
Silt, loess | 1 × 10-2–1 × 102 |
Glacial till | 1 × 10-5–1 × 101 |
TABLE 2.4.1 (Cont.)
Soil Type | Saturated Hydraulic Conductivity, K (m/yr) |
Unweathered marine clay | 1 × 10-5–1 × 10-2 |
Rocks | |
Shale | 1 × 10-6–1 × 10-2 |
Unfractured metamorphic and igneous rocks | 1 × 10-7–1 × 10-3 |
Sandstone | 1 × 10-3–1 × 101 |
Limestone and dolomite | 1 × 10-2–1 × 101 |
Fractured metamorphic and igneous rocks | 1 × 10-1–1 × 103 |
Permeable basalt | 1 × 101–1 × 105 |
Karst limestone | 1 × 101–1 × 105 |
Source: Adapted from Freeze and Cherry (1979). |
TABLE 2.4.2 Representative Values of Saturated Hydraulic Conductivity of Different Soil Textures
Texture | Saturated Hydraulic Conductivity, K (m/yr) |
Sand | 5.55 × 103 |
Loamy sand | 4.93 × 103 |
Xxxxx loam | 1.09 × 103 |
Silty loam | 2.27 × 102 |
Loam | 2.19 × 102 |
Xxxxx xxxx loam | 1.99 × 102 |
Silty clay loam | 5.36 × 10 |
Clay loam 7.73 × 10
Xxxxx xxxx 6.84 × 10
Silty clay 3.21 × 10
Clay 4.05 × 10
Source: Xxxxx and Xxxxxxxxxx (1978).
TABLE 2.4.3 Estimated Saturated Hydraulic Conductivities for Fine-Grained Materials
Grain-Size Class
Saturated Hydraulic Conductivity, K (103 m/yr)
Clay <0.0001
Xxxx, xxxxxx 0.1–0.4
TABLE 2.4.3 (Cont.)
Grain-Size Class | Saturated Hydraulic Conductivity, K (103 m/yr) |
Silt, slightly xxxxx | 0.5 |
Silt, moderately xxxxx | 0.8–0.9 |
Silt, very xxxxx | 1.0–1.2 |
Xxxxx silt | 1.2 |
Silty sand | 1.4 |
Source: EPA (1986). |
TABLE 2.4.4 Estimated Saturated Hydraulic Conductivities for Sands and Gravels According to Degree of Sorting and Silt Contenta
Saturated Hydraulic Conductivity, K (103m/yr) | ||||||
Degree of Sorting | Silt Content | |||||
Grain-Size Class or Range | Poor | Moderate | Well | Slight | Moderate | High |
Very fine sand | 1 | 2 | 3 | 3 | 2 | 1 |
Very fine to fine sand | 3 | 3 | -b | 3 | 2 | 1 |
Very fine to medium sand | 4 | 5 | - | 4 | 3 | 2 |
Very fine to coarse sand | 5 | - | - | 4 | 3 | 3 |
Very fine to very coarse sand | 7 | - | - | 6 | 4 | 3 |
Very fine sand to fine gravel | 8 | - | - | 7 | 6 | 4 |
Very fine sand to medium gravel | 11 | - | - | 9 | 7 | 5 |
Very fine sand to coarse gravel | 14 | - | - | 12 | 10 | 7 |
Fine sand | 3 | 4 | 6 | 4 | 3 | 2 |
Fine to medium sand | 6 | 7 | - | 5 | 4 | 3 |
Fine to coarse sand | 6 | 8 | - | 6 | 5 | 4 |
Fine to very coarse sand | 8 | - | - | 7 | 5 | 4 |
Fine sand to fine gravel | 10 | - | - | 8 | 7 | 5 |
Fine sand to medium gravel | 13 | - | - | 10 | 8 | 6 |
Fine sand to coarse gravel | 16 | - | - | 12 | 10 | 8 |
Medium sand | 7 | 9 | 10 | 7 | 6 | 4 |
Medium to coarse sand | 8 | 10 | - | 8 | 6 | 5 |
Medium to very coarse sand | 9 | 12 | - | 8 | 7 | 5 |
Medium sand to fine gravel | 11 | - | - | 9 | 8 | 6 |
Medium sand to medium gravel | 15 | - | - | 13 | 9 | 7 |
Medium sand to coarse gravel | 18 | - | - | 15 | 12 | 9 |
Coarse sand | 9 | 12 | 15 | 10 | 8 | 6 |
Coarse to very coarse sand | 10 | 15 | - | 10 | 8 | 6 |
Coarse sand to fine gravel | 13 | 16 | - | 12 | 10 | 8 |
Coarse sand to medium gravel | 16 | - | - | 13 | 10 | 8 |
Coarse sand to coarse gravel | 20 | - | - | 15 | 11 | 10 |
Very coarse sand | 12 | 16 | 21 | 13 | 10 | 8 |
TABLE 2.4.4 (Cont.)
Saturated Hydraulic Conductivity, K (103m/yr) | ||||||
Degree of Sorting | Silt Content | |||||
Grain-Size Class or Range | Poor | Moderate | Well | Slight | Moderate | High |
Very coarse to fine gravel | 15 | 24 | - | 13 | 12 | 10 |
Very coarse to medium gravel | 19 | 25 | - | 16 | 14 | 11 |
Very coarse sand to coarse gravel | 23 | - | - | 18 | 15 | 12 |
Fine gravel | 18 | 24 | 30 | 25 | 16 | 12 |
Fine to medium gravel | 22 | 37 | - | 22 | 19 | 15 |
Fine to coarse gravel | 27 | 37 | - | 26 | 21 | 16 |
Medium gravel | 27 | 26 | 45 | 27 | 22 | 18 |
Medium to coarse gravel | 33 | 52 | - | 33 | 27 | 21 |
Coarse gravel | 37 | 52 | 67 | 37 | 32 | 26 |
a Reduce conductivities by 10% if grains are subangular. b A hyphen indicates that no data are available. Source: EPA(1986). | ||||||
TABLE 2.4.5 Default Hydraulic Conductivity Values Used in RESRAD (onsite) and RESRAD-OFFSITE
Parameter Name | Unit | Default Value | Code- Accepted Values | References | Description |
Contaminated-zone hydraulic conductivity for Cover and Contaminated Zone | m/yr | 10 | 10-3–1010 | Yu et al. 1993; EPA 1996 | The measure of the soil’s ability to conductively transmit water when subjected to a hydraulic gradient. The hydraulic conductivity depends on the soil grain size, the structure of the soil matrix, the type of soil fluid, and the relative amount of soil fluid (saturation) present in the soil matrix. |
Saturated-zone hydraulic conductivity | m/yr | 100 | 10-3–1010 | Yu et al. 1993; EPA 1996 | See contaminated-zone hydraulic conductivity (above). |
Unsaturated-zone hydraulic conductivity | m/yr | 10 | 10-3–1010 | Yu et al. 1993; EPA 1996 | See contaminated-zone hydraulic conductivity (above). |
2.4.2 Measurement Methodology
The saturated hydraulic conductivity, K, of water in soil (or the intrinsic permeability, k, of the soil) can be measured by both field and laboratory experiments. Either way, the experimental measurement of K (or k) consists in determining the numerical value for the coefficient in Darcy’s equation.
The methodology used for the experimental determination of K (or k) in either laboratory or field experiments is based on the following procedures (Bear 1972):
1. Assume a flow pattern (such as one-dimensional flow in a porous medium) that can be described analytically by Xxxxx’x law;
2. Perform an experiment reproducing the chosen flow pattern and measure all measurable quantities in Equation (2.4.3), including fluid density, dynamic viscosity, flow velocity, and the gradient of the hydraulic head; and
3. Compute the coefficient K (or k) by substituting the measured quantities into Equation (2.4.3).
Many different laboratory or field experiments can be used to determine the coefficient K (or k).
An extensive discussion on the respective measurement methodologies for laboratory and field experiments is presented by Xxxxx and Xxxxxxx (1986) and Xxxxxxxxx and Xxxxxxx (1986), respectively. For FUSRAP sites, the standard methods used for determining saturated hydraulic conductivity in soil materials are those described by the American Society for Testing and Materials (ASTM 1992a-o), the U.S. Environmental Protection Agency (EPA 1986), the
U.S. Department of the Army (DOA 1970), and the U.S. Department of the Interior (DOI 1990a,b). Brief descriptions of these pertinent standard methods are presented in Table 2.4.6.
Laboratory tests are carried out on small samples of soil materials collected during core- drilling programs. Because of the small sizes of the soil samples handled in the laboratory, the results of these tests are considered a point representation of the soil properties. If the soil samples used in the laboratory test are truly undisturbed samples, the measured value of K (or k) should be a true representation of the in situ saturated hydraulic conductivity at that particular sampling point.
Laboratory methods may be used to evaluate the vertical and horizontal hydraulic conductivity in soil samples. For instance, in undisturbed samples of either cohesive or cohesionless soils, the values of K obtained through laboratory tests correspond to the direction in which the sample was taken, that is, generally vertical. The conductivity of disturbed (remolded) samples of cohesionless soils obtained in the laboratory can be used to approximate the actual value of K in the undisturbed (natural) soil in the horizontal direction (DOA 1970). For fine-grained soils, the undisturbed cohesive sample can be oriented accordingly, to obtain the hydraulic conductivity in either the vertical or horizontal direction.
In contrast to laboratory methods for measuring conductivity in soil samples, field methods, in general, involve a large region of the soil. Consequently, the results obtained from field methods should reflect the influences of both the vertical and horizontal directions and should represent an average value of K. This situation is especially important in highly stratified soils where the values of K measured from field methods would reflect the domination of the most permeable layer in the soil profile. However, by appropriately selecting the specific method to be used in the field, the in situ values of the vertical and horizontal components of K could be determined independently in each layer of stratified soils.
Selection of a specific method for a particular application will depend on the objectives to be achieved. Because of the difficulty in obtaining a perfectly undisturbed sample of unconsolidated soil, the K value determined by laboratory methods may not accurately reflect the respective value in the field. Therefore, field methods should be used whenever the objective is to characterize the physical features of the subsurface system in question as accurately as possible. Field methods, however, are usually more expensive than laboratory methods and, consequently, when the question of cost becomes decisive, or when actual representation of field conditions is not of fundamental importance and in situ hydraulic conductivity is not available, laboratory methods may be used to determine the saturated hydraulic conductivity K. The inclusion of more factors such as mud content (Xxxxx et al. 2015) into empirical hydraulic equations has shown improvement of accuracy of the K estimate. Note that for saturated conditions, field methods are superior to laboratory measurements; however, even field measurements can represent local conditions (e.g., slug tests) and can have errors associated with them (e.g., skin effects). According to Xxxxx and Xxxxxxx (2001), slug tests may be thought of as representing the harmonic mean or one-dimensional flow; tracer tests, the geometric mean or two-dimensional flow, and multi-well pumping tests, the arithmetic mean or the three- dimensional flow field. Depending on the scale being represented and the problem being solved, one method may be preferred over another.
35
TABLE 2.4.6 Standard Laboratory and Field Methods for Measuring Saturated Hydraulic Conductivity, K, in Soil Materials
Method Type | Method Specification | Application | Remarks | References |
Laboratory | Constant-head conductivity test with permeameter cylinder | Disturbed (remolded) samples of cohesionless coarse-grained soils with K > 1.0 × 102 m/yr. | The conductivity of disturbed (remolded) cohesionless soil is generally used to approximate the conductivity of its original, undisturbed state in a horizontal direction. | DOA (1970) EPA (1986) ASTM (1992m) Xxxxx and Xxxxxxx (1986) |
Falling-head conductivity test with permeameter cylinder | Disturbed (remolded) samples of cohesionless fine-grained soils with K < 1.0 × 102 m/yr. | The conductivity of disturbed (remolded) cohesionless soil is generally used to approximate the conductivity of its original, undisturbed state in a horizontal direction. | DOA (1970) EPA (1986) ASTM (1992m) Xxxxx and Xxxxxxx (1986) | |
Conductivity test with sampling tubes | Undisturbed samples of cohesionless soil that cannot be removed from the sampling tube without excessive disturbance. | The measured conductivity corresponds to the direction in which the sample was taken (generally vertical); may be performed under constant-head or falling-head flow conditions, depending on the estimated conductivity of the sample. | DOA (1970) | |
Conductivity test with pressure chamber | Cohesive fine-grained soil samples in the undisturbed, disturbed (remolded), or compacted state in a fully saturated condition. | Should be used only in soils that are originally fully saturated; can be performed under conditions of loading expected in the field; leakage along the sides of the sample can be prevented; usually performed under falling-head flow conditions. | DOA (1970) EPA (1986) | |
Conductivity test with back pressure | Cohesive fine-grained soil samples in the undisturbed, disturbed (remolded), or compacted state that are not fully saturated. | The additional pressure (back pressure) applied to the pore fluid of the soil sample reduces the size of the gas bubbles in the pores, increasing the degree of water saturation; usually performed under constant-head flow conditions. | DOA (1970) EPA (1986) ASTM (1992m) | |
Conductivity test with consolidometer | Cohesive fine-grained soil samples in a fully saturated condition. | Can be used as an alternative method to the conductivity test with pressure chamber. | DOA (1970) |
TABLE 2.4.6 (Cont.) | ||||
Method Type | Method Specification | Application | Remarks | References |
Laboratory | Grain-size-based empirical method | To evaluate the intrinsic permeability, k, in disturbed samples of soil materials with known grain-size distribution. [After determining k, the saturated hydraulic conductivity, K, can then be evaluated from Equation (2.4.2).] | The intrinsic permeability, k, can be predicted from the expression k = cda, where c = constant found through regression analysis; d = the mean or particle diameter; and a = exponent constant, ranging from 1.65 to 1.85. | ASTM (1992n) |
Field | Auger-hole method | Saturated soil materials near the ground surface in the presence of a shallow water table. | The method consists of pumping the water out of an auger-hole extending below the water table and then measuring the rate of the rise of the water in the hole; most widely used procedure to measure the saturated hydraulic conductivity in saturated soils; the measured result is dominated by the average value of the horizontal conductivity of the profile. | Amoozegar and Xxxxxxx (1986) |
Piezometer method | Saturated soil materials near the ground surface in the presence of a shallow water table. | The method consists of installing a piezometer tube or pipe into an auger hole with a cavity at the bottom; water is removed from the tube and the rate of the rise of the water in the tube is measured; can be used to measure either horizontal or vertical hydraulic conductivity; in stratified soils, the method can be used to measure K in each individual layer. | Amoozegar and Xxxxxxx (1986) | |
36
TABLE 2.4.6 (Cont.) | ||||
Method Type | Method Specification | Application | Remarks | References |
Single-well (slug) test in moderately permeable formations under unconfined conditions | Saturated soil materials of moderate K in aquifers under unconfined conditions. | Pump-out test method developed primarily for groundwater systems; the method consists of removing a slug of water instantaneously from a well and measuring the recovery of the water in the well; applicable to xxxxx that fully or partially penetrate the interval of interest in the unconfined aquifer; the measured K primarily reflects the value in the horizontal direction. | EPA (1986) | |
Field | Single-well (slug) test in moderately permeable formations under confined conditions | Saturated soil materials of moderately hydraulic conductivity in testing zones under confined conditions, entirely open to the well screen or open borehole. | Pump-out test method developed primarily for groundwater systems; the method consists of removing a lug of water instantaneously from a well and measuring the recovery of the water in the well; used in confined aquifer (saturated zone of the soil under confined conditions); the method assumes that the tested zone is uniform in all radial directions from the test well. | EPA (1986) |
Single-well (modified slug) test in extremely tight formations under confined conditions | Saturated soil materials with low to extremely low conductivity such as silts, clays, and shales. (For K as low as 1.0 × 10-5 m/yr). | Pump-out test method developed primarily for groundwater systems; the test is conducted by suddenly pressurizing a packed-off zone of the soil in a portion of a borehole or well within the confined zone and then monitoring the pressure decay afterwards; used in confined aquifer (saturated zone of the soil under confined conditions). | EPA (1986) | |
37
TABLE 2.4.6 (Cont.) | ||||
Method Type | Method Specification | Application | Remarks | References |
Constant-head | To measure field-saturated | Pump-in test consisting of measuring the rate at | Amoozegar and Xxxxxxx | |
conductivity test by the | hydraulic conductivity of soil | which water flows out of an uncased well into the | (1986) | |
well permeameter | materials in the unsaturated | soil under constant-head flow conditions; specially | ASTM (1992) | |
method (also referred | (vadose) zone near the ground | used to determine the field-saturated hydraulic | DOI (1990a) | |
to as shallow-well | surface. | conductivity in unsaturated zones of the soil (but | ||
pumping, or dry-auger | can also be used in saturated zones); for a very high | |||
hole, method) | Soil types ranging from sand, | groundwater condition, a “pump-out” test for | ||
silt and clay mixtures, with | saturated soils is often more satisfactory than any | |||
K larger than 1.0 × 102 m/yr, | “pump-in” type of test; the calculated K is | |||
to relatively clean sand or | dominated by the conductivity of the most | |||
xxxxx xxxxxx with | permeable layer of the soil profile; in uniform soils, | |||
K <1.0 × 104 m/yr. | the measured K reflects the conductivity in the | |||
horizontal direction; requires a large quantity of | ||||
water and a long time (several days) for execution. | ||||
Field | Double-tube method | To measure field-saturated hydraulic conductivity of oil materials in the unsaturated (vadose) zone, near the ground surface. | Utilizes two concentric cylinders installed in an auger hole; water is introduced into these cylinders and K is evaluated by measuring the flow in the cylinders; can measure field saturated K in the horizontal and vertical directions; the method requires over 200 L of water and two to six hours for completion. | Amoozegar and Xxxxxxx (1986) ASTM (1992n) |
Field | Cylindrical permeameter method (also referred to as ring infiltrometer test method) | To measure field-saturated hydraulic conductivity of soil materials in the unsaturated (vadose) zone near the ground surface. Soil materials with K ranging between 1.0 × 10-3 and 1.0 × 103 m/yr. | The method consists of ponding water within a cylindrical ring placed over the soil surface and measuring the volumetric rate of water needed to maintain a constant head; measures the field- saturated K in the vertical direction near the ground surface; a time-consuming procedure, requiring in excess of 100 L of water; variations of the method include the single-ring and double-ring infiltrometers. | Amoozegar and Xxxxxxx (1986) ASTM (1992i,n) |
38
TABLE 2.4.6 (Cont.) | ||||
Method Type | Method Specification | Application | Remarks | References |
Air-entry permeameter method | To measure field-saturated hydraulic conductivity of soil materials in the unsaturated (vadose) zone near the ground surface. | Fast technique to determine the field saturated K; requires approximately 10 L of water; is a variation of the single-ring infiltrometer method. | Amoozegar and Xxxxxxx (1986) ASTM (1992n) | |
Constant-head conductivity test in single drill hole | To measure field-saturated hydraulic conductivity of soil materials at any depth within the unsaturated (vadose) zone. Soil or rock materials with K ranging between 1.0 × 102 and 1.0 × 104 m/yr. | Pump-in test consisting of injecting water into an isolated interval of a drill hole in soil or rock under constant-head flow conditions; the only currently available test that can measure field-saturated K at large depths within the unsaturated zone; designed to determine an approximate value of K in a specific interval of a drill hole. | Amoozegar and Xxxxxxx (1986) ASTM (1992n) DOI (1990b) | |
39
2.4.2.1 Laboratory Methods
In the laboratory, the value of K can be determined by several different instruments and methods such as the permeameter, pressure chamber, and consolidometer (DOA 1970). A common feature of all these methods is that a soil sample is placed in a small cylindrical receptacle representing a one-dimensional soil configuration through which the circulating liquid is forced to flow. Depending on the flow pattern imposed through the soil sample, the laboratory methods for measuring hydraulic conductivity are classified as either a constant-head test with a steady-state flow regimen or a falling-head test with an unsteady-state flow regimen.
Constant-head methods are primarily used in samples of soil materials with an estimated K above 1.0 × 102 m/yr, which corresponds to coarse-grained soils such as clean sands and gravels. Falling-head methods, on the other hand, are used in soil samples with estimated values of K below 1.0 × 102 m/yr (DOA 1970). A list of standard laboratory methods for determining K, with variations of the constant-head and falling-head flow conditions, is presented in Table 2.4.6. Also listed in Table 2.4.6, as a laboratory method for measuring K, is the grain-size-based empirical method, in which the intrinsic permeability, k, of the soil sample is empirically determined from the otherwise laboratory-measured grain size distribution of the soil sample.
Important considerations regarding the laboratory methods for measuring K are related to the soil sampling procedure and preparation of the test specimen and circulating liquid. The sampling process, if not properly conducted, usually disturbs the matrix structure of the soil and results in a misrepresentation of the actual field conditions. Undisturbed sampling of soils is possible, but it requires the use of specially designed techniques and instruments (Xxxxx and Xxxxxxx 1986).
A detailed guide on the standard methods for soil sampling is presented in
ASTM D 4700–91, Standard Guide for Soil Sampling from the Vadose Zone (ASTM 1992l). Relatively undisturbed soil samples, suitable for the determination of hydraulic conductivity in the laboratory, could be obtained, for example, by using the thin-walled tube sampling method in ASTM D 1587–83, Standard Practice for the Thin-Walled Tube Sampling of Soils
(ASTM 1992c). In this technique, a relatively undisturbed soil sample is obtained by pressing a thin-walled metal tube into the soil, removing the soil-filled tube, and sealing its ends to prevent physical disturbance in the soil matrix.
Selecting the test fluid is also of fundamental importance for the laboratory determination of the saturated hydraulic coefficient. The objective is to have the test fluid mimic the actual properties of the soil fluid as closely as possible. When an inappropriate test fluid is selected, the test sample can get clogged with entrapped air, bacterial growths, and fines. To avoid such problems, a standard test solution such as a deaerated 0.005-mol calcium sulfate (CaSO4) solution, saturated with thymol (or sterilized with another substance such as formaldehyde), should be in the permeameter, unless there are specific reasons to choose another solution (Xxxxx and Xxxxxxx 1986).
2.4.2.2 Constant-Head Method
The constant-head test with the permeameter is one of the most commonly used methods for determining the saturated hydraulic conductivity of coarse-grained soils in the laboratory.
The test operates in accordance with the direct application of Xxxxx’x law to a soil liquid configuration representing a one-dimensional, steady flow of a percolating liquid through a saturated column of soil from a uniform cross-sectional area. In this method, a cylindrical soil sample of cross-sectional area A and length L is placed between two porous plates that do not provide any extra hydraulic resistance to the flow. A constant head difference, H2 - H1, is then applied across the test sample. By measuring the volume V of the test fluid that flows through the system during time t, the saturated hydraulic conductivity K of the soil can be determined directly from Xxxxx’x equation:
K = VL
⎡⎣ At ( H2 − H1 )⎤⎦
(2.4.4)
To improve the results, it is recommended that the test be performed several times under different head differences, H2 - H1. It is also recommended that the quantity of liquid collected be sufficient to provide at least three significant figures in the measured volume. In a simple version of the constant-head permeameter, the lower limit of the measurement of K is approximately
1 × 101 m/yr, which corresponds to the lower limit of the conductivity of xxxxx xxxx soils. For lower values of K, it is recommended that either an enhanced version of the constant-head permeameter (i.e., one that has a more sensitive method of measuring the volume flow rate) or the falling-head permeameter be used (Xxxxx and Xxxxxxx 1986). Table 2.4.6 presents variations of the constant-head method for measuring saturated hydraulic conductivity of soil materials in the laboratory.
2.4.2.3 Falling-Head Method
The falling-head test with the permeameter is primarily used for determining the K (or k) value of fine-grained soils in the laboratory. Like the constant-head method, the falling-head test also operates in accordance with direct application of Xxxxx’x law to a one-dimensional, saturated column of soil with a uniform cross-sectional area. The falling-head method differs from the constant-head method in that the liquid that percolates through the saturated column is kept in an unsteady-state flow regimen in which both the head and the discharged volume vary during the test. In the falling-head test method, a cylindrical soil sample of cross-sectional area A and length L is placed between two highly conductive plates. The soil sample column is connected to a standpipe of cross-sectional area a, in which the percolating fluid is introduced into the system. Thus, by measuring the change in head in the standpipe from H1 to H2 during a specified interval of time t, the saturated hydraulic conductivity can be determined as follows (Xxxxx and Xxxxxxx 1986):
K = ⎛ aL ⎞ ln ⎛ H1 ⎞
(2.4.5)
⎜ At ⎟ ⎜ H ⎟
⎝ ⎠ ⎝ 2 ⎠
The lower limit of K, which can be measured in a falling-head permeameter, is about 1× 10-2 m/yr. This value corresponds approximately to the lower limit of conductivity of silts and coarse clays (Xxxxx and Xxxxxxx 1986).
A common problem encountered in using either the constant-head or falling-head test with the permeameter is related to the degree of saturation achieved within the soil samples during the test. Air bubbles are usually trapped within the pore space, and although they tend to disappear slowly by dissolving into the deaerated water, their presence in the system may alter the measured results. Therefore, after using these instruments to measure K, it is always recommended that the degree of saturation of the sample be verified by measuring the sample’s volumetric water content and comparing the result with the total porosity calculated from the particle density.
For a more accurate laboratory measurement of K in soil samples in which the presence of air bubbles becomes critical, the conductivity test with back pressure is recommended. In this method, additional pressure (back pressure) is applied to the pore fluid of the soil sample, which reduces the size of the gas bubbles in the pores and, consequently, increases the degree of water saturation.
2.4.2.4 Field Methods
The several methods developed for in situ determination of saturated hydraulic conductivity of soils can be separated into two groups: (1) those that are applicable to sites near or below a shallow water table and (2) those that are applicable to sites well above a deep water table or in the absence of a water table. More specifically, these groups are applicable to sites located, respectively, in the saturated and unsaturated zones of the soil. In either group (similarly to the laboratory methods), the value of K is obtained from Xxxxx’x law after measuring the gradient of the hydraulic head at the site and the resulting soil water flux. Table 2.4.6 lists several standard methods used for in situ determination of K in saturated and unsaturated regions of the soil.
Field Methods Used in Saturated Regions of the Soil. Many in situ methods have been developed for determining the saturated hydraulic conductivity of saturated soils within a groundwater formation under unconfined and confined conditions. These methods include (1) the auger-hole and piezometer methods, which are used in unconfined shallow water table conditions (Amoozegar and Xxxxxxx 1986), and (2) well-pumping tests, which were primarily developed for the determination of aquifer properties used in the development of confined and unconfined groundwater systems (EPA 1986).
Auger-Hole Method. The auger-hole method is the field procedure most commonly used for in situ determination of saturated hydraulic conductivity of soils. This method has many possible variations (Amoozegar and Xxxxxxx 1986). In its simplest form, it consists of the preparation of a cavity partially penetrating the aquifer, with minimal disturbance of the soil.
After preparation of the cavity, the water in the hole is allowed to equilibrate with the groundwater; that is, the level in the hole becomes coincident with the water table level. The
actual test is started by removing the entire amount of water from the hole and measuring the rate of the rise of the water level within the cavity.
Because of the three-dimensional aspect of the flow pattern of the water near the cavity, there is no simple equation for accurately determining the conductivity. Numerous available semiempirical expressions, however, can be used for approximating the saturated hydraulic conductivity for different soil configurations. These expressions are functions of the geometrical dimensions of the auger hole and the aquifer and the measured rate at which the water level in the hole changes with time (Amoozegar and Xxxxxxx 1986).
The auger-hole method is applicable to an unconfined aquifer with homogeneous soil properties and a shallow water table. In its simplest form, this method provides an estimate of the average horizontal component of the saturated hydraulic conductivity of the soil within the aquifer. Enhanced variations of the method have been developed to account for layered soils and for the determination of either horizontal or vertical components of saturated hydraulic conductivity. Results obtained by the auger-hole method are not reliable for cases in which
(1) the water table is above the soil surface, (2) artesian conditions exist, (3) the soil structure is extensively layered, or (4) highly permeable small strata occur.
Piezometer Method. The piezometer method, like the auger-hole method, is applicable for determining the saturated hydraulic conductivity of soils in an unconfined aquifer with a shallow water table level. Unlike the auger-hole method, however, the piezometer method is appropriately designed for applications in layered soil aquifers and for determining either horizontal or vertical components of the saturated hydraulic conductivity.
This method consists of installing a piezometer tube or pipe into an auger hole drilled through the subsurface system without disturbing the soil. The piezometer tube should be long enough to partially penetrate the unconfined aquifer. The walls of the piezometer tube are totally closed except at its lower extremity, where the tube is screened open to form a cylindrical cavity of radius r and height hc within the aquifer. The water in the piezometer tube is first removed to clean the system and is then allowed to equilibrate with the groundwater level.
Similarly to the auger-hole method, the piezometer method consists of removing the water from the pipe and then measuring the rate of the rise of the water within the pipe. The saturated hydraulic conductivity is then evaluated as a function of the geometrical dimension of the cavity in the piezometer tube, the dimensions of the aquifer, and the measured rate of rise of the water table in the tube. The value for the conductivity is calculated with the help of a nomograph and tables (Amoozegar and Xxxxxxx 1986).
Depending on the relative length (hc) of the cavity as compared with its radius (r), the piezometer method can be used to determine the horizontal or vertical component of the saturated hydraulic conductivity. Thus, if hc is large compared to r, the results obtained reflect the horizontal component of K. Otherwise, if hc is small compared to r, then the vertical component of K is estimated. The piezometer method is especially suitable for determining the conductivity of individual layers in stratified subsurface systems.
Well-Pumping (Slug) Methods. The well-pumping (slug) test is applicable for in situ determination of the saturated hydraulic conductivity in soil materials of unconfined and confined aquifers. This method consists of removing a slug of water instantaneously from a well and measuring the recovery of the water in the well. Variations of the well-pumping test, called single-well tests (EPA 1986), are listed in Table 2.4.6.
In contrast to the auger-hole and piezometer methods, the results of which reflect an in situ average of a relatively small region of soil around the created cavity in the soil, well- pumping tests also provide an in situ representation of the soil hydraulic conductivity, but averaged over a larger representative volume of the soil. The measured results of K primarily reflect the value in the horizontal direction. (Further references for these methods can be found in EPA (1986), Freeze and Cherry (1979), and Xxxxxxxxx and Xxxxxxx (1986).)
Field Methods Used in the Unsaturated Region of the Soil. Measuring the saturated hydraulic conductivity of unsaturated soils located above the water table (or in the absence of a water table) by in situ methods is more difficult than measuring K for saturated soils. The important difference is that the original unsaturated soil must be artificially saturated to perform the measurements. An extra-large quantity of water may be needed to saturate the medium, which results in a more elaborate and time-consuming measurement. The results of these in situ measurements of K are commonly called the field-saturated hydraulic conductivity.
Many in situ methods have been developed for determining the field-saturated hydraulic conductivity of soil materials within the unsaturated (vadose) zone of the soil. As listed in Table 2.4.6, the available standard methods for measuring field-saturated K include (1) the shallow-well pump-in or dry auger-hole, (2) the double-tube, (3) the ring infiltrometer, (4) the air-entry permeameter, and (5) the constant-head test in a single drill hole. A complete guide for comparing these standard methods is presented in ASTM D5126-90, Standard Guide for Comparison of Field Methods for Determining Hydraulic Conductivity in the Vadose Zone (ASTM 1992n). Further detailed discussion on these standard methods can also be found in the work of Xxxxxxxxx and Xxxxxxx (1986).
2.4.3 Data Input Requirements
In RESRAD (onsite) and RESRAD-OFFSITE, the user is requested to input a saturated hydraulic conductivity value in units of meters per year (m/yr) for three soil materials: contaminated, unsaturated, and saturated zones.
The vertical infiltration of water within the contaminated zone and through the unsaturated region of the soil, the subsequent vertical leaching, and the transport of contaminants into the underlying aquifer are the important aspects of the problem being modeled.
Consequently, in RESRAD (onsite) and RESRAD-OFFSITE, the saturated hydraulic conductivity values related to the contaminated and unsaturated zones of the soil should represent the vertical component of K. For isotropic soil materials, the vertical and horizontal components of K are the same; for anisotropic soils, however, the vertical component of K is typically one or two orders of magnitude lower than the horizontal component.
The major concern within the saturated zone is related to the horizontal transport of the contaminants that have infiltrated through the unsaturated zone and reached the aquifer.
Therefore, the input value for the saturated hydraulic conductivity (K) of the soil material in the saturated zone should reflect the horizontal component of K.
The estimation of the values of K to be used in RESRAD (onsite) and RESRAD- OFFSITE can be performed at different levels of site-specific accuracy, depending on the amount of information available. For generic use of the code, a set of default values of K is defined as 10 m/yr for the contaminated and unsaturated zones and 100 m/yr for the saturated zone. These values approximately represent the condition of an anisotropic sedimentary soil material, that is, silt, loess, or silty sand, in which the vertical component of K is one order of magnitude lower than the horizontal component. The code accepted value for hydraulic conductivity ranges between 10-3 and 1010 m/yr for all the three soil materials, as shown in Tables 1.1.1 and 1.1.2.
If the geological stratigraphy and the soil textures at the site are known, a better (i.e., more accurate and site-specific) estimation of K can be performed with the help of
Table 2.4.1 through Table 2.4.4. However, if values in the literature are used in place of actual site data, no more than one significant digit is appropriate.
For an accurate site-specific estimation of the input data for RESRAD, the values of K should be measured either in the laboratory or in field experiments according to one of the standard methods listed in Table 2.4.6.
Because of the intrinsic difficulties of the methods available for in situ measurements of field-saturated K in unsaturated regions of the soil, it is recommended that laboratory methods be used for determining the vertical component of K in the contaminated and unsaturated zones. In these cases, either variation of the constant-head or falling-head method can be used, depending solely on the actual values of K being measured. As mentioned previously, the constant-head
method is more applicable for large values of K (in the range of 100 − 106 m/yr), and the falling-
head method is more applicable for lower values of K (in the range of 10−2 − 102 m/yr).
Determination of the horizontal component of K in the saturated zone of the soil can be accomplished either by laboratory (i.e., constant-head and falling-head) or field methods
(i.e., auger-hole, piezometer, and well-pumping). In the laboratory, the value of the horizontal component of K in cohesionless soil materials can be approximated by the conductivity of a disturbed soil sample obtained by the permeameter method. For cohesive soil materials, the undisturbed cohesive soil sample can then be oriented in the horizontal direction to obtain the appropriate value of K. In the field, most of the methods available for the determination of K in the saturated zone will reflect the value in the horizontal direction.
The saturation ratio can be estimated by using the following equation (Xxxxx and Xxxxxxxxxx 1978):
1
R = ⎛ I ⎞2b +3
K
s ⎜ ⎟
⎝ sat ⎠ (2.4.6)
where
I = infiltration rate (m/yr),
Ksat = saturated hydraulic conductivity (m/yr), and
b = soil-specific exponential parameter (dimensionless).
When the medium is saturated, Rs equals unity. Under unsaturated infiltration conditions, the saturation ratio is a function of the infiltration rate, the saturated hydraulic conductivity, and the texture of the soil, as shown in Equation (2.4.6). The volumetric water content of the unsaturated zone is calculated by
θ = Rs ⋅θsat
(2.4.7)
The calculated volumetric water content is checked against the field capacity of the unsaturated soil and porosity. The field capacity sets the lower limit of the volumetric water content and is used to replace the calculated value when the calculated value is smaller. Once the volumetric water content is set to the field capacity, the saturation ratio is recalculated by using Equation (2.4.7). The porosity, on the other hand, sets the upper boundary of the volumetric water content and is used to replace the calculated value when the calculated value is larger.
2.5 SOIL-SPECIFIC EXPONENTIAL b PARAMETER
2.5.1 Definition
The soil-specific exponential b parameter is one of several hydrological parameters used to calculate the radionuclide leaching rate of the contaminated zone. (See also precipitation rate, irrigation rate, runoff coefficient, evapotranspiration coefficient, hydraulic conductivity, and soil porosity.) The soil-specific b parameter is an empirical and dimensionless parameter that is used to evaluate the saturation ratio (or the volumetric water saturation), Rs, of the soil, according to a soil characteristic function called the conductivity function (i.e., the relationship between the unsaturated hydraulic conductivity, K, and the saturation ratio, Rs).
It has been suggested that a power function is an acceptable form of representing the conductivity function. As cited by Xxxxx and Xxxxxxxxxx (1978), Xxxxxxxx (1974) derived a partly empirical and partly theoretical conductivity function on the basis of the power function model; this function proved to be reasonably accurate over a large number of cases. Xxxxxxxx suggested the following power expression to represent the working relationship for the conductivity function:
s
where
k = R(2b+3) , (2.5.1)
k = relative conductivity (or relative permeability, dimensionless),
Rs = saturation ratio (dimensionless), and
b = fitting parameter, called the soil-specific exponential parameter, which must be determined experimentally.
The relative conductivity, k, at any location in the unsaturated zone is defined as a ratio of the unsaturated hydraulic conductivity, K, at that point, to the saturated hydraulic conductivity, Ksat. Thus, k can be expressed as follows:
k = K Ksat
(2.5.2)
Substituting the definition of the relative permeability k into Equation (2.5.1) yields
K
s
Ksat
= R(2b+3)
(2.5.3)
or
⎝ ⎠
⎛ 1 ⎞
R = ⎛ K
⎞⎜ 2b+3 ⎟
(2.5.4)
K
s ⎜ ⎟
⎝ sat ⎠
In downward water infiltration into the unsaturated upper layer of the soil, the infiltration rate, Ir (see also precipitation rate), can be approximated by the unsaturated hydraulic conductivity, K (Hillel 1980a). Therefore, substituting Ir for K in Equation (2.5.4) yields
⎝ ⎠
⎛ 1 ⎞
R = ⎛ Ir
⎞⎜ 2b+3 ⎟
(2.5.5)
K
s ⎜ ⎟
⎝ sat ⎠
Equation (2.5.5) is used internally in the RESRAD (onsite) model to evaluate the volumetric water saturation, Rs, in all unsaturated regions of the soil system. According to Equation (2.5.5), under unsaturated infiltration conditions, the saturation ratio Rs is a function of the infiltration rate Ir, the saturated hydraulic conductivity Ksat, and the texture of the soil, as determined by the fitting parameter b. When the medium is fully saturated, Ir equals Ksat, and Rs equals unity.
2.5.2 Measurement Methodology
The soil-specific b parameter is an empirical fitting parameter and, therefore, must be determined experimentally. For each type of soil, the best estimate of b can be obtained by adjusting the best-fit values of the soil to an experimentally determined curve of relative permeability versus saturation, according to the power function model proposed above, Equation (2.5.1).
Determining the conductivity function of a soil sample experimentally by measuring the relative permeability and the saturation is not an easy laboratory task because of many technical and procedural difficulties. Yet some data have been reported in the literature that demonstrate reasonable agreement with the proposed model. For example, Xxxxx and Xxxxxxxxxx (1978) have reported that Campbell’s model (Xxxxxxxx 1974) for the conductivity function has proven to be acceptable under different conditions of soil saturation over a wide range of b values (0.17–13.6) and even for values of saturation, Rs, near unity (i.e., full saturation). Table 2.5.1 lists representative values of the soil-specific exponential b parameter for various soil textures.
Section 2.1.2 provides a discussion on soil textures.
2.5.3 Data Input Requirements
In RESRAD (onsite) and RESRAD-OFFSITE, the user is requested to define an input value for the soil-specific b parameter for (1) the contaminated zone, (2) the unsaturated zone strata, and (3) the saturated zone. Input for the saturated-zone b parameter is required only if the water table drop rate (Section 2.10) is greater than zero.
TABLE 2.5.1 Representative Values of Soil-Specific Exponential b Parameter
Texture | Soil-Specific Exponential Parameter, b |
Sand | 4.05 |
Loamy sand | 4.38 |
Xxxxx loam | 4.9 |
Silty loam | 5.3 |
Loam | 5.39 |
Xxxxx xxxx loam | 7.12 |
Silty clay loam | 7.75 |
Clay loam | 8.52 |
Xxxxx xxxx | 10.4 |
Silty clay | 10.4 |
Clay | 11.4 |
Source: Xxxxx and Xxxxxxxxxx (1978). | |
Reported measured data indicate that values of b vary within the range of 0.17–13.6 (Xxxxx and Xxxxxxxxxx 1978). A default value of 5.3 was adopted in the RESRAD (onsite) and RESRAD-OFFSITE models. This value represents the condition of a silty loam soil material. Whenever possible, however, site-specific input data for b should be used in the RESRAD calculation. The range of b accepted by the code varies from 0 to 15 for cover and contaminated zone and unsaturated zone, and from 10-34 to 15 for saturated zone, as shown in Table 2.5.2.
A relatively more accurate value of parameter b for site-specific soil materials can be obtained from the data listed in Table 2.5.1. For most applications, this approach should suffice because of the difficulties in obtaining laboratory determinations of the soil conductivity function.
2.6 EROSION RATE
2.6.1 Definition
The erosion rate is the average volume of soil material that is removed from one place to another by running water, waves and currents, wind, or moving ice per unit of ground surface area and per unit of time. The erosion rate represents the average depth of soil that is removed from the ground surface per unit of time at the site and is expressed in units of length per time (LT-1).
TABLE 2.5.2 Default Soil-specific Exponential b Parameters Used in RESREAD (onsite) and RESRAD-OFFSITE
Parameter Name | Unit | Default Value | Code- Accepted Values | References | Description |
Cover and contaminated zone b parameter | - | 5.3 | 0–15 | Yu et al. 1993; EPA 1996; Xxxxx and Xxxxxxxxxx 1978 | An empirical and dimensionless parameter that is used to evaluate the saturation ratio (or the volumetric water saturation) of the soil according to a soil characteristic function called the conductivity function. |
Saturated zone b parameter | - | 5.3 | 10-34–15 | ||
Unsaturated zone, soil- specific b parameter | - | 5.3 | 0–15 |
2.6.2 Measurement Methodology
Erosion rates can be estimated by means of the Universal Soil Loss Equation (USLE), an empirical model that has been developed for predicting the rate of soil loss by sheet and rill erosion, or its revised version RUSLE (Xxxxxx et al. 1997). However, orders-of-magnitude errors
can result from using the USLE method without proper orientation. An appropriate guide for using the USLE method can be obtained from the U.S. Soil Conservation Service (SCS), which conducts county soil surveys on a regular basis. The SCS office near the site should be able to provide the USLE parameters mapped out for the site-specific soils and cover types for the area of interest. In addition to the USLE model, which is commonly used to predict the average annual soil loss from a watershed, some physics-based models such as SIBERIA (Willgoose 2005) and the CHILD (Channel-Hillslope Integrated Landscape Development) (Xxxxxx 2011) model are also available for calculating the evolution of complex topography and landscape.
Although these models provide more details about soil erosion, they usually require much more information and are computationally expensive.
If sufficient site-specific data are available, a site-specific erosion rate can be calculated by using the USLE method. Xxxxxxxxxx and Xxxxx (1978) and Xxxxxx (1979) discuss details of the calculation. Estimates based on the range of erosion rates for typical sites in humid areas east of the Mississippi River (based on model site calculations for locations in New York, New Jersey, Ohio, and Missouri) can also be used (Knight 1983). For example, for a site with a 2% slope, these model calculations predict a range of 8 × 10-7 to 3 × 10-6 m/yr for natural succession vegetation, 1 × 10-5 to 6 × 10-5 m/yr for permanent pasture, and 9 × 10-5 to 6 × 10-4 m/yr for row- crop agriculture. The rate increases by a factor of about 3 for a 5% slope, 7 for a 10% slope, and 15 for a 15% slope. If these generic values are used for a farm/garden scenario in which the dose contribution from food ingestion pathways is expected to be significant, an erosion rate of
6 × 10-4 m/yr should be assumed for a site with a 2% slope. This would lead to erosion of 0.6 m of soil in 1,000 yr. A proportionately higher erosion rate must be used if the slope exceeds 2%. An erosion rate of 6 × 10-5 m/yr, leading to erosion of 0.06 m of soil in 1,000 yr, can be used for a site with a 2% slope if it can be reasonably shown that the farm/garden scenario is unreasonable; for example, if the site is, and will likely continue to be, unsuitable for agricultural use.
Erosion rates are more difficult to estimate for arid than for humid sites. Although water erosion is generally more important than wind erosion, the latter can also be significant. Water erosion in the West is more difficult to estimate because it is likely to be due to infrequent heavy rainfalls for which the empirical constants used in the USLE may not be applicable. Long-term erosion rates are generally lower for sites in arid locations than for sites in humid locations.
A more detailed discussion and data on soil erosion are presented in Soil Physics (Xxxxxxxx and Xxxxxx 1979), Universal Soil Loss Equation: Past, Present, and Xxxxxx (Xxxxxxxx and
Swan 1979), and the Nature and Properties of Soils (Xxxxx 1984).
2.6.3 Data Input Requirements
In RESRAD (onsite), the user is requested to input a value for the annual average erosion rate for the cover zone and the contaminated zone. These input values of the erosion rate are given in units of meters per year (m/yr).
For generic use of the code, a default value of the annual erosion rate equal to 0.001 m/yr (as shown in Table 2.6.1) was adopted in RESRAD (onsite). This value is about the same as the
national average of erosion rate on cropland in 1982, according to the national resources inventory conducted by the USDA’s NRCS and the Center for Survey Statistics and Methodology (CSSM) at Iowa State University in 2012, as shown in Figure 2.6.1 (USDA NRCS and CSSM 2015). For a particular site, however, a more accurate site-specific estimation of the erosion rates for both the cover and the contaminated zones should be attempted. Some reported studies on specific sites (e.g., the study on the Western New York Nuclear Service Center [DOE 2010] and the study by Xxxxxx et al. [1998]) may also provide useful information for users to determine their own site-specific erosion rate. The erosion rate of the contaminated zone becomes significant only if and when the cover zone is completely eroded, thus exposing the contaminated zone to the erosive effects of the environmental elements. If there is no initial cover, a greater erosion rate will remove the contaminated material faster. This may lead to lower doses than found for an initial cover case for an on-site receptor using RESRAD (onsite) code. However, because of the transport of contamination through erosion to off-site locations, a greater erosion rate may result in higher doses for an off-site receptor using RESRAD-OFFSITE code.
A site-specific estimation of the erosion rate for the cover and contaminated zones can be performed by means of the USLE or the revised USLE (RUSLE).
The USLE is directly used in RESRAD-OFFSITE to estimate soil erosion in contaminated and agricultural areas. The USLE parameters, the rainfall and runoff factor, soil erodibility factor, the slope length-steepness factor, the cover and management factor, and support practice factor are discussed by Xx et al. (2007).
TABLE 2.6.1 Default Erosion Rate Values Used in RESRAD
Parameter Name | Unit | Default Value | Code- Accepted Values | References | Description |
Cover erosion rate | m/yr | 0.001 | 0–5 | Yu et al. 1993 | The average volume of cover material that is removed per unit of ground surface area and per unit of time. Erosion rates can be estimated by means of the universal soil loss equation. |
Contaminated- zone erosion rate | m/yr | 0.001 | 0–5 | Yu et al. 1993 | The average volume of source material that is removed per unit of ground surface area and per unit of time. |
FIGURE 2.6.1 Erosion Rate on Cropland in the United States (Source: USDA NRCS and CSSM 2015)
2.7 HYDRAULIC GRADIENT
2.7.1 Definition
The hydraulic gradient is the change in hydraulic head per unit of distance of the groundwater flow in a given direction. The hydraulic gradient, Jx, in the flow direction x is expressed as follows:
J = h1 − h2
x Δx
(2.7.1)
where h1 and h2 represent the hydraulic head at points 1 and 2, respectively, and Δ x is the distance between these two points. Mathematically, the hydraulic gradient is a vector that can be expressed as grad h. The norm of the vector represents the maximum slope of the hydraulic gradient; its orientation represents the direction along the maximum slope. The hydraulic gradient is a dimensionless parameter, usually represented as a fraction rather than as a percentage.
In an unconfined (water table) aquifer, the horizontal hydraulic gradient of groundwater flow is approximately the slope of the water table. In a confined aquifer, it represents the difference in potentiometric surfaces over a unit distance. The potentiometric surface is the elevation to which water rises in a well that taps a confined aquifer. It is an imaginary surface
analogous to a water table. In general, the hydraulic gradient of groundwater flow in a highly permeable geologic material, such as sand or gravel, is far less than that in a geologic material with a low permeability, such as silt or clay.
2.7.2 Measurement Methodology
The hydraulic head at a point in the saturated zone can be measured in the field by installing a piezometric nest at the site. A piezometer is basically a tube or pipe long enough to be introduced through the unsaturated zone down into the saturated zone. Its walls must be completely sealed along all its length, but it must be open to the atmosphere at the top and to the water flow at the bottom. The water level measured inside the piezometer, as compared with a defined reference level (such as mean sea level), gives the hydraulic head of the aquifer at the point of measurement.
The distribution of the hydraulic head in a groundwater system is actually three- dimensional. Thus, with the installation of three or more piezometers spatially distributed in an aquifer, it is possible to determine the spatial distribution of the hydraulic head at the site. If the distances between the piezometers are known, the hydraulic gradient of the dominant aquifer flow at the site can be evaluated. A detailed description of piezometer nests has been given by Xxxxxx and Xxxxxx (1979).
Based on the technical survey of 400 sites across the United States, Xxxxxx et al. (1990) developed a hydrogeologic database and provided the box plot of hydraulic gradient for
2.7.3 Data Input Requirements
In RESRAD (onsite) and RESRAD-OFFSITE, the user is requested to input a value for the hydraulic gradient in the dominant groundwater flow direction in the underlying aquifer at the site. This parameter is dimensionless and should be entered as a decimal fraction rather than as a percentage. This parameter is needed for RESRAD (onsite) and RESRAD-OFFSITE to calculate the water flow rate per unit of cross-sectional area (i.e., Xxxxx velocity) in the saturated zone.
For generic use of the codes, a default value of 0.02 was adopted for the hydraulic gradient in the RESRAD (onsite) and RESRAD-OFFSITE models, as shown in Table 2.7.1. Because the hydraulic gradient varies significantly from one site to another, site-specific information should be applied for more accurate use of the code whenever possible.
1 For a lognormal distribution (with median m and geometric standard deviation g ), 68% of the distribution lies between m / g and m × g .
Site-specific data on the hydraulic gradient and the general flow pattern of the groundwater system at the site can be obtained by installing a piezometric nest in the area, as suggested above. RESRAD users should also consider contacting a local or state hydrologist or geologist as a possible source of site-specific information.
TABLE 2.7.1 Default Hydraulic Gradient Values Used in RESRAD (onsite) and RESRAD-OFFSITE
Parameter Name | Unit | Default Value | Code- Accepted Values | Reference | Description |
Saturated-zone hydraulic gradient | - | 0.02 | 10-10–10 | Yu et al. 1993 | The change in hydraulic head per unit of distance in the groundwater flow direction. In an unconfined (water table) aquifer, the horizontal hydraulic gradient of groundwater flow is approximately the slope of the water table. In a confined aquifer, it represents the difference in potentiometric surfaces over a unit distance. |
2.8 LENGTH OF CONTAMINATED ZONE PARALLEL TO THE AQUIFER FLOW
2.8.1 Definition
The length, l, of the contaminated zone parallel to the aquifer flow is the maximum horizontal distance measured in the contaminated zone, from its upgradient edge to the downgradient edge, along the direction of the groundwater flow in the underlying aquifer.
The parameter l is used in the RESRAD (onsite) and RESRAD-OFFSITE codes to evaluate the dilution of the contaminated inflow water (which percolates the contaminated zone vertically and reaches the aquifer underneath) by the uncontaminated inflow groundwater in the Nondispersion Model for a well located near the contaminated zone.
2.8.2 Measurement Methodology
To evaluate the value of parameter l at a specific site, it is first necessary to determine the hydraulic gradient of groundwater flow at the site. As described in Section 2.7, the groundwater flow direction in the aquifer can be determined locally by installing a piezometric nest composed of three or more piezometers spatially distributed throughout the hydrogeological system. With a known groundwater flow direction and the horizontal extent of the contaminated zone, the
parameter l can be determined by measuring the largest horizontal length of the contaminated zone parallel to the groundwater flow direction.
2.8.3 Data Input Requirements
In the RESRAD (onsite) and RESRAD-OFFSITE codes, the user is required to input a value of l, that is, the length of the contaminated zone parallel to the groundwater flow that represents the conditions at the site. The dimensions of l should be entered in units of meters (m).
A default value of 100 m was adopted in the RESRAD (onsite) and RESRAD-OFFSITE codes for parameter l. The default value of 100 m is the square root of the default contaminated zone area of 10,000 m2. Whenever possible, however, site-specific information should be applied for more accurate use of the code.
2.9 WATERSHED AREA FOR NEARBY STREAM OR POND
2.9.1 Definition
A watershed is a region contoured by an imaginary line connecting ridges or summits of high land and drained by or draining into a river, river system, or a body of water such as a lake or pond. The watershed area is the surface area of the draining region above the discharge measuring points. This parameter is expressed in units of length squared (l2). In the RESRAD (onsite) and RESRAD-OFFSITE codes, the watershed area parameter represents the area of the region draining into the nearby stream or pond located at the vicinity of the site.
The watershed area parameter is used in the RESRAD model to evaluate the dilution factor for the contamination of the water at the nearby stream or pond as it gets mixed with the inflow of water from the contaminated aquifer. Thus, the evaluation of the dilution factor for the ground/surface water pathway is based on the following assumptions (Xxxxxxx et al. 1989):
1. The nearby body of water is a pond;
2. The inflow and outflow of water in the pond are in equilibrium;
3. The average annual inflow of radioactivity into the pond is equal to the average annual quantity of radioactivity that is leached from the contaminated zone into the groundwater system; and
4. The infiltrating water flow through the contaminated zone is vertically downward.
Under these conditions and assumptions, the dilution factor is then defined as the ratio of the average annual volume of water that percolates through the contaminated zone to the average
annual total inflow of water into the pond. More specifically, the dilution factor is calculated internally in the code as the ratio of the contaminated zone area (AREA) to the watershed area (WAREA).
2.9.2 Measurement Methodology
The area of the watershed draining toward the pond located at the vicinity of the site can be evaluated by using a small-scale morphologic map of the region.
2.9.3 Data Input Requirements
In the RESRAD (onsite) and RESRAD-OFFSITE codes, the user is requested to input a value for the area of the watershed region draining into the stream or pond located in the vicinity of the site. The dimensions of the watershed area should be entered in units of square meters (m2).
A default value of one million (1 × 106) m2 for the watershed area was adopted in the RESRAD model. If found to significantly affect the results, site-specific information should be applied for more accurate use of the code.
Site-specific information on the watershed area can be obtained from small-scale hydrological and morphological maps covering the region under study. In the RESRAD codes, the watershed area must be larger than or equal to the area of the contaminated zone. The code will issue a warning if this condition is violated and will not proceed with the calculations until the violation is corrected.
2.10 WATER TABLE DROP RATE
2.10.1 Definition
The water table drop rate is the rate, in units of length per time (lT-1), at which the depth of the water table is lowered. The level of the water table in a groundwater system fluctuates seasonally because of the erratically temporal variations of the processes involved in the hydrologic cycle (Section 3.1), as well as extra use of the water from the system. Under normal circumstances, the level of the water table is approximately stationary if averaged over long periods of time such as one year. For unusually high consumptive use of groundwater in the region, however, the water table may experience a significant drop during the annual period. In these cases, the average annual water table drop rate is not zero and results in the creation of an increase in the unsaturated-zone thickness over time. This process of increasing the unsaturated- zone thickness is modelled in the RESRAD (onsite) code. This parameter is not used in the RESRAD-OFFSITE code.
2.10.2 Measurement Methodology
The site-specific water table drop rate can be estimated by observing the change of the water level of a monitoring well appropriately installed at the site. It can also be estimated by consulting water table records of past decades.
2.10.3 Data Input Requirements
In RESRAD (onsite), the user is required to input a value for the average annual water table drop rate that represents conditions at the site. The water table drop rate should be expressed in units of meters per year (m/yr).
A default value of 0.001 m/yr was adopted in the RESRAD (onsite) code for the water table drop rate. This value is the same as the default value used for the erosion rate. Whenever possible, however, site-specific information should be applied for more accurate use of the code.
2.11 WELLPUMP INTAKE DEPTH
2.11.1 Definition
The parameter well-pump intake depth is the screened depth of a well within the aquifer (the saturated zone). The well-pump intake depth is measured in units of length (l). Based on the technical survey of 400 sites across the United States, Xxxxxx et al. (1990) developed a hydrogeologic database and provided the box plot of the saturated thickness of aquifer for
12 groups of hydrogeologic environments (see Figure 9 of Xxxxxx et al. [1990] for details). Their research indicates that the saturated thickness of aquifer follows a lognormal distribution. The median of the national distribution of the saturated thickness of aquifer is 30.0 ft (or 9.09 m).1
2.11.2 Data Input Requirements
In RESRAD (onsite), the user is required to input a value for the well-pump intake depth that represents conditions at the site. Its dimensions should be given in units of meters (m). This parameter is required for calculating the dilution factor for the nondispersion model and the well water concentration, as discussed in Appendixes E and K in Yu et al. (2001) and Chapter 3 of Xx et al, (2007). A default value of 10 m was adopted in the RESRAD model for the well-pump intake depth, as shown in Table 2.11.1. For more accurate use of the code, however, site-specific
TABLE 2.11.1 Default Well-pump Intake Depth Value Used in RESRAD
Parameter Name | Unit | Default Value | Code-Accepted Values | Reference | Description |
Well-pump intake depth (below water table) | m | 10 | 10-5–1,000 | Yu et al. 1993 | The screened depth of a well within the aquifer (the saturated zone). |
data should be applied whenever possible. In RESRAD-OFFSITE, the user is required to input a value for the depth of the aquifer contributing to the well or surface water body (Yu et al. 2007).
2.12 THICKNESS OF UNCONTAMINATED UNSATURATED ZONE
2.12.1 Definition
The uncontaminated unsaturated zone is the portion of the uncontaminated zone that lies below the bottom of the contaminated zone and above the water table. The RESRAD (onsite) and RESRAD-OFFSITE codes provide for up to five different horizontal strata within this zone. Each stratum is characterized by six radionuclide-independent parameters: (1) thickness of the layer, (2) soil density, (3) total porosity, (4) effective porosity, (5) soil-specific b parameter, and
(6) hydraulic conductivity. Based on the technical survey of 400 sites across the United States, Xxxxxx et al. (1990) developed a hydrogeologic database and provided the box plot of the depth to top of aquifer for 12 groups of hydrogeologic environments (see Figure 9 of Xxxxxx et al. [1990] for details). Their research indicates that the depth to top of aquifer follows a lognormal distribution. The median of the national distribution of the depth to top of aquifer is 15.0 ft (or
2.12.2 Data Input Requirements
In RESRAD (onsite) and RESRAD-OFFSITE, the user is required to input a value for each stratum used in the calculation. Default values are supplied by the code for all parameters of an active stratum; however, the use of site-specific data is strongly recommended.
2.13 DISTRIBUTION COEFFICIENTS
2.13.1 Definition
The distribution coefficient, Kd, is the ratio of the mass of solute species adsorbed or precipitated on the solids per unit of dry mass of the soil, S, to the solute concentration in the liquids, C. The distribution coefficient represents the partition of the solute in the soil matrix and soil water, assuming that equilibrium conditions exist between the soil and solution phases. A linear Freundlich isotherm, which assumes complete reversibility of ion adsorption, has been extensively used to correlate the relationship between S and C, that is,
S = Xx X .
(2.13.1)
The transfer of radionuclides from the liquid to the solid phase or vice versa may be controlled by mechanisms such as adsorption and precipitation, depending on the radionuclides. The dimensions of the distribution coefficient are given in units of length (l) cubed per mass (M) (l3/M).
In the literature, distribution coefficients measured from adsorption conditions abound, but it is well known that these experimental Kd values are not constant when used with soils. The time elapsed since the incorporation of the radionuclide in the soil affects the distribution coefficient because of the aging effect (IAEA 2010a); a fraction of the radionuclide may become fixed by the solid phase over time. The Kd values are dependent on the soil’s physical and chemical characteristics, which do not necessarily remain constant over the long term because soils are dynamic systems. Soil properties affecting the distribution coefficient include
the texture of soils (sand, loam, clay, or organic soils) (Xxxxxxxx and Xxxxxxxx 1991;
Xxx-Xxxxxx et al. 2009a; Xxxxxxxxxx et al. 2009; Xxx-Xxxxxx et al. 2009b); the organic matter content of the soils; pH values (Coughtrey et al. 1985; Xxx-Xxxxxx et al. 2009a;
Xxxxxxxxxx et al. 2009; Xxx Xxxxxx et al. 2009b); the soil solution ratio (Xxxxxxxx et al. 1983); the solution or pore water concentration (Xxxxxx 1982; Xxxxxxxx 1985; Xxxxxxxx et al. 1987; Xxxxxxxx and Xxxxxxxx 1990); and the presence of competing cations and complexing agents (Gee et al. 1980, Xxxxxx 1982; Xxx et al. 1983; Xxxxxxx et al. 1984; Xxxxxxxx 1985; Xxxxxx and Xxxxxx 1987; Bond and Smiles 1988). Because of its dependence on many soil properties, the value of the distribution coefficient for a specific radionuclide in soils can range over several orders of magnitude under different conditions. To reduce the variability, the Kd values can be grouped on the basis of fundamental soil properties, such as soil texture and organic matter content (IAEA 2010a; Xxxxxxxx 2011; Xxx-Xxxxxx et al. 2009a; Xxxxxxxxxx et al. 2009;
Xxx Xxxxxx et al. 2009b; Xxxxxxxxx 1981).
2.13.2 Measurement Methodology
2.13.2.1 Experimental Methods
The two most common experimental techniques for the determination of Kd are the batch and column methods. Usually, the batch method is used to measure the distribution coefficient, Kd, under saturated equilibrium conditions. The column method is used to approach a more “natural” soil condition.
Batch Method. Measurement of the distribution coefficient can be performed quickly by the batch method with any radionuclide in any soil material or rock, independent of the porosity, brittleness, or other properties of the soil or rock. In most instances, the soil material or rock is continually agitated to facilitate mixing and contact. At specified times, to approach equilibrium conditions, the solid and solution are separated and the resultant distribution of the nuclide is determined. In the batch system, radionuclide desorption and adsorption are affected by the following: agitation effects (Barney and Xxxxx 1980); solid-liquid separation techniques; and limitation of analytical determination, that is, multiple species of soil or rock cannot be differentiated if present (Serne and Xxxxxx 1981).
The ASTM C1733 test method has been developed as a standard batch method (ASTM 2010d) to measure the distribution coefficient of inorganic species under steady-state conditions. This test method determines the Kd of chemical species by quantifying uptake onto solid materials by batch sorption techniques. This method can be applied directly to
unconsolidated material samples or to disaggregated portion of samples. The sorption is strongly dependent on concentration of the species of interest in solution, pH, temperature, rock and soil properties including mineralogy (surface charge and energy), particle size distribution, and biological conditions. The method recommends considering all ionic species present in the migrating solution and using groundwater representative of the test zone (but containing added tracers) as contact liquid. The method also recommends running each concentration in duplicate, doing the analysis for five or more concentrations, and determining the time required for the tracer/solid system to achieve constant concentrations at the highest tracer concentration to be used in the experiment. The method further recommends keeping a 25:1 liquid-to-mass ratio, measuring the liquid in terms of mass, and collecting a small aliquot of liquid each time for analysis. The contact periods should differ by at least a one-day period. Before taking a sample for analysis, shake the mixture and allow it to settle for several minutes. Remove an appropriate quantity of liquid, filter it, and keep it for analysis. The soil solution mixture can also be separated by centrifugation at a minimum setting of 1,400 g for 20 minutes. The distribution ratio can then be calculated as
K = mass of
solute on the solid phase per unit mass of solid
phase .
(2.13.2)
d mass of
solute in solution per unit volume of the liquid
phase
Column Method. Column experiments are used to simulate the migration of radionuclides through soils under saturated and/or unsaturated conditions. They allow observation of radionuclide migration rates without significant soil particle alteration caused by grinding, as in batch experiments, and produce more representative site-specific results. (Even removing a core sample to the laboratory results in alteration of the soil from its field condition.)
Typical equipment used in column experiments includes a reservoir to the column, a cylindrical holder to contain the crushed or intact soil being tested, and a sample collector for the column effluent. For experimentation on intact and fissured soil with low permeability, a high- pressure apparatus has to be used. The associated equipment costs, time constraints, experimental complications, and uncertainty in data reduction usually discourage potential users of the column system. Several operational problems with column experiments have been observed by numerous investigators: (1) homogeneity of column packing (Xxxxxxx et al. 1962; Xxxxx 1967; Xxxxxx et al. 1974), (2) potential short-circuit effects (Xxxxxx 1981; Xxxxx and Xxxxxxx 1986), and (3) residence time required for experimentation. To bridge the gap between batch and column experiments, a case study of cesium absorption on granite was done by
Xxxx et al. (2009).
Theoretical models have been developed to describe solute transport in soil columns.
Consider a situation in which water containing a dissolved tracer is introduced into a tracer-free soil column with a known dry density and volumetric water content. The hydrodynamic dispersion (i.e., the mechanical dispersion and molecular diffusion) of radionuclides throughout the column and the adsorption of radionuclides into the soil cause the initial sharp tracer front near the top end of the soil column to spread out downward. A mass balance equation for the radionuclide concentration in the liquid phase can be derived as follows:
R ∂C = D ∂C -υ ∂C ,
(2.13.3)
∂t ∂ x2 ∂x
where
R = retardation factor,
D = coefficient of hydrodynamic dispersion,
v = average pore water velocity, and
C = radionuclide concentration in the water.
The retardation factor R is related to the distribution coefficient Kd of the radionuclide as follows:
R= 1+ ρb K d
θ
(2.13.4)
where
ρb = dry soil density, and
θ = volumetric water content of the soil.
Therefore, Kd can be calculated if R is known. The solution to Equation (2.13.3) for a semi- infinite system is (Xxxxxxx and Xxxxxxxx 1952)
erfc +
C(x,t) = Co ⎧ ⎡ Rx −υt ⎤
υx )erfc⎡ Rx +υt ⎤⎫ , (2.13.5)
2 ⎨ ⎢ 2(DRt)1/ 2 ⎥
exp(
D
⎢ 2(DRt)1/ 2 ⎥⎬
⎩ ⎣ ⎦ ⎣ ⎦⎭
where Co is the initial radionuclide concentration applied to the system. The relative effluent concentration, C′, expressed in terms of two dimensionless parameters, the column Peclet number
(P) and the number of pore volumes (T), is derived as follows:
C'(T ) = 1 erfc⎡(
P )1/ 2 (R − T )⎤ + 1 exp(P)erfc⎡(
P )1/ 2 (R + T )⎤ , (2.13.6)
2 ⎢⎣
4RT
⎦⎥ 2
⎣⎢ 4RT ⎥⎦
where
C′ = C(L,t)/ C0 ,
(2.13.7)
T =υt /L ,
(2.13.8)
and
P=υL/D .
(2.13.9)
The average interstitial or pore-water velocity is represented by v and is approximately equivalent to the ratio of the water flow rate to the volumetric water content. The length of the soil column is represented by L. The parameter L, in the case of field-measured concentration- time curves, simply refers to the soil depth at which the concentration was observed. The following expression is frequently used to describe displacement experiments (Danckwerts 1953; Xxxxx et al. 1956):
C(x,t)= C0 erfc ⎡ Rx -υt ⎤ .
(2.13.10)
2 ⎢ 2(DRt)1/2 ⎥
⎣ ⎦
This equation provides a close approximation to Equation (2.13.5) for relatively large values of P (>20). In terms of the Peclet number (P) and the number of pore volumes (T), when applied to the effluent concentration, Equation (2.13.10) can be written as follows:
C '(T ) = 1 erfc⎡( P )1/ 2 (R − T )⎤
2 ⎢⎣ 4RT ⎥⎦
(2.13.11)
Many empirical methods based on the measured relative effluent concentration (C′) versus the number of pore volumes (T) have been used for the analysis of P and R. These include the trial-and-error, slope, lognormal plot, and least-squares methods (Rifai et al. 1956; Xxx Xxxxxxxxx and Xxxxxxxx 1986). The parameters P and R can also be calculated by using the method of moments (Aris 1958; Xxxxxxxxxx et al. 1978; Skopp 1985; Xxxxxxxx 1985; Jury and Xxxxxxx 1985) and methods for directly determining the coefficients Kd and D from the location and peak concentration of a short or instantaneous surface-applied tracer pulse (Xxxxxxx and Xxxxxx 1972; Xxxxxx et al. 1974; Xx et al. 1984). (Application of these methods is discussed in the original studies.)
2.13.2.2 Empirical Determination of the Distribution Coefficient
In addition to the experimental methods for determining the distribution coefficient (Kd), Xxxx and Xxxxx (1983), Xxxx et al. (1984), and Xxxxxxxx and Xxxxxxxx (1989) proposed an empirical approach to calculate Kd for radionuclide i from the soil-to-plant concentration ratio (Biv), on the basis of the strong correlation between Biv and Kd. Xxxxxxxx and Xxxxxxxx (1990) proposed the following correlation equation:
ln Kd = a + b ( lnBiv ) ,
(2.13.12)
where a and b are constants. The value for the coefficient b is -0.5, on the basis of experimental data. The value of a depends on soil type: for xxxxx soil, a = 2.11; for loamy soil, a = 3.36; for clayey soil, a = 3.78; and for organic soil, a = 4.62. Equation (2.13.12) provides a method of estimating the distribution coefficient from the plant-soil concentration ratio, especially when experimental or literature data are not available. For actinides and transuranics, this approach may not be valid (IAEA 2010a).
2.13.3 Summary of Literature Review
In 2003, the International Atomic Energy Agency (IAEA) launched the program on Environmental Modeling for Radiation Safety (EMRAS), and one Working Group under this program worked on revising Kd values and transfer parameters for a large number of elements. Tables 2.13.1–2.13.5 list the Kd data developed for different soil types by the EMRAS Working Group (IAEA 2010a, Xxx-Xxxxxx et al. 2009a, Vandenhove et al. 2009, Xxx-Xxxxxx et al. 2009b). The data include geometric mean, geometric standard deviation, minimum and maximum values, and the mean and standard deviation of the underlying normal distribution. The data in these tables are from field and laboratory experiments with various contamination sources. The soils were grouped according to the sand and clay percentages and the organic matter content. For certain radionuclides, Kd values were also grouped by using the “cofactor” criterion. Table 2.13.6 lists the correlations between Kd and soil properties. Table 2.13.7 lists the Kd for some elements grouped on the basis of pH values. For some elements, the Kd values can also be grouped on
the basis of other soil properties [water content (θ) and organic matter content (I)
(Xxx-Xxxxxx et al. 2009b)]. Xxxxxxxx (2011) provided relationships for predicting the variations in
Kd values on the basis of soil properties (Table 2.13.8), such as soil pH, clay content, and organic carbon content. The data in the EMRAS compilation (IAEA 2010a; Xxx-Xxxxxx et al. 2009a, b; Xxxxxxxxxx et al. 2009) was mainly based on short-term sorption studies, and the data of Xxxxxxxx (2011) represented desorption of indigenous elements. Table 2.13.9 lists the geometric mean Kd values for different soil types.
2.13.4 Data Input Requirements
The default distribution coefficients used in the RESRAD (onsite) and RESRAD- OFFSITE codes are listed in Table 2.13.10. From Tables 2.13.1–2.13.9, it can be seen that Kd is quite variant; that is, it assumes different values under different circumstances. Because Kd is one of the important input parameters that has a strong influence on the calculated results in the RESRAD (onsite) and RESRAD-OFFSITE codes, a site-specific value, if available, should always be used for risk assessment. In its decommissioning guidance (Xxxxxxx et al. 2006), the
U.S. Nuclear Regulatory Commission (NRC) encourages licensees to use sensitivity analysis to identify the importance of Kd on the resulting dose either (1) to demonstrate that a specific value used in the analysis is conservative or (2) to identify whether site-specific data should be obtained (if the licensee believes Kd is overly conservative).
In addition to the direct input of Kd values from the screen, the RESRAD (onsite) code provides four optional methods for deriving the distribution coefficient. The first method requires inputting a greater-than-zero value for the elapsed time since material placement (TI) and provision of the groundwater concentration of the radionuclide, which is measured at the same time as the radionuclide soil concentration. The second method uses the non-zero input xxxxx rate (default is 0) to derive Kd. The third method is based on the correlation between the plant-soil concentration ratio and the water-soil distribution coefficient, which can be invoked by setting the Kd value to -1 on the input screen. The last method uses a solubility limit to derive an effective distribution coefficient. Only one of the four methods can be used in each RESRAD (onsite) execution. If more than one of the requirements is satisfied, RESRAD (onsite) will always choose according to the following order: the solubility limit method first, the groundwater concentration method second, the xxxxx rate method third, and the plant/soil concentration ratio method last.
2.14 XXXXX RATE
2.14.1 Definition
The xxxxx rate is the fraction of the available radionuclide leached out from the contaminated zone per unit of time. It is assumed that the leaching process is driven by equilibrium distribution of the contaminant between the soil matrix and soil water. The xxxxx rate is used in RESRAD (onsite) for calculating the source factor for adjusting radionuclide concentrations in the contaminated zone.
TABLE 2.13.1 Kd Data for Each Element for Sand Soil Type
Element | N | GM | GSD | Min | Max | µ | σ |
Ac | 1 | 450 | NAa | NA | NA | NA | NA |
Ag | 3 | 130 | 5 | 36 | 695 | 4.87 | 1.61 |
Am | 17 | 1,000 | 7 | 67 | 37,000 | 6.91 | 1.95 |
As | 4 | 210 | 5 | 25 | 1,350 | 5.35 | 1.61 |
Be | 1 | 240 | NA | NA | NA | NA | NA |
Bi | 2 | NA | NA | 120 | 490 | NA | NA |
Br | 1 | 15 | NA | NA | NA | NA | NA |
Cab | 7 | 3 | 4 | 0.7 | 28 | 1.1 | 1.39 |
Cd | 30 | 110 | 8 | 2 | 1,770 | 4.7 | 2.08 |
Ce | 3 | 400 | 1 | 316 | 490 | 5.99 | 0 |
Cl | 3 | 0.5 | 4 | 0.1 | 1.1 | −0.69 | 1.39 |
Cm | 5 | 3,400 | 14 | 186 | 30,920 | 8.13 | 2.64 |
Co | 18 | 260 | 18 | 5 | 36,756 | 5.56 | 2.89 |
Cr | 9 | 8 | 8 | 1 | 100 | 2.08 | 2.08 |
Csb | 114 | 530 | 6 | 10 | 35,210 | 6.27 | 1.79 |
Cu | 2 | NA | NA | 128 | 333 | NA | NA |
Dy | 1 | 820 | NA | NA | NA | NA | NA |
Fe | 4 | 320 | 1 | 220 | 424 | 5.77 | 0 |
Ga | 1 | 310 | NA | NA | NA | NA | NA |
H | 1 | 0.1 | NA | NA | NA | NA | NA |
Hf | 2 | NA | NA | 450 | 3,270 | NA | NA |
Ho | 1 | 240 | NA | NA | NA | NA | NA |
I | 37 | 4 | 8 | 0.01 | 134 | 1.39 | 2.08 |
I-all | 48 | 4 | 7 | 0.01 | 134 | 1.39 | 1.95 |
In | 1 | 240 | NA | NA | NA | NA | NA |
IO3 | 6 | 4 | 5 | 0.4 | 41 | 1.39 | 1.61 |
Kb | 60 | 3 | 3 | 0.7 | 179 | 1.1 | 1.1 |
La | 1 | 5,300 | NA | NA | NA | NA | NA |
Lu | 1 | 5,100 | NA | NA | NA | NA | NA |
Mgb | 6 | 1 | 4 | 0.4 | 16 | 0 | 1.39 |
Mn | 13 | 980 | 14 | 40 | 79,044 | 6.89 | 2.64 |
Mo | 2 | NA | NA | 7 | 82 | NA | NA |
Na | 6 | 2 | 4 | 0.4 | 23 | 0.69 | 1.39 |
Nb | 2 | NA | NA | 160 | 187 | NA | NA |
Ni | 26 | 130 | 10 | 3 | 7250 | 4.87 | 2.3 |
Np | 8 | 14 | 4 | 3 | 108 | 2.64 | 1.39 |
P | 2 | NA | NA | 9 | 760 | NA | NA |
Pa | 1 | 540 | NA | NA | NA | NA | NA |
Pbc | 9 | 220 | 4 | 25 | 1,349 | 5.39 | 1.39 |
Pd | 2 | NA | NA | 55 | 127 | NA | NA |
Pm | 1 | 450 | NA | NA | NA | NA | NA |
Poc | 14 | 100 | 6 | 17 | 7,020 | 4.61 | 1.79 |
Pu | 11 | 400 | 4 | 33 | 6,865 | 5.99 | 1.39 |
Rac | 20 | 3,100 | 8 | 49 | 40,000 | 8.04 | 2.08 |
Rb | 1 | 55 | NA | NA | NA | NA | NA |
Ru | 3 | 36 | 6 | 5 | 172 | 3.58 | 1.79 |
Sb | 19 | 17 | 6 | 0.6 | 472 | 2.83 | 1.79 |
TABLE 2.13.1 (Cont.) | |||||||
Element | N | GM | GSD | Min | Max | µ | σ |
Sc | 1 | 670 | NA | NA | NA | NA | NA |
Se | 15 | 56 | 5 | 4 | 1616 | 4.03 | 1.61 |
Si | 1 | 33 | NA | NA | NA | NA | NA |
Sm | 1 | 240 | NA | NA | NA | NA | NA |
Sn | 2 | NA | NA | 130 | 169 | NA | NA |
Srb | 65 | 22 | 6 | 0.4 | 2,424 | 3.09 | 1.79 |
Ta | 2 | NA | NA | 240 | 379 | NA | NA |
Tb | 1 | 5,400 | NA | NA | NA | NA | NA |
Tc | 5 | 0.04 | 3 | 0.01 | 0.1 | −3.22 | 1.1 |
Te | 1 | 180 | NA | NA | NA | NA | NA |
Thc | 12 | 700 | 11 | 35 | 100,000 | 6.55 | 2.4 |
Tm | 1 | 330 | NA | NA | NA | NA | NA |
Uc | 50 | 110 | 12 | 0.7 | 66,667 | 4.7 | 2.48 |
V | 1 | 180 | NA | NA | NA | NA | NA |
Y | 5 | 22 | 2 | 10 | 47 | 3.09 | 0.69 |
Zn | 17 | 110 | 23 | 0.9 | 27,815 | 4.7 | 3.14 |
Zr | 4 | 32 | 16 | 2 | 600 | 3.47 | 2.77 |
Note: N = number of observations; GM = geometric mean; GSD = geometric standard deviation; Min = minimum; Max = maximum; µ = mean of the underlying normal distribution; and σ = standard deviation of the underlying normal distribution. For “sand” soil type, sand fraction ≥ 65% and clay fraction <18%. a NA = not applicable. b Source: Xxx-Xxxxxx et al. (2009a). c Source: Vandenhove et al. (2009). Source: Xxx-Xxxxxx et al. (2009b), except as noted. | |||||||
TABLE 2.13.2 Kd Data for Each Element for Loam Soil Type
Element | N | GM | GSD | Min | Max | µ | σ |
Ac | 1 | 1,500 | NAa | NA | NA | NA | NA |
Ag | 1 | 120 | NA | NA | NA | NA | NA |
Am | 31 | 4,200 | 6 | 50 | 48,309 | 8.34 | 1.79 |
As | 1 | 1,000 | NA | NA | NA | NA | NA |
Ba | 1 | 0.4 | NA | NA | NA | NA | NA |
Be | 1 | 810 | NA | NA | NA | NA | NA |
Bi | 1 | 400 | NA | NA | NA | NA | NA |
Br | 1 | 49 | NA | NA | NA | NA | NA |
Cab | 21 | 8 | 3 | 2 | 89 | 2.08 | 1.1 |
Cd | 5 | 100 | 7 | 9 | 1,700 | 4.61 | 1.95 |
Ce | 4 | 3,000 | 3 | 652 | 8,100 | 8.01 | 1.1 |
Cl | 10 | 0.4 | 3 | 0.04 | 0.9 | −0.92 | 1.1 |
Cm | 9 | 19,000 | 2 | 6809 | 51,900 | 9.85 | 0.69 |
Co | 71 | 810 | 15 | 2 | 103,595 | 6.7 | 2.71 |
Cr | 9 | 45 | 23 | 1 | 1585 | 3.81 | 3.14 |
Csb | 191 | 3,500 | 4 | 39 | 55,100 | 8.16 | 1.39 |
Cu | 1 | 490 | NA | NA | NA | NA | NA |
Fe | 12 | 890 | 2 | 291 | 2,231 | 6.79 | 0.69 |
Hf | 1 | 1,500 | NA | NA | NA | NA | NA |
Ho | 1 | 810 | NA | NA | NA | NA | NA |
I | 74 | 7 | 5 | 0.2 | 531 | 1.95 | 1.61 |
I-all | 129 | 8 | 4 | 0.2 | 538 | 2.08 | 1.39 |
IO3 | 41 | 9 | 4 | 1 | 538 | 2.2 | 1.39 |
Kb | 81 | 20 | 4 | 2 | 911 | 3 | 1.39 |
Mgb | 20 | 5 | 3 | 0.9 | 45 | 1.61 | 1.1 |
Mn | 56 | 1,100 | 8 | 60 | 77,079 | 7 | 2.08 |
Mo | 1 | 130 | NA | NA | NA | NA | NA |
Na | 20 | 5 | 2 | 0.3 | 26 | 1.61 | 0.69 |
Nb | 5 | 2,500 | 3 | 540 | 8370 | 7.82 | 1.1 |
Ni | 14 | 180 | 5 | 8 | 1163 | 5.19 | 1.61 |
Np | 12 | 23 | 4 | 1.3 | 117 | 3.14 | 1.39 |
P | 2 | NA | NA | 30 | 380 | NA | NA |
Pa | 1 | 1,800 | NA | NA | NA | NA | NA |
Pbc | 5 | 10,000 | 3 | 3,600 | 43,000 | 9.21 | 1.1 |
Pd | 1 | 180 | NA | NA | NA | NA | NA |
Poc | 27 | 230 | 4 | 12 | 1,830 | 5.44 | 1.39 |
Pu | 27 | 950 | 4 | 100 | 9,610 | 6.86 | 1.39 |
Rac | 19 | 1,100 | 17 | 12 | 120,000 | 7 | 2.83 |
Rac | 17 | 710 | 14 | 12 | 80,000 | 6.57 | 2.64 |
Rb | 1 | 180 | NA | NA | NA | NA | NA |
Ru | 3 | 300 | 3 | 82 | 990 | 5.7 | 1.1 |
Sb | 92 | 61 | 3 | 4 | 2,065 | 4.11 | 1.1 |
Se | 101 | 220 | 3 | 12 | 1,606 | 5.39 | 1.1 |
Si | 1 | 110 | NA | NA | NA | NA | NA |
Sm | 1 | 810 | NA | NA | NA | NA | NA |
Sn | 1 | 450 | NA | NA | NA | NA | NA |
Srb | 120 | 57 | 5 | 2 | 2,549 | 4.04 | 1.61 |
Ta | 1 | 810 | NA | NA | NA | NA | NA |
TABLE 2.13.2 | |||||||
Element | N | GM | GSD | Min | Max | µ | σ |
Tc | 14 | 0.07 | 3 | 0.01 | 0.1 | −2.66 | 1.1 |
Thc | 6 | 18,000 | 4 | 5,000 | 250,000 | 9.8 | 1.39 |
Uc | 84 | 310 | 12 | 0.9 | 38,710 | 5.74 | 2.48 |
Zn | 48 | 2,400 | 4 | 211 | 153,070 | 7.78 | 1.39 |
Zr | 2 | NA | NA | 2,200 | 8,100 | NA | NA |
Note: N = number of observation; GM = geometric mean; GSD = geometric standard deviation; Min = minimum; Max = maximum; µ = mean of the underlying normal distribution; and σ = standard deviation of the underlying normal distribution. When soil is not of sand, clay, or organic soil type, it is classified as loam soil type. a NA = not applicable. b Source: Xxx-Xxxxxx et al. (2009a). c Source: Vandenhove et al. (2009). Source: Xxx-Xxxxxx et al. (2009b), except as noted. | |||||||
Reported leaching mechanisms have included diffusion, dissolution, ion exchange, corrosion and surface effects. Diffusion has traditionally been considered to be the most important leaching mechanism. However, it has been indicated that dissolution is also important for waste containing soluble salts and that ion exchange is important when sorbents such as zeolites or clay are included in the waste form.
A literature survey on leaching mechanisms by Colombo et al. (1985) indicates that factors that affect leaching have been divided into three categories: (1) system factors,
(2) leachant factors, and (3) composition of contamination site form. System factors include time, temperature, pressure, radiation environment and ratio of waste form surface area to leachant volume. Xxxxx rate is a function of time and the functional dependence typically changes over the long term. Therefore, changes in xxxxx rate should be taken into account when long-term xxxxx rate is used. Temperature is generally the first parameter to be varied in attempts to analyze rate processes. For example, the leachability of cement increases with temperature (Colombo et al. 1985).
Leachant factors include the effects of pH, oxidation potential (Eh), flow rate or replacement frequency, and composition. The solubility of most cations is strongly dependent on pH. The high pH limits the solubility of most radionuclides with the notable exception of cesium. Eh controls the oxidation state, and thus the solubility of elements such as cobalt with multiple oxidation states. Ames and Xxx (1978) reported the Eh-pH diagrams predicting the presence of different solids for elements that exist in more than one oxidation state. Appendix J of User’s
TABLE 2.13.3 Kd Data for Each Element for Clay Soil Type
Element | N | GM | GSD | Min | Max | µ | σ |
Ac | 1 | 2,400 | NAa | NA | NA | NA | NA |
Ag | 1 | 180 | NA | NA | NA | NA | NA |
Am | 1 | 8,100 | NA | NA | NA | NA | NA |
Be | 1 | 1,300 | NA | NA | NA | NA | NA |
Bi | 1 | 670 | NA | NA | NA | NA | NA |
Br | 1 | 74 | NA | NA | NA | NA | NA |
Cab | 5 | 16 | 3 | 6 | 49 | 2.77 | 1.1 |
Cd | 4 | 130 | 15 | 7 | 2721 | 4.87 | 2.71 |
Ce | 3 | 910 | 15 | 122 | 20,000 | 6.81 | 2.71 |
Cl | 5 | 0.2 | 3 | 0.06 | 0.9 | −1.61 | 1.1 |
Cm | 1 | 5,400 | NA | NA | NA | NA | NA |
Co | 10 | 3,800 | 6 | 540 | 99,411 | 8.24 | 1.79 |
Cr | 5 | 14 | 20 | 1 | 1,500 | 2.64 | 3 |
Csb | 36 | 5,500 | 4 | 566 | 375,000 | 8.61 | 1.39 |
Cu | 2 | NA | NA | 101 | 2733 | NA | NA |
Fe | 4 | 1,600 | 1 | 1,185 | 2,240 | 7.38 | 0 |
Hf | 1 | 2,400 | NA | NA | NA | NA | NA |
Ho | 1 | 1,300 | NA | NA | NA | NA | NA |
I | 13 | 7 | 6 | 1 | 123 | 1.95 | 1.79 |
I-all | 19 | 11 | 5 | 1 | 180 | 2.4 | 1.61 |
Kb | 12 | 43 | 3 | 9 | 294 | 3.76 | 1.1 |
Mgb | 4 | 7 | 3 | 2 | 29 | 1.95 | 1.1 |
Mn | 10 | 4,500 | 13 | 139 | 57,215 | 8.41 | 2.56 |
Mo | 1 | 90 | NA | NA | NA | NA | NA |
Na | 4 | 2 | 6 | 0.2 | 11 | 0.69 | 1.79 |
Nb | 3 | 2,400 | 2 | 900 | 4,729 | 7.78 | 0.69 |
Ni | 12 | 930 | 2 | 247 | 3,187 | 6.84 | 0.69 |
Np | 2 | NA | NA | 20 | 55 | NA | NA |
P | 1 | 49 | NA | NA | NA | NA | NA |
Pa | 1 | 2,700 | NA | NA | NA | NA | NA |
Pbc | 2 | NA | NA | 5,396 | 127,544 | NA | NA |
Pd | 1 | 270 | NA | NA | NA | NA | NA |
Poc | 1 | 732 | NA | NA | NA | NA | NA |
Pu | 10 | 1,800 | 2 | 430 | 7,600 | 7.5 | 0.69 |
Rac | 6 | 38,000 | 12 | 696 | 950,000 | 10.55 | 2.48 |
Rac | 4 | 13,000 | 10 | 696 | 100,000 | 9.47 | 2.3 |
Rb | 1 | 270 | NA | NA | NA | NA | NA |
Ru | 4 | 500 | 2 | 203 | 989 | 6.21 | 0.69 |
Sb | 18 | 140 | 2 | 38 | 614 | 4.94 | 0.69 |
Se | 33 | 240 | 3 | 22 | 2,130 | 5.48 | 1.1 |
Si | 1 | 180 | NA | NA | NA | NA | NA |
Sm | 1 | 1,300 | NA | NA | NA | NA | NA |
Sn | 1 | 670 | NA | NA | NA | NA | NA |
Srb | 19 | 95 | 4 | 9 | 747 | 4.55 | 1.39 |
Ta | 1 | 1,300 | NA | NA | NA | NA | NA |
Tc | 3 | 0.09 | 10 | 0.02 | 1 | -2.41 | 2.3 |
Thc | 7 | 4,500 | 3 | 800 | 24,000 | 8.41 | 1.1 |
TABLE 2.13.3 (Cont.) | |||||||
Element | N | GM | GSD | Min | Max | µ | σ |
Uc | 12 | 28 | 7 | 3 | 480 | 3.33 | 1.95 |
Zn | 8 | 2,445 | 2 | 480 | 6,945 | 7.8 | 0.69 |
Zr | 2 | NA | NA | 3300 | 10,300 | NA | NA |
Note: N = number of observation; GM = geometric mean; GSD = geometric standard deviation; Min = minimum; Max = maximum; µ = mean of the underlying normal distribution; and σ = standard deviation of the underlying normal distribution. For “clay” soil type, clay fraction ≥35%. a NA = not applicable. b Source: Xxx-Xxxxxx et al. (2009a). c Source: Vandenhove et al. (2009). Source: Xxx-Xxxxxx et al. (2009b), except as noted. | |||||||
Manual for RESRAD Version 6 (Xx et al. 2001) describes estimating the effective distribution coefficient on the basis of radionuclide solubility when the stability-pH diagrams for radionuclides are provided. Leachant flow rate or replacement frequency affects the degree of saturation of the leachant with respect to leached material. Porosity in a solid is a major factor affecting diffusion within the solid. Changes in porosity due to dissolution of soluble material or other factors may affect long-term leachability.
TABLE 2.13.4 Kd Data for Each Element for Organic Soil Type
Element | n | GM | GSD | Min | Max | µ | σ |
Ac | 1 | 5,400 | NAa | NA | NA | NA | NA |
Ag | 2 | NA | NA | 4,400 | 15,000 | NA | NA |
Am | 13 | 2,500 | 5 | 210 | 110,000 | 7.82 | 1.61 |
Be | 1 | 3,000 | NA | NA | NA | NA | NA |
Bi | 1 | 1,500 | NA | NA | NA | NA | NA |
Br | 1 | 180 | NA | NA | NA | NA | NA |
Cab | 1 | 110 | NA | NA | NA | NA | NA |
Cd | 13 | 650 | 6 | 10 | 7,000 | 6.48 | 1.79 |
Ce | 1 | 3,000 | NA | NA | NA | NA | NA |
Cl | 2 | NA | NA | 0.1 | 1.2 | NA | NA |
Cm | 3 | 7,400 | 2 | 5,056 | 12,000 | 8.91 | 0.69 |
Co | 17 | 87 | 9 | 4 | 5,800 | 4.47 | 2.2 |
Cr | 6 | 160 | 10 | 8 | 2,905 | 5.08 | 2.3 |
Csb | 108 | 270 | 7 | 4 | 95,000 | 5.6 | 1.95 |
Cu | 4 | 320 | 3 | 76 | 883 | 5.77 | 1.1 |
Fe | 3 | 1,400 | 3 | 521 | 4,900 | 7.24 | 1.1 |
Hf | 1 | 5,400 | NA | NA | NA | NA | NA |
TABLE 2.13.4 (Cont.) | |||||||
Element | n | GM | GSD | Min | Max | µ | σ |
Ho | 1 | 3,000 | NA | NA | NA | NA | NA |
I | 9 | 36 | 4 | 8 | 581 | 3.58 | 1.39 |
I-all | 11 | 32 | 3 | 8 | 581 | 3.47 | 1.1 |
IO3 | 1 | 13 | NA | NA | NA | NA | NA |
Kb | 76 | 19 | 3 | 2 | 134 | 2.94 | 1.1 |
Mn | 3 | 160 | 4 | 36 | 490 | 5.08 | 1.39 |
Mo | 2 | NA | NA | 18 | 27 | NA | NA |
Nb | 1 | 2,000 | NA | NA | NA | NA | NA |
Ni | 8 | 1,100 | 2 | 406 | 4,990 | 7 | 0.69 |
Np | 4 | 810 | 1 | 500 | 1,200 | 6.7 | 0 |
P | 1 | 110 | NA | NA | NA | NA | NA |
Pa | 1 | 6,600 | NA | NA | NA | NA | NA |
Pbc | 5 | 2500 | 3 | 880 | 10,266 | 7.82 | 1.1 |
Pd | 1 | 670 | NA | NA | NA | NA | NA |
Pu | 6 | 760 | 4 | 90 | 2951 | 6.63 | 1.39 |
Rac | 1 | 200 | NA | NA | NA | NA | NA |
Rb | 1 | 670 | NA | NA | NA | NA | NA |
Ru | 1 | 66,000 | NA | NA | NA | NA | NA |
Sb | 3 | 75 | 8 | 8 | 540 | 4.32 | 2.08 |
Se | 2 | NA | NA | 230 | 1,800 | NA | NA |
Si | 1 | 400 | NA | NA | NA | NA | NA |
Sm | 1 | 3,000 | NA | NA | NA | NA | NA |
Sn | 1 | 1,600 | NA | NA | NA | NA | NA |
Srb | 37 | 110 | 6 | 3 | 6,500 | 4.7 | 1.79 |
Ta | 1 | 3,000 | NA | NA | NA | NA | NA |
Tc | 11 | 3 | 3 | 0.9 | 11 | 1.1 | 1.1 |
Thc | 5 | 730 | 44 | 19 | 80,000 | 6.59 | 3.78 |
Uc | 9 | 1,200 | 6 | 33 | 7,600 | 7.09 | 1.79 |
Y | 2 | NA | NA | 260 | 375 | NA | NA |
Zn | 12 | 570 | 8 | 10 | 7,630 | 6.35 | 2.08 |
Zr | 2 | NA | NA | 23 | 7,300 | NA | NA |
Note: N = number of observations; GM = geometric mean; GSD = geometric standard deviation; Min = minimum; Max = maximum; µ = mean of the underlying normal distribution; and σ = standard deviation of the underlying normal distribution. For “organic” soil type, organic fraction >20%. a NA = not applicable. b Source: Xxx-Xxxxxx et al. (2009a). c Source: Vandenhove et al. (2009). Source: Xxx-Xxxxxx et al. (2009b), except as noted. | |||||||
TABLE 2.13.5 Kd Data for Each Element for Generic Soil Type
Element | N | GM | GSD | Min | Max | µ | σ |
Ac | 4 | 1,700 | 3 | 450 | 5,400 | 7.44 | 1.10 |
Ag | 9 | 380 | 7 | 36 | 15,000 | 5.94 | 1.95 |
Am | 62 | 2,600 | 6 | 50 | 110,000 | 7.86 | 1.79 |
As | 7 | 550 | 5 | 25 | 2,991 | 6.31 | 1.61 |
Be | 5 | 990 | 3 | 240 | 3,000 | 6.9 | 1.10 |
Bi | 6 | 480 | 2 | 120 | 1,500 | 6.17 | 0.69 |
Br | 4 | 56 | 3 | 15 | 180 | 4.03 | 1.10 |
Cab | 34 | 8 | 3 | 0.7 | 110 | 2.08 | 1.10 |
Cd | 61 | 150 | 9 | 2 | 7,000 | 5.01 | 2.20 |
Ce | 11 | 1,200 | 5 | 122 | 20,000 | 7.09 | 1.61 |
Cl | 22 | 0.3 | 3 | 0.04 | 1.2 | -1.2 | 1.10 |
Cm | 18 | 9,300 | 4 | 186 | 51,900 | 9.14 | 1.39 |
Co | 118 | 480 | 16 | 2 | 103,595 | 6.17 | 2.77 |
Cr | 31 | 40 | 20 | 1 | 7,943 | 3.69 | 3.00 |
Csb | 469 | 1,200 | 7 | 4 | 375,000 | 7.09 | 1.95 |
Cu | 11 | 530 | 3 | 76 | 2,733 | 6.27 | 1.10 |
Dy | 2 | NAa | NA | 820 | 2,100 | NA | NA |
Fe | 23 | 880 | 2 | 220 | 4,900 | 6.78 | 0.69 |
Ga | 2 | NA | NA | 280 | 310 | NA | NA |
Hf | 6 | 2,500 | 3 | 450 | 8,500 | 7.82 | 1.10 |
Ho | 4 | 930 | 3 | 240 | 3,000 | 6.84 | 1.10 |
I | 157 | 5 | 6 | 0.01 | 581 | 1.61 | 1.79 |
I-all | 250 | 7 | 5 | 0.01 | 581 | 1.95 | 1.61 |
In | 2 | NA | NA | 240 | 730 | NA | NA |
IO3 | 67 | 8 | 4 | 0.4 | 538 | 2.08 | 1.39 |
Kb | 237 | 13 | 4 | 0.7 | 911 | 2.56 | 1.39 |
Mgb | 30 | 4 | 3 | 0.4 | 45 | 1.39 | 1.10 |
Mn | 83 | 1,200 | 9 | 36 | 79,044 | 7.09 | 2.20 |
Mo | 9 | 38 | 3 | 7 | 130 | 3.64 | 1.10 |
Na | 30 | 3 | 3 | 0.2 | 26 | 1.1 | 1.10 |
Nb | 11 | 1,500 | 4 | 160 | 8,370 | 7.31 | 1.39 |
Ni | 64 | 280 | 7 | 3 | 7,250 | 5.63 | 1.95 |
Np | 26 | 36 | 6 | 1.3 | 1200 | 3.58 | 1.79 |
P | 6 | 87 | 5 | 9 | 760 | 4.47 | 1.61 |
Pa | 4 | 2,000 | 3 | 540 | 6,600 | 7.6 | 1.10 |
Pbc | 23 | 2,100 | 10 | 25 | 127,544 | 7.65 | 2.30 |
Pd | 6 | 180 | 2 | 55 | 670 | 5.19 | 0.69 |
Pm | 2 | NA | NA | 450 | 450 | NA | NA |
Poc | 42 | 180 | 5 | 12 | 7,020 | 5.19 | 1.61 |
Pu | 62 | 740 | 4 | 32 | 9,610 | 6.61 | 1.39 |
Rac | 51 | 2,500 | 13 | 12 | 950,000 | 7.82 | 2.56 |
Rac,d | 47 | 1,800 | 10 | 12 | 100,000 | 7.5 | 2.30 |
Rb | 4 | 210 | 3 | 55 | 670 | 5.35 | 1.10 |
Ru | 15 | 270 | 8 | 5 | 66,000 | 5.6 | 2.08 |
Sb | 152 | 62 | 4 | 0.6 | 2065 | 4.13 | 1.39 |
Sc | 2 | NA | NA | 670 | 3,500 | NA | NA |
Se | 172 | 200 | 3 | 4 | 2,130 | 5.3 | 1.10 |
TABLE 2.13.5 (Cont.) | |||||||
Element | N | GM | GSD | Min | Max | µ | σ |
Si | 4 | 130 | 3 | 33 | 400 | 4.87 | 1.10 |
Sm | 4 | 930 | 3 | 240 | 3,000 | 6.84 | 1.10 |
Sn | 12 | 1,600 | 6 | 130 | 31,000 | 7.38 | 1.79 |
Srb | 255 | 52 | 6 | 0.4 | 6500 | 3.95 | 1.79 |
Ta | 5 | 780 | 3 | 240 | 3000 | 6.66 | 1.10 |
Tb | 2 | NA | NA | 5,400 | 6600 | NA | NA |
Tc | 33 | 0.2 | 9 | 0.01 | 11 | -1.61 | 2.20 |
Te | 2 | NA | NA | 180 | 790 | NA | NA |
Thc | 46 | 1,900 | 10 | 19 | 250,000 | 7.55 | 2.30 |
Uc | 178 | 200 | 12 | 0.7 | 66,667 | 5.3 | 2.48 |
V | 2 | NA | NA | 180 | 410 | NA | NA |
Y | 7 | 47 | 4 | 10 | 375 | 3.85 | 1.39 |
Zn | 92 | 950 | 11 | 0.9 | 153,070 | 6.86 | 2.40 |
Zr | 11 | 410 | 21 | 2 | 10,300 | 6.02 | 3.04 |
Note: N = number of observations; GM = geometric mean; GSD = geometric standard deviation; Min = minimum; Max = maximum; µ = mean of the underlying normal distribution; and σ = standard deviation of the underlying normal distribution. For generic soil type, the data includes all soil types combined including sand, loam, clay, organic, and the “unspecified” soil type reported in the original reference sources. a NA = not applicable. b Source: Xxx-Xxxxxx et al. (2009a). c Source: Vandenhove et al. (2009). d Values excluding one dataset. Source: Xxx-Xxxxxx et al. (2009b), except as noted. | |||||||
TABLE 2.13.6 Correlations between Kd and Soil Main Properties for Selected Elements
Element – Soil Type | Regression Equations | Number of Observations | Correlation Coefficient | % Variance Explained |
Cd – All soils | Log Kd = 0.8(0.4) + 0.21(0.07) × pH | 55 | 0.38 | 13 |
Log Kd = −0.1(0.5) + 0.34(0.08) × pH + 0.4(0.1) × log(OM) | 54 | 0.49 | 24 | |
Cd – Mineral soils | Log Kd = −0.7(0.4) + 0.41(0.06) × pH | 43 | 0.71 | 49 |
Co – All soils | Log Kd = −0.7(0.3) + 0.63(0.05) × pH | 113 | 0.75 | 56 |
Log Kd = −1.5(0.4) + 0.74(0.06) × pH + 0.5(0.2) × log(OM) | 110 | 0.77 | 59 |
TABLE 2.13.6 (Cont.) | ||||
Element – Soil Type | Regression Equations | Number of Observations | Correlation Coefficient | % Variance Explained |
Co – Mineral soils | Log Kd = −1.2(0.4) + 0.71(0.06) × pH | 97 | 0.76 | 58 |
Cr(VI) – All soils | Log Kd = 4.7(0.6)–0.52(0.08) × pH | 12 | -0.89 | 78 |
Cs – All soils | Log Kd = 0.94(0.04) × log(RIP/Kss) | 257 | 0.78 | 65 |
Cu – Mineral soils | Log Kd = −3(1) + 0.8(0.1) × pH | 5 | 0.95 | 88 |
I – All soils | Log Kd = 0.63(0.04) + 0.6(0.1) × log(OM) | 227 | 0.55 | 30 |
Log Kd = −1.4(0.4) + 0.6(0.1) × log(Fe) | 124 | 0.44 | 18 | |
Log Kd = −0.6(0.4) + 0.7(0.1) × log(OM) + 0.3(0.1) × log(Fe) | 124 | 0.63 | 39 | |
Ni – All soils | Log Kd = 0.1(0.3) + 0.34(0.05) × pH | 58 | 0.68 | 46 |
Log Kd = −1.6(0.5) + 0.55(0.06) × pH + 0.27(0.09) × log(clay) | 38 | 0.82 | 67 | |
Log Kd = −0.7(0.3) + 0.41(0.04) × pH + 0.7(0.1) × log(OM) | 58 | 0.84 | 70 | |
Ni – Mineral soils | Log Kd = −0.6(0.3) + 0.43(0.04) × pH | 51 | 0.82 | 66 |
Log Kd = −1.6(0.5) + 0.55(0.06) × pH + 0.27(0.09) × log(clay) | 38 | 0.82 | 67 | |
Log Kd = -0.9(0.3) + 0.45(0.04) × pH + 0.6(0.1) × log(OM) | 51 | 0.86 | 74 | |
Pb – All soilsa | Log Kd = 1.25(0.45) + 0.37(0.08) × pH | 21 | 0.52 | 68 |
Sr – All soils | Log Kd = −0.05(0.09) + 0.86(0.03) × log(CEC/(Ca + Mg)ss) | 96 | 0.95 | 90 |
U – Soil adequate for agriculturea | Log Kd = −0.77(0.11) × pH + 7.7 (0.7) | 110 | 0.3 | 20 |
Zn – All soils | Log Kd = −0.1(0.5) + 0.52(0.08) × pH | 88 | 0.55 | 30 |
Log Kd = −1.0(0.6) + 0.6(0.1) × pH + 0.5(0.2) × log(OM) | 86 | 0.59 | 35 | |
Zn – Mineral soils | Log Kd = −1.2(0.5) + 0.71(0.09) × pH | 75 | 0.69 | 47 |
Log Kd = −1.8(0.6) + 0.8(0.9) × pH + 0.5(0.2) × log(OM) | 73 | 0.71 | 50 | |
Note: Values in brackets show the uncertainty in the number; OM = organic matter content, RIP = radiocesium interception potential (mmol/kg), Kss = concentration of K in soil solution (cmolc/L), CEC = cation exchange capacity (cmolc/kg), (Ca + Mg)ss = concentration of Ca and Mg in soil solution (cmolc/L). a Source: Xxxxxxxxxx et al. (2009). Source: Xxx-Xxxxxx et al. (2009b), except as noted. | ||||
TABLE 2.13.7 Kd Values Grouped According to pH Values
Element | Soil Group | Number of Observations | Geometric Mean | Geometric Standard Deviation | Minimum | Maximum |
Cd | pH<5 | 8 | 11 | 3 | 2 | 64 |
5≤pH<6.5 | 11 | 18 | 4 | 6 | 250 | |
pH≥6.5 | 24 | 380 | 6 | 4 | 4,360 | |
Co | pH<5 | 21 | 12 | 5 | 2 | 153 |
5≤pH<6.5 | 50 | 1,100 | 5 | 29 | 99,941 | |
pH≥6.5 | 26 | 4,600 | 4 | 547 | 103,595 | |
Ni | pH<5 | 10 | 15 | 2 | 3 | 48 |
5≤pH<6.5 | 11 | 58 | 4 | 7 | 1,100 | |
pH≥6.5 | 30 | 820 | 4 | 40 | 7,250 | |
Pba | 3≤pH≤6.4 | 13 | 570 | 6 | 25 | 6,200 |
6.4<pH≤8.3 | 8 | 7,900 | 7 | 301 | 127,544 | |
Tha | pH<5 | 11 | 1,275 | 15 | 19 | 10,200 |
5≤pH<8 | 26 | 3,261 | 8 | 100 | 100,000 | |
pH≥8 | 6 | 310 | 7 | 35 | 3,200 | |
Ua | pH<5 | 36 | 71 | 11 | 0.7 | 6,700 |
5≤pH<7 | 77 | 740 | 8 | 2.6 | 66,667 | |
pH≥7 | 61 | 68 | 8 | 0.9 | 6,160 | |
Zn | pH<5 | 9 | 8 | 8 | 1 | 301 |
5≤pH<6.5 | 49 | 1,600 | 6 | 6 | 30,157 | |
pH≥6.5 | 17 | 4,300 | 4 | 437 | 153,070 | |
a Source: Vandenhove et al. (2009). Source: Xxx-Xxxxxx et al. (2009b), except as noted. | ||||||
TABLE 2.13.8 Regression Equations for Kd Values for Some Nuclides
Element | Regression Equation | Number of Soils | Geometric Standard Deviation | Soil Organic Carbon (%), 5th/95th Percentiles |
As | Log(Kd) = 2.39 + 0.085 × pH | 178 | 1.8 | 1.1/4.7 |
Cd | Log(Kd) = 2.35 + 0.114 × pH | 150 | 1.4 | 0/5.0 |
Ce | Log(Kd) = 1.84 + 0.469 × pH – 0.00162 × clay × pH | 209 | 2.0 | 0/4.7 |
Cl | 1.4 L/kg for mineral soils and 150 L/kg for organic soils | 11/3 | NAa | NA |
Co | Log(Kd) = 1.46 + 0.247 × pH + 0.00709 × clay | 342 | 7.5 | 0.27/30 |
TABLE 2.13.8 (Cont.) | ||||
Element | Regression Equation | Number of Soils | Geometric Standard Deviation | Soil Organic Carbon (%), 5th/95th Percentiles |
Cr | Log(Kd) = 1.61 + 0.29 × pH + 0.381 × log(organic carbon) – CrIII; 9.4 L/kg – CrVI | 83; 51 | 3.0; 2.0 | 0.29/30; 0.06/8.0 |
Csb | Log(Kd) = 3.03 + 0.101 × pH + 0.0117 × clay | 470 | 5.6 | 0.09/40 |
Cu | Log(Kd) = 2.47 + 0.0656 × pH + 0.00726 × clay | 205 | 1.4 | 0/4.7 |
Fe | Log(Kd) = 2.01 + 0.00442 × clay × pH | 44 | 3.2 | 0.81/31 |
Ho | Log(Kd) = 2.15 + 0.338 × pH – 0.00094 × clay × pH | 161 | 1.7 | 0.0/4.8 |
I | Log(Kd) = 0.953 + 0.701 × log(organic carbon) | 114 | 8.1 | 0.19/49 |
La | Log(Kd) = 3.26 + 0.234 × pH – 0.0448 × clay + 0.00517 × clay × pH | 227 | 1.8 | 0.0/4.7 |
Mnc | Log(Kd) = −0.330 + 0.457 × pH | 402 | 15 | 0.4/7.7 |
Mo | Log(Kd) = 3.22–0.212 × pH + 0.0125 × clay | 215 | 1.9 | 0.44/4.8 |
Nb | Log(Kd) = 2.45 + 0.348 × pH + 0.0960 × clay - 0.0159 × clay × pH | 92 | 2.8 | 0.0/8.6 |
Nd | Log(Kd) = 2.98 + 0.271 × pH – 0.0112 × clay + 0.204 × log(organic carbon) | 228 | 1.9 | 3.5/5.5 |
Nid | Log(Kd) = 0.816 + 0.229 × pH | 410 | 2.5 | 0.3/14 |
Np | Log(Kd) = −1.71 + 0.332 × pH + 0.960 × log(organic carbon) + 0.00740 × clay × pH | 159 | 5.7 | 0.42/40 |
Pa | 1380 L/kg for mineral soils and 6600 L/kg for organic soils | 4 | NA | NA |
Pb | Log(Kd) = 1.96 + 0.276 × pH + 0.294 × log(organic carbon) | 362 | 6.4 | 0.3/9.8 |
Pu | Log (Kd) = 1.77 + 0.193 × pH + 0.637× log(organic carbon) | 175 | 3.9 | 0.1/4.9 |
Ra | Log(Kd) = −2.64 + 0.676 × pH | 38 | 30 | 0.01/9.9 |
Sb | Log(Kd) = 3.24 – 0.107 × pH + 0.00614 × clay | 197 | 1.4 | 0.0/4.7 |
Se | Log(Kd) = 2.02 + 0.0929 × pH − 0.00964 × clay | 123 | 2.0 | 0.6/30 |
TABLE 2.13.8 (Cont.) | ||||
Element | Regression Equation | Number of Soils | Geometric Standard Deviation | Soil Organic Carbon (%), 5th/95th Percentiles |
Sm | Log(Kd) = 2.77 + 0.273 × pH + 0.00852 × clay + 0.253 × log(organic carbon) | 218 | 1.8 | 0.0/4.8 |
Sn | 2100 L/kg | 32 | 1.7 | 0.18/8.6 |
Sr | Log(Kd) = 2.93 – 0.224 × pH + 0.0217 × clay | 481 | 4.9 | 0.09/14 |
Tc | 2.1 L/kg if aerobic Log(Kd) = −0.0243 + 0.253 × pH + 0.531 × log(organic carbon) if anaerobic | 118, 33 | 3.8, 1.9 | 0.06/59, 0.18/54 |
Th | Log(Kd) = 1.90 + 0.346 × pH | 39 | 12 | 0.8/35 |
Tl | Log(Kd) = 4.08 – 0.0842 × pH + 0.0181 × clay | 170 | 1.5 | 0/4.7 |
Tm | Log(Kd) = 1.94 + 0.369 × pH =0.00150 × clay × pH | 87 | 2.1 | 0.0/8.6 |
U | Log(Kd) = 9.05–0.989 × pH + 0.00290 × clay × pH where pH ≥5.5 and Log(Kd) = 1.75 + 0.0145 × clay × pH where pH <5.5 | 318, 28 | 4.7, 11 | 0.9/50, 1.8/50 |
W | 6020 L/kg | 19 | 2.2 | 0.9/10 |
Yb | Log(Kd) = 2.71 + 0.244 × pH – 0.000962 × clay × pH | 203 | 1.8 | 0.0/4.7 |
a Not applicable b For desorption of indigenous Cs, the Kd values will be 4.2-fold higher than predicted by the equation, and for sorption of new Cs-137, they will be 4.2-fold lower. c For desorption of indigenous Mn, the Kd values will be 4.0-fold higher than predicted by the equation, and for sorption of new Mn-54, they will be 4.0-fold lower. d For desorption of indigenous Ni, the Kd values will be 6.2-fold higher than predicted by the equation, and for sorption of new Ni, they will be 6.2 fold lower. | ||||
TABLE 2.13.9 Summary of Geometric Mean Kd
Values (cm3/g) for Each Element by Soil Type
Soil Type | |||||
Element | Sand | Loam | Clay | Organic | Generic |
Ac | 450 | 1,500 | 2,400 | 5,400 | 1,700 |
Ag | 130 | 120 | 180 | NAa | 380 |
TABLE 2.13.9 (Cont.) | |||||
Soil Type | |||||
Element | Sand | Loam | Clay | Organic | Generic |
Am | 1,000 | 4,200 | 8,100 | 2,500 | 2,600 |
As | 210 | 1000 | NA | NA | 550 |
Ba | NA | 0.4 | NA | NA | NA |
Be | 240 | 810 | 1,300 | 3,000 | 990 |
Bi | NA | 400 | 670 | 1,500 | 480 |
Br | 15 | 49 | 74 | 180 | 56 |
Cab | 3 | 8 | 16 | 110 | 8 |
Cd | 110 | 100 | 130 | 650 | 150 |
Ce | 400 | 3,000 | 910 | 3,000 | 1,200 |
Cl | 0.5 | 0.4 | 0.2 | NA | 0.3 |
Cm | 3,400 | 19,000 | 5,400 | 7,400 | 9,300 |
Co | 260 | 810 | 3,800 | 87 | 480 |
Cr | 8 | 45 | 14 | 160 | 40 |
Csb | 530 | 3,500 | 5,500 | 270 | 1,200 |
Cu | NA | 490 | NA | 320 | 530 |
Dy | 820 | NA | NA | NA | NA |
Fe | 320 | 890 | 1,600 | 1,400 | 880 |
Ga | 310 | NA | NA | NA | NA |
H | 0.1 | NA | NA | NA | NA |
Hf | NA | 1,500 | 2,400 | 5,400 | 2,500 |
Hg | NA | NA | NA | NA | 6,300 |
Ho | 240 | 810 | 1,300 | 3,000 | 930 |
I-all | 4 | 8 | 11 | 32 | 7 |
IO3 | 4 | 9 | NA | 13 | 8 |
I- | 4 | 7 | 7 | 36 | 5 |
In | 240 | NA | NA | NA | 730 |
Ir | NA | NA | NA | NA | 3 |
Kb | 3 | 20 | 43 | 19 | 13 |
La | 5,300 | NA | NA | NA | NA |
Lu | 5,100 | NA | NA | NA | NA |
Mgb | 1 | 5 | 7 | NA | 4 |
Mn | 980 | 1,100 | 4,500 | 160 | 1,200 |
Mo | NA | 130 | 90 | NA | 38 |
Na | 2 | 5 | 2 | NA | 3 |
Nb | NA | 2,500 | 2,400 | 2,000 | 1,500 |
Ni | 130 | 180 | 930 | 1,100 | 280 |
Np | 14 | 23 | NA | 810 | 36 |
P | NA | NA | 49 | 110 | 87 |
Pa | 540 | 1,800 | 2,700 | 6,600 | 2,000 |
Pbc | 220 | 10,000 | 2,500 | 2,100 | |
Pd | NA | 180 | 270 | 670 | 180 |
Pm | 450 | NA | NA | NA | NA |
Poc | 100 | 230 | 732 | NA | 180 |
Pt | NA | NA | NA | NA | 24 |
Pu | 400 | 950 | 1800 | 760 | 740 |
TABLE 2.13.9 (Cont.) | |||||
Soil Type | |||||
Element | Sand | Loam | Clay | Organic | Generic |
Rac | 3,100 | 1,100 | 38,000 | 200 | 2,500 |
Rac, d | NA | 710 | 13,000 | NA | 1,800 |
Rb | 55 | 180 | 270 | 670 | 210 |
Rh | NA | NA | NA | NA | 4 |
Ru | 36 | 300 | 500 | 66,000 | 270 |
Sb | 17 | 61 | 140 | 75 | 62 |
Sc | 670 | NA | NA | NA | NA |
Se | 56 | 220 | 240 | NA | 200 |
Si | 33 | 110 | 180 | 400 | 130 |
Sm | 240 | 810 | 1,300 | 3,000 | 930 |
Sn | NA | 450 | 670 | 1,600 | 1,600 |
Srb | 22 | 57 | 95 | 110 | 52 |
Ta | NA | 810 | 1,300 | 3,000 | 780 |
Tb | 5,400 | NA | NA | NA | NA |
Tc | 0.04 | 0.07 | 0.09 | 3 | 0.2 |
Te | 180 | NA | NA | NA | 790 |
Thc | 700 | 18,000 | 4,500 | 730 | 1,900 |
Tm | 330 | NA | NA | NA | NA |
Uc | 110 | 310 | 28 | 1,200 | 200 |
V | 180 | NA | NA | NA | NA |
Y | 22 | NA | NA | NA | 47 |
Zn | 110 | 2,400 | 2445 | 570 | 950 |
Zr | 32 | NA | NA | NA | 410 |
a NA = not applicable. b Source: Xxx-Xxxxxx et al. (2009a). c Source: Vandenhove et al. (2009). d Estimates exclude data with very low Ca2+ concentration in external solution. Source: Xxx-Xxxxxx et al. (2009b), except as noted. | |||||