Influence of Coupling Erosion 

and Hydrology on the 

Long-Term Performance of 

Engineered Surface Barriers

Office of Nuclear Regulatory Research

NUREG/CR-7200

Influence of Coupling Erosion 

and Hydrology on the 

Long-Term Performance of 

Engineered Surface Barriers

Manuscript Completed: May 2016

Date Published: May 2016

Prepared by:

Crystal L. Smith and Craig H. Benson

Geological Engineering

University of Wisconsin-Madison

1415 Engineering Drive

Madison, WI 53706

Jacob Philip, NRC Project Manager

Office of Nuclear Regulatory Research

NUREG/CR-7200

iii

ABSTRACT

Design strategies were evaluated that couple erosion and hydrology for barriers over low 

level radioactive waste (LLW) disposal facilities by conducting long-term (1000 yr)

parametric simulations with a landform evolution and hydrologic models. Topography of 

the Grand Junction Uranium Mill Tailings Disposal Site in Grand Junction, CO was used 

to define a realistic geometry. The most significant differences in maximum erosion 

depths were attributed to climate and vegetation. Approximately 4 m greater maximum 

erosion depth was estimated in semi-arid climates compared to humid climate for 

simulations with a rip-rap or gravel admixture surface. Vegetation decreased erosion in 

the semi-arid climate by 1.5 m, and by 4 m in the humid climate. Vegetation also 

increased the amount of evapotranspiration that occurred, decreasing percolation into 

the waste. Short slopes, slopes with a low grade, and slopes with small grade 

differences at the nickpoint decreased erosion. The humid climate had the least erosion 

when terraced slopes were utilized. Due to higher erosion rates in the semi-arid climate, 

natural and concave slopes that promote deposition produced the least erosion. Overall,

a rip-rap surface layer prevented erosion most effectively for any type of topography, 

climate, or cover type. However, covers with a riprap surface had higher percolation 

rates. In contrast, a gravel admixture surface had slightly greater erosion, but was more 

effective in limited percolation.
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v

CONTENTS

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

CONTENTS...................................................................................................v

LIST OF FIGURES.........................................................................................vii

LIST OF TABLES..........................................................................................xiii

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

ACKNOWLEDGMENTS................................................................................xvii

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

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

2.1 Factors Affecting Fluvial Erosion ..........................................................2-1

2.2 Erosion Models.................................................................................2-6

2.2.1 Empirical Erosion Models......................................................... 2-6

2.2.2. Landform Evolution Models ..............................................................2-14

3. METHODS............................................................................................................3-1

3.1 Reference Site – Grand Junction Uranium Mill Tailings Disposal Site...........3-1

3.1.1 Engineered Barriers.................................................................3-1

3.1.2 Materials...............................................................................3-1

3.2 Modeling Erosion with SIBERIA........................................................... 3-4

3.2.1 Parameterization.....................................................................3-7

3.2.2 DTM Formulation using SIBERIA..............................................3-12

3.2.3 SIBERIA Inputs and Control Parameters....................................3-13

3.3 SVFLUX........................................................................................3-13

4. RESULTS AND DISCUSSION...................................................................4-1

4.1 Effect of Type of Surface Layer on Erosion.............................................4-1

4.1.1 Influence of Climate and Vegetation on Erosion.............................4-3

4.1.2 Influence of Barrier Type on Erosion....................................... 4-10

4.1.3 Hydrologic Comparison of Barrier Type and Surface Layer Type.....4-10

4.2 Effect of Slope Length and Grade on Erosion........................................4-16

4.3 Effect of Slope Shape on Erosion....................................................... 4-18

5. SUMMARY AND PRACTICAL IMPLICATIONS.............................................5-1

6. REFERENCES.......................................................................................6-1

APPENDIX A: WEPP SENSITIVITY ANALYSIS TO INITIAL SOIL WATER 

CONTENT AND ALBEDO.................................................................. A-1

APPENDIX B: SIBERIA PREDICTIONS FOR COVERS WITH WATER 

BALANCE BARRIERS....................................................................... B-1

APPENDIX C: SVFLUX PREDICTIONS FOR RESISTIVE AND WATER 

BALANCE COVERS.......................................................................... C-1
vi

APPENDIX D: SIBERIA PREDICTIONS FOR UNIFORM SIDE SLOPE 

TOPOGRAPHY.................................................................................. D-1

APPENDIX E: TOPOGRAPHIC MAPS USED IN SIBERIA ........................................ E-1

APPENDIX F: SIBERIA PREDICTIONS FOR SHALLOW AND DEEP CONCAVE 

SIDE SLOPES......................................................................................F-1

APPENDIX G: SIBERIA PREDICTIONS FOR LEAST ERODED SURFACES...........G-1

APPENDIX H: STEPS FOR RUNNING SIBERIA LANDFORM EVOLUTION 

MODEL USING A DIGITAL TERRAIN MODEL AND VIEWING 

MODEL OUTPUT............................................................................... H-1

APPENDIX I: A SAMPLE LAYER.MODEL FILE USED IN SIBERIA............................I-1

APPENDIX J: THE SIBERIA.SETUP FILE USED IN SIBERIA ...................................J-1
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LIST OF FIGURES

Fig. 2.1. Slope shapes (a) uniform slope, (b) convex slope, and (c) concave 

slope...........................................................................................................2-2

Fig. 2.2. Interrill erosion area (a) and rill erosion area (b). Photo courtesy of 

USDA Natural Resource Conservation Service...........................................2-4

Fig. 2.3. Schematic of the armoring process: (a) original surface, (b) armored 

surface (adapted from Willgoose and Sharmeen, 2006)..............................2-5

Fig. 2.4. Conservation of mass for a segment along the overland flow path on a 

hillslope (adapted from

http://www.ars.usda.gov/Research/docs.htm?docid=6014).........................2-9

Fig. 2.5. Watershed and hillslope erosion processes evaluated by WEPP 

(adapted from USDA-ARS 1995). .............................................................2-12

Fig. 3.1. Topography of Grand Junction Uranium Mill Tailings Disposal Site in 

Grand Junction, CO, the reference site for this study. .................................3-2

Fig. 3.2. Resistive barrier profile (a) and water balance barrier profile (b). ................3-3

Fig. 4.1. Maximum erosion and average elevation predicted by SIBERIA for the 

reference site with a resistive barrier comparing rip-rap, topsoil, and 

gravel admixture surface layers: (a) semi-arid climate and (b) humid 

climate. .......................................................................................................4-2

Fig. 4.2. Elevation predicted for reference site with SIBERIA for a resistive 

barrier in a semi-arid climate: (a) rip-rap surface layer, (b) gravel 

admixture surface layer, and (c) topsoil surface layer. Elevation is 

shown in m and denoted by the color bar above. ........................................4-4

Fig. 4.3. Plan view of reference site with a resistive barrier in a semi-arid 

climate showing number of layers remaining intact across surface as 

predicted by SIBERIA: (a) rip-rap surface layer, (b) gravel admixture 

surface layer, and (c) topsoil surface layer. The color scale is layers of 

the barrier remaining intact ranging from one (tailings, red shading) to 

eight (deposition, blue shading). Green shading is all five layers of the 

cover plus the tailings layer remaining intact (six). ......................................4-6

Fig. 4.4. Elevation predicted for reference site predicted with SIBERIA for a 

resistive barrier in a humid climate: (a) rip-rap surface layer, (b) gravel 

admixture surface layer, and (c) topsoil surface layer. Elevation is 

shown in m and denoted by the color scale above......................................4-7

Fig. 4.5. Plan view of reference site predicted with SIBERIA for a resistive 

barrier in a humid climate: (a) rip-rap surface layer, (b) gravel 

admixture surface layer, and (c) topsoil surface layer. The color scale 

is layers of the barrier remaining intact ranging from one (tailings, red 
viii

shading) to eight (deposition, blue shading). Green shading is all five 

layers of the cover plus the tailings layer remaining intact (six). ..................4-8

Fig. 4.6. Maximum erosion and average elevation predicted by SIBERIA for the 

reference site with a resistive barrier comparing gravel admixture 

surfaces with and without vegetation: (a) semi-arid climate and (b) 

humid climate............................................................................................4-12

Fig. 4.7. Maximum erosion and average elevation predicted by SIBERIA for 

resistive and water balance barriers with a rip-rap surface layer: (a) 

semi-arid climate and (b) humid climate....................................................4-13

Fig. 4.8. End-of-year cumulative flux above the tailings predicted by SVFLUX 

for the typical year and wettest year in a semi-arid climate: (a) 

resistive barrier and (b) water balance barrier. Negative flux indicates 

downward flow into the tailings..................................................................4-14

Fig. 4.9. End-of-year cumulative flux above the tailings predicted by SVFLUX 

for the typical year and wettest year in a humid climate: (a) resistive 

barrier and (b) water balance barrier. Negative flux indicates 

downward flow into the tailings..................................................................4-15

Fig. 4.10. Topography representing balanced side slopes with 20% maximum 

side slopes and 5.3% maximum top slope, referred to herein as the 

modified topography. ................................................................................4-17

Fig. 4.11. Maximum erosion and average elevation change predicted by 

SIBERIA for the reference site with rip-rap surface layer and a 

resistive barrier for various slope lengths: (a) semi-arid climate and (b) 

humid climate............................................................................................4-20

Fig. 4.12. Maximum erosion depth at 1000-yr for a 14.7% and 15.5% grade 

difference using a rip-rap surface over a resistive barrier in semi-arid 

and humid climates with slope length of 28 and 41 m. ..............................4-21

Fig. 4.13. Terraced (a), shallow concavity, 30% initial slope (b), deep concavity, 

60% initial slope (c), and natural hillside slopes (d) used to evaluate 

influence of topography on erosion. ..........................................................4-22

Fig. 4.14. Maximum erosion, maximum deposition, and average elevation 

change predicted by SIBERIA for resistive barriers with a rip-rap 

surface and uniform, terraced, concave (semi-arid: deep concave, 

humid: shallow concave), or natural side slopes: (a) semi-arid climate 

and (b) humid climate. ..............................................................................4-23

Fig. 4.15. Number of layers intact after 1000 years in a semi-arid climate 

predicted by SIBERIA for a resistive barrier with a rip-rap surface: (a) 

terraced side slopes, (b) concave side slopes (deep), and (c) natural 

side slopes................................................................................................4-25
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Fig. 4.16. Number of layers intact after 1000 years in a humid climate predicted 

by SIBERIA for a resistive barrier with a rip-rap surface: (a) terraced 

side slopes, (b) concave side slopes (shallow), and (c) natural side 

slopes. ......................................................................................................4-26

Fig. 4.17. Maximum erosion, maximum deposition, and average elevation 

change predicted by SIBERIA for resistive barriers with a gravel 

admixture surface and uniform, terraced, concave (semi-arid: shallow, 

humid: deep), or natural side slopes: (a) semi-arid climate and (b) 

humid climate............................................................................................4-27

Fig. 4.18. Number of layers intact after 1000 years in a semi-arid climate 

predicted by SIBERIA for a resistive barrier with a gravel admixture 

surface: (a) terraced side slopes, (b) concave side slopes (shallow), 

and (c) natural side slopes. .......................................................................4-28

Fig. 4.19. Number of layers intact after 1000 years in a humid climate predicted 

by SIBERIA for a resistive barrier with a gravel admixture surface: (a) 

terraced side slopes, (b) concave side slopes (deep), and (c) natural 

side slopes................................................................................................4-30

Fig. 4.20. Maximum erosion, maximum deposition, and average elevation 

change predicted by SIBERIA for resistive barriers with a topsoil 

surface and uniform, terraced, concave (semi-arid: shallow, humid: 

deep), or natural side slopes: (a) semi-arid climate and (b) humid 

climate. .....................................................................................................4-31

Fig. 4.21. Number of layers intact after 1000 years in a semi-arid climate 

predicted by SIBERIA for a resistive barrier with a topsoil surface: (a) 

terraced side slopes, (b) concave side slopes (shallow), and (c) 

natural side slopes....................................................................................4-32

Fig. 4.22. Number of layers intact after 1000 years in a humid climate predicted 

by SIBERIA for a resistive barrier with a topsoil surface: (a) terraced 

side slopes, (b) concave side slopes (deep), and (c) natural side 

slopes. ......................................................................................................4-34

Fig. B.1. Maximum erosion, maximum deposition, and average elevation 

change predicted by SIBERIA for rip-rap, topsoil, and gravel 

admixture surface layer for a water balance barrier using the 

representative site topography: (a) semi-arid climate and (b) humid 

climate. ...................................................................................................... B-2

Fig. B.2. Erosion predicted by SIBERIA for a rip-rap surface with a water 

balance barrier in a semi-arid climate using the representative site 

topography: a) elevation predictions of the surface after 1000 years of 

erosion and, b) number of layers remaining intact after 1000 years of 

erosion, plan view. ..................................................................................... B-3

Fig. B.3. Erosion predicted by SIBERIA for a gravel admixture surface with a 

water balance barrier in a semi-arid climate using the representative 
x

site topography: a) elevation predictions of the surface after 1000 

years of erosion and, b) number of layers remaining intact after 1000 

years of erosion, plan view......................................................................... B-4

Fig. B.4. Erosion predicted by SIBERIA for a topsoil surface with a water 

balance barrier in a semi-arid climate using the representative site 

topography: a) elevation predictions of the surface after 1000 years of 

erosion and, b) number of layers remaining intact after 1000 years of 

erosion, plan view. ..................................................................................... B-5

Fig. B.5. Erosion predicted by SIBERIA for a rip-rap surface on a water balance 

barrier in a humid climate using the representative site topography: a) 

elevation predictions of the surface after 1000 years of erosion and b) 

number of layers remaining intact after 1000 years of erosion, plan 

view. .......................................................................................................... B-6

Fig. B.6. Erosion predicted by SIBERIA for a gravel admixture surface on a 

water balance barrier in a humid climate using the representative site 

topography: a) elevation predictions of the surface after 1000 years of 

erosion and b) number of layers remaining intact after 1000 years of 

erosion, plan view. ..................................................................................... B-7

Fig. B.7. Erosion predicted by SIBERIA for a topsoil surface on a water balance 

barrier in a humid climate using the representative site topography: a) 

elevation predictions of the surface after 1000 years of erosion and b) 

number of layers remaining intact after 1000 years of erosion, plan 

view. .......................................................................................................... B-8

Fig. C.1. Predictions from SVFLUX of precipitation, evapotranspiration, soilwater storage, and cumulative percolation for resistive and water 

balance barriers in a semi-arid climate. Some simulations required 

less years than others to stabilize. The last year of each simulation is 

the wettest year. Positive percolation is into the tailings, negative is 

out. ............................................................................................................C-2

Fig. C.2. Predictions from SVFLUX of precipitation, evapotranspiration, soilwater storage, and cumulative percolation for resistive and water 

balance barriers in a humid climate. Some simulations required less 

years than others to stabilize. The last year of each simulation is the 

wettest year. Positive percolation is into the tailings, negative is out. ......... C-3

Fig. D.1. Maximum erosion, maximum deposition, and average elevation 

change predicted by SIBERIA for rip-rap, topsoil, and gravel 

admixture surfaces with 41 m side slopes and a resistive barrier: (a) 

semi-arid climate and (b) humid climate..................................................... D-2

Fig. D.2. Maximum erosion, maximum deposition, and average elevation 

change in resistive and water balance barriers predicted by SIBERIA 

with 41 m side slopes and a rip-rap surface layer: (a) semi-arid 

climate and (b) humid climate. ................................................................... D-3
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Fig. D.3. Elevation predicted for a rip-rap surface with various slope lengths 

and angles in a semi-arid climate: (a) 53 m side slopes, 15.3% side 

slopes, 2% top slope, (b) 28 m side slopes, 18.5% side slopes, 3% 

top slope, and (c) 41 m side slopes, 20% side slopes, 5.3% top slope.

Elevation is shown in m and denoted by the color scale above.................. D-4

Fig. D.4. Plan view predicted for a rip-rap surface with various slope lengths 

and angles in a semi-arid climate: (a) 53 m side slopes, 15.3% side 

slopes, 2% top slope, (b) 28 m side slopes, 18.5% side slopes, 3% 

top slope, and (c) 41 m side slopes, 20% side slopes, 5.3% top slope....... D-5

Fig. D.5. Elevation predicted for a rip-rap surface with various slope lengths 

and angles in a humid climate: (a) 53 m side slopes, 15.3% side 

slopes, 2% top slope, (b) 28 m side slopes, 18.5% side slopes, 3% 

top slope, and (c) 41 m side slopes, 20% side slopes, 5.3% top slope.

Elevation is shown in m and denoted by the color scale above.................. D-6

Fig. D.6. Plan view predicted for a rip-rap surface with various slope lengths 

and angles in a humid climate: (a) 53 m side slopes, 15.3% side 

slopes, 2% top slope, (b) 28 m side slopes, 18.5% side slopes, 3% 

top slope, and (c) 41 m side slopes, 20% side slopes, 5.3% top slope....... D-7

Fig. E.1. Topographic map of the representative site. .............................................. E-2

Fig. E.2. Modified site topography used to create uniform, terraced, concave, 

and natural side slopes. See Fig. 4.13 for side slope views with top 

and side slope grades................................................................................ E-3

Fig. F.1. Maximum erosion, maximum deposition, and average elevation 

change for resistive barrier in a semi-arid climate: a comparison of 

shallow and deep concavity for (a) a rip-rap surface, and (b) a topsoil 

surface........................................................................................................F-3

Fig. F.2. Maximum erosion, maximum deposition, and average elevation 

change for resistive barrier in a humid climate: a comparison of 

shallow and deep concavity for (a) a rip-rap surface, and (b) a gravel 

admixture surface. ......................................................................................F-4

Fig. G.1. Elevation predictions from SIBERIA of the topography producing the 

least erosion with a resistive barrier in a semi-arid climate: (a) rip-rap 

surface layer with deep concavity and (b) gravel admixture surface 

layer with shallow concavity. ......................................................................G-2

Fig. G.2. Plan view SIBERIA predictions of the topography producing the least 

erosion with a resistive barrier in a semi-arid climate: (a) rip-rap 

surface layer with deep concavity and (b) gravel admixture surface 

layer with shallow concavity. ......................................................................G-3
xii

Fig. G.3. Elevation predictions from SIBERIA of the topography producing the 

least erosion with a resistive barrier in a humid climate: (a) rip-rap 

surface layer with terraces and (b) gravel admixture surface layer with 

terraces......................................................................................................G-4

Fig. G.4. Plan view SIBERIA predictions of the topography producing the least 

erosion with a resistive barrier in a humid climate: (a) rip-rap surface 

layer with terraces and (b) gravel admixture surface layer with 

terraces......................................................................................................G-5
xiii

LIST OF TABLES

Table 2.1. Summary of key aspects of erosion codes evaluated for this study. .........2-7

Table 3.1. Material properties of surface layers, resistive barrier layers, water 

balance barrier layers, and waste (Benson et al. 2008 and 2010), 

Particle size fractions by Unified Soil Classification System. Organic 

matter by loss on ignition...........................................................................3-5

Table 3.2. Hydraulic properties used in the hydraulic modeling portion of this 

study..........................................................................................................3-6

Table 3.3. Summary of parameterization and SIBERIA simulations in the 

literature. ...................................................................................................3-8

Table 3.4. Fluvial sediment transport parameters for resistive barriers used in 

the SIBERIA simulations..........................................................................3-10

Table 3.5. Fluvial sediment transport parameters for water balance barriers 

used in SIBERIA simulations. ..................................................................3-11

Table 3.6. SIBERIA input and control parameters for erosion, runoff and 

sediment transport...................................................................................3-14

Table 3.7. Vegetation parameter input to SVFLUX...................................................3-16

Table 4.1. Erosion process for fluvial erosion parameters m1 and n1 based on 

climate and surface layer type. ..................................................................4-5

Table 4.2. Side slope length, side slope grade, top slope grade, and grade 

difference compared with SIBERIA simulations to determine effects 

of slope length and grade. .......................................................................4-19

Table A.1. Effects of initial soil water content on discharge and sediment loss in 

WEPP. All other factors held constant. ..................................................... A-2

Table A.2. Effects of soil albedo on discharge and sediment loss in WEPP............... A-3

Table F.1. Best case scenario for concave side slopes based on climate and 

surface material.........................................................................................F-2
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EXECUTIVE SUMMARY

The objective of this study was to evaluate design strategies that couple erosion and 

hydrology for barriers of low level radioactive waste (LLRW) disposal facilities. This 

objective was met by conducting long-term (1000 yr) parametric simulations with the 

SIBERIA landform evolution model and the SVFLUX hydrologic model.

Landform evolution modeling considered four main factors affecting fluvial erosion: (1) 

climate, (2) soil, (3) vegetation, and (4) topography. Several scenarios were evaluated 

for semi-arid and humid sites. The topography of the Grand Junction Uranium Mill 

Tailings Disposal Site in Grand Junction, CO was used as a realistic starting point, and

modifications were made to the topography, soil surface layer, cover type, and 

vegetation. The topographic changes included a modified cover with a central high point 

and more balanced slope lengths with uniform slopes, and modified cover with terraced, 

concave, and natural side slopes. Three types of surface layers were evaluated: rip-rap, 

topsoil, and topsoil mixed with gravel (gravel admixture). Conventional resistive barriers 

and water balance barriers with a capillary break were evaluated. Simulations were 

conducted with and without vegetation with native plants for each climate.

Hydraulic modeling was conducted using a one-dimensional profile for semi-arid and 

humid climates. Simulations were conducted using normal and wettest year precipitation 

data. Rip-rap, topsoil, and gravel admixture surface layers were used over resistive and 

water balance barriers in simulations to evaluate cumulative percolation into the waste.

Climate and use of vegetation produced significant differences in maximum erosion 

depths. The semi-arid climate had approximately 4 m greater maximum erosion depth 

than the humid climate for simulations with a rip-rap or gravel admixture surface. A 

topsoil surface in the semi-arid climate had approximately 2.5 m greater maximum 

erosion than the humid climate. Vegetation decreased the amount of erosion in the 

semi-arid climate by 1.5 m and 4 m in the humid climate. Vegetation also increased the 

amount of evapotranspiration that occurred, decreasing percolation into the waste. 

The resistive barrier produced less erosion than the water balance barrier in the semiarid climate. Neither allowed percolation into the waste. Percolation was high for the 

water balance cover in the humid climate and non-existent for the resistive cover. Both 

covers performed identically in the landform evolution predictions for the humid climate.

Short slopes, slopes with a low grade, and slopes with small grade differences at the 

nickpoint were found to decrease erosion. The humid climate had the least erosion when 

terraced slopes were utilized. Due to higher erosion rates in the semi-arid climate, 

natural and concave slopes that promote deposition produced the least erosion.

Overall, the rip-rap surface layer prevented the most erosion over any type of 

topography, climate, or cover type. However, covers with a riprap surface layer 

transmitted more percolation. In contrast, the gravel admixture surface had slightly 

greater erosion, but prevented percolation in typical year simulations for both climates.
xvi
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ACKNOWLEDGMENTS

This study was supported by the US Nuclear Regulatory Commission via an Interagency 

Agreement with the US Geological Survey. Support was also provided by the US 

Department of Energy under Cooperative Agreement Number DE-FC01-06EW07053 

entitled ‘The Consortium for Risk Evaluation with Stakeholder Participation III. The 

opinions, findings, conclusions, or recommendations expressed herein are those of the 

author and do not necessarily represent the views of the US Nuclear Regulatory 

Commission, the US Geological Survey, or the US Department of Energy.
xviii
1-1

1 INTRODUCTION

Engineered barriers are used in waste containment facilities to limit human and 

animal contact with waste, to control ingress and egress of gases, and to limit 

exposure of waste to water sources by controlling percolation (Sackschewsky et al. 

1995, Benson 2001, Walter and Dubreuilh 2007). Barriers for low-level radioactive 

waste (LLRW) and uranium mill tailings sites are designed to control percolation, 

radon emission, and erosion for a service life of at least 1000 yr (EPA 1983). Erosion 

can severely diminish the integrity of the barrier (Waugh et al. 1994, Anderson and 

Stormont 1997, 2005, Stormont 2003) by exposing buried waste, or reduce the 

barrier thickness sufficiently to make the waste more susceptible to percolation

(Richardson and Waugh 1996).

The main objective of this study was to assess the coupling of erosion control 

strategies and hydrological performance of engineered barriers. Two models were 

chosen to evaluate how design strategies affect erosion and hydrology of barriers.

Erosion was modeled using the SIBERIA landform evolution model, whereas 

hydrology was modeled using the variably saturated flow model SVFLUX. Climate, 

material used for the surface layer, barrier type (resistive vs. water balance), 

topography of the landform, erosion protection systems, and vegetation were varied 

systematically to assess how they influence erosion and percolation.

The SIBERIA landform evolution model was used to predict the long-term erosion of 

surface barriers for LLRW facilities. Multiple scenarios with different surface 

materials, barrier types, and topography were predicted with SIBERIA. The variably 

saturated flow code SVFLUX was used to predict the hydrology of barrier scenarios 

simulated in the SIBERIA model. The objective was to determine how modifications 

made to prevent erosion impact the hydrology of barriers. The SVFLUX predictions

were used in conjunction with the SIBERIA predictions to evaluate the barrier

system as a whole when comparing barrier scenarios designed to prevent erosion.

This report consists of the five sections. Section 2 of this report includes background 

information on erosion processes and erosion models. Section 3 includes a

description of the reference site, materials used, and modeling methods. Results of 

the erosion and hydrologic modeling are presented and discussed in Section 4.

Implications of coupling erosion and hydrologic barrier performance and best case 

scenarios are summarized in Section 5.
1-2
2-1

2 BACKGROUND

2.1 Factors Affecting Fluvial Erosion

Soil erodibility is the inherent susceptibility of the soil to erosive forces such as 

rainfall and overland flow. The USDA method to estimate erodibility is based on the 

particle size distribution, organic matter content, soil structure (e.g. granular, platy), 

and hydraulic conductivity (Wischmeier and Smith 1978, Toy et al. 2002). Soil 

erodibility depends on soil structure, texture, organic matter, water content, clay 

mineralogy, density, and chemical and biological characteristics of the soil (Foster et 

al. 1995). Larger particle sizes are easier to detach but more difficult to transport (i.e. 

clay soils are more difficult to detach but easier to transport than sandy soils) 

(Fangmeier et al. 2006). Fine-grained soils have attractive forces that must be 

overcome for erosion to occur (Toy et al. 2002). Granular soils do not have attractive 

forces, and are easier to detach (Fangmeier et al. 2006).

Vegetation can increase rainfall interception, retard erosion, increase plant residue 

on the surface, and restrain soil movement (Fangmeier et al. 2006). Land uses that 

incorporate vegetation have lower erosion than land uses with bare soil.

Topographic features that affect erosion include slope length, steepness, shape, and 

the size and shape of the watershed (Morgan 1995). Steep slopes can accelerate 

detachment and sediment transport by decreasing the stability of particles. Long 

slope lengths tend to concentrate flow, with sheet flow generally transitioning to 

concentrated flow within 30 m (Wischmeier and Smith 1978). Keeping slope lengths 

less than 30 m can significantly reduce development of rills and gullies (Wischmeier 

and Smith 1978).

Uniform, convex, and concave slopes are shown in Fig. 2.1. Concave slopes are

flatter at the base of the slope and deliver less sediment to the base than convex 

slopes because most deposition occurs immediately following a section of steep 

slope (Toy et al. 2002). Variations in erosion to due to shape are influenced by the 

location of overland flow processes on the hillslope in relation to the steepness of 

the slope. By placing the flatter slope towards the base, as with a concave slope,

concentration is avoided and rills disperse over the flatter slope (Fangmeier et al. 

2006).

There are two types of areas where overland flow causes erosion: interrill areas and 

rill areas (Toy et al. 2002), as shown in Fig. 2.2 Rill areas are small channels where 

flow concentrates. Rill location depends on the topography of the surface and can 

change with surface disruption (e.g., tilling). Overland flow causes detachment and 

erosion in rill areas, whereas raindrop impact and sheet flow cause detachment and 

erosion in interrill areas (USDA-ARS 2010b). Detachment in rills occurs when the 

sediment load in the overland flow is less than the transport capacity of the flow.
2-2

 (a) (b) (c)

Fig. 2.1. Slope shapes (a) uniform slope, (b) convex slope, and (c) concave slope.
2-3

Thus, sediment load can also control detachment (Fangmeier et al. 2006).

Transport capacity is the amount of sediment that overland flow is capable of moving 

and is a function of the runoff rate, slope steepness, and hydraulic resistance (Toy et 

al. 2002). Deposition occurs when the sediment load in surface water is greater than 

the transport capacity of the flow. The largest particles are deposited first, and the

smaller particles deposit further downstream (Willgoose and Sharmeen 2006).

Gully erosion is the most destructive form of erosion (Morgan 1995). Gullies are 

large channels that form in concentrated flows that have enough shear stress and 

carry enough abrasive sediment to cut into the surface by removing sediment. This 

first incision into the surface is called head-cutting and it begins downstream towards 

the channel outlet. Head-cutting moves upslope within the channel over time, 

incising the surface and creating the gully (Toy et al. 2002).

Erosion can be mitigated using several methods: (1) vegetating the surface layer, (2) 

decreasing slope steepness, (3) decreasing slope length, and (4) modifying the 

surface material. Vegetation reduces erosion by decreasing raindrop impact (i.e. by 

interception), decreasing interrill erosion, and if the plant stems are dense, limiting rill 

formation. Plant litter and biomass on the surface bind the surface soil so that it is 

less erodible, and surface biomass dissipates energy during water contact. Both of 

the factors are influenced by plant species and coverage.

Other surface materials such as rip-rap and gravel admixtures have been used 

successfully to control erosion on covers (Waugh et al. 1994). Rip-rap controls 

erosion by providing stability on the surface with a sufficiently large weight to resist 

movement by flow (Toy et al. 2002). Rip-rap has been successfully used on 

spillways and severely unstable slopes (Fangmeier et al. 2006). Gravel admixtures 

control erosion via natural surface armoring (Fig. 2.3). Over time, as overland flow 

events occur, the surface soil becomes more resistant to erosion than the underlying 

layer (Willgoose and Sharmeen 2006). Adding large particles expedites the armoring

process by decreasing the amount of finer and more erodible soil (Willgoose and 

Sharmeen 2006). Reducing the steepness of the slope reduces velocity which slows 

channel development by head-cutting. Decreasing slope length decreases the size 

of the drainage area that a channel services. Long slopes tend to increase the 

accumulation of concentrated overland flow (Wischmeier and Smith 1978).
2-4

Fig. 2.2. Interrill erosion area (a) and rill erosion area (b). Photo courtesy of USDA 

Natural Resource Conservation Service

(a) (b)
2-5

Fig. 2.3. Schematic of armoring process: (a) original surface and (b) armored 

surface (adapted from Willgoose and Sharmeen, 2006).
2-6

2.2 Erosion Models

Two empirical erosion models and six landform evolution models were evaluated 

when selecting an erosion model to use in this study. Key aspects of the erosion 

models that were considered are summarized in Table 2.1. Empirical erosion models 

provide an average soil loss per unit area, but provide no information on erosion 

patterns on the land surface. Landform evolution models are process-based 

representations of the mechanisms of erosion on a landform that couple hydrology, 

fluvial erosion, hillslope erosion processes, tectonic uplift, and climate (Coulthard 

2001). Landform evolution models predict erosion patterns on the land surface, 

when erosion occurs, and where erosion starts.

2.2.1 Empirical Erosion Models

Empirical erosion models are used to compute an average soil loss per unit area.

The most common are the Revised Universal Soil Loss Equation (RUSLE2) (USDAARS 2010a) and the Water Erosion Prediction Project (WEPP) model (USDA-ARS 

1995). RUSLE2 and WEPP were developed for agricultural purposes by the United 

States Department of Agriculture - Agricultural Research Service (USDA-ARS) 

jointly with the Natural Resources Conservation Service (NRCS).

2.2.1.1 RUSLE2

The RUSLE2 model is used for conservation planning and erosion estimates in the 

United States (Walter and Dubreuilh 2007). RUSLE2 (USDA-ARS 2010a), and its 

predecessor, the Universal Soil Loss Equation (USLE) (Wischmeier and Smith 1978)

use mechanistic and empirical equations to predict erosion. A schematic of the 

erosion processes in RUSLE2 is in Fig. 2. RUSLE2 is a modification of the original 

USLE model and is based on an updated evaluation of standard plot data (USDAARS 2008) and more recent field data (USDA-ARS 2010b) regarding erosion. USLE 

and RUSLE2 are based on Eq. 2.1 (USDA-ARS 2010b):

A=RKLSCP (2.1)

where A is the average annual soil loss per unit area (tons/acre/yr), R is the average 

annual erosivity of rainfall and runoff [(ft-tonsf/ac)(in/hr)/yr = R-units], K is the soil 

erodibility factor (tons/ac/R-unit), LS is the length-slope factor (dimensionless), C is

the barrier factor (dimensionless), and P is the conservation practice factor 

(dimensionless).

The R-factor is based on rainfall intensity and energy including the terminal velocity 

of raindrops. High intensity and energy are able to erode the surface with greater 

speed and depth (Walter and Dubreuilh 2007).
2-7

Table 2.1. Summary of key aspects of erosion codes evaluated for this study.

Variable/

Process RUSLE2 WEPP SIBERIA ARMOUR CAESAR GOLEM CAS

Type of 

surface

General slope or 

watershed

General slope 

or watershed DTM DTM DTM DTM DTM 

Empirical or 

Mechanistic Empirical MechanisticEmpirical

Mechanistic Mechanistic Mechanistic Mechanistic

Mech

anist

Grid type Not applicable Not applicable Rectangular Rectangular Rectangular

Fixed 

Rectangula

r 1km2 or 

50m2

TIN ≥

Relevant 

Site Size Watershed

Hillslope or 

640 acre field 

size

Watershed Watershed Watershed Regional or 

Watershed

Regi

Scale 

Relevant 

Time Scale Annual Up to 100 

years

highly 

erodible <

1000 yr; 

hard 

surface

<100,000 

yr

highly 

erodible <

1000 yr; 

hard surface

<100,000 yr

10 to 10,000 

years

100,000 -

10,000,000 

yr

Millio

years

Erosion 

Calculations Empirical Shear stress

Conservati

on of mass 

and 

channel 

initiation 

function

Conservation of 

mass and 

shear stress

Multiple flow 

algorithm

Conservation of 

mass

Conserva

mass

2-7
2-8

Table 2.1. Summary of key aspects of erosion codes evaluated for this study (continued).

Variable/

Process RUSLE2 WEPP SIBERIA ARMOUR CAESAR GOLEM CAS

Fluvial 

Erosion/

Diffusive 

Erosion

Fluvial and 

Diffusive 

Erosion

Fluvial and 

Diffusive 

Erosion

Fluvial and 

Diffusive 

Erosion

Fluvial 

Erosion

Fluvial and 

Diffusive 

Erosion

Fluvial and 

Diffusive 

Erosion

Fluvi

Eros

Vegetation 

Capabilities Yes Yes, many 

built in crops

Not 

directly, 

can be 

calibrated 

with model 

parameters

Not directly, 

can be 

calibrated 

with model 

parameters

Yes

Not 

directly, 

can be 

calibrated 

with model 

parameters

Not 

direc

can b

calib

with 

para

Determinatio

n of Erosion

Average Annual 

Rates

Average 

Annual Rates

Average 

Annual 

Rates

Average 

Annual 

Rates

Event 

Based

Event 

Based

Aver

Annu

Rate

Unique 

Capabilities Agriculture Agriculture

Evolves 

catchment 

throughout 

simulation, 

layers, 

output at 

any time

Armoring of 

surface

Divergent 

flow (e.g. 

alluvial fans 

or braided 

rivers)

Landslides, 

weathering, 

sediment 

production

Grap

outpu

mode

evolu

References

Wischmeier and 

Smith (1978), 

USDA-ARS 

(2010a), USDAARS (2010b)

Foster et al. 

(1995), USDAARS (1995), 

Flanigan and 

Nearing 

(1995)

Willgoose 

et al. (91 a, 

b, c; 1994), 

Willgoose 

(05a)

Sharmeen 

(2000), 

Willgoose 

and 

Sharmeen 

(2006)

Coulthard et 

al. (98, 99, 

00), 

Coulthard 

and Macklin 

(2000)

Tucker and 

Slingerland 

(1994)

Brau

Sam

(1997

2-8
2-9

Fig. 2.4. Conservation of mass for a segment along the overland flow path on a 

hillslope (adapted from

http://www.ars.usda.gov/Research/docs.htm?docid=6014).

Sediment load

from upslope

Sediment addition by

interrill erosion

Outgoing

sediment load

Sediment addition

by rill erosion Deposition
2-10

The K-factor is based on the composition of the soil, namely the percentages of clay, 

silt, very fine sand, and organic matter (Wischmeier and Smith 1978). High organic 

matter decreases the erosion potential of soil, whereas erosion increases with clay 

and silt content (Walter and Dubreuilh 2007). Very fine sand is defined as particles 

greater than 0.050 mm and smaller than 0.10 mm. High very fine sand content also 

increases erosion because fine sand has little binding forces (USDA-ARS 2008).

The K-factor also empirically accounts for perviousness of the soil (rapid to very 

slow) and soil structure (very fine granular to blocky, platy or massive) based on the 

texture and saturated hydraulic conductivity of the material (Wischmeier and Smith 

1978). 

The parameter LS is based on the slope length and slope percentage. Slope length 

is important because the drainage area increases, overland flow increases, and 

detachment and transport of soil increases as the slope length increases (Toy et al. 

2002). High slopes increase the velocity of overland flow causing greater soil 

detachment and transport.

The surface cover factor, C, is the ratio of erosion for a type of barrier and practice to 

the erosion for two years of fallow conditions (the standard plot), and is used to 

compare the relative effect of management practices and cropping on erosion rates

(Wischmeier and Smith 1978). Soil conservation practices affect the P-factor. They 

include contouring, strip cropping, and a combination of terracing and contouring. All 

reduce erosion and are reflected in a lower P.

The USLE and RUSLE2 equations were developed to compare any site to the 

standard plot using statistical relationships and produce an average annual soil loss 

for that site. The standard plot is 22.1 m long by 1.83 m wide at a 9% slope with 

tillage up and down the slope that has been fallow for a minimum of 2 yr. In several 

locations throughout the United States, standard plots were developed and 

monitored to gather statistical data regarding erosion. Data from these plots were 

used to develop USLE and RUSLE2. Most of the standard plots were developed in 

agricultural areas of the eastern United States where humid climates are prevalent,

making RUSLE2 less useful for other land uses and climates (USDA-ARS 2010a).

The semi-empirical equations and statistical correlations employed by RUSLE2 can 

result in less accurate erosion estimations, and they are relevant specifically for 

conditions under which the expressions were derived. Walter and Dubreuilh (2007)

reviewed previous studies on the accuracy of RUSLE2 and its predecessors, USLE 

and RUSLE, and found that soil loss generally is over predicted for rates less than 

23 Mg/ha-yr, and under predicted soil loss for rates greater than 23 Mg/ha-yr.

2.2.1.2 WEPP

WEPP (Foster et al. 1995) has been used mainly by the United States Department 

of Agriculture for evaluating agricultural practices (Fig. 2.). WEPP uses mathematical 

descriptions of the physical processes of runoff, raindrop impact, and rain splash to 
2-11

model detachment, erosion, and deposition on hillslopes rather than the statistical 

correlations of the standard plot as in RUSLE2. Interrill erosion is conceptualized as 

a process of sediment delivery to the rill. The sediment load is a function of the 

interrill erosion and the rill erosion. The sediment continuity equation (Eq. 2.2) is 

used to describe the movement of sediment to a rill (all equations in Section 2.2.1.2 

are from USDA-ARS 1995):

dG 

dx = Df + Di (2.2)

where G is the sediment load (kg/m•s), x is the distance downslope (m), Di is the 

interrill sediment delivery to the rill (kg/m2•s), and Df is the rill erosion rate (kg/m2•s). 

The rill erosion rate is calculated when the hydraulic shear stress of the flow 

exceeds the critical shear stress of the soil. If the sediment transport capacity, Tc, 

has already been exceeded rill erosion does not occur.

Rill erosion is described by:

Df = Dc �1 -

G

Tc

� (2.3)

where Dc is the detachment capacity by rill flow (kg/m2•s) and Tc is the sediment 

transport capacity within the rill (kg/m•s). The detachment capacity is calculated by 

Eq. 2.4 when the hydraulic shear stress of rill flow exceeds the critical shear stress 

of the soil:

Dc = Kr (τf - τc) (2.4)

where Kr is the rill erodibility parameter (s/m), τf is the flow shear stress (Pa), and τc

is the critical shear stress of the soil (Pa). Deposition of particles in a rill is calculated 

by Eq. 2.5 when the sediment load is greater than the sediment transport capacity 

(G > Tc):

Df = 

βVf

q (Tc - G) (2.5)
2-12

Fig. 2.5. Watershed and hillslope erosion processes evaluated by WEPP (adapted 

from USDA-ARS 1995).
2-13

where β is the raindrop-induced turbulence coefficient, Vf is the effective fall velocity 

for the sediment (m/s), and q is the flow discharge per unit width (m2/s) (Foster et al. 

1995).

WEPP can be used to model hillslopes and watersheds with or without existing 

channels and sub-watersheds. Watershed properties such as channel and 

impoundment characteristics as well as the outlet information are input variables

(USDA-ARS 1995).

The water balance portion of WEPP is calculated using kinematic wave equations 

and infiltration is calculated using a modified Green–Ampt infiltration equation

(USDA-ARS 1995). The plant growth component increases and decreases biomass 

above and below ground by calculating potential plant growth based on solar 

radiation, water availability, and temperature. Eq. 2.2 is the erosion component of 

WEPP that estimates the change in sediment load in the flow with the distance down 

slope using the shear stress of the material (Flanagan and Nearing 1995).

Climate, slope, soil, and management are the major input variables in WEPP. WEPP 

includes the stochastic weather generator, CLIGEN, which includes at least 25 years 

of precipitation and temperature data. CLIGEN has been parameterized by historical 

data from 1200 National Climatic Data Center weather stations in the United States.

Each station has been collecting daily, hourly, and 15 minute precipitation and 

temperature data for at least 25 yr. By selecting the nearest weather station, 

precipitation, snowfall, storm duration, peak rainfall, time to peak, storm frequency, 

air temperature, dew point temperature, solar radiation, wind speed, and wind 

direction are all modeled within WEPP using the CLIGEN weather generator

(Flanagan and Nearing 1995). Different climates can by modeled by simply selecting 

weather stations in the desired climates.

Slope inputs consist of steepness, length, width, and shape. Shapes that can be 

modeled include concave, convex, complex, and uniform. Soil characteristics include 

the soil depth, percent sand content, percent clay content, percent rock content, 

percent organic content, cation exchange capacity (CEC), soil albedo, and initial 

water content. Soil types can either be chosen from an extensive database within 

WEPP, or modified by input of soil characteristics (Flanagan and Nearing 1995). The 

user can specify or have the model calculate interill erodibility, rill erodibility, critical 

shear, and effective hydraulic conductivity. Land use practices that describe different 

plants and tillage and management practices can be selected from the management 

section of WEPP (USDA-ARS 1995). 

WEPP also determines the on-site and off-site effects of erosion and the particle 

size distribution for the sediment leaving the site. WEPP outputs can be adjusted by 

the user to obtain runoff and sediment loss on a storm-by-storm, monthly, annual, or 

average annual basis. Time sensitive estimates of runoff, erosion, sediment delivery, 

and sediment enrichment as well as spatial distribution of sediment loss on the 

hillslope are calculated and output in text files and on the interface. Predictions from 
2-14

WEPP have been validated against 12 sites for approximately 1000 plot years of 

natural runoff and erosion data (Flanagan and Meyer 2010).

2.2.2 Landform Evolution Models

Landform evolution models predict the geometry of a watershed over time by routing 

water across a grid network and representing erosion by changing the grid 

elevations to reflect the evolving geomorphic characteristics of the site (Willgoose 

2005a, Coulthard et al. 2007). Some landform evolution models (e.g. ARMOUR, 

CHILD) use a short-term event-based time scale, whereas others calculate longterm average annual erosion (e.g. SIBERIA, CAESAR, GOLEM, and CASCADE) for 

intervals of tens to thousands of years. The following landform evolution models 

were evaluated in this study: SIBERIA, ARMOUR, CAESAR, GOLEM, CASCADE, 

and CHILD. These models were included because they have been used in practice 

and tested and verified. Other landform evolution models were available but were 

not considered because they have not been verified or used in practice.

2.2.2.1 SIBERIA

The SIBERIA (Willgoose et al. 1991c, 1994) landform evolution model is a 

mechanistic model that predicts fluvial and diffusive sediment transport for a 

watershed-sized area (Willgoose et al. 1991a, 1991b, and Willgoose 2005a) and has 

been used for mine site rehabilitation (Evans and Willgoose 2000, Hancock et al. 

2000, Hancock et al. 2003, Hancock and Turley 2006, Hancock et al. 2010).

SIBERIA is unique because (1) it uses digital terrain maps (DTMs) to determine 

watershed size and drainage areas and (2) efficiently adjusts the landform with time 

as erosion occurs (Willgoose 2005a).

SIBERIA models fluvial and diffusive sediment transport, channel network 

development, runoff, and tectonic uplift processes and predicts the evolving 

landform using two partial differential equations: (1) a continuity equation for 

sediment transport and elevation change and (2) a channel indicator equation to 

identify whether a point is a channel or hill slope. SIBERIA uses the finite-difference 

method on a DTM with rectangular grid spacing to move water and sediment in the 

direction of the steepest slope using the continuity equation (Eq. 2.6).

∂z

∂t =c0(x, y)+

1

ρs(1-n)

�

∂qsx

∂x

+

∂qsy

∂y � +Dz �

∂

2

z

∂x2 +

∂

2

z

∂y2� (2.6)

where z is elevation, t is time, c0(x, y) is the rate of tectonic uplift, ρs is the density of 

the solids, n is the porosity of material before erosion and after deposition, q is the 
2-15

discharge per unit width, x and y are horizontal coordinates, Dz is the erosive 

diffusivity (Willgoose et al. 1991a).

Channel growth is a function of hillslope form, discharge from upstream to the 

channel head, and the resistance of the hillslope to channel formation. The channel 

indicator equation (Eq. 2.7) is used to describe the transition point between a 

hillslope and a channel (Willgoose 2005a). 

∂Y

∂t =dt �0.0025

a

at

+ �-0.1Y

Y2

1+9Y2�� (2.7)

where t is time, dt is the rate constant for channel growth, a is the channel initiation 

function, at is the channel initiation threshold, and Y is the indicator variable for 

channelization (Y=0, hillslope mode; Y=1, channel mode) (Willgoose et al. 1991a).

The channel indicator equation is based on the channel initiation threshold which is 

dependent on the resistance of the watershed to channelization.

In SIBERIA, erosion is modeled by combining fluvial and diffusive sediment transport 

processes. The fluvial processes depend on the discharge and slope in the steepest 

downhill direction. Diffusive processes, which include soil creep, rain splash, and 

rockslides, are modeled using a spatially constant Fickian diffusion term. The 

sediment transport constitutive equations are used to calculate the sediment 

transport rate (Hancock et al. 2003). Eq. 2.8 quantifies sediment transport in 

SIBERIA:

qs=qsf+qsd (2.8)

where qs is the sediment transport rate per unit width, qsf is the fluvial sediment 

transport term, and qsd is the diffusive transport term. Eq. 2.9 quantifies rill and 

channel erosion:

qsf=β1qm1Sn1 (2.9)
2-16

where q is the discharge per unit width, S is the slope in the steepest downslope 

direction, β1, m1, and n1 are fluvial sediment transport parameters, and qsf is defined 

above. Eq. 2.10 quantifies soil creep, rain splash, and other diffusive processes:

qsd=DS (2.10)

where D is diffusivity and qsd and S are described above.

Runoff, sediment transport, and channel characteristics can be modeled in SIBERIA 

with multiple options (Willgoose 2005a). SIBERIA only simulates Hortonian runoff

(points on the watershed that are saturated cause runoff). Thus, fluvial erosion and 

sediment transport occurs at saturated points. Sediment transport is either transport 

limited or source limited. Transport-limited flow assumes an unlimited amount of 

sediment can be removed from the surface. Source-limited processes recognize a 

finite sediment amount exists and can only transport that amount of sediment. Two 

types of channel characteristics can be modeled: the fixed channel model fixes the 

channel in place forever once it is created; the stochastic channel model allows 

channels to advance and retreat in response to climate fluctuations.

Tectonic uplift processes are also modeled in SIBERIA. There are three options for 

incorporating tectonic uplift: (1) continuous spatially uniform uplift over a specified 

time, (2) continuous, tilting uplift over a specified time, (3) spatially uniform, cyclic 

uplift with either a sinusoidal uplift, square wave uplift, or pulse uplift over the whole 

simulation time (Willgoose 2005a). Uplift is added to the change in elevation over 

time over each grid space.

Hancock and Willgoose (2001) and Dinwiddie and Walter (2008) have conducted 

validation studies for SIBERIA. Hancock and Willgoose (2001) performed a 

laboratory validation study using a landscape simulator box equipped with a rainfall 

simulator to erode the sediment and stereo digital photogrammetry to analyze the 

results. The photogrammetry was compared with 3D erosion predictions from 

SIBERIA. They found that “...the landscapes produced by SIBERIA are visually 

representative of what would occur for field scale watersheds.”

Dinwiddie and Walter (2008) evaluated the predictions of three SIBERIA simulations 

for physically realistic and expected landscape evolution. Physical characteristics of 

slope angle, surface roughness, and magnitude of the coefficient of fluvial sediment 

transport (β1) were evaluated relative to expected behavior, (1) more erosion should 

occur on steeper slopes than shallower slopes, (2) multidirectional, branching 

channelized erosion should occur on a rough slope, whereas unidirectional erosion 

should occur on a smooth slope, and (3) as the magnitude of the coefficient of fluvial 

sediment transport increases, erosion should also increase. Each expected result 
2-17

was validated by comparing each to the 3D SIBERIA predictions. The erosion 

predictions indicated that SIBERIA adequately predicted erosion to the set

expectations.

2.2.2.2 ARMOUR

The ARMOUR model (Sharmeen 2000) was developed for modeling surface 

armoring of the soil, erosion of the surface, and deposition of the eroded sediment

(Willgoose and Sharmeen 2006). ARMOUR is driven by precipitation events and can 

model single events or multiple events over time allowing for time varying runoff and 

erosion.

The main part of the ARMOUR model, surface armoring, depends on the shear 

stress of flow moving over the surface. A schematic of the armoring process is 

shown in Fig. 2.3. Over time, as overland flow events occur, the surface soil layer 

becomes coarser than the underlying layer, a process called armoring (Willgoose 

and Sharmeen 2006). As flow passes over the surface, selective erosion of fine 

particles occurs, making the remaining fine particles more difficult to remove. Coarse 

particles within the soil help bind the remaining fines and form a desert pavement.

Desert pavements are natural formations consisting of a surface layer comprised of

closely packed gravel and fines that is one to two particles thick (McFadden et al. 

1987).

The ARMOUR model extends this theory to unsteady flow conditions creating a 

surface armor that changes with time and varying runoff conditions (Sharmeen 

2000). At any point in time, the concentration of particles in each size class constant 

over the depth of overland flow, but varies spatially. Simultaneous erosion and 

deposition cannot occur. Sediment flux is determined by the median diameter (d50) 

of the sediment and both cohesive and non-cohesive sediment can be modeled.

Erosion, deposition, time varying runoff, and surface armor development in 

ARMOUR are calculated using shear stress mechanisms and a mass balance 

equation (Willgoose and Sharmeen 2006). The differential equations used in 

ARMOUR include a mass balance equation to determine the change in elevation 

over time and an equation to determine the potential rate of erosion or deposition for 

each size class of the surface material (Sharmeen 2000, Willgoose and Sharmeen 

2006). ARMOUR is one-dimensional and uses the finite-difference method to solve 

the partial differential equations. 

The mass balance equation in ARMOUR is:

∂z

∂t =

∂qs

∂x =�∂qs, k∂x

M

k

 (2.11) 
2-18

where z is the elevation, t is time, qs is the sediment flux, M is the number of different 

size classes in the sediment mixture, k is the size class, and x is the position on the 

hillslope. The erosion or deposition potential is based on the size class and the 

availability of particles of that size class on the surface, and is defined by:

∂Pk

∂x = �

∂Rk

∂t �∂Rj∂t

M

j

� �

∂qs

∂x (2.12)

where Pk is the potential depth of material entrained/deposited in each size class, Rk

is the rate of sediment entrainment or deposition for each size class, j is the node, 

and Rj is the rate of sediment entrainment or deposition at node j. Sediment 

transport is based on a size threshold of sediment entrainment based on the shear 

stress at the bottom of the flow (Willgoose and Sharmeen 2006).

Like SIBERIA, ARMOUR can simulate transport-limited and source-limited sediment 

transport processes. However, ARMOUR can track many different fractions of 

sediment trapped in overland flow, whereas SIBERIA can only track one sediment 

fraction (Willgoose 2005b).

Willgoose and Sharmeen (2006) used predictions from ARMOUR, field runoff and 

erosion data, concentration peaks of runoff events, and depletion of fines on the 

surface, to compare to results from rainfall simulator trials. ARMOUR was able to 

adequately replicate the rainfall simulator experiments after calibration.

2.2.2.3 CAESAR

The CAESAR landform evolution model (Coulthard et al. 1998, 1999, 2000) predicts

fluvial erosion processes using a high-resolution rectangular grid (1 to 50 m).

CAESAR has been applied to land use and climate change (Coulthard et al. 2000), 

sediment waves and alluvial fan evolution (Coulthard et al. 1999), large watersheds 

with large scale grids (400 km2 watershed with 50 m grid spacing) (Coulthard and 

Macklin 2000), and time spans ranging from 10 to 10,000 years.

CAESAR is simplified by limiting overland flow to channels using the Chezy-Manning 

equation. Because interrill erosion is not modeled, Coulthard et al. (2000) 

recommend that CAESAR predictions be used qualitatively rather than 

quantitatively. Overland flow routing is performed cell-to-cell requiring any channel to 

be the width of the cell, making channel sizes unrealistic and either eliminating or 

making small rills very large.
2-19

Spatial variation in surface materials is not available, but multiple particle sizes may 

be routed through the watershed. The overland flow routing equation is:

Q=UA=

1

n

h2⁄3�SA (2.13)

where Q is the discharge, U is the flow velocity, A is the cross sectional area of the 

flow, n is Manning’s coefficient, h is the flow depth, and S is the average 

downstream slope (Coulthard et al. 2002, Van De Wiel et al. 2007).

Sediment transport is determined by:

qi

=

FiU*

3

Wi

*

(s-1)g (2.14)

where qi is the sediment transport rate for the ith sediment fraction, Fi is the fractional 

volume of sediment in the active layer, U* is the shear velocity, Wi* is a function 

relating the fractional transport rate to the total transport rate, s is the ratio of 

sediment to water density, and g is gravimetric acceleration (Van De Wiel et al. 

2007).

Unlike the other landform evolution models, CAESAR allows for divergent flow (e.g. 

alluvial fans, braided rivers). CAESAR also performs a grain-size sorting for 

deposition layers for up to nine grain sizes, along with soil creep and mass 

movement processes. Although some interrill erosion processes are modeled in 

CAESAR, Welsh et al. (2009) suggest that CAESAR should increase the level of 

slope process representation, especially for studies where hillslope processes are 

an essential and important part of the fluvial system. At small time scales, CAESAR 

is ineffective as it fails to incorporate long-term rock weathering, soil generation, and 

tectonic uplift processes (Coulthard 2001). Long run times are a major drawback to 

the high-resolution capabilities of CAESAR (Coulthard 2000).

Welsh et al. (2009) performed a validation study on CAESAR using two subwatersheds in the French Alps from 1826 to 2005. The site has a long history of 

research focused on historical documentation of the geomorphology, land use, and 

environmental changes. The uncertainty of the records was ±10 yr. Comparing

CAESAR modeling and the decadal DTM patterns in two watersheds produced a 

broad similarity in the overall patterns of erosion, deposition, and sediment 
2-20

discharge. Realistic simulations of the behavior of larger flood and sediment events

at the decadal time scale were also found in the study by Welsh et al. (2009).

2.2.2.4 GOLEM

The GOLEM model (Tucker and Slingerland 1994) was developed for regional scale 

landform evolution processes and geologic time frames (100,000 to 10,000,000 

years). GOLEM includes the erosion processes of overland flow, bedrock 

weathering, sediment transport, stream incision, slope failure, diffusive hillslope 

transport, and uplift (Tucker and Slingerland 1994). Two modes of operation are 

available for modeling erosion: watershed mode is used when hillslope-scale 

processes of weathering, soil creep, landslides, and channel initiation are desired;

regional-scale mode operates for large-scale studies where channel evolution, but 

not individual hillslope processes are required. In either mode, GOLEM tracks the 

thickness of a surficial sediment layer and can handle multiple soil and rock types 

with varying resistance to erosion in either layers or regions.

GOLEM routes water over a rectangular grid. Spacing of the DTM is fixed to 1 km2

for regional-scale mode and 50 m2 for watershed mode. Water and sediment flow 

from each grid cell in the direction of the steepest slope to one of the eight 

surrounding cells. Sediment transport by overland flow is transport-limited, supplylimited, or a third case that uses transport and supply-limited sediment transport

(e.g., channel incision and weathering). The continuity of mass equation that 

describes the changing elevation of the landform in GOLEM is:

∆h

∆t

=

Qs

(in)-Qs(out)

∆x2 (2.15)

where Δh is the change in the elevation of a cell, Δt is the change in time, Qs is 

volumetric sediment flux in and out of the cell, and Δx2 is the surface area of the cell.

The GOLEM model is different from SIBERIA and ARMOUR because GOLEM

quantifies sediment production in terms of bedrock erosion. GOLEM also is limited to 

a single output time and a single grain size with sediment transport and deposition

modeling. No validation studies on GOLEM were identified.

2.2.2.5 CASCADE

The CASCADE model (Braun and Sambridge 1997) was created for mountain-range

scale and geological time scales (millions of years) with spatial resolution on the 

order of 1 km. CASCADE runs on fixed 100-yr time steps and uses a “bucket”

algorithm to route water through the system using the finite-element method. The 
2-21

“bucket” algorithm gives each node on the grid a set amount of water (a bucket) to 

convey along to the next lowest neighbor (i.e. the next nod with the lowest 

elevation). Water is transferred until all nodes are connected by the flow paths. This 

simplified fluvial process should only be used for the low-resolution, large-scale, 

long-term simulations because CASCADE lacks the spatial resolution in SIBERIA, 

CAESAR, and CHILD.

CASCADE uses an irregular grid rather than the rectangular grid used in SIBERIA, 

ARMOUR, CAESAR, and GOLEM. Irregular grid spacing eliminates the directional 

bias that creates artificial symmetry invoked by rectangular grids invoke (Braun and 

Sambridge 1997). Irregular grid spacing can also easily incorporate irregular 

watershed boundaries and spatial variability in resolution size, for instance a 

watershed with both flat and steep areas could have wide grid spacing in the flat 

land and dense grid spacing in the steep areas.

No validation studies for CASCADE were identified.

2.2.2.6 CHILD

The CHILD model (Tucker et al. 1997) is based on a short-term and event-based 

time scale (Coulthard 2001). Events are based on rainfall intensity and duration and 

drive the unsaturated flow model selected (four available). Storm events have been

enlarged for larger time scales to incorporate several years of erosion and 

deposition into a single storm event. Enlarging a storm event consists of calibrating 

the event to the amount of erosion and deposition for a set time period. In this 

manner, an event can be many years in a simulation. The sediment transport rules, 

a meandering model, and overbank deposition are driven by the calculation of 

channel width and depth within each node.

The continuity of mass equation that drives sediment transport is:

dVi

dt =� Qji

Ni

j=1

 (2.16)

where i and j are nodes, Vi is the volume or mass stored at node i, t is time, Ni is the 

number of nodes connected to node i, and Qji is the total flux from node j to i (Tucker 

et al. 2001). The equation for changes in surface elevation due to erosion or 

deposition is:
2-22

dzi

dt =

�∑ Qsj

n

j=1 �-Qsi

(1-v)Ai

 (2.17)

where zi is the elevation at node i, t is time, n is the number of nodes flowing directly 

into i, Qs is the sediment flux, v is the sediment porosity, and Ai is the Voronoi area 

of node i (Tucker et al. 1997). The equations for fluvial sediment transport (Eq. 2.16)

and elevation change (Eq. 2.17) are solved using the finite-difference method across 

the irregular grid network.

CHILD can account for vegetative growth and allows user-specified grain sizes and 

can record the age of deposits to develop an alluvial stratigraphy within the model

using the irregular grid network (Tucker et al. 1997). This elaborate fluvial system is 

more suited for shorter time periods because of its higher resolution; however 

CHILD has been used for simulations over millions of years.

The disadvantages of the CHILD model are the complexity of the grid which uses an 

irregular network with a Voronoi diagram and overall complexity of the code (Tucker 

et al. 2001). No validation studies for CHILD were identified.
3-1

3 METHODS

3.1 Reference Site – Grand Junction Uranium Mill Tailings Disposal Site

The Grand Junction Uranium Mill Tailings Disposal Site in Grand Junction, Colorado 

was used as a reference site for this study (DOE Office of Legacy Management 

2009). The topographic map of the reference site is shown below in Fig. 3.1. The

surface area of the disposal cell is approximately 390,000 m2, the side slopes are

20% and range from 15 to 60 m long, and the top slope is 2% and ranges from 450 

m to 770 m long. The depth of the tailings is approximately 22 m and the disposal 

cell is approximately 12 m above the original ground surface. The barrier slopes to 

the south and west. The existing topography was used as a base scenario. The 

footprint of the site and the total elevation change were held constant in all 

simulations. Modifications to the topography during modeling included changes to 

the slope and slope length.

3.1.1 Engineered Barriers

Two types of barriers were evaluated, a resistive barrier and a water balance barrier.

The barrier profiles are shown in Fig. 3.2. The resistive barrier includes a compacted 

fine-textured soil barrier to control water and gas flow and is based on the barrier

system employed in Grand Junction, CO (Benson et al. 2010). The water balance 

barrier stores water during wetter periods and then releases stored water through 

evaporation and transpiration (Benson et al. 2008), and is based on the final cover 

employed in Monticello, UT.

3.1.2 Materials

The surface layers were assumed to be topsoil, rip-rap, and topsoil blended with 

gravel (40% by weight), referred to herein as a gravel admixture.

The resistive barrier consisted of a surface layer, a bedding layer (only if rip-rap was 

used as the top layer), a frost protection layer, a radon barrier, and a transition layer.

The bedding layer and transition layer were classified as poorly graded gravel. The 

frost protection layer and radon barrier were classified as clayey sand. A summary of 

the particle size characteristics assumed for the barrier materials is shown in Table 

3.1. Material properties of surface layers, resistive barrier layers, water balance barrier 

layers, and waste (Benson et al. 2008 and 2010), Particle size fractions by Unified Soil 

Classification System. Organic matter by loss on ignition..

The water balance barrier consists of the top layer, a bedding layer (only if rip-rap is 

used), a water storage and frost protection layer, a biointrusion layer, and a sand 

layer (capillary break). The water storage and frost protection layers were assumed 

to be sandy silt, the animal intrusion layer was assumed to be poorly graded gravel 

with silt and sand, and the sand layer was assumed to be poorly graded sand.
3-2

Fig. 3.1. Topography of Grand Junction Uranium Mill Tailings Disposal Site in Grand 

Junction, CO, the reference site for this study.

631 m

631 m

807 m

452 m

Max Elevation = 1606 m

Min Elevation = 1584 m

1606 m

1584 m
3-3

305 mm

150 mm

610 mm

610 mm

915 mm

Remaining

Surface layer

Bedding layer 

(Rip-rap only)

Frost protection layer

Radon barrier

Transition layer

Tailings

305 mm

150 mm

900 mm

300 mm

300 mm

300 mm

Remaining

Surface layer

Bedding layer 

(Rip-rap only)

Water Storage and

Frost Protection Layer

Animal Intrusion Layer

Water Storage and

Frost Protection Layer

Sand and Capillary Break

Tailings

(a) (b)

Fig. 3.2. Resistive barrier profile (a) and water balance barrier profile (b).
3-4

Particle size distributions assumed for the water balance barrier materials are 

summarized in Table 3.1.

The tailings were assumed to behave similar to silt and were assigned properties of 

Boardman silt (Boardman, OR) from the University of Wisconsin-Madison soil bank

(Gurdal et al. 2003, Benson and Gurdal 2013).

Saturated and unsaturated hydraulic properties of the soils are summarized in Table 

3.. Hydraulic conductivity and soil water characteristic curves (SWCC) of each soil

were obtained from Benson et al. (2008, 2010). Methods described in Benson et al. 

(2007, 2011) were used to account for pedogenesis.

Van Genuchten’s equation (1980) was used to describe the SWCC:

θ=θr+(θs-θr) � 1

[1+(αψ)n]m� (3.1) 

where θ is the volumetric water content at suction (ψ), θr is the residual volumetric 

water content, θs is the saturated volumetric water content, α and n are the van 

Genuchten parameters, and m = 1-1/n. 

3.2 Modeling Erosion with SIBERIA 

SIBERIA has high spatial resolution, the ability to model layers of different materials, 

and has been validation with field and laboratory experiments. Because of these 

characteristics, SIBERIA was used for predicting erosion.

The fluvial sediment transport equation is:

qs=β1qm1Sn1 (3.2)

where qs is the sediment flux per unit width (m3/year/width), q is the discharge per 

unit width (m3/year/width), S is the slope in the steepest downhill direction (m/m), β1

is the rate constant for sediment transport (dimensionless), and m1 and n1 are 

parameters of the model (dimensionless) (Willgoose et al. 1991a).
3-5

Table 3.1. Material properties of surface layers, resistive barrier layers, water balance barrier layers, and wa

(Benson et al. 2008 and 2010), Particle size fractions by Unified Soil Classification System. Orga

by loss on ignition.

Cover 

Section

Material 

Description

Particle Size 

Characteristics

Thickness Dry

Density Particle Size Fractions (%) 

(mm) (kg/m3) Sand Silt Clay Gravel

Surface 

Layers

Rip-rap

Poorly graded 

gravel with silt and 

sand

305 2700 20 10 0 70 

Gravel Admixture Silty gravel with 

sand 305 2510 24 24 12 40 

Topsoil Silty sand 305 1553 40 40 20 0 

Resistive 

Cover 

Layers

Bedding Layer 

(Rip-rap surface 

only)

Poorly graded 

gravel 150 2338 3.3 0.1 3.3 93.3 

Frost Protection 

Layer Clayey sand 610 2028 47.8 12.4 39.8 0 

Radon Barrier Clayey sand 610 1865 45 11.6 43.4 0 

Transition Layer Poorly graded 

gravel 915 1234 3.3 0.1 3.3 93.3 

Water 

Balance 

Cover 

Layers

Waste

Bedding Layer 

(Rip-rap surface 

only)

Poorly graded 

gravel 150 2338 3.3 0.1 3.3 93.3 

Water Storage 

and Frost 

Protection Layer

Sandy elastic silt 900 1443 22.3 49 25.8 2.9 

Animal Intrusion 

Layer

Poorly graded 

gravel with silt and 

sand

300 2510 20 10 0 70 

Water Storage 

and Frost 

Protection Layer

Sandy elastic silt 300 1443 22.3 49 25.8 2.9 

Sand Layer and 

Capillary Break

Poorly graded 

sand 300 1551 85 5 0 10 

Tailings Silt Remaining 1404 10 85 5 0 

3-5
3-6

Table 3.2. Hydraulic properties used in the hydraulic modeling portion of this study.

Cover Section Material 

Description

Saturated 

hydraulic 

conductivity, 

Ks (m/d)

SWCC van Genuchten Parameters

θr θs α (kPa-1) n

Surface Layers

Rip-rap 10800 0.04 0.40 0.60 1.40

Gravel Admixture 0.86 0.04 0.40 0.03 1.26

Topsoil 0.86 0.04 0.40 0.02 1.27

Resistive Cover 

Layers

Bedding Layer 130 0.05 0.25 0.44 1.36

Frost Protection 

Layer 0.055 0.00 0.38 0.04 1.30

Radon Barrier 0.055 0.00 0.38 0.04 1.30

Transition Layer 108 0.06 0.25 0.57 1.36

Water Balance 

Cover Layers

Bedding Layer 130 0.05 0.25 0.44 1.36

Water Storage and 

Frost Protection 

Layer

0.13 0.00 0.41 0.03 1.27

Animal Intrusion 

Layer 0.13 0.00 0.41 0.03 1.27

Sand Layer and 

Capillary Break 130 0.05 0.25 0.44 1.36

Waste Tailings 0.043 0.00 0.99 0.02 1.30

3-6
3-7

The fluvial sediment transport equation can be parameterized using field data or a 

validated computational erosion model. Field calibration consists of fitting the 

parameters β1, m1, and n1 to site-specific and soil-specific sediment transport and 

hydrology data from natural rainfall events or a rainfall simulator. This method is data 

intensive and is described in detail by Willgoose and Riley (1998) and Hancock et al. 

(2000). SIBERIA can also be calibrated using another erosion model to determine a 

target erosion rate for the site. A previously validated model such as RUSLE2, 

CREAMS, or WEPP can be used for this method (Willgoose, personal 

communication, 2010).

3.2.1 Parameterization

SIBERIA has been successfully parameterized and run for many sites in Australia 

and Argentina. Table 3.3 summarizes parameterization methods, the fluvial erosion 

parameters, and erosion depths from several from several sites simulated with 

SIBERIA, and input and control parameters used in SIBERIA.

The fluvial sediment transport parameters in SIBERIA (Eq. 2.9) were obtained by 

matching erosion rates predicted by SIBERIA to average erosion rates predicted by 

WEPP. WEPP was used in this study to calibrate SIBERIA because it is mechanistic 

and input parameters for WEPP are readily available. Multiple slope lengths with the 

slope width equal to the grid spacing (10 m) used in SIBERIA were simulated with 

WEPP to determine the average annual soil loss and average annual runoff for the 

site. Slope lengths were varied in the WEPP simulations to represent the different 

slope lengths of the top (450 m to 770 m) and side slopes (15 m to 60 m). 

When multiple layers are modeled in SIBERIA, each layer is assigned a unique β1, 

whereas the same m1 and n1 are used to represent the entire barrier. SIBERIA 

parameters m1 and n1 were calibrated to the surface layer. The fluvial sediment 

transport parameters are summarized in Table 3.4 (resistive barrier) and Table 3.5 

(water balance barrier).

The following steps were followed to obtain the fluvial erosion parameters m1 and n1: 

(1) WEPP was run for an individual soil layer, (2) the predicted average annual 

runoff rate and sediment loss were recorded for 2% and 20% slopes with varying 

slope lengths found on the reference site (15 to 770 m), (3) the erosion rate was 

computed from eroded depth over the slope, the bulk density of the soil, and the 

area, and (4) the m1 and n1 parameters were obtained by fitting the log10 transform 

of Eq. 3.2 to WEPP predictions of q and qs using linear regression:

log qs = log β1 ∙ m1 log q ∙ n1 log S (3.3)
3-8

Table 3.3. Summary of parameterization and SIBERIA simulations in the literature.

β1 m1 n1

Waste rock dump 

and pit, Nabarlek 

uranium mine, 

Northern Territory, 

Australia

Armour of coarse 

material with negligible 

vegetation cover. 

24463 2.52 0.69 12 m 36 km2 1000

0.281 

m m

eros

Airstrip, Nabarlek 

uranium mine, 

Northern Territory, 

Australia

All-weather bitumen 

surface surrounded by 

bare, compacted soil, 

no vegetative cover.

22899 2.24 0.69 12 m 36 km2 1000

0.145 

m m

eros

Tin Camp Creek 

Catchment 1 (C1), 

western Arnhem 

Land, Northern 

Territory, Australia

1067 1.7 0.69 10 m 2032 m2 10,000

0.16 m

m m

eros

Tin Camp Creek 

Catchment 2 (C2), 

western Arnhem 

Land, Northern 

Territory, Australia

384 1.69 0.69 10 m 2947 m2 10,000

0.064 

m m

eros

Section 6, Tom 

Price mine, NW 

Western Australia

0.0007 2.53 2.67 1 km2 20 to

Section 10 East, 

Parraburdoo, NW 

Western Australia

0.075 1.11 1.5 0.94 km2 20 to

Site Site Characteristics Soil Charactersitics Calibration/Parameter 

selection

Parameter Values Watershed 

Size

Years 

Simulated Ero

Short, high intensity 

storms. Wet-dry 

tropical environment. 

Annual rainfall of 

1400 mm. 

Used the ERA Ranger 

Mine and the Jabiluka 

project sediment loss 

and runoff data from 

rainfall simulator 

experiments.

Grid 

Spacing

Representation of the 

pre-mined Ranger 

Mine site. Short, 

high intensity storms. 

Average annual 

rainfall is 1400 mm. 

Slopes are generally 

15 to 50%. 

Vegetation is annual 

grasses in the wet 

Red, loamy material 

and shallow gravely lam 

with some micaceous 

silty yellow earths. 

Minor solodic soils on 

alluvial flats. Gravelly 

cobble quartz lag on 

slope surfaces and hill 

crests.

Sediment loss, rainfall, 

and runoff field data for 

discrete rainfall events 

were used to calibrate 

the erosion and 

hydrology models.

No vegetation. 

Average annual 

rainfall of 281 mm. 

Rocky spoil mainly 

comprised of hematite. 

Different particle size 

distributions due to 

mechanical processes 

of blasting, handling, 

Sediment concentration 

data from rainfall 

simulator experiments 

was used to calibrate 

the sediment discharge 

equation.

10 m 100 

3-8
3-9

Table 3.3. Summary of parameterization and SIBERIA simulations in the literature (continued).

β1 m1 n1

High rainfall (400 

mm/year). Arid climate, 

Evaporation rate = 1385 

mm/year. Intense storms.

0.00225 1.5 2.1 

Low Rainfall/Low Incision 

(160 mm/year) 0.00075 1.5 2.1 

Low Rainfall/High Incision 

(160 mm/year) 0.00075 2.0 2.1 

Waste rock dump cover, 

unvegetated, unripped. 

High intensity storms (973-

1480 mm/year). Average 

slope of 2.8%.

Fine material overlying 

a hard pan-like surface 

which developed cracks 

during the prolonged 

dry season. 

0.00027 1.59 0.69 30 m 1.6 km2 1000 

Waste rock dump cover, 

vegetated, ripped. High 

intensity storms (973-1480 

mm/year). Vegetated with 

low shrubs and grasses. 

Average slope of 1.2%. 

Top-soiled, surface 

ripped and revegetated 

area. 

0.000005 1.59 0.69 30 m 1.6 km2 1000 

Scinto 6 mine, 

ERA Ranger Mine, 

Northern Territory, 

Australia

High intensity storms (973-

1480 mm/year). 52-58% 

batter slope. Vegetation 

had little effect on 

hydrology.

Dumped, precambrian 

volcanic waste rock.

Rainfall, runoff, and 

sediment data were 

measured from 9 actual 

rainfall event on site. This 

data was used to 

parameterize the DISTFW 

rainfall-runoff model which 

was used to derive longterm average parameters 

for SIBERIA.

0.003 1.68 0.69 0.5 m 1600 m2 50

ERA Ranger Mine, 

Northern Territory, 

Australia

Data from natural storm 

events was used in the 

DISTFW rainfall-runoff 

model to determine long 

term average parameters 

for SIBERIA.

Watershed 

Size

Years 

Simulated 

Xstrata Alumbrera 

copper mine, 

Argentina

Benign waste rock 

dumped to create a 

rough humpy surface. 

Humps range in height 

from 2 to 3m.

Data from Sheridan et. al. 

using the particle size 

distributions of the soil 

and spoil materials were 

used in calibration to 

provide are range of values 

for β1, m1, and n1.

2 m 0.25 km2 1000

Site Site Characteristics Soil Charactersitics Calibration/Parameter 

selection

Parameter Values Grid 

Spacing

3-9
3-10

Table 3.4. Fluvial sediment transport parameters for resistive barriers used in the SIBERIA simulations

Surface Layer Material β1 m1 n1 β1 m1 n

Vegetated Rip-rap 0.00200 0.00014

Bedding Layer 2.10000 0.0299

Frost Protection Layer 1.84000 0.0223

Radon Barrier 7.30000 0.0620

Transition Layer 2.10000 0.0299

Tailings 1.05000 0.0175

Vegetated Gravel Admixture 0.0050 0.00008

Frost Protection Layer 4.29000 0.00984

Radon Barrier 17.5000 0.02400

Transition Layer 4.90000 0.01345

Tailings 2.42000 0.00763

Vegetated Topsoil 6.000E-11 5.70E-05

Frost Protection Layer 2.170E-09 0.00403

Radon Barrier 2.980E-09 0.00828

Transition Layer 2.390E-09 0.0055

Tailings 1.220E-09 0.00313

Resistive Covers Semi Arid - Big Mountain Humid - Bluestem Pra

Rip-rap

1.201 4.166 1.114 0.6

Topsoil

4.651 3.925 1.416 1.0

Gravel Admixture

1.205 4.586 1.265 0.7

3-10
3-11

Table 3.5. Fluvial sediment transport parameters for water balance barriers used in SIBERIA simulatio

Surface Layer Material β1 m1 n1 β1 m1 

Vegetated Rip-rap 0.002 0.00014

Bedding Layer 2.1 0.0299

Water Storage/Frost Protection 1.59 0.0176

Animal Intrusion 0.91 0.0178

Water Storage/Frost Protection 1.59 0.0176

Sand and Capillary Break 0.14 0.00385

Tailings 1.05 0.0175

Vegetated Gravel Admixture 0.005 0.00008

Water Storage/Frost Protection 3.7 0.00771

Animal Intrusion 2.1 0.00778

Water Storage/Frost Protection 3.7 0.00771

Sand and Capillary Break 0.32 0.0019

Tailings 2.42 0.00763

Vegetated Topsoil 6.000E-10 5.70E-05

Water Storage/Frost Protection 1.88E-09 0.00316

Animal Intrusion 1.05E-09 0.00319

Water Storage/Frost Protection 1.88E-09 0.00316

Sand and Capillary Break 1.57E-10 0.00089

Tailings 1.220E-09 0.00313

Gravel Admixture

1.205 4.586 1.265 

Topsoil

4.651 3.925 1.416 

Water Balance Covers Semi Arid - Big Mountain Humid - Bluestem 

Rip-rap

1.201 4.166 1.114 

3-11
3-12

Multiple linear regressions were conducted using SYSTAT12 (Systat Software, Inc., 

Chicago, IL) to obtain unique m1 and n1 parameters for each soil type and climate.

To calibrate the β1 parameter, WEPP and SIBERIA need to produce the same 

average erosion rate for a simple slope. The average slope from the reference site 

was used with the width equal to the grid spacing of the DTM (11% slope, 10 m 

wide). WEPP was run using 60 yr simulations, the minimum required to quantify 

erosional response to ± 10% (Nearing 2004). The average erosion rate was 

compiled as the product of the average sediment loss and time divided by the bulk 

density. SIBERIA was then run with the same simple slope. The β1 fluvial erosion 

parameter was systematically modified so that the SIBERIA average erosion rate 

was equal to the WEPP average erosion rate. This process was used to obtain the 

fluvial sediment transport parameters for the 12 soil types for both semi-arid and 

humid climates.

Soil types were defined in WEPP using percent sand, percent clay, percent rock, 

organic content, and depth of each layer to represent all soils used in the barrier

scenarios. The soil properties used in WEPP are in Table 3.1. Cation exchange

capacity (CEC) can also be input to WEPP, but was not available for the various soil 

types in this study. Thus, CEC was held constant at 8.0 meq/100 g to represent soil 

with a high sand content and low water holding capacity (Holtz and Kovacs 1981).

A sensitivity analysis on the soil albedo and initial water content showed that neither 

had a significant effect on predicted discharge or sediment flux, so both were held 

constant for each soil type (Appendix A). Albedo was set at the mean albedo of the 

earth, 0.36. Initial water content was set at 17%, the average water content of each 

soil layer, measured previously by Benson et al. (2008, 2010). The sites include the 

reference site and another disposal facility in Monticello, UT that employs the water 

balance barrier used in this study. The interrill erodibility, rill erodibility, critical shear, 

and effective hydraulic conductivity WEPP input parameters were estimated by 

WEPP based on the particle size distribution for use in the calculations for discharge 

and sediment flux.

Weather data for two sites were generated by the CLIGEN weather generator in 

WEPP (Flanagan and Nearing 1995) for use in the WEPP simulations. These sites 

were calibrated using meteorological data from the Grand Junction WB AP CO

(Grand Junction, CO) and the Pittsburgh WB AP 2 PA (Pittsburgh, PA) stations in 

the National Climatic Data Center. The sites were chosen because of nearby 

existing disposal sites for uranium mill tailings and their representation of semi-arid 

(Grand Junction, CO) and humid (Pittsburgh, PA) climates.
3-13

3.2.2 DTM Formulation using SIBERIA

A digital terrain model (DTM) was created for SIBERIA by (1) saving an AutoCAD

drawing (.dwg) that includes site topographic information as a .dxf file, (2) using the 

EAMS MOSCOW interface to select the .dxf file to turn into a DTM, (3) enter the 

coordinates to be gridded, and (4) enter the desired spacing between nodes. This 

process outputs a DTM in the form of a grid.raw file for using site topography in 

SIBERIA.

3.2.3 SIBERIA Inputs and Control Parameters

The SIBERIA inputs include the topography in the form of a DTM, soil types with 

their unique β1 parameters and layer depths, the m1 and n1 parameters of the 

surface layer, the bulk density of the surface layer, and the USLE barrier factor. The 

barrier factor from USLE was used to account for varying particle sizes on the 

surface (i.e. rip-rap, gravel admixture, and topsoil). The barrier factor was calculated 

by:

C=exp(-bfg) (3.4)

where C is the barrier factor (USLE), b is the coefficient that describes the relative 

effectiveness of the ground barrier, and fg is the percent ground barrier (Toy et al. 

1998, USDA-ARS 2008). Vegetation was accounted for when calibrating the fluvial 

sediment transport parameters β1, m1, and n1, using WEPP.

SIBERIA also requires control parameters to define the duration of the simulation, 

time period between outputs, erosion file output, time step, and mode for running the 

erosion, runoff, and sediment transport models. The duration of the simulation was 

set to 1000 yr to be consistent with the design life for disposal facilities for low-level 

radioactive waste (US EPA 1983). Output was selected for 1, 5, 10, 30, 60, 100, 

500, and 1000 yr to obtain estimates of when and where erosion occurs. The modes 

used for erosion, runoff, and sediment transport are in Table 3. and account for the 

layered system defined in the layer.model file. Steps for running SIBERIA are 

outlined in Appendix H, the layer.model file is described in Appendix I, and the 

sample siberia.setup file is in Appendix J.

3.3 SVFLUX

Hydraulic modeling was conducted with the variably saturated flow model SVFLUX, 

which Bohnhoff et al. (2009) provides reliable hydrological predictions for covers 

when parameterized realistically. The resistive and water balance barriers described 

in Section 3.1.1 were used as the base profiles. The surface layer was changed for 

each simulation to evaluate how the differences between surface layer materials 

affect hydrology. SVFLUX simulations were run for both semi-arid (Grand Junction, 

CO) and humid (Pittsburgh, PA) climates. SVFLUX input includes climate, 

vegetation, and soil data.
3-14

Table 3.6. SIBERIA input and control parameters for erosion, runoff and sediment 

transport.

Parameter 

Type SIBERIA Description Parameter Description Value

Duration of simulation 

(years)

Years of simulation from beginning 

to end 1000

Time step (years) The resolution used within SIBERIA 0.01

Period between output of 

diagnostic statistics (years)

Time peroid between output of 

summary statistics to the DOS 

window

100

Times of erosion output Time in years of when erosion files 

are output

1, 5, 10, 30, 

60, 100, 500, 

and 1000

Mode for Sediment 

Transport Model

The default fluvial erosion model 

where parameters β1, m1, and n1 are 

spatially constant and the 

layer.model file is used

4

Input File: Sediment 

Transport Model

The input file for the layer β1 and 

depth specifications

File: 

layer.model

Bulk density of the soil Bulk density of the surface layer 

(tonnes/m3

)

Varies by 

material

Cover factor USLE's Cover factor used to 

differentiate between particle sizes

Varies by 

material

Hydrology 

Parameters Mode for Runoff Model Spatially constant fluvial erosion 0

Advanced 

Parameters 

#2

Mode for Sediment 

Transport Solver

Solution method of the physical 

transport equation where the 

layer.model file is used

8

Varies by 

material

Run 

Parameters

Erosion 

Parameters

Coefficient of the fluvial 

transport relationship β1 for the soil layer Varies by material

Exponent on discharge in 

the fluvial transport 

relationship

m1 for the surface layer Varies by 

material

Exponent on slope in the 

fluvial transport relationship n1 for the surface layer
3-15

SVFLUX solves Richards’ equation, the governing partial differential equation for 

unsaturated flow:

∂θ

∂t = -∂∂z �KΨz

∂Ψ

∂z � +

∂KcΨ

∂z

+

∂

∂z �-Kv

∂Ψ

∂z � (3.5)

where θ is volumetric water content, t is time, KΨz is hydraulic conductivity, Ψ is 

matric suction, z is the vertical component, Kv is the diffusive conductivity, and KcΨ is 

the total water conductivity (hydraulic conductivity + diffusive conductivity).

SVFLUX simulations were conducted using a typical precipitation year and the 

maximum precipitation year for each climate. The typical precipitation year was 

defined as the year having annual precipitation as close as possible to the average 

annual precipitation (1969 in Grand Junction, 231 mm; 2010 in Pittsburgh, 961 mm).

The maximum precipitation year was defined as the year with the maximum annual 

precipitation (1965 in Grand Junction, 382 mm; 2004 in Pittsburgh, 1458 mm). Daily 

data were obtained for precipitation, temperature, and wind speed from the High 

Plains Regional Climate Center and the Northeast Regional Climate Center (HPRCC 

and NRCC 2011).

Precipitation was assumed to begin at 12 hr and end at 19.2 hr on days with rainfall 

events. Daily average solar radiation, wind speed, relative humidity, and temperature 

were used in conjunction with the Penman method (Penman 1948) to define

potential evaporation. Actual evaporation was defined by the Wilson-Penman 

equation (Wilson et al. 1994).

Mountain Big Sagebrush was assumed to be the prominent vegetation in the semiarid climate and Bluestem Prairie Grass was assumed to be the prominent 

vegetation in the humid climate. The vegetation parameters input into SVFLUX are 

in Table 3.. The leaf area index (LAI), plant limiting factor, and potential root uptake 

were specified for both vegetation types (Table 3.) (Kirkham 2005, Klett et al. 2010, 

White 2010, USDA-Bureau of Reclamation 2011). In SVFLUX, the LAI was

generated using the dates for the start of germination and the date when plants 

cease to transpire. The LAI was set to excellent growth giving a maximum LAI of 3 

during the peak of the growing season. The plant limiting factor was generated using 

the moisture wilting point and the moisture limiting point for the plant based on the 

climate (Benson 2011). The potential root uptake (depth where roots can extract

water) was specified as 2 m.

The saturated hydraulic conductivity, residual and saturated volumetric water 

content, and van Genuchten’s α, n, and m parameters input to SVFLUX are in Table 

3..
3-16

Table 3.7. Vegetation parameter input to SVFLUX.

SVFLUX

Vegetation 

Parameter

Units Mountain Big 

Sagebrush

Bluestem 

Prairie Source

Growing season 

start date day 120 114 Allen (2010), 

Klett et al. 

(2010), Grand 

Valley Project 

(2011)

Growing season

end date day 310 280

Wilting point kPa -4000 -1500

Benson (2011), 

Kirkham (2005) Limiting point kPa -1000 -800

Max. root depth m 2 2

Max Leaf Area Index 

(LAI) -- 3 3 Foster et al. (1995)
3-17

A one-dimensional simulation was conducted for each case using the profile shown 

in Fig. 3.2. To minimize the impact of the unit gradient boundary at the lower 

boundary, the tailings layer was assumed to be 5 m thick. Sensitivity analysis 

indicated that a thicker tailings layer had no impact on the solution. The upper

boundary was assigned as a climatic flux boundary. The typical year climate data

were applied each year for the first 3 to 5 yr until a steady condition was reached 

(i.e. initial conditions no longer affected predictions). The maximum precipitation 

year was then applied for one year.
3-18
4-1

4 RESULTS AND DISCUSSION

4.1 Effect of Type of Surface Layer on Erosion

Vegetated rip-rap, topsoil, and gravel admixture surfaces were simulated to 

determine how type of surface layer affects erosion. Each surface was simulated in

semi-arid and humid climates using resistive and water balance barriers.

Topography representative of the Grand Junction, CO site was used for all 

simulations as a base topography so that surface layer effects could be compared 

while keeping site topography constant.

Predictions of maximum erosion and average elevation for a resistive barrier with 

rip-rap, topsoil, and gravel admixture surface layers are shown in Fig. 4.1.

Predictions for semi-arid and humid climates are shown in Fig. 4.1 (a) and (b), 

respectively. The following nomenclature is defined as follows:

• Maximum erosion corresponds to the maximum depth of erosion for any node 

over the DTM. Maximum erosion can occur at one node or at multiple nodes.

Maximum erosion indicates the greatest depth of erosion predicted for the site.

• Average elevation is the average elevation for each node on the DTM. Average 

elevation is a good indication of the average amount of erosion that is occurring 

over the site.

These definitions of maximum erosion and average elevation are used throughout 

this report. Predictions are shown for up to 1000 yr, which is the minimum design life 

for LLRW disposal facilities.

The relative magnitudes of maximum erosion between the surface layer types in Fig. 

4.1 indicate that a rip-rap surface layer produces less maximum erosion over a 

1000-yr period than the topsoil and gravel admixture surface layers in either climate.

In both semi-arid and humid climates, all surfaces had a similar average elevation.

However, maximum erosion evolved more rapidly with the topsoil surface, less 

rapidly for the gravel admixture surface, and slowest for the rip-rap surface.

Once the erosion level is below the surface layer (the only layer varied between 

simulations) erosion should occur at the same rate. However, Fig. 4.1 shows that 

erosion occurs at different rates for the same layers beneath the surface. This 

difference is due to the calibrated fluvial erosion parameters, m1 and n1. Although a 

unique β1 parameter is used for each layer, the same m1 and n1 must be applied to 

each layer. This is a limitation of the SIBERIA model when evaluating layered soil 

systems. Thus the layers below the surface are eroded by the same processes as 

the surface layer regardless of their own soil properties.
4-2

Time (yr)

0 200 400 600 800 1000 1200

Elevation Change (m) -2

-4

-6

-8

0

 

Average Elevation

Maximum Erosion

Time (yr)

0 200 400 600 800 1000 

Elevation Change (m) -2

-4

-6

-8

0

 

Average Elevation

Maximum Erosion

(a) Semi-arid (b) Humid

Fig. 4.1. Maximum erosion and average elevation predicted by SIBERIA for the reference site with a re

comparing rip-rap, topsoil, and gravel admixture surface layers: (a) semi-arid climate and (b) 

Topsoil 

Rip-rap

Gravel Admixture

Zero Change

Surface Layer

Bedding Layer

Frost Protection Layer

Radon Barrier

Transition Layer

Tailings

4-2
4-3

A 3D depiction of surface elevation at 1000 yr of erosion is shown in Fig. 4.2 for (a)

rip-rap, (b) gravel admixture, and (c) topsoil surface layers. The gravel admixture 

surface and the rip-rap surface show no gullies and little visible erosion. Erosion of 

the topsoil surface shows gully formation as the primary source of erosion. The scale 

is exaggerated to 20V:1H to magnify the elevation change, which causes the base of 

the slope to have vertical yellow or black streaks. These streaks are an artifact of the 

graphics software used to prepare the images and should be ignored.

A plan view of the (a) rip-rap, (b) gravel admixture, and (c) topsoil surfaces is shown 

in Fig. 4.3 in terms of the number of layers remaining intact on the barrier. There are 

eight layers shown, with five layers for the barrier, one for the tailings, and two 

deposition layers. One layer remaining intact (red on the scale) means that the 

tailings layer has been partially eroded. Six layers remaining intact (green on the 

scale) indicates that none of the layers in the barrier has been fully penetrated. Eight 

layers intact (blue on the scale) indicates deposits of eroded material above the 

original surface of the cover.

The processes that drive erosion are determined by the calibrated fluvial erosion 

parameters, m1 and n1 (Kirkby 1971 and Hancock 2004). Table 4.1 shows the m1

and n1 input to the model and the erosion processes predicted for each climate and 

surface layer type. The erosion predictions from Fig. 4.2 and Fig. 4.3 follow the 

erosion process outlined from Kirkby (1971), with rip-rap and gravel admixture 

surfaces having soil wash erosion and deep gully formation in the topsoil surface.

For the rip-rap and gravel admixture surface layers, erosion occurs only in the side 

slopes and over the entire side slope as soil wash (not in defined gullies). The plan 

view of the gravel admixture surface, Fig. 4.3 (b), shows a similar erosion pattern as 

the rip-rap surface, but erosion occurs over a slightly larger in area. The plan view of 

the topsoil surface, Fig. 4.3 (c), shows that gully erosion occurs rather than soil 

wash. The maximum erosion depth for the topsoil surface is the same as the 

maximum erosion depth for the gravel admixture surface.

The surface layers with larger particle sizes have the least maximum erosion. As 

particles sizes get smaller with the gravel admixture (40% gravel and 60% topsoil) 

and topsoil surfaces, the erosion depth increases, with the greatest depth in the 

cover with a topsoil surface.

4.1.1 Influence of Climate and Vegetation on Erosion

Predictions of surface elevation for the rip-rap and gravel admixture surface layers in 

a humid climate are shown in Fig. 4.4. In contrast to the soil wash erosion in the 

semi-arid climate (Fig. 4.3, Fig. 4.4), rip-rap and gravel admixture surfaces erode in 

gullies. Erosion occurs in similar locations, on the side slopes and across the 

nickpoint into the top slope, but the erosion depth is greater in the gravel admixture 

surface (Fig. 4.1).
4-4

Semi-Arid Climate

Red = Lowest elevation Blue = Highest elevation

(a) Rip-rap (b) Gravel admixture (c) Topsoil

Fig. 4.2. Elevation predicted for reference site with SIBERIA for a resistive barrier in a semi-arid climat

surface layer, (b) gravel admixture surface layer, and (c) topsoil surface layer. Elevation is sh

denoted by the color bar above.

4-4
4-5

Table 4.1. Erosion process for fluvial erosion parameters m1 and n1 based on 

climate and surface layer type.

Climate Surface Layer m1 n1

Erosion Process 

(Kirkby 1971)

Semi-Arid 

Climate

Rip-rap 1.201 4.166 Soil wash with gullying

Gravel 

Admixture 1.205 4.586 Soil wash with gullying

Topsoil 4.651 3.925 Gullying

Humid Climate

Rip-rap 1.114 0.698 Soil wash on an 

armored surface

Gravel 

Admixture 1.265 0.789 Soil wash on an armored surface

Topsoil 1.416 1.045 Soil wash
4-6

Semi-Arid Climate

Red = High erosion Blue = Deposition

(a) Rip-rap (b) Gravel admixture (c) Topsoil

Fig. 4.3. Plan view of reference site with a resistive barrier in a semi-arid climate showing number of la

intact across surface as predicted by SIBERIA: (a) rip-rap surface layer, (b) gravel admixture 

and (c) topsoil surface layer. The color scale is layers of the barrier remaining intact ranging 

(tailings, red shading) to eight (deposition, blue shading). Green shading is all five layers of t

the tailings layer remaining intact (six).

4-6
4-7

Humid Climate

Red = Lowest elevation Blue = Highest elevation

(a) Rip-rap (b) Gravel admixture (c) Topsoil

Fig. 4.4. Elevation predicted for reference site predicted with SIBERIA for a resistive barrier in a humid 

rap surface layer, (b) gravel admixture surface layer, and (c) topsoil surface layer. Elevation i

and denoted by the color scale above.

4-7
4-8

Humid Climate

Red = High erosion Blue = Deposition

(a) Rip-rap (b) Gravel admixture (c) Topsoil

Fig. 4.5. Plan view of reference site predicted with SIBERIA for a resistive barrier in a humid climate: (a

surface layer, (b) gravel admixture surface layer, and (c) topsoil surface layer. The color scale 

barrier remaining intact ranging from one (tailings, red shading) to eight (deposition, blue sha

shading is all five layers of the cover plus the tailings layer remaining intact (six).

4-8
4-9

The plan view (Fig. 4.5) shows that erosion occurs in the same location in the rip-rap 

and gravel admixture layers, by the same mechanism (gully formation), and that 

erosion is deeper in the gravel admixture than in the rip-rap. In contrast, more 

extensive gullying occurs with the topsoil surface, with longer and deeper gullies.

Maximum erosion in the semi-arid climate is much greater than maximum erosion in 

the humid climate for all three surface layer types (Fig. 4.1). All surface layers in the 

semi-arid climate had a maximum erosion of 6 to 7 m and the humid climate had a 

maximum erosion of 3.5 to 5.5 m, despite greater rainfall in the humid climate. For 

example, consider the plan views of the rip-rap surface layers in the semi-arid 

climate (Fig. 4.3 a) and the humid climate (Fig. 4.5 a). Erosion occurs across the 

side slopes as soil wash in the semi-arid climate, whereas erosion is in defined 

gullies in the humid climate. Semi-arid climates have less rainfall compared to humid 

climates (average annual rainfall is 230 mm in Grand Junction, CO compared to 961 

mm in Pittsburgh, PA), but often have more fluvial erosion than humid climates 

because of sparse vegetative cover (Hudson 1987). These effects can be 

exacerbated when the surface is modified due to other factors, such as fire.

Monthly average precipitation data were analyzed for potential causes of greater 

erosion in the semi-arid climate. Precipitation data from the normal annual

preciptiation cycle for the three consecutive months with the greatest precipitation for 

both Grand Junction, CO and Pittsburgh, PA were explored for connections with the 

growing cycle for each climate. The three consecutive months with greatest rainfall 

for Grand Junction occur in March, April, and May, with 31.6% of the annual rainfall

(NRCC 2009). Much of the rainfall occurs prior to the start of the growing season 

(April 30 to November 6) (Grand Valley Project 2011). In contrast, 31.4% of the 

annual rainfall for Pittsburgh occurs in May through July (NRCC 2009); i.e. after the 

growing season begins (April 24 to October 6) (Allen 2010 and Klett et al. 2010).

Significant rainfall prior to the start of the growing season may be the cause of 

greater erosion seen in the semi-arid climate. The opportunity to establish vegetation 

prior to the period of greatest rainfall may significantly reduce erosion in the humid 

climate. Precipitation and growing season data are included in the WEPP 

calibrations of the fluvial erosion parameter β using the built-in climate and plant 

databases.

The calibrated n1 fluvial erosion parameter also corresponds to erosion 

mechanisms, and controls the type of erosion over the landscape (Kirkby 1971 and 

Hancock 2004). Descriptions of erosion processes corresponding to the fluvial 

erosion parameters are in Table 4.1. An n1 of 1 to 2 corresponds to soil wash without 

gullying and n1 = 0.7 is reasonable for an armored surface. An n1 of > 2 represents 

gullying. For the semi-arid climate, n1 ranged from 3.9 to 4.6, indicating gullying 

occurs. For the humid climate, n1 ranged from 0.7 to 1.0, indicating surface armoring 

occurs. These erosion mechanisms are consistent with erosion rates associated with 

areas of higher rainfall intensity (semi-arid climate) and lower rainfall intensity (humid

climate).
4-10

Vegetative cover for this study was the average cover established by the USDA 

(Foster et al. 1995) for each type of vegetation (Big Mountain Sagebrush for a semiarid climate and Bluestem Prairie Grass for a humid climate): 30% for the semi-arid 

climate and 56% for the humid climate. Vegetative cover for the humid climate was 

reduced to 30% for a resistive barrier with a gravel admixture surface to test if the 

differences in percent vegetative cover between climates affected erosion predicted 

by the model. The fluvial erosion parameters had no change after lowering the

vegetative cover percentages, meaning that a change in percentage vegetative 

cover of this magnitude did not impact the model predictions.

Erosion of vegetated gravel admixture and un-vegetated gravel admixture surface 

layers for a resistive barrier is compared in Fig. 4.6. In the semi-arid climate, the

vegetated gravel admixture has less maximum erosion and a higher average 

elevation than un-vegetated gravel admixture (Fig. 4.6 (a)). With vegetation, the

average elevation depth is in the bedding layer (layer 2) rather than the much 

deeper transition layer (layer 5) with an un-vegetated surface. For the humid climate,

the vegetated gravel admixture had 6 m less maximum erosion and the average 

elevation was 4 m higher than the un-vegetated gravel admixture over the 1000-yr 

design life of the cover. Vegetation has the same decreasing effect on erosion of the 

topsoil and rip-rap surface layers. Vegetation was also found to have the same 

decreasing effect on erosion for water balance barriers. All subsequent erosion 

simulations were performed using vegetated surface layers.

4.1.2 Influence of Barrier Type on Erosion

Maximum erosion and average elevation for water balance and resistive barriers in 

(a) semi-arid and (b) humid climates are shown in Fig. 4.7. In a semi-arid climate, 

the maximum erosion and average elevation for a water balance barrier fall slightly

deeper than the maximum erosion and average elevation for a resistive barrier.

There is no difference between maximum or average erosion in the water balance 

and resistive barriers in a humid climate. Additional figures showing predictions are 

in Appendix A for resistive barriers and Appendix B for water balance barriers.

The difference in average erosion depth between water balance and resistive 

barriers in a semi-arid climate appears to begin in the third layer of the water 

balance barrier. The difference between the two barriers is due to the higher silt 

content for the water storage layer (third layer of the water balance barrier) 

compared to the frost protection layer (third layer of the resistive barrier) (49% silt in 

the water storage layer, 12% silt in the frost protection layer), as erodibility increases 

with silt content (Fangmeier et al. 2006). 

4.1.3 Hydrologic Comparison of Barrier Type and Surface Layer Type

Cumulative percolation from the barrier was predicted using SVFLUX for water 

balance and resistive barriers with rip-rap, gravel admixture, and topsoil surface 
4-11

layers. Simulations were conducted for semi-arid and humid sites. Predictions are 

shown in Fig. 4.8 for the semi-arid climate and in Fig. 4.9 for the humid climate.
4-12

Time (yr)

0 200 400 600 800 1000 1200

Elevation Change (m) -10

-12

-14

-16

-2

-4

-6

-8

0

 

 

 

Average Elevation

Maximum Erosion

Time (yr)

0 200 400 600 800 100

Elevation Change (m) -10

-12

-14

-16

-2

-4

-6

-8

0

 

 

 

Average Elevatio

Maximum Erosio

(a) Semi-arid (b) Humid

Fig. 4.6. Maximum erosion and average elevation predicted by SIBERIA for the reference site with a re

comparing gravel admixture surfaces with and without vegetation: (a) semi-arid climate and (

climate.

Surface Layer

Bedding Layer

Frost Protection Layer

Radon Barrier

Transition Layer

Tailings

Zero Change

Un-vegetated Gravel Admixture

Vegetated Gravel Admixture

 

4-12
4-13

Time (yr)

0 200 400 600 800 1000 1200

Elevation Change (m) -2

-4

-6

-8

0

 

 

Average Elevation

Maximum Erosion

Time (yr)

0 200 400 600 800 100

Elevation Change (m) -2

-4

-6

-8

0

 

 

Average Elevation

Maximum Erosion

(a) Semi-arid (b) Humid

Fig. 4.7. Maximum erosion and average elevation predicted by SIBERIA for resistive and water balanc

rip-rap surface layer: (a) semi-arid climate and (b) humid climate.

Resistive Cover

Water Balance Cover

Tailings, Resistive

Tailings, Water Balance

Zero Change

4-13
4-14

Semi-Arid Climate Topsoil

Gravel Admixture

Rip-rap

Topsoil

Gravel Admixture

Rip-rap

End-of-year Cumulative Flux at Base (mm) -100

-200

0

200

100

Typical Wettest

Topsoil

Gravel Admixture

Rip-rap

Topsoil

End-of-year Cumulative Flux at Base (mm) -100

-200

0

200

100

Typical We

(a) Resistive barrier (b) Water balance barrier

Fig. 4.8. End-of-year cumulative flux above the tailings predicted by SVFLUX for the typical year and w

semi-arid climate: (a) resistive barrier and (b) water balance barrier. Negative flux indicates d

into the tailings.

4-14
4-15

Humid Climate Topsoil

Gravel Admixture

Rip-rap

Topsoil

Gravel Admixture

Rip-rap

End-of-year Cumulative Flux at Base (mm) -100

-200

0

200

100

Typical Wettest

Topsoil

Gravel Admixture

Rip-rap

Topsoil

Gravel Admixture

End-of-year Cumulative Flux at Base (mm) -100

-200

-300

-400

-500

0

100

Typical Wett

(a) Resistive barrier (b) Water balance barrier

Fig. 4.9. End-of-year cumulative flux above the tailings predicted by SVFLUX for the typical year and w

humid climate: (a) resistive barrier and (b) water balance barrier. Negative flux indicates dow

the tailings.

4-15
4-16

Negative percolation in Fig. 4.8 and Fig. 4.9 is downward flow (i.e. into the tailings). 

Additional figures showing SVFLUX predictions for precipitation, evapotranspiration, 

soil-water storage, and cumulative percolation are in Appendix C.

In the semi-arid climate (Fig. 4.8), the barriers with a rip-rap surface transmit 

percolation into the tailings (negative flux) regardless of barrier type or typical or 

wettest year simulations. The resistive barrier with topsoil and gravel admixture 

surface layers had upward flow out of the tailings (positive flux) for typical and 

wettest year simulations (Fig. 4.8 (a)). In contrast, percolation into the tailings 

occurred in the wettest year for all surface layer types with a water balance barrier, 

and only with the rip-rap surface for the typical year (Fig. 4.8 (b)). Topsoil and gravel 

admixture surfaces with water balance barriers had upward flux (out of the tailings) 

for the typical year simulation.

In the humid climate (Fig. 4.9), both barrier types with a rip-rap surface had 

percolation into the tailings (negative flux) for the typical and wettest year 

simulations. Resistive barriers with topsoil and gravel admixture surfaces had 

upward flow for both the typical and wettest year simulations (Fig. 4.9 (a)) due to 

evapotranspiration of water stored in finer-textured soil layers.

Barriers with a gravel admixture surface layer were most effective in controlling both 

erosion and percolation. Although percolation was slightly lower in some cases when 

topsoil was used for the surface layer, the gravel admixture layer was much more 

effective in controlling erosion than the topsoil layer. In contrast, the rip-rap surface 

layer was most effective in controlling erosion, but barriers with a rip-rap surface 

layer consistently transmitted the most percolation.

A gravel admixture surface includes both fine and coarse soil within a single surface 

layer. This combination of particle sizes provides the surface with a high interlock of 

soil particles, helping prevent erosion (Toy et al 1998), and higher soil water storage,

with the finer soil allowing the barrier to store water until evapotranspiration can 

occur (Kirkham 2005). The fine-textured soil in the gravel admixture surface also 

allows water to move upward to the surface for evaporation. In contrast, the 

permeable rip-rap layer promotes infiltration during precipitation events, and the 

caplillary break formed between the coarse rip-rap and finer underlying layers traps 

water within the cover, reducing evapotranspiration and increasing percolation.

4.2 Effect of Slope Length and Grade on Erosion

Slope length and grade difference at the nickpoint (i.e. the location of the change in 

grade between the top and side slopes) both affect erosion. To evaluate the effect of 

slope length and slope grade, the topography was modified to be symmetrical in 

both base and peak (Fig. 4.10). This new topography had one base elevation 

representing a disposal site on a level surface and with a mound shape.
4-17

Fig. 4.10. Topography representing balanced side slopes with 20% maximum side 

slopes and 5.3% maximum top slope, referred to herein as the modified 

topography.
4-18

When changing the topography, the same lowest base elevation and highest peak 

elevation were maintained so that the storage volume of the new topography would 

remain similar to the storage volume of the reference site described in Section 4.1. 

Three cases with different side slope length (distance between top and bottom of the 

side slope) were evaluated to compare how different slope lengths and angles 

influence erosion. The side slope lengths were 53 m, 41 m, and 28 m, with 

corresponding side slope grades of 15.3, 20.0, and 18.5% (Table 4.2).

Maximum erosion and average elevation are shown in Fig. 4.11 for a rip-rap cover

with 53-m, 28-m, and 41-m side slope lengths in the (a) semi-arid and (b) humid 

climates. For both climates (Fig. 4.11), the 41-m long slope has less maximum 

erosion and a higher average elevation than the 53-m and 28-m slopes. The 41-m 

slope has approximately 5 m less maximum erosion than the 28-m long slope in the 

semi-arid climate, and approximately 4 m less maximum erosion than the 28-m long 

slope in the humid climate. 

When the slope angle is held constant, an increase in slope length increases the 

amount and depth of erosion for both climates. For example, the 53-m slope has 

deeper maximum erosion than the 41-m slopes; 7 m deeper in the semi-arid climate 

and 5 m deeper in the humid climate. Slope grade also has an effect, with larger 

slope grades producing more erosion (e.g. the 28-m slopes have greater maximum 

erosion than the 41-m slopes because slope grade difference at the nickpoint is 

larger; the nickpoint is where erosion begins to occur, and is typically where the 

deepest erosion occurs). Fig. 4.12 shows the effect of grade difference on erosion 

for semi-arid and humid climates; the larger maximum erosion associated with the 

28-m slope is concomitant with the larger grade difference associated with the 28-m 

slope (15.5%). Additional figures showing different slope lengths and angles are 

Appendix D.

4.3 Effect of Slope Shape on Erosion

Terraced, concave, natural, and uniform slopes (Fig. 4.13) were simulated with 

SIBERIA to compare the effect of slope shape on erosion. Shallow and deep 

concave side slopes were evaluated to compare differences between a shallow 

(30%) initial slope and a deep (60%) initial slope. The uniform side slope shape is 

the modified mound shape from Section 4.2. Rip-rap, gravel admixture, and topsoil 

surface layers were used for the simulations. Topographic views of the four slope 

shapes are in Appendix E.

Predictions of maximum erosion, maximum deposition, and average elevation 

change for the various slope shapes with a rip-rap surface are shown in Fig. 4.14 for 

barriers in (a) semi-arid and (b) humid climates. Predictions labeled concave 

correspond to the shallow or deep concave slope that produced the least maximum 

erosion and least average elevation change for that surface type. In Fig. 4.14, the
4-19

Table 4.2. Side slope length, side slope grade, top slope grade, and grade difference 

compared with SIBERIA simulations to determine effects of slope length 

and grade.

Side Slope 

Length Side Slope Grade Top Slope Grade Grade Difference

53 m 15.3% 2.0% 13.3%

41 m 20.0% 5.3% 14.7%

28 m 18.5% 3.0% 15.5%
4-20

Time (yr)

0 200 400 600 800 1000 1200

Elevation Change (m)

-10

-12

-14

-2

-4

-6

-8

2

0

 

 

 

 

Average Elevation

Maximum Erosion

Time (yr)

0 200 400 600 

Elevation Change (m)

-10

-12

-14

-2

-4

-6

-8

2

0

 

 

 

 

Averag

Maxim

(a) Semi-arid (b) Humid

Fig. 4.11. Maximum erosion and average elevation change predicted by SIBERIA for the reference 

surface layer and a resistive barrier for various slope lengths: (a) semi-arid climate and 

28 m side slopes

41 m side slopes

53 m side slopes 

Surface Layer

Bedding Layer

Frost Protection Layer

Radon Barrier

Transition Layer

Tailings

Zero Change

 

4-20
4-21

Semi-Arid Climate Humid Climate

Maximum Erosion Depth (m)

0

2

4

6

8

10

12

14

14.7 % Grade Difference

15.5 % Grade Difference

41 m

28 m

41 m

28 m

Fig. 4.12. Maximum erosion depth at 1000-yr for a 14.7% and 15.5% grade 

difference using a rip-rap surface over a resistive barrier in semi-arid and 

humid climates with slope lengths of 28 and 41 m.
4-22

(a) Terraced

(b) Shallow Concavity 

(c) Deep Concavity

(d) Natural Hillside

Fig. 4.13. Terraced (a), shallow concavity, 30% initial slope (b), deep concavity, 60% 

initial slope (c), and natural hillside slopes (d) used to evaluate influence 

of topography on erosion.

4% 9 m

2:1

 40 m

2%

4%

60 m

10 m

4%

60 m

10 m

4%

64 m

10 m
4-23

Rip-rap Surface

Time (yr)

0 200 400 600 800 1000 1200

Elevation Change (m) -2

-4

-6

-8

4

2

0

 

 

 

 

 

Average Elevation

Maximum Erosion

Maximum Deposition

Time (yr)

0 200 400 600 800 

Elevation Change (m) -2

-4

-6

-8

4

2

0

 

 

 

 

 

Average Elevat

Maximum Eros

Maximum Depos

(a) Semi-Arid (b) Humid

Fig. 4.14. Maximum erosion, maximum deposition, and average elevation change predicted by SIBER

barriers with a rip-rap surface and uniform, terraced, concave (semi-arid: deep concave, hu

concave), or natural side slopes: (a) semi-arid climate and (b) humid climate.

Uniform side slopes

Terraced side slopes 

Concave side slopes

Natural side slopes 

Surface Layer

Bedding Layer

Frost Protection Layer

Radon Barrier

Transition Layer

Tailings

Zero Change

4-23
4-24

semi-arid climate has deep concave slopes and the humid climate has shallow 

concave slopes. In semi-arid environments, the deep concave slope has the least 

maximum erosion, whereas the terraced slope has the greatest maximum erosion.

In contrast, in humid climates, terraced side slopes had the least maximum erosion 

and natural side slopes had the greatest maximum erosion. Additional figures 

comparing shallow and deep concave slopes are in Appendix F.

Images showing the number of intact layers for a rip-rap surface in a semi-arid 

climate are shown in Fig. 4.15 for (a) terraced, (b) concave, and (c) natural side

slopes. Concave side slopes have approximately 2 m more maximum deposition 

and 1 m less maximum erosion than terraced side slopes. On-site deposition plays a 

part in keeping the cover intact for concave side slopes (Fig. 4.15, blue shading). 

Sediment is deposited at the base of the steepest slope section in a concave slope,

allowing more layers to build up at the base. Deposition is shown by the number of 

layers remaining intact over 6 (blue shading). Deposition at the toe of the slope also 

occurs on natural slope shapes, whereas terraced side slopes do not show

deposition (Fig. 4.15 (a)).

The effect of slope shape on erosion predictions for a rip-rap surface was

significantly different in the humid climate. At least 3 layers (no evident red or deep 

red shading) remained intact over the 1000-year simulation for terraced slopes (Fig. 

4.16). As observed for the semi-arid simulation, deposition was not significant for 

terraced slopes in the humid climate (blue shading not evident). Natural and 

concave slopes had more erosion at the top of the slope (red shading), indicating 

that the head-cut progression was more advanced than with terraced side slopes. 

Deposition was approximately 2 m at the base of both natural and concave slopes. 

This deposition limits erosion depth at the base of the slopes, but the advanced 

head-cutting created deeper erosion further up slope.

The steepness of the slope immediately at the transition point between the top slope 

and side slope is a reason for the advance head-cutting on the natural and concave

slopes in the humid climate. The side slope for the natural and concave slopes has a 

steeper slope for a longer length, causing erosion to easily move upwards. Terraced 

slopes limit head-cutting by having short lengths of steep slope sections and several 

small “step” grade changes, rather than one large grade change. Shorter slopes 

prevent large quantities of overland flow (Toy et al. 2002, Fangmeier et al. 2006),

and shallow slopes slow the movement of the rill head-cut by reducing the velocity of 

the flow (Willgoose and Sharmeen 2006); both limit erosion.

The predictions for a gravel admixture surface with the four slope shapes in both 

climates are shown in Fig. 4.17. At 1000 yr, there is no observable difference in 

either maximum erosion or average elevation change between the slope shapes for 

the semi-arid climate. Concave and natural slopes have about 1.5 m more 

deposition (blue shading) at the base of the slope than uniform and terraced slopes

(Fig. 4.18).
4-25

Rip-rap Surface (Semi-Arid Climate)

(a) Terraced (b) Concave (c) Natural

Fig. 4.15. Number of layers intact after 1000 years in a semi-arid climate predicted by SIBERIA for a re

with a rip-rap surface: (a) terraced side slopes, (b) concave side slopes (deep), and (c) natu

4-25
4-26

Rip-rap Surface (Humid Climate)

(a) Terraced (b) Concave (c) Natural 

Fig. 4.16. Number of layers intact after 1000 years in a humid climate predicted by SIBERIA for a resis

a rip-rap surface: (a) terraced side slopes, (b) concave side slopes (shallow), and (c) natura

4-26
4-27

Gravel Admixture Surface

Time (yr)

0 200 400 600 800 1000 1200

Elevation Change (m) -2

-4

-6

-8

4

2

0

 

 

 

 

 

Average Elevation

Maximum Erosion

Maximum Deposition

Time (yr)

0 200 400 600 800 

Elevation Change (m) -2

-4

-6

-8

4

2

0

 

 

 

 

 

Average Elevati

Maximum Eros

Maximum Depositio

(a) Semi-Arid (b) Humid

Fig. 4.17. Maximum erosion, maximum deposition, and average elevation change predicted by SIBER

barriers with a gravel admixture surface and uniform, terraced, concave (semi-arid: shallow, 

or natural side slopes: (a) semi-arid climate and (b) humid climate.

Uniform side slopes

Terraced side slopes 

Concave side slopes

Natural side slopes 

Surface Layer

Bedding Layer

Frost Protection Layer

Radon Barrier

Transition Layer

Tailings

Zero Change

4-27
4-28

Gravel Admixture Surface (Semi-Arid Climate)

(a) Terraced (b) Concave (c) Natural 

Fig. 4.18. Number of layers intact after 1000 years in a semi-arid climate predicted by SIBERIA for a re

with a gravel admixture surface: (a) terraced side slopes, (b) concave side slopes (shallow), 

side slopes.

4-28
4-29

Erosion is significant on the side slopes for all four slopes shapes, but the deep 

erosion on the side slopes occurs over a smaller area for concave and natural 

slopes.

Gravel admixture surfaces on terraced side slopes in a humid climate have the least 

maximum erosion (Fig. 4.17 (b)), with the 1000-yr maximum erosion in the transition 

layer. The average elevation change for all slope shapes is in the surface layer.

Natural and concave slopes have the greatest amount of maximum erosion, and 

have a maximum deposition of approximately 2 m and 3 m, respectively.

Erosion on natural and concave slopes progresses further up slope than erosion on

terraced slopes (Fig. 4.19, red shading), as was found in the simulations for the riprap surface in a humid climate (Fig. 4.16).

The differences between erosion for the four slope shapes in semi-arid and humid 

climates for the rip-rap and gravel admixture surfaces can be explained by the 

maximum amount of erosion (Fig. 4.14 and Fig. 4.17). For all slopes in the semi-arid 

climate, the rip-rap surface had approximately 4 m greater maximum erosion,

creating more sediment movement than in a humid climate. A similar situation 

occurred for the gravel admixture surface in the semi-arid climate; all slope shapes 

had approximately 4 m greater maximum erosion depth than slope shapes in the 

humid climate with the same gravel admixture surface. Concave and natural slope 

shapes have a flatter grade at the base of the slope, which creates a sediment trap

that promotes deposition.

Deposition is important in the more eroded semi-arid climate because sediment fills 

eroded regions near the base, keeping sediment on the slope (blue shading; Fig. 

4.15b, c) and Fig. 4.18b, c), rather than migrating off site (no blue shading evident, 

Fig. 4.15a, Fig. 4.18a). Terraced slopes produce the least maximum erosion for riprap and gravel admixture surfaces in a humid climate (Fig. 4.14b and Fig. 4.17b).

Terraces have many short slopes whereas concave and natural slope shapes have 

long slope lengths. Sediment deposition is not significant on the terraced slopes

because less erosion occurs on the short slopes.

Predictions are shown in Fig. 4.20 for resistive barriers with topsoil surfaces in (a) 

semi-arid and (b) humid climates. The deepest rills and greatest deposition in the 

semi-arid climate occur in the concave side slope. Terraced and natural slopes have 

the least maximum erosion. Terraced slopes have shorter slope lengths and natural 

slopes have less abrupt changes in grade than slopes with a concave shape. The 

concave slope also has more branches within its rill system, indicating the rills on the 

concave slope began much earlier than the straighter rills on the terraced and 

natural slopes (Fig. 4.21). 
4-30

Gravel Admixture Surface (Humid Climate)

(a) Terraced (b) Concave (c) Natural 

Fig. 4.19. Number of layers intact after 1000 years in a humid climate predicted by SIBERIA for a resis

a gravel admixture surface: (a) terraced side slopes, (b) concave side slopes (deep), and (c) 

slopes.

4-30
4-31

Topsoil Surface

Time (yr)

0 200 400 600 800 1000 1200

Elevation Change (m) -2

-4

-6

-8

2

0

 

 

 

 

 

Average Elevation

Maximum Erosion

Maximum Deposition

Time (yr)

0 200 400 600 800 

Elevation Change (m) -2

-4

-6

-8

2

0

 

 

 

 

 

Average Elev

Maximum Er

Maximum Depo

(a) Semi-Arid (b) Humid

Fig. 4.20. Maximum erosion, maximum deposition, and average elevation change predicted by SIBER

barriers with a topsoil surface and uniform, terraced, concave (semi-arid: shallow, humid: de

side slopes: (a) semi-arid climate and (b) humid climate.

Uniform side slopes

Terraced side slopes 

Concave side slopes

Natural side slopes 

Surface Layer

Bedding Layer

Frost Protection Layer

Radon Barrier

Transition Layer

Tailings

Zero Change

4-31
4-32

Topsoil Surface (Semi-Arid Climate)

 

(a) Terraced (b) Concave (c) Natural 

Fig. 4.21. Number of layers intact after 1000 years in a semi-arid climate predicted by SIBERIA for a re

with a topsoil surface: (a) terraced side slopes, (b) concave side slopes (shallow), and (c) na

slopes.

4-32
4-33

Predictions of maximum erosion and average erosion depths for a topsoil surface in 

a humid climate are shown in Fig. 4.20 (b). After 1000 years, the concave and 

natural slopes have about 1 m more deposition than terraced slopes Sediment is 

deposited at the base of the concave slope (blue shading) shown in Fig. 4.22. This 

increased deposition does have a small effect on maximum erosion depth, with 

concave and natural slopes having less maximum erosion than terraced slopes (Fig. 

4.20 (b)). The topsoil in the humid climate behaves similarly to rip-rap and gravel 

admixture in the semi-arid climate because erosion is more widespread for a topsoil 

surface in a humid climate due to the smaller particle size of topsoil. The three 

surfaces in the humid climate can be compared by the following figures: rip-rap, Fig. 

4.16; gravel admixture, Fig. 4.19; topsoil, Fig. 4.22. Additional figures showing the 

elevation and surface views of the scenarios producing the least erosion are in 

Appendix G.
4-34

Topsoil Surface (Humid Climate)

(a) Terraced (b) Concave (c) Nat

Fig. 4.22. Number of layers intact after 1000 years in a humid climate predicted by SIBERIA for a resis

a topsoil surface: (a) terraced side slopes, (b) concave side slopes (deep), and (c) natural si

4-34
5-1

5 SUMMARY AND PRACTICAL IMPLICATIONS

The objective of this study was to evaluate strategies to control erosion and 

percolation through barriers used for LLRW disposal sites. Two models were used to 

evaluate strategies; the SIBERIA landform evolution model was used to predict

erosion and the SVFLUX hydrologic model was used to predict percolation into the 

stored waste (tailings in this study). Predictions from these two models were used to 

assess barrier design strategies in semi-arid and humid climates in terms of ability to 

limit erosion and percolation into the tailings. Type of barrier, type of surface layer,

presence of vegetation, and type of side slope topography were evaluated for their 

effects on erosion and hydrology.

Three surface layers were evaluated: topsoil, rip-rap, and gravel admixture. Armored 

surfaces such as rip-rap and gravel admixture had less erosion than finer textured 

surfaces, such as topsoil. However, armoring a barrier with rip-rap transmits more 

percolation than any other surface layer in either climate due to water trapping 

induced by the textural contrast between the rip-rap and underlying finer layers. In 

contrast, a gravel admixture surface layer erodes more than a rip-rap surface, but 

transmits less percolation in either climate.

Incorporating vegetation reduces erosion and promotes evapotranspiration, 

decreasing percolation. For the examples that were evaluated, vegetation reduced

erosion by 1.5 m in the semi-arid climate and 4 m in the humid climate over 1000 

years. Barriers that employ a surface layer employing a gravel admixture and 

planted with native vegetation are expected to provide a good balance between 

effective control of erosion and percolation. Rip-rap could be used on side slopes 

outside the limits of waste to control erosion in areas where erosive effects are more 

significant and percolation is not important.

Slope length and grade difference at the nickpoint affect erosion. Erosion is greater 

for longer slopes and slopes with a large-grade difference at the nickpoint between 

the top and side slopes. Grade difference may be more important than slope length; 

therefore reducing changes in grade at the nickpoint will reduce erosion. Creating a 

smoother nickpoint, as in natural side slopes, will slow the erosion process and yield 

less deep erosion in upslope regions. Slope lengths should be kept as short as 

practical and grade differences as small as practical to reduce erosion.

Slope shape affects both erosion and deposition of sediment. In areas where larger

amounts of erosion occur (i.e. semi-arid climates), erosion can be mitigated through 

the use of concave or natural slopes that deposit eroded sediment on site. Terraced 

slopes with an armored surface prevent the most erosion in a humid climate.

Terraces cause a smaller erosion rate due to the use of many short slope lengths.

Use of “bands” of rip-rap on side slopes (alternating rip-rap with other material), 

humps at the end of each terrace to aide on-site deposition, and chemicals to limit 
5-2

both erosion and percolation (i.e. bentonite, sodium nitrate, gypsum) should be 

evaluated in future studies. Other future work should expand the use of native 

vegetation to include more varieties and the strategic placement of various varieties

so they may have the greatest effect on controlling erosion and percolation. 
6-1

6 REFERENCES

Allen, Z. (2010, April 13). Fire Weather Operating Plan, Retrieved April 25, 2011, 

from National Weather Service: http://www.erh.noaa.gov/pbz/fxwx/ops_plan_10.htm

Anderson, C., and Stormont, J. (1997). Prediction of long-term erosion from landfill 

covers in the southwest, Conference Proceedings, International Containment 

Technology Conference, February 9-12, 1997, St. Petersburg, FL. USA, 389-395.

Anderson, C., and Stormont, J. (2005). Gravel Admixtures for Erosion Protection in 

Semi-Arid Climates. In J. Briaud, and S. Bhatia (Ed.), Geo-Frontiers 2005 Congress 

Geotechnical Special Publication No. 135 Erosion of Soils and Scour of 

Foundations, American Society of Civil Engineers, Austin, TX, USA.

Benson, C. (2001). Waste Containment: Strategies and Performance, Australian 

Geomechanics, 36 (4).

Benson, C. (2011, April 18). Water Balance Modeling, University of WisconsinMadison, Madison, WI, USA.

Benson, C., Lee, S., Wang, X., Albright, W., and Waugh, W. (2008). Hydraulic 

Properties and Geomorphology of the Earthen Component of the Final Cover at the 

Monticello Uranium Mill Tailings Repository, Geo Engineering Report No. 08-04, 

University of Wisconsin-Madison, Desert Research Institute, and US Department of 

Energy Environmental Sciences Laboratory.

Benson, C., Sawangsuriya, A., Trzebiatowski, B., and Albright, W. (2007). 

Postconstruction Changes in the Hydraulic Properties of Water Balance Cover Soils, 

Journal of Geotechnical and Geoenvironmental Engineering, 133 (4), 349-359.

Benson, C., Waugh, W., Albright, W., and Smith, G. (2010). The RECAP Test 

Sections at the Grand Junction Disposal Site: Construction Documentation and 

Instrument Calibration, Geological Engineering, University of Wisconsin-Madison, 

Madison, WI, USA.

Benson, C. and Gurdal, T. (2013), Hydrologic Properties of Final Cover Soils, 

Foundation Engineering in the Face of Uncertainty, GSP No. 229, J. Withiam et al., 

Eds., ASCE, Reston VA, 283-297.

Benson, C., Albright, W., Fratta, D., Tinjum, J., Kucukkirca, E., Lee, S., Scalia, J., 

Schlicht, P., Wang, X. (2011), Engineered Covers for Waste Containment: 

Changes in Engineering Properties & Implications for Long-Term Performance 

Assessment, NUREG/CR-7028, Office of Research, U.S. Nuclear Regulatory 

Commission, Washington. 
6-2

Bohnhoff, G., Ogorzalek, A., Benson, C., Shackelford, C., and Apiwantragoon, P. 

(2009), Field Data and Water-Balance Predictions for a Monolithic Cover in a 

Semiarid Climate, J. Geotech. and Geoenvironmental Eng., 135(3), 333-348. 

Braun, J., and Sambridge, M. (1997). Modelling landscape evolution on geological

time scales: a new method based on irregular spatial discretization, Basin Research, 

9, 27-52.

Coulthard, T. (2001). Landscape evolution models: a software review, Hydrological 

Processes, 15, 165-173.

Coulthard, T., and Macklin, M. (2000). How sensitive are river systems to climate 

and land-use changes? A model based evaluation, Journal of Quarternary Science.

Coulthard, T., Maklin, M., and Kirkby, M. (2002). A cellular model of Holocene 

upland river basin and alluvial fan evolution, Earth Surface Processes and 

Landforms, 27, 269-288.

Coulthard, T., Hicks, D., and Van De Wiel, M. (2007). Cellular Modelling of river 

catchments and reaches: Advantages, limitations and prospects, Geomorphology 

90, 192-207.

Coulthard, T. , Kirkby, M., and Macklin, M. (1998). Non-linearity and spatial 

resolution in a cellular automaton model of a small upland basin, Hydrology and 

Earth System Sciences, 2, 257-264.

Coulthard, T., Kirkby, M., and Macklin, M. (2000). Modelling geomorphic response to 

environmental change in an upland catchment, Hydrological Processes, 14, 2031-

2045.

Coulthard, T., Kirkby, M., and Macklin, M. (1999). Modelling the impacts of Holocene 

environmental change on the fluvial and hillslope morphology of an upland 

landscape, using a cellular automaton approach, Fluvial Processes and 

Environmental Change, 31-47.

Dinwiddie, C., and Walter, G. (2008). Software validation test plan and report for 

EAMS Version 2.09 and SIBERIA Version 8.33, Center for Nuclear Waste 

Regulatory Analyses. U.S. Nuclear Regulatory Commission.

DOE Office of Legacy Management. (2009, May 5). Grand Junction, Colorado, 

Processing Site and Disposal Site, U.S. Department of Energy Office of Legacy 

Management, Grand Juncation, CO, United States of America.

USEPA. (1983). Standards for the Disposal of Uranium Mill Tailings, 40 CFR 192,

Washington, D.C., USA.
6-3

Evans, K., and Willgoose, G. (2000). Post-mining landform evolution modelling: 2. 

Effects of vegetation and surface ripping, Earth Surface Processes and Landforms, 

25, 803-823.

Fangmeier, R., Elliot, W., Workman, S., Huffman, R., and Schwab, G. (2006). Soil 

and Water Conservation Engineering (5th ed.), Thomson Delmar Learning, Clifton 

Park, NY, USA.

Flanagan, D., and Meyer, C. (2010, December 8). WEPP: Spilling the Secrets of 

Water Erosion, Retrieved December 9, 2010 from 

http://www.ars.usda.gov/is/AR/archive/apr97/wepp0497.htm?pf=1

Flanagan, D., and Nearing, M. (1995). NSERL Report No. 10 USDA - Water Erosion 

Prediction Project Hillslope Profile and Watershed Model Documentation, USDAARS National Soil Erosion Research Laboratory, West Lafayette, IN, USA.

Foster, G., Flanagan, D., Nearing, M., Lane, L., Risse, L., and Finkner, S. (1995). 

NSERL Report No. 10 Technical Documentation: USDA-Water Erosion Prediction 

Project (WEPP), National Soil Erosion Research Laboratory USDA-ARS-MWA, 

West Lafayette, IN, USA.

Grand Valley Project. (2011, May 10). Retrieved May 13, 2011, from United States 

Department of the Interior, Bureau of Reclamation: 

http://www.usbr.gov/projects/Project.jsp?proj_Name=Grand%20Valley%20Projectan

dpageType=ProjectDataPage

Gurdal, T., Benson, C., and Albright, W. (2003). Hydrologic properties of final cover 

soils from the alternative cover assessment program, Geo-Engineering Report No. 

03-02, Geo-Engineering Program, University of Wisconsin – Madison, Madison, WI, 

USA.

Hancock, G. (2004). The use of landscape evolution models in mining rehabilitation 

design, Environmental Geology, 46, 562-573.

Hancock, G., and Turley, E. (2006). Evaluation of proposed waste rock dump 

designs using the SIBERIA erosion model, Environmental Geology, 49, 765-779.

Hancock, G., and Willgoose, G. (2001). Use of a landscape simulator in the 

validation of the SIBERIA catchment evolution model: Declining equilibrium 

landforms, American Geophysical Union, 37 (7), 1981-1992.

Hancock, G., Evans, K., Willgoose, G., Moliere, D., Saynor, M., and Loch, R. (2000). 

Medium-term erosion simulation of an abandoned mine site using the SIBERIA 

landscape evolution model, Australian Journal of Soil Research, 38, 249-263.
6-4

Hancock, G., Loch, R., and Willgoose, G. (2003). The design of post-mining 

landscapes using geomorphic priciples, Earth Surface Processes and Landforms, 

28, 1097-1110.

Hancock, G., Lowry, J., Coulthard, T., Evans, K., and Moliere, D. (2010). A 

catchment scale evaluation of the SIBERIA and CAESAR landscape evolution 

models, Earth Surface Processes and Landforms, 35, 863-875.

Hancock, G., Lowry, J., Moliere, D., and Evans, K. (2008). An evaluation of an 

enhanced soil erosion and landscape evolution model: a case study assessment of 

the former Nabarlek uranium mine, Northern Territory, Australia, Earth Surface 

Processes and Landforms, 33, 2045-2063.

Holtz, R. and Kovacs, W. (1981). An Introduction to Geotechnical Engineering. 

Prentice Hall, Upper Saddle River, NJ, USA.

Hudson, N. (1987). Soil and water conservation in semi-arid areas, Food and

Agriculture Organization of the United Nations, Ampthill, Bedford, U.K.

Kirkby, M. (1971). Hillslope process-response models based on the continuity 

equation, Slopes Form and Process, 15-30.

Kirkham, M. (2005). Principles of Soil and Plant Water Relations, Elsevier Inc., 

Burlington, MA, USA.

Klett, J., Fahey, B., and Cox, R. (2010, May 12). Native Shrubs for Colorado 

Landscapes, Retrieved April 21, 2011, from Colorado State University Extension: 

http://www.ext.colostate.edu/pubs/garden/07422.html

McFadden, L., Wells, S., and Jercinovich, M. (1987). Influences of eolian and 

pedogenic processes on the origin and evolution of desert pavements, Geology, 15, 

504-508.

Morgan, R. (1995). Soil Erosion and Conservation, Longman Group Limited, Essex, 

England.

Nearing, M. (2004). Capabilities and limitations of erosion models and data, 13th 

International Soil Conservation Organisation Conference, Brisbane: Conserving Soil 

and Water for Society: Sharing Solutions, 1-6.

Penman, H. (1948). Natural evapotranspiration from open water, bare soil and 

grass, Proceedings of the Royal Society A, London, 120-145.

Richardson, G. and Waugh, W.J. (1996). The design of final covers systems for arid 

and semi-arid regions of the west, 3rd International Symposium on Environmental 

Geotechnology, June 10-12, 1996.
6-5

Sackschewsky, M., Kemp, C., Link, S., and Waugh, W. J. (1995). Soil water balance 

changes in engineered soil surfaces, Journal of Environmental Quality, 24, 352-359.

Sharmeen, S. (2000). Modelling the long-term evolution of mine spoils, soil erosion 

and soil development, PhD Thesis, University of Newcastle, Australia, Department of 

Civil, Surveying, and Environmental Engineering.

SoilVision Systems Ltd. (2004-2010). SVOFFICE Overview, Retrieved March 22, 

2011 from http://www.soilvision.com/subdomains/svoffice.com/index.shtml

Stormont, J., and Anderson, C. (2003). Erosional stability of the proposed Lee Acres 

cover, Report to Cheney – Walters – Echols, University of New Mexico, 

Albuquerque, NM, USA.

Toy, T., Foster, G., and Galetovic, J. (1998). Guidelines for the Use of the Revised 

Universal Soil Loss Equation (RUSLE) Version 1.06 on Mined Lands, Construction 

Sites, and Reclaimed Lands, The Office of Technology Transfer, Western Regional 

Coordinating Center, Office of Surface Mining, Denver, CO, USA.

Toy, T., Foster, G., and Renard, K. (2002). Soil Erosion: Processes, Prediction, 

Measurement, and Control. John Wiley and Sons, Inc., New York, NY, USA.

Tucker, G., and Slingerland, R. (1994). Erosional dynamics, flexural isostasy, and 

long-lived escarpments: A numerical modeling study, Journal of Geophysical 

Research, 99 (B6), 12229-12243.

Tucker, G., Gasparini, N., Lancaster, S., and Bras, R. (1997). An Integrated Hillslope 

and Channel Evolution Model as an Investigation and Prediction Tool, Year 2 annual 

report DACA99-95-R-0020, Department of Civil and Environmental Engineering. 

Massachusetts Institute of Technology, Cambridge, MA, USA.

Tucker, G., Gasparini, N., Lancaster, S., and Gras, R. (1997). An integrated hillslope 

and channel evolution model as an investigation and prediction tool, Technical 

Report prepared for the U.S. Army Corps of Engineers.

Tucker, G., Lancaster, S., Gasparini, N., Bras, R., and Rybarczyk, S. (2001). An 

object-oriented framework for distributed hydrologic and geomorphic modeling using 

triangulated irregular networks, Computers and Geosciences, 27, 959-973.

USDA-ARS. (2008). Draft User's Reference Guide Revised Universal Soil Loss

Equation Version 2, USDA-Agricultural Research Service, Washington, D.C., USA.

USDA-ARS. (2010). Revised Universal Soil Loss Equation 2 - RUSLE2 

Development. Retrieved February 23, 2011 from 

http://www.ars.usda.gov/Research/docs.htm?docid=6027
6-6

USDA-ARS. (2010 (2)). Revised Universal Soil Loss Equation 2 - How RUSLE2 

Computes Rill and Interrill Erosion, Retrieved February 23, 2011 from 

http://www.ars.usda.gov/Research/docs.htm?docid=6014

USDA-ARS. (1995). WEPP User Summary, USDA-ARS-MWA, National Soil Erosion 

Research Laboratory, West Lafayette, IN, USA.

Van De Wiel, M., Coulthard, T., Macklin, M., and Lewin, J. (2007). Embedding 

reach-scale fluvial dynamics within the CAESAR cellular automaton landscape 

evolution model, Geomorphology 90 , 283-301.

Walter, G., and Dubreuilh, P. (2007). Evaluation of approaches to simulate 

engineered cover performance and degradation, U.S. Nuclear Regulatory 

Commission. Center for Nuclear Waste Regulatory Analyses, San Antonio, TX, 

USA.

Waugh, W., Thiede, M., Bates, D., Cadwell, L., Gee, G., and Kemp, C. (1994). Plant 

cover and water balance in gravel admixtures at an arid waste-burial site, Journal of 

Environmental Quality, 23, 676-685.

Welsh, K., Dearing, J., Chiverrell, R., and Coulthard, T. (2009). Testing a cellular 

modelling approach to simulating late-Holocene sediment and water transfer from 

catchment to lake in the French Alps since 1826, The Holocene, 19 (5), 785-798.

White, R. (2010). Fire Weather Operating Plan, Retrieved May 13, 2011, from 

National Weather Service, Pittsburgh, PA: 

http://www.erh.noaa.gov/pbz/fxwx/ops_plan_10.htm

Willgoose, G. (2010, December 6). Personal interview, C. L. Smith, Interviewer.

Willgoose, G. (2005b). Mathematical Modeling of Whole Landscape Evolution,

Annual Review of Earth and Planetary Sciences, 33, 443-459.

Willgoose, G. (2005a). User Manual for SIBERIA, Retrieved March 1, 2010, from 

Telluric Research: http://www.telluricresearch.com/index.html

Willgoose, G., and Riley, S. (1998). Application of a catchment evolution model to 

the prediction of long-term erosion on the spoil heap at Ranger uranium mine: Initial 

analysis, Supervising Scientist Report 132, Supervising Scientist, Canberra .

Willgoose, G., and Sharmeen, S. (2006). A One-dimensional model for simulating 

armouring and erosion on hillslopes: 1. Model development and event-scale 

dynamics, Earth Surface Processes and Landforms, 31, 970-991.

Willgoose, G., Bras, R., and Rodriguiz-Iturbe, I. (1991a). A coupled channel network 

growth and hillslope evolution model: 1. Theory, Water Resourses Research, 27 (7), 

1671-1684.
6-7

Willgoose, G., Bras, R., and Rodriguez-Iturbe, I. (1991b). A physically based 

coupled network growth and hillslope evolution model: 2 Applications, Water 

Resources Research, 27 (7), 1685-1696.

Willgoose, G., Bras, R., and Rodriguez-Iturbe, I. (1991c). Results from a new model 

of river basin evolution, Earth Surface Processes and Landforms, 16, 237-254.

Wilson, G., Fredlund, D., and Barbour, S. (1994). Coupled soil-atmosphere modeling 

for soil evaporation, Canadian Geotechnical Journal, 31, 151-161.

Wischmeier, W., and Smith, D. (1978). Predicting rainfall-erosion losses: A guide to 

conservation planning, Agriculture Handbook 537, U.S. Department of Agriculture, 

Washington, D.C., USA.

APPENDIX A

WEPP Sensitivity Analysis to Initial Soil Water Content and Albedo

A-1

Appendix A: WEPP Sensitivity Analysis to Initial Soil Water Content and Albedo

A sensitivity analysis was performed to determine if the initial soil water content and the soil albedo 

had an effect on sediment loss within WEPP. The following tables represent these sensitivity 

analyses. The figures and tables in this appendix coincide with Section 3.2.1.
A-2

Table A.1. Effects of initial soil water content on discharge and sediment 

loss in WEPP. All other factors held constant.

Initial Soil Water Content Discharge, q Sediment Loss, qs

% mm/yr kg/m2

17 0.43 0.004

16 0.43 0.004

15 0.43 0.004

10 0.43 0.004

20 0.43 0.004

80 0.43 0.004

0 0.43 0.004
A-3

Table A.2. Effects of soil albedo on discharge and sediment loss in WEPP.

All other factors held constant.

Soil Albedo Discharge, q Sediment Loss, qs

- mm/yr kg/m2

0.25 0.43 0.004

0.35 0.43 0.004

0.5 0.43 0.004

0.9 0.53 0.005

0.75 0.44 0.005

0.6 0.44 0.005

0.1 0.43 0.004

B-1

APPENDIX B

SIBERIA Predictions for Covers with Water Balance Barriers
B-1
B-1

Appendix B: SIBERIA Predictions for Covers with Water Balance Barriers

Erosion predicted by SIBERIA is shown for rip-rap, gravel admixture, and topsoil 

surface layers with a water balance barrier for the semi-arid and humid climate. The 

site topography used is the reference site, shown in Figure 3.1. The figures in this 

appendix coincide with Section 4.1.2. 
Water Balance Barrier – Representative Site Topography

Time (yr)

0 200 400 600 800 1000 1200

Elevation Change (m) -2

-4

-6

-8

2

0

 

 

 

 

Maximum Erosion

Average Elevation Change

Maximum Deposition

Time (yr)

0 200 400 600 800 

Elevation Change (m) -2

-4

-6

-8

2

0

 

 

 

 

Maximum Ero

Average Elevation Ch

Maximum Depo

(a) (b)

Figure B.1. Maximum erosion, maximum deposition, and average elevation change predicted by SIB

topsoil, and gravel admixture surface layer for a water balance barrier using the represen

topography: (a) semi-arid climate and (b) humid climate.

Topsoil

Rip-rap

Gravel Admixture

Surface Layer

Bedding Layer

Water Storage Layer

Animal Intrusion Layer

Sand Capillary Break

Clay Barrier Layer

Tailings

Zero Change

 

B-2
Water Balance Barrier – Rip-rap Surface – Semi-Arid Climate

(a) Elevation (b) Layers remaining intact

Figure B.2. Erosion predicted by SIBERIA for a rip-rap surface with a water balance barrier in a sem

using the representative site topography: a) elevation predictions of the surface after 100

erosion and, b) number of layers remaining intact after 1000 years of erosion, plan view.

B-3
Water Balance Barrier – Gravel Admixture Surface – Semi-Arid Climate

(a) Elevation (b) Layers remaining intact

Figure B.3. Erosion predicted by SIBERIA for a gravel admixture surface with a water balance barrie

climate using the representative site topography: a) elevation predictions of the surface a

of erosion and, b) number of layers remaining intact after 1000 years of erosion, plan vie

B-4
Water Balance Barrier – Topsoil Surface – Semi-Arid Climate

(a) Elevation (b) Layers remaining intact

Figure B.4. Erosion predicted by SIBERIA for a topsoil surface with a water balance barrier in a sem

using the representative site topography: a) elevation predictions of the surface after 100

erosion and, b) number of layers remaining intact after 1000 years of erosion, plan view.

B-5
Water Balance Barrier – Rip-rap Surface – Humid Climate

(a) Elevation (b) Layers remaining intact

Figure B.5. Erosion predicted by SIBERIA for a rip-rap surface on a water balance barrier in a humid 

the representative site topography: a) elevation predictions of the surface after 1000 yea

b) number of layers remaining intact after 1000 years of erosion, plan view.

B-6
Water Balance Barrier – Gravel Admixture Surface – Humid Climate

(a) Elevation (b) Layers remaining intact

Figure B.6. Erosion predicted by SIBERIA for a gravel admixture surface on a water balance barrier 

climate using the representative site topography: a) elevation predictions of the surface a

of erosion and b) number of layers remaining intact after 1000 years of erosion, plan view

B-7
Water Balance Barrier – Topsoil Surface – Humid Climate

(a) Elevation (b) Layers remaining intact

Figure B.7. Erosion predicted by SIBERIA for a topsoil surface on a water balance barrier in a humid 

the representative site topography: a) elevation predictions of the surface after 1000 yea

b) number of layers remaining intact after 1000 years of erosion, plan view.

B-8
APPENDIX C

SVFLUX Predictions for Resistive and Water Balance Covers
C-1
C-1

Appendix C: SVFLUX Predictions for Resistive and Water Balance Covers 

The following figures show precipitation, evapotranspiration, soil-water storage, and 

cumulative percolation for resistive and water balance barriers for both resistive and 

water balance covers. Predictions are shown by climate. The figures in this appendix 

coincide with Section 4.1.3.
SVFLUX Predictions – Semi-Arid Climate

Figure C.1. Predictions from SVFLUX of precipitation, evapotranspiration, soil-water storage, and cu

percolation for resistive and water balance barriers in a semi-arid climate. Some simulati

less years than others to stabilize. The last year of each simulation is the wettest year. P

percolation is into the tailings, negative is out.

C-2
SVFLUX Predictions – Humid Climate

Figure C.2. Predictions from SVFLUX of precipitation, evapotranspiration, soil-water storage, and cu

percolation for resistive and water balance barriers in a humid climate. Some simulations 

years than others to stabilize. The last year of each simulation is the wettest year. Positiv

into the tailings, negative is out.

C-3

APPENDIX D

SIBERIA Predictions for Uniform Side Slope Topography
D-1
D-1

Appendix D: SIBERIA Predictions for Uniform Side Slope Topography

The following figures contain erosion predictions by SIBERIA for uniform side slope 

topography. These figures were used to evaluate different slope lengths and angles 

for uniform side slopes. The figures in this appendix coincide with Section 4.2. 
Uniform Side Slope Topography

Time (yr)

0 200 400 600 800 1000 1200

Elevation Change (m) -2

-4

-6

-8

2

0

 

 

Maximum Deposition

Average Elevation Change

Maximum Erosion

Time (yr)

0 200 400 600 800 

Elevation Change (m) -2

-4

-6

-8

2

0

 

 

Maximum Dep

Average Elevation C

Maximum E

(a) Semi-arid (b) Humid

Figure D.1. Maximum erosion, maximum deposition, and average elevation change predicted by 

topsoil, and gravel admixture surfaces with 41 m side slopes and a resistive barrier: (

and (b) humid climate.

Rip-rap Surface

Topsoil Surface

Gravel Admixture Surface

Surface Layer

Bedding Layer

Frost Protection Layer

Bedding Layer

Transition Layer

Tailings

Zero Change

 

D-2
Resistive vs. Water Balance Covers – Uniform Side Slopes

Time (yr)

0 200 400 600 800 1000 1200

Elevation Change (m) -2

-4

-6

-8

2

0

 

 

Maximum Deposition

Average Elevation Change

Maximum Erosion

Time (m)

0 200 400 600 80

Elevation Change (m) -2

-4

-6

-8

2

0

 

 

Maximum Depo

Average Elevation 

Maximum Ero

(a) Semi-arid (b) Humid

Figure D.2. Maximum erosion, maximum deposition, and average elevation change in resistive an

barriers predicted by SIBERIA with 41 m side slopes and a rip-rap surface layer: (a) s

and (b) humid climate.

Resistive Cover

Water Balance Cover 

Tailings, Resistive

Tailings, Water Balance

Zero Change

 

D-3
Semi-Arid Climate

(a) 53 m side slopes (b) 28 m side slopes (c) 41 m side slop

Figure D.3. Elevation predicted for a rip-rap surface with various slope lengths and angles in a se

53 m side slopes, 15.3% side slopes, 2% top slope, (b) 28 m side slopes, 18.5% side 

slope, and (c) 41 m side slopes, 20% side slopes, 5.3% top slope. Elevation is shown 

by the color scale above.

D-4
Semi-Arid Climate

(a) 53 m side slopes (b) 28 m side slopes (c) 41 m side slop

Figure D.4. Plan view predicted for a rip-rap surface with various slope lengths and angles in a se

53 m side slopes, 15.3% side slopes, 2% top slope, (b) 28 m side slopes, 18.5% side 

slope, and (c) 41 m side slopes, 20% side slopes, 5.3% top slope.

D-5
Humid Climate

(a) 53 m side slopes (b) 28 m side slopes (c) 41 m side slop

Figure D.5. Elevation predicted for a rip-rap surface with various slope lengths and angles in a hu

m side slopes, 15.3% side slopes, 2% top slope, (b) 28 m side slopes, 18.5% side slo

and (c) 41 m side slopes, 20% side slopes, 5.3% top slope. Elevation is shown in m a

color scale above.

D-6
Humid Climate

(a) 53 m side slopes (b) 28 m side slopes (c) 41 m side slop

Figure D.6. Plan view predicted for a rip-rap surface with various slope lengths and angles in a hu

m side slopes, 15.3% side slopes, 2% top slope, (b) 28 m side slopes, 18.5% side slo

and (c) 41 m side slopes, 20% side slopes, 5.3% top slope.

D-7

APPENDIX E

Topographic Maps Used in SIBERIA
E-1
E-1

Appendix E: Topographic Maps Used in SIBERIA

Topography used in this study was changed to show the effects of slope length and 

angle and the effects of slope shape on erosion. The following figures show the 

topography used in this study in creating the DTMs for input into SIBERIA. The 

figures in this appendix coincide with Section 4.2.
E-1

Representative Site Topography

Figure E.1. Topographic map of the representative site.

E-2
E-1

Modified, Uniform Site Topography

Figure E.2. Modified site topography used to create uniform, terraced, concave, 

and natural side slopes. See Fig. 4.13 for side slope views with top and 

side slope grades

E-3
E-1
APPENDIX F

SIBERIA Predictions for Shallow and Deep Concave Side Slopes

Appendix F: SIBERIA Predictions for Shallow and Deep Concave Side Slopes

The following tables and figures pertain to the evaluation of shallow and deep 

concave side slopes for use with various surface layer soil types and both the semiarid and humid climate. The figures and tables in this appendix coincide with Section 

4.3.

F-1
Table F.1. Best case scenario for concave side slopes based on climate and 

surface material.

Climate Surface Material Best Case Concavity Scenario

Humid

Rip-rap Shallow

Gravel Admixture Shallow

Semi-Arid

Rip-rap Deep

Topsoil Shallow

F-2
Shallow vs. Deep Concavity – Semi-Arid Climate

(a) Rip-rap (b) Topsoil

Figure F.1. Maximum erosion, maximum deposition, and average elevation change for resistive b

climate: a comparison of shallow and deep concavity for (a) a rip-rap surface, and (b) 

Time (yr)

0 200 400 600 800 1000 1200

Elevation Change (m) -2

-4

-6

4

2

0

 

 

Maximum Deposition

Average Elevation Change

Maximum Erosion

Time (yr)

0 200 400 600 800 

Elevation Change (m) -2

-4

-6

-8

4

2

0

 

Maximum Dep

Average Elevation C

Maximum E

Shallow Concavity

Deep Concavity

Surface Layer

Bedding Layer

Frost Protection Layer

Radon Barrier

Transition Layer

Tailings

Zero Change

 

F-3
Shallow vs. Deep Concavity – Humid Climate

(a) Rip-Rap (b) Gravel Admixture

Figure F.2. Maximum erosion, maximum deposition, and average elevation change for resistive b

climate: a comparison of shallow and deep concavity for (a) a rip-rap surface, and (b) 

surface.

Time (yr)

0 200 400 600 800 1000 1200

Elevation Change (m) -1

-2

-3

4

3

2

1

0

 

Maximum Deposition

Average Elevation Change

Maximum Erosion

Time (yr)

0 200 400 600 800 

Elevation Change (m) -1

-2

-3

4

3

2

1

0

 

 

Maximum De

Average Elevation 

Maximum 

Shallow Concavity

Deep Concavity

Surface Layer

Bedding Layer

Frost Protection Layer

Radon Barrier

Transition Layer

Tailings

Zero Change

 

F-4
APPENDIX G

SIBERIA Predictions for Least Eroded Surfaces
G-1
G-1

Appendix G: SIBERIA Predictions for Least Eroded Surfaces

The following figures show SIBERIA predictions showing the best case erosion 

scenario based on surface layer type, climate, and slope shape. The figures show 

3D and plan views of erosion over the surface. The figures in this appendix coincide 

with Section 4.3.
G-1

Best Case Scenario – Semi-Arid Climate

(a) Rip-rap (b) Gravel admixture

Figure G.1. Elevation predictions from SIBERIA of the topography producing the least erosion with a 

in a semi-arid climate: (a) rip-rap surface layer with deep concavity and (b) gravel admixt

layer with shallow concavity.

G-2
G-1

Best Case Scenario – Semi-Arid Climate

(a) Rip-rap (b) Gravel admixture

Figure G.2. Plan view SIBERIA predictions of the topography producing the least erosion with a resis

semi-arid climate: (a) rip-rap surface layer with deep concavity and (b) gravel admixture s

with shallow concavity.

G-3
G-1

Best Case Scenario – Humid Climate

(a) Rip-rap (b) Gravel admixture

Figure G.3. Elevation predictions from SIBERIA of the topography producing the least erosion with a 

in a humid climate: (a) rip-rap surface layer with terraces and (b) gravel admixture surfac

terraces.

G-4
G-1

Best Case Scenario – Humid Climate

(a) Rip-rap (b) Gravel admixture

Figure G.4. Plan view SIBERIA predictions of the topography producing the least erosion with a resis

humid climate: (a) rip-rap surface layer with terraces and (b) gravel admixture surface lay

G-5
G-1
APPENDIX H

Steps for Running SIBERIA Landform Evolution Model Using a 

Digital Terrain Model and Viewing Model Output
H-1
H-2

Appendix H: Steps for Running SIBERIA Landform Evolution Model Using a 

Digital Terrain Model and Viewing Model Output

To begin modeling with SIBERIA, an AutoCAD drawing of the existing site 

topography from the Grand Junction, CO reference site was first obtained to be used 

to create the digital terrain model. The gridding suite in EAMS had trouble reading 

files with several layers and hidden lines and would not grid the drawing. The 

unnecessary lines of the AutoCAD drawing were removed so only the contour lines 

of the area to be modeled remained. After these edits, the drawing was saved as a 

.dxf file.

Using EAMS, the .dxf file was imported for the gridding process. To grid everything 

in the .dxf file, the area of interest was kept as the default inputs, all four directions = 

-1. Grid spacing was selected as 10 m. The .dxf gridding resulted in two additional 

files, one .raw file and one .grid.raw file. The .grid.raw file stores coordinate and 

elevation information of the DTM and is used as the site input in SIBERIA.

After gridding the DTM, layers of the barrier, output file types, and output data were 

specified. The layer.model file located with the program files was modified to include 

layers of soil that constitute the barrier. This file can be opened and modified in a 

text editor program such as Notepad or WordPad. The individual layers of the barrier 

were specified using the layer capping command which places layers of a specified 

thickness and erodibility (β1) above the DTM elevations. This keeps the shape of the 

site true, but adds the thickness of the barrier to the elevation of the true land 

surface. The layer.model file must be specified in the erosion parameters portion of 

SIBERIA. An example of the layer.model file used is shown in Appendix C.

The siberia.setup file was modified in a text editor program and is where outputs 

recorded and reported are selected. The siberia.setup file is explained both within 

the file itself and in the SIBERIA User Manual (Willgoose 2005a). Critical output 

selections included: showing the model screen, the maximum, minimum, and mean 

change in elevation at a point from the start of the simulation, the erosion loss in 

units of weight per area, the sediment flux, the minimum and average amount of soil 

layers completely intact, and the output of the grid coordinates as time progresses in 

the form of a .xyz file. The siberia.setup file used in this study is in Appendix D.

Once the DTM was gridded, the layer.model file has been modified, and the 

siberia.setup file has been modified SIBERIA can be set up to run. Under the 

SIBERIA menu Input from Gridded RAW was selected. This brought up a window 

with output file type, start time, number of outputs and where a unique file name 

were be specified. The output file type was selected as .rst2 for ease of use in the 

EAMS Viewer. The start time was set to zero. The number of outputs was set to 10, 

at times 1, 5, 10, 30, 60, 100, 300, 500, 700, and 1000, to view erosion as in occurs 

H-1
H-3

and relative erosion rates at different times. Next, EAMS opened a window to select 

a database file. The database file is used to store parameter information. Several 

database files including a default file were included in the siberia_parameters.sdb 

database. From this database, the default file was selected and edited to include the 

desired parameters. A new database file was created by selecting edit parameters, 

modifying the parameters, and saving the file within the database. This was 

beneficial for multiple runs using the same base parameters as when the sediment 

transport equation parameter calibration is taking place, or when only a few 

parameters were required to change. The parameters selected for the database file 

were that of the top layer, except the parameter β1. This parameter was the 

erodibility of the bottom layer. The top layers were included in the layer.model file. 

The parameters modified from default are in Table 3.4.

Control parameters to define the duration of the simulation, time period between 

outputs, erosion file output, time step, and modes for running the erosion, runoff, and 

sediment transport models. The time step was set sufficiently small (0.01 yr) so that 

erosion events could be captured. The output settings used in the siberia.setup file 

include having SIBERIA output elevation data at each output time in an .xyz format, 

the amount of sediment being transported, the elevation change (maximum erosion, 

maximum deposition, and average change in elevation), and the erosion loss in 

tons/hectare. Once the setup of the model was complete, SIBERIA was run by 

selecting “Prepare and Run SIBERIA”.

Once SIBERIA had finished running the output was viewed with the viewer program 

in the EAMS suite. Open in the File menu was selected to find the file labeled with 

the file name specified followed by the year (i.e. 700). Only two files can be opened 

at one time. The outputs selected in the siberia.setup file were viewed by selecting 

Statistics in the File menu. The statistics were reported as a minimum, maximum, 

and mean for the entire DTM (i.e. the minimum Z Change is the greatest erosion 

depth found at any one point on the DTM).

Graphs of the DTM and corresponding changes were viewed by selecting Draw in 

the Surface menu. The graphs shown in this study were the Elevation and Layer_No 

selections. Modifications to the viewer graphs were made by right clicking and using 

the viewing, lighting, and rendering menus. Position was changed with the number 

pad on a computer keyboard. Vertical exaggeration was useful for smaller elevation 

changes. If desired another program can be used for graphing by using the .xyz file 

that contains the coordinates of each point on the grid at the specified time.

H-2
APPENDIX I

A Sample layer.model File Used in SIBERIA
I-0
I-1

Appendix I: A Sample layer.model File Used in SIBERIA

sa_vrr_gj_layer

SIBERIA EXTERNAL

This is a siberia models input file. The first line of the file

above is fixed and should not be edited. The next three lines (i.e these lines

are for file description data and can be modified by the user

#

#

=================================================================================

===

==

# This file contains the extnded models information for SIBERIA

# (including regional variations in runoff, erosion and tectonics, layering)

#

=================================================================================

===

==

#

# The format of this file is as a series of example commands giving the

# general format of the commands. The commands can be in any order and there

# are no limits on the number of commands in the file. Each command is a

# single line of information.

#

# We suggest that you copy the appropriate command line examples and edit copies

# so that you always have copies of the original correct form of the command.

#

# NB 1. All commands are independent of each other so that runoff and erosion

# commands can be entered independently. However, the runoff commands are

dependent

# on each other with subsequent runoff commands working on the result of

previous

# runoff commands if the regions over which they apply are overlapping. The same

# is true of the erosion commands, tectonics, layers, etc.

#

# In particular, if you have regions

# of different material you may change the runoff for that region and not the

erosion

# model if that is appropriate (and vice versa) or you may change both if

# appropriate, or you may change one 'absolute' and one 'relative' if desired.

#

# 2. These commands assume that the erosion model and the runoff model are

initially

# everywhere uniform and determined by the b1, m1, n1, b3, n3 parameters

specified in

# the RST2 file.

#

# Compatible with SIBERIA V8.29

# =============================

# UPDATE HISTORY

# --------------

# 1/12/2003 Additions to for region based uplift and aggradation (V8.20)
I-2

# 7/ 4/2004 Additions to support new LAYERS module (V8.25)

# 11/2004 Further modifications for LAYERS module (V8.28)

#

#

=================================================================================

===

==

# EROSION commands

#

=================================================================================

===

==

#

# These commands are read in SIBERIA when the parameter ModeErode=3 and

# the EROSION file parameter=-1 is set to this file.

#

# The EROSION commands come in two forms:

# --------------------------------------

# GENERAL EROSION MODEL

# ---------------------

# The most general form of the erosion commands from left to right is

# - 'EROSION' indicating this is an erosion command (starts in column 1)

# - one of either 'ABSOLUTE' or 'RELATIVE' indicating

# ABSOLUTE: the erosion parameters are as given

# RELATIVE: the erosion parameters given are multipied with

# the erosion parameters at that point previously

# given .... ie. this changes the parameters by a relative amount

# - the parameters b1, m1, n1. For RELATIVE these are interpretted as

multipliers

# - the region file for applying those parameters (it must inside '')

#

# The command below replaces the erosion model over the region defined by

test1.rgn

# with an erosion model with b1(new)=0.01, m1(new)=0.6, n1(new)=0.7

#

#EROSION ABSOLUTE 0.01 0.6 0.7 'control\test1.rgn'

#

# The command below replaces the erosion model over the region defined by

test2.rgn

# with an erosion model with b1(new)=0.05, m1(new)=0.2, n1(new)=0.3

# NB. Because this command after the test1.rgn command where

# test1.rgn and test2.rgn overlap test2.rgn overwrites test1.rgn

#

#EROSION ABSOLUTE 0.05 0.2 0.3 'control\test2.rgn'

#

# The command below modifies the erosion model over the region defined by

test3.rgn

# with an erosion model with b1(new)=b1(old)*0.1

# m1(new)=m1(old)*0.7

# n1(new)=n1(old)*1.2

# NB. Because this command after the test1.rgn and test2.rgn commands where

# test1.rgn, test2.rgn and test3.rgn overlap test3.rgn overwrites the other

files
I-3

#

#EROSION RELATIVE 0.1 0.7 1.2 'control\test.rgn'

#

#

# ERODIBILITY ONLY EROSION MODEL

# ------------------------------

#

# A more specific form of the erosion command only modifies the erodibility

# and is of the form

# - 'ERODIBILITY' indicating this is an erosion command (starts in column 1)

# - one of either 'ABSOLUTE' or 'RELATIVE' indicating

# ABSOLUTE: the erosion parameters are as given

# RELATIVE: the erosion parameters given are multipied with

# the erosion parameters at that point previously

# given .... ie. this changes the parameters by a relative amount

# - the parameter b1. For RELATIVE these are interpretted as multipliers

# - the region file for applying those parameters (it must inside '')

#

# The command below modifies the erosion model over the region defined by

test3.rgn

# with an erosion model with b1(new)=b1(old)*0.1

#

#ERODIBILITY RELATIVE 0.1 'control\test.rgn'

#

#

#

#

=================================================================================

===

==

# RUNOFF commands

#

=================================================================================

===

==

#

# These commands are read in SIBERIA when the parameter ModeRunoff=3 and

# the RUNOFF file parameter=-2 is set to this file.

#

# The general form of the erosion commands from left to right is

# - 'RUNOFF' indicating this is an runoff command (starts in column 1)

# - one of either 'ABSOLUTE' or 'RELATIVE' indicating

# ABSOLUTE: the runoff parameters are as given

# RELATIVE: the runoff parameters given are multipied with

# the runoff parameters at that point previously

# given .... ie. this changes the parameters by a relative amount

# - the parameters b3, m3. For RELATIVE these are interpretted as multipliers

# - the region file for applying those parameters (it must inside '')

#

#

# The command below replaces the runoff model over the region defined by test0.rgn

# with a runoff model with b3(new)=1.0, m3(new)=0.8

#
I-4

#RUNOFF ABSOLUTE 1.0 1.0 'test1.rgn'

#

#

# The command below updates the runoff model over the region defined by

test1_2.rgn

# with a runoff model with b3(new)=b3(old)*2.0, m3(new)=m3(old)*0.9

#

#RUNOFF RELATIVE 2.0 0.9 'control\test1_2.rgn'

#

#

# The command below updates the runoff model over the region defined by test0.rgn

# with a runoff model with b3(new)=b3(old)*0.5, m3(new)=m3(old)*1.0

#

#RUNOFF RELATIVE 0.5 1.0 'control\test.rgn'

#

#

#

=================================================================================

===

==

# CHANNEL commands

#

=================================================================================

===

==

#

#

# These commands are read in SIBERIA when the parameter ModeChannel=3 and

# the CHANNEL file parameter=-6 is set to this file.

#

# The general form of the erosion commands from left to right is

# - 'CHANNEL' indicating this is an runoff command (starts in column 1)

# - one of either 'ABSOLUTE' or 'RELATIVE' indicating

# ABSOLUTE: the runoff parameters are as given

# RELATIVE: the runoff parameters given are multipied with

# the runoff parameters at that point previously

# given .... ie. this changes the parameters by a relative amount

# - the parameters b5, m5, n5. For RELATIVE these are interpretted as

multipliers

# - the region file for applying those parameters (it must inside '')

#

#CHANNEL RELATIVE 0.5 1.0 1.0 'control\test.rgn'

#

#

#

=================================================================================

===

==

# UPLIFT commands

#

=================================================================================

===

==
I-5

#

#

# These commands are read in SIBERIA when the parameter ModeChannel=4 and

# the UPLIFT file parameter=-3 is set to this file.

#

# The general form of the erosion commands from left to right is

# - 'UPLIFT' indicating this is an runoff command (starts in column 1)

# - one of either 'ABSOLUTE' or 'RELATIVE' indicating

# ABSOLUTE: the uplift parameters are as given

# RELATIVE: this mode is ignored in the current version (NB. RELATIVE or

# ABSOLUTE must still be input).

# - one parameter: the uplift rate/timestep.

# - the region file for applying this parameters (it must inside '')

#

#UPLIFT ABSOLUTE 0.5 1.0 1.0 'control\test.rgn'

#

#

#

=================================================================================

===

==

# KNOWN AGGRADATION/DEGRADATION rate commands

#

=================================================================================

===

==

#

#

# These commands are read in SIBERIA when the parameter ModeChannel=4 and

# the UPLIFT file parameter=-3 is set to this file.

#

# The general form of the erosion commands from left to right is

# - 'UPLIFT' indicating this is an runoff command (starts in column 1)

# - one parameter: the known aggradation/timestep. Note is a positive number is

input

# this is interpretted as aggradation, whereas if a negative number if input

this

# is intrepretted as a degradation

# - the region file for applying this parameters (it must inside '')

#

#AGGRADATION 0.5 'control\test.rgn'

#

#

#

#

#

#

#

#

=================================================================================

===

==

# LAYERS MODULE commands
I-6

#

=================================================================================

===

==

#

# Whenever a LAYERS file and ModeErode=4 is specified the file is read for all

# commands that start with LAYERS.

#

# ALL lines starting with other commands (e.g. RUNOFF, UPLIFT) are ignored. Note

# that RUNOFF and EROSION and ERODIBILITY commands conflict with LAYERS and errors

# may occur if ModeErode=3 or ModeRunoff=3 is set in addition to a LAYER file.

#

# LAYER commands can be divided into four kinds.

#

# - LAYER CONTROL. These commands allow the user to control the internal

# computational behaviour of the LAYER model (e.g. maximum thickness of

layers)

# - LAYER PARAMETERS. These commands provide information about the erosion/runoff

# model parameters that are to be used for subsequent LAYER commands (or

until

# they are superseded by a new LAYER parameter command).

# - LAYER ELEVATION. These commands input the elevation properties of

# the layer being created. The properties of the LAYER being created are

those

# input by the most recent LAYER PARAMETER commands.

# - LAYER MASKING. These commands input information on the spatial extent of

# the LAYER currently being created. These commands allow you to create a

LAYER

# that is restricted in spatial extent so that it doesn't have to barrier the

# entire computational domain.

# - LAYER DETACHMENT. These commands input information of the detachment

limitation

# of the material in that layer.

#

#

# LAYER CONTROL COMMANDS

# ----------------------

#

# - the maximum thickness of a layer created by SIBERIA during deposition. This

does

# not preclude the user from inputting a thicker layer but all layers generated

by

# the computations will have a maximum thickness as below. NB thin layers can

# significantly increase the memory consumption of the code and this increase

# may be superlinear (i.e. halving the layer thickness may increase memory

# consumption by more than a factor of 2).

#

#LAYER THICKNESS 0.1

#

#

# LAYER PARAMETER COMMANDS

# ----------------------

#
I-7

# - the general format of these commands is as for the EROSION/RUNOFF models

# for region input at the top of this file, except that a region file is not

# input as part of the command line. For instance for EROSION parameters input

# is:

# - 'EROSION' indicating this is an erosion command (starts in column 1)

# - one of either 'ABSOLUTE' or 'RELATIVE' indicating

# ABSOLUTE: the erosion parameters are as given

# RELATIVE: the erosion parameters given are multipied with

# the erosion parameters at that point previously

# given .... ie. this changes the parameters by a relative amount

# (initially the parameters are those set in the parameters input

# at the start)

# DEFAULT: sets the parameters back to the default values (those

# input in the parameters input at the start). This can be handy

# for resetting parameters when you have input lots of layers

with

# RELATIVE parameters.

# - the parameters. For RELATIVE these are interpretted as multipliers

# on the last value for the parameters.

# - there are parameters for the layer detachment limitation model are grouped

# at the end of the layer section

#

#

# - Erosion model parameters 'b1,m1,n1'

#

#LAYER EROSION RELATIVE 0.1 0.2 0.3

#LAYER EROSION ABSOLUTE 1.0 2.0 3.0

#LAYER EROSION DEFAULT

#

# - Erodibility parameter 'b1'

#

#LAYER ERODIBILITY RELATIVE 0.1

#LAYER ERODIBILITY ABSOLUTE 0.3

#LAYER ERODIBILITY DEFAULT

#

#

# - Runoff model parameters 'b3,m3'

#

#LAYER RUNOFF RELATIVE 0.5 0.95

#LAYER RUNOFF ABSOLUTE 0.1 0.5

#LAYER RUNOFF DEFAULT

#

# - Maximum slope parameter 's0max'

#

#LAYER ANGLE_OF_REPOSE RELATIVE 0.5

#LAYER ANGLE_OF_REPOSE ABSOLUTE 0.2

#LAYER ANGLE_OF_REPOSE DEFAULT

#

# - Creep parameter 'dZ'

#

#LAYER CREEP RELATIVE 0.6

#LAYER CREEP ABSOLUTE 0.01

#LAYER CREEP DEFAULT
I-8

#

#

# LAYER ELEVATION COMMANDS

# ----------------------

#

# - the commands for input of the elevations for the layers. NB the input

elevations

# are for the base of the layer unless otherwise noted (i.e. the layer extends

# upwards from the elevations input.

#

# - a layer barriering the surface of thickness given. The top of the capping layer

# is the landform surface and the bottom of the capping is 'thickness' below

that

# surface

#

LAYER ERODIBILITY ABSOLUTE 2.10

LAYER CAPPING 2.590

LAYER ERODIBILITY ABSOLUTE 7.30

LAYER CAPPING 1.675

LAYER ERODIBILITY ABSOLUTE 1.84

LAYER CAPPING 1.065

LAYER ERODIBILITY ABSOLUTE 2.10

LAYER CAPPING 0.455

LAYER ERODIBILITY ABSOLUTE 0.002

LAYER CAPPING 0.305

#

# - a layer with base horizontal and with the layer's base at the elevation given

#LAYER Z 25.2

#

# - a layer that is a bilinear spline. the 1st 4 values are the coordinates of the

# four corners of the rectangular

# region (in node coordinates), and the 2nd four values are the elevations at

the

# four corners in the order SW, SE, NW, NE corners.

# NB. the spline extends over the

# whole domain and the corner coordinates are ONLY used to determine the

elevations

# of the interpolated/extrapolated surface not the spatial extent of the surface

# NB: BILINEAR_CLAMPED restricts the layer to the box specified.

#

#LAYER BILINEAR 1 20 1 30 10.0 20.0 22.0 35.0

#LAYER BILINEAR_CLAMPED 1 20 1 30 10.0 20.0 22.0 35.0

#

# - a layer that has as its base the elevations as read from the rst2 file,

# with the elevations offset by

# the specified value (i.e. a negative offset is a lower elevation). NB the

areal

# extent of the RST2 file must match the RST2 file of the landform DEM.

#

#LAYER DEM -2.1 'TEST.RST2'

#

#

# LAYER MASKING COMMANDS
I-9

# ----------------------

#

# - these commands specify over what part of the domain the layer will be created.

If a

# mask is input and active then the layer will be created for the region

specified

# by the mask and will not be created outside the mask. For all other cases the

# layer will barrier the entire region.

#

# - the mask is that part of the domain specified by the region file. The mask

# is automatically activated after input of the region file.

#

#LAYER REGION_MASK 'TEST.RGN'

#

# - the mask is that a rectangle defined by the coordinates. The cordinates

# are in the order LOWX,HIGHX,LOWY,HIGHY where the rectangle coordinates

# are (LOWX,LOWY) and (HIGHX,HIGHY). The mask

# is automatically activated after input of the region file.

#

#LAYER REGION_CLIP 0 10 5 35

#

# - Any mask that has been input can be inactivated (i.e. turned off). In the

event

# that the is needed again then it can activated by setting REGION_ACTIVE ON.

NB.

# This command does not delete the mask ... it only turns it off ... it can

always be

# turned back on again later (unless the mask is overwritten with another RGN

file in

# the meantime by a #LAYER REGION_FILE command).

#

#LAYER REGION_ACTIVE OFF

#

# - If a mask has been input from a region file then this activates it (i.e. turns

it

# on). If no region file has been input then the command is ignored.

#

#LAYER REGION_ACTIVE ON

#

#

# LAYER DETACHMENT MODEL COMMANDS

# -------------------------------

#

# - Relative Detachment Rate (Default is 1.0)

# To turn detachment limitation ON (once ON it cannot be turned off)

#

#LAYER DETACHMENT ON

#

# - Set the Relative detachment rate for that layer's material

#

#LAYER DETACHMENT RELATIVE 0.6

#LAYER DETACHMENT ABSOLUTE 0.01

#LAYER DETACHMENT DEFAULT
I-10
APPENDIX J

The siberia.setup File Used in SIBERIA
J-12
J-1

APPENDIX J: The siberia.setup File Used in SIBERIA

siberia

#

#

# ===================================================================|

# |

# SIBERIA LICENSE AGREEMENT |

# ------------------------- |

# |

# Please read the following licence information carefully. This |

# computer program ("SIBERIA") is licensed, not sold, to you for use|

# only under the terms of this license, and the copyright owner |

# reserves any rights not expressly granted to you. You own the |

# computer media on which SIBERIA is originally and subsequently |

# recorded or fixed, but the copyright owner retains ownership |

# of all copies of SIBERIA itself |

# |

# Unless otherwise stated this licence entitles you to |

# (a) copy this code onto a single computer, |

# (b) make backup copies of this software, |

# |

# You may not |

# (a) remove these license agreement, disclaimer, copyright, or |

# limitation of damages notices from this source code, |

# (b) distribute this software to others, |

# (c) rent,lease, resell, distribute, network, or create |

# derivative products works based upon this software, or |

# any part thereof. |

# (d) modify the software in this file without the written |

# permission of the copyright owner. |

# (e) disclose this source code and algorithms to |

# unlicensed users |

# |

# This Licence is effective until terminated. This Licence will |

# terminate automatically without notice from the copyright owner |

# If you fail to comply with any provision of this Licence. Upon |

# termination of this Licence you must destroy this software and |

# all copies thereof. You may terminate the Licence at any time |

# by destroying this software and any copies thereof. |

# |

#--------------------------------------------------------------------|

# |

# COPYRIGHT NOTICE |

# ---------------- |

# |

# The SIBERIA software is Copyright 1993-2004 by |

# |

# Professor Garry Raymond Willgoose, |

# Earth and Biosphere Institute |

# School of Geography |

# University of Leeds, UK, LS2 9JT |

# |
J-2

# SIBERIA and EAMS are distributed by: |

# |

# Telluric Research, |

# Scone, Australia |

# |

# g.r.willgoose@leeds.ac.uk, |

# |

# |

#--------------------------------------------------------------------|

# |

# DISCLAIMER |

# ---------- |

# |

# SIBERIA is provided 'as is' without warranty of any kind |

# either express or implied, including without limitation any |

# warranty with respect to its merchantability, or its fitness for |

# any particular purpose. The entire risk as to the quality and |

# performance of SIBERIA is with you. Should SIBERIA |

# prove defective, you (and not the copyright owner), assume the |

# entire cost of all necessary servicing, repair or correction. |

# |

# The copyright owner does not warrant that the functions contained |

# in SIBERIA will meet your requirements or that the operation |

# of SIBERIA will be uninterrrupted or error free or that defects |

# in SIBERIA will be corrected |

# |

#--------------------------------------------------------------------|

# |

# LIMITATION OF DAMAGES |

# --------------------- |

# |

# In no event will the copyright owner be liable (i) to you for any |

# incidental, consequential or indirect damages (including damages |

# for loss of business profits, business interruption, loss of |

# business information, and the like) arising out of the use of or |

# inability to use SIBERIA even if the copyright owner has been |

# advised of the possibility of such damages, or (ii) for any |

# claim by any other party. |

# |

# ====================================================================

#

#

# HOW TO USE THIS FILE

# ----------------------

#

# This file controls the operation of SIBERIA. Its name should always be

'siberia.setup'

# (all in lower case on Unix or Mac OSX machines) and it should be situated in

the

# directory in which SIBERIA is being run.

# If the file exists in that directory then SIBERIA reads it automatically.

# If the file does not exist then SIBERIA simply continues on without it,

choosing default
J-3

# values where necessary.

#

# To make this file easier to use all of the allowable commands are listed below.

The commands

# are the lines all in UPPER CASE while the comments and explanations are the

lines in lower

# case.

#

# If a line starts in column 1 with either of # or ! character then that line is

treated

# as a comment and is ignored by SIBERIA. To make a command active all you have

to do

# is to uncomment the appropriate line (i.e. remove the # or ! from the first

column).

# To inactivate it you simply add the # or ! to the first column again.

Explanations

# for the commands are provided immediately above the commands.

#

# There are a number of commands that turn some mode in the model off or on.

There are always

# three options for these modes. ON = (turn that mode on), OFF = (turn that mode

off),

# DEFAULT = (do whatever the code decides is best in the circumstances). If you

do not

# enable one these three options then the code chooses DEFAULT automatically.

NOTE: the

# default action may not always be the same as it may vary with size of the

problem being

# solved, whether SIBERIA detects that is being run of a multiprocessor machine,

etc, so if

# you absolutely must have some form of behaviour then specify it otherwise

SIBERIA may run

# differently on different machines

#

# FILE REVISION HISTORY

# -----------------------

# - updated for V8.28 5/ 4/2005 (GRW)

#

#

#

#

=================================================================================

===

==

# -- To echo whatever is output to the screen to a file called (in the example

command below

# it is 'junk.output') uncomment the line starting ECHO

# -- To NOT echo to a file uncomment the line starting NOECHO

# -- ECHO_INCR appends a unique number to the filename to ensure that it doesn't

overwrite

# the output file from previous runs of siberia

#
J-4

=================================================================================

===

==

#

#ECHO junk.output

#NOECHO

#ECHO_INCR siberia.output

#

ECHO_INCR siberia.output

#

#

=================================================================================

===

==

# -- To have the program halt at the end of the run without the window automatically

closing

# then uncomment the line PAUSE_AT_END ON.

# -- To have the window automatically close at the end of the run then uncomment the

line

# PAUSE_AT_END OFF

# -- To have the program do whatever its default behaviour is with the window at the

end

# of the run then uncomment line then uncomment PAUSE_AT_END DEFAULT.

#

=================================================================================

===

==

#

#PAUSE_AT_END ON

#PAUSE_AT_END OFF

#PAUSE_AT_END DEFAULT

#

PAUSE_AT_END OFF

#

#

=================================================================================

===

==

# -- To allow RST output files to be overwritten uncomment the line RST_OVERWRITE

ON.

# -- To stop RST output files from being overwritten uncomment the line

RST_OVERWRITE OFF

# -- To have the program do whatever its default behaviour (typically this is to NOT

# overwrite the RST files) uncomment RST_OVERWRITE DEFAULT.

#

=================================================================================

===

==

#

#RST_OVERWRITE ON

#RST_OVERWRITE OFF

RST_OVERWRITE DEFAULT

#
J-5

#

=================================================================================

===

==

# PARALLEL OPTIONS

# ----------------

# This option is to set the maximum no of threads that the parallel

implementation

# of SIBERIA can use. The code will use this number of threads and attempt to get

# that many number of processors from the computer. This option is ignored if

the

# standard serial version of code is being used. If this option is not used then

# the code grabs a default (typically small but > 1) number of processors. On

shared

# parallel supercomputers choosing a large number of threads may slow the

starting of

# the code until the requested number of processors become available.

#

=================================================================================

===

==

#

NO_THREADS 1

#

#

=================================================================================

===

==

# EAMS COMPATIBILITY OPTIONS

# --------------------------

# Output the elevation data in an xyz format (identical to the format read by EAMS)

# in addition to the output in the .rst2 files. This option is also useful in EAMS

# for output back to mine management and CAD (e.g. AutoCad) packages.

#

=================================================================================

===

==

#

XYZ_FILE

#

#

=================================================================================

===

==

# OUTPUT OF SUPPLEMENTARY CALCULATION DATA

# ----------------------------------------

# The following OUTPUT commands provide supplementary information to what is

# in the RST file. The data below are output in a .RSU file. A maximum of 10

# datsets may be output.

#

# There are two forms of the OUTPUT command

# OUTPUT : This outputs the specified data set into an RSU file which is

# a text column format used by all of the software in the EAMS
J-6

suite

# and which is easily readable into data analysis programs (e.g.

EXCEL

# Kaleidograph, SigmaPlot).

# OUTPUT_BIN : In addition to the RSU file this form also outputs the dataset

into

# a binary file (the filename is name.abbrev.bin where 'name' is

the

# same as the RST and RSU files, 'abbrev' is a self evident

# abbreviation for the dataset requested) that can be streamed

into

# visualisation packages like IDL, EXPLORER etc.

# The format is 2 4byte integers (the x and y dimensions of the

grid)

# followed by the data in 4byte floating point (by the x

dimension first).

# Note is you request more than one dataset to be OUTPUT_BIN

then each

# dataset requested goes into a seperate file with the

appropriate

# name.

#

=================================================================================

===

==

#

# the amount of sediment being transported (cubic metres/timestep/m width)

analytically

# derived from the transport equation.

#

OUTPUT SED_FLUX

#

#

# the potential and actual sediment transport (cubic metres/timestep/m width) as

determined by

# the transport-detachment limited transport model (i.e. ModeSolver=8).

# They may not match SED_FLUX exactly due to time discretisation error.

#

#OUTPUT SED_FLUX_POTENTIAL

#OUTPUT SED_FLUX_ACTUAL

#

#

# the amount of sediment removed/timestep in units of height at any pt in the grid

at the

# the requested time.

#

OUTPUT YIELD

#

# the average amount of sediment removed/timestep in units of height averaged over

the

# total catchment draining through that node.

#

OUTPUT AVEYIELD
J-7

#

# the change in elevation at a point from the start of the simulation (+ve increase

# in elevation -ve decrease in elevation).

#

OUTPUT ZCHANGE

#

# the change in elevation from the start of the simulation averaged over the

catchment

# draining through that point at that point in time (ie. the catchment area used for

# calculating the average elevation for the initial conditions is NOT the catchment

# draining through that point at the beginning, but rather that catchment at the

simulation

# time for output)

#

OUTPUT AVEZCHANGE

#

# the channel initiation function at that point

#

#OUTPUT GULLYPOT

#

# the log of the channel initiation function at that point

#

#OUTPUT LOGGULLYPOT

#

# the suggested steady state elevation for area-slope equilibrium based on the

# erosion parameters used in the simulation) NOT YET IMPLEMENTED.

#

#OUTPUT ZSUGGEST

#

# the change in elevations required to modify the existing elevations so that

# the elevations would comply with the area-slope equilibrium based on the erosion

# parameters used in the simulation. (NOT YET IMPLEMENTED)

#

#OUTPUT DZSUGGEST

#

# the erosion loss in weight units at a point (simply the elevation loss divided

# by the bulk density). This assumes that the units of height are metres and the

# units of length for the grid spacing are also metres.

#

OUTPUT TONNESHECTARE

#

# the erosion loss in weight units averaged over the catchment draining through

# at that point (simply the elevation loss divided

# by the bulk density). This assumes that the units of height are metres and the

# units of length for the grid spacing are also metres.

#

OUTPUT AVETONNESHECTARE

#

# the stability number for every point in the domain for the last timestep

#

#OUTPUT STABILITY

#

# the area-slope number for every point in the domain. It is calculated as
J-8

# area*slope^((m1*m3-1)/n1) and for a landform with optimal shape in equilibrium

# with tectonic uplift should be constant everywhere in the domain

#

#OUTPUT AREASLOPE

#

# the area-slope-elevation number for every point in the domain. It is calculated

as

# area*slope^((m1*m3-1)/n1)/Zave^(1/n1) where Zave is the average elevation of the

# catchment draining though that point. For a landform with optimal shape

# with erosion down to a flat plain this should be constant everywhere

#

#OUTPUT AREASLOPEELEVATION

#

# The Mean annual discharge used in the erosion model

#

OUTPUT DISCHARGE_MEANANNUAL

#

#

# SOILS MODEL OUTPUTS

# -------------------

# The outputs that follow can only be output when the soils model is turned ON.

#

#OUTPUT SOILMOISTURE

#

# - Bedrock properties can only be output for ModeSoils=2

#

#OUTPUT BEDROCK_Z

#OUTPUT BEDROCK_SLOPE

#OUTPUT BEDROCK_AREA

#OUTPUT BEDROCK_DIRECTIONS

#

#

#

# LAYERS MODEL OUTPUTS

# -------------------

# The outputs that follow can only be output when the layering model is turned ON.

#

#

# The B1 of the surface Layer (equivalent to OUTPUT LAYER_1_B1 except SURFACE_B1

will

# give the surface B1 even if the layers model is used)

OUTPUT SURFACE_B1

# The B1 of the flow

#OUTPUT FLOW_B1

# Number of layers at that node

OUTPUT LAYER_NO

# Layer properties for the top 5 layers

# ... note if the layer doesn't exist then zeros are output

# ... OUTPUT LAYER_1_B1 is equivalent to OUTPUT SURFACE_B1 and is provided to

display

# B1 when layers is not used (SURFACE_B1 doesn't need the layers model while

# LAYER_1_B1 does).

#OUTPUT LAYER_1_B1
J-9

#OUTPUT LAYER_2_B1

#OUTPUT LAYER_3_B1

#OUTPUT LAYER_4_B1

#OUTPUT LAYER_5_B1

#

#OUTPUT LAYER_1_Z

#OUTPUT LAYER_2_Z

#OUTPUT LAYER_3_Z

#OUTPUT LAYER_4_Z

#OUTPUT LAYER_5_Z

#

#

#

# The Detachment-Limitation Model

# -------------------------------

# This model is only available in combination with the LAYERS module

# so the output commands are a subset of the LAYERS commands (and LAYERS

# model has to be activated to enable the detachment model)

#

# The detachment rate for the material in the flow

#OUTPUT LAYER_FLOW_DETACHMENT

#

# The detachment rate of the material for the various layers (note LAYER=1

# is equivalent to the detachment rate for the surface)

#OUTPUT LAYER_1_DETACHMENT

#OUTPUT LAYER_2_DETACHMENT

#OUTPUT LAYER_3_DETACHMENT

#OUTPUT LAYER_4_DETACHMENT

#OUTPUT LAYER_5_DETACHMENT

#

#

#

#

# INTERNAL MODEL STATES

# ---------------------

# These commands provide diagnostic output of the internal model operations. They

# are primarily available to aid debugging of the code operation and provided here

# as a memory aid for the developer.

#

# States that control the stability/mass balance of the solver

#

# Elevation changes of predictor

#OUTPUT PREDICTOR_SED

#

# Elevation changes of corrector

#OUTPUT CORRECTOR_SED

#

# Difference between elevation changes of predictor and corrector

#OUTPUT PREDCORRECT_SED_DIFF

#

# Relative difference between elevation changes of predictor and corrector

#OUTPUT PREDCORRECT_SED_RATIO

#
J-10

#

# The weights generated by the Dinfinity algorithm

#

#OUTPUT DINFWEIGHTS

#

# A domain mask 0=outside computational domain, 1=inside computational domain

#OUTPUT DOMAIN






NUREG/CR

-7200 Influence of Coupling Erosion and Hydrology on the Long-Term 

Performance of Engineered Surface Barriers