final 2002-30 research - minnesota department of...
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Evaluation of Water Flow Through Pavement
Systems
2002-30 Final Report
Res
earc
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Technical Report Documentation Page 1. Report No. 2. 3. Recipients Accession No. MN/RC - 2002-30 4. Title and Subtitle 5. Report Date
June 2002 6.
EVALUATION OF WATER FLOW THROUGH PAVEMENT SYSTEMS 7. Author(s) 8. Performing Organization Report No. Paola Ariza and Bjorn Birgisson 9. Performing Organization Name and Address 10. Project/Task/Work Unit No.
11. Contract (C) or Grant (G) No.
University of Florida Civil and Coastal Engineering Department P.O. Box 116580 Gainesville, FL 32611-6580 (C) 79080
12. Sponsoring Organization Name and Address 13. Type of Report and Period Covered
Final Report 14. Sponsoring Agency Code
Minnesota Department of Transportation 395 John Ireland Boulevard Mail Stop 330 St. Paul, Minnesota 55155 15. Supplementary Notes http:// www.lrrb.org/PDF/200230.pdf 16. Abstract (Limit: 200 words) Most research on the effects of moisture in pavement has been based on conditions of total saturation with loss of pavement strength calculated using saturated flow assumptions. Yet roadbeds reach full saturation only when positive total heads are present (e.g., surface ponding, etc.) and distributed in such a manner that saturation of the pavement system is reached. Most dense graded pavement base layers tend to be unsaturated most of the time. The flow of water through unsaturated soil (unsaturated flow) is primarily a function of matric suction and gravity. Matric suction varies with saturation and changes over the course of a rainfall event. The authors propose a first step toward a comprehensive approach to drainage and pavement design that integrates the true effects of moisture on pavement moduli and mechanistic-empirical pavement design. The authors used SEEP/W and DRIP software to analyze data collected at the Minnesota Road Research project (Mn/ROAD Cell 33, Cell 34, and Cell 35). The SEEP/W software modeled unsaturated flow under transient conditions through layered systems under complex boundary conditions and material characterizations. Results establish that SEEP/W is a valuable tool for modeling unsaturated flow that can predict results comparable to field studies. The time to drain calculated based on unsaturated flow theory will generally be longer than that evaluated under saturated flow assumptions. The study also looked at the edge drains and under drains and found that under drains alone did not significantly improve drainage, but collector pipes or edge drains used in combination with under drains are very effective in reducing the amount of moisture in the soil.
17. Document Analysis/Descriptors 18. Availability Statement pavements drainage finite elements soil water characteristics curve
hydraulic conductivity curveunsaturated flow edge drains under drains
No restrictions. Document available from: National Technical Information Services, Springfield, Virginia 22161
19. Security Class (this report) 20. Security Class (this page) 21. No. of Pages 22. Price Unclassified Unclassified 166
EVALUATION OF WATER FLOW THROUGH PAVEMENT SYSTEMS
Final Report
Prepared by
Paola Ariza, Bjorn Birgisson, Ph.D., P.E.
UNIVERSITY OF FLORIDA Civil and Coastal Engineering Department
P.O. Box 116580 Gainesville, FL 32611-6580
June 2002
Published by:
Minnesota Department of Transportation Office of Materials & Road Research
1400 Gervais Avenue MS 645 Maplewood, MN 55109
This report represents the results of research conducted by the authors and does not necessarily represent the views or policy of the Minnesota Department of Transportation. This report does not contain a standard or specified technique. The authors and the Minnesota Department of Transportation and/or Center for Transportation Studies do not endorse products or manufacturers. Trade or manufacturers’ names appear herein solely because they are consid-ered essential to this report.
TABLE OF CONTENTS
Page CHAPTER 1 INTRODUCTION.......................................................................................... 1 1.1 Objectives ............................................................................................... 2 1.2 Scope of Report....................................................................................... 3 CHAPTER 2 LITERATURE REVIEW............................................................................... 4 2.1 Current State-of-the-Practice .................................................................. 4 2.1.1 Effects of drainage on pavement design life............................... 5 2.1.2 Summary of current practice....................................................... 7 2.2 Positive Drainage Systems...................................................................... 8 2.2.1 Open graded base course ............................................................ 8 2.2.2 Edge drains ................................................................................. 8 2.2.3 Use of geotextiles for drainage improvement............................. 9 2.3 Unsaturated Flow Through Pavements................................................... 9 2.3.1 Soil water characteristic curves ................................................ 11 2.3.2 Hydraulic conductivity models ................................................. 20 2.3.3 Effects of layering on pavement drainage ................................ 22 CHAPTER 3 RESEARCH METHODOLOGY ................................................................. 25 3.1 Selection of Analysis Tools .................................................................. 25 3.1.1 SEEP/W .................................................................................... 26 3.1.2 DRIP ......................................................................................... 26 3.2 Materials and Pavement Sections ......................................................... 28 3.2.1 Pavement sections..................................................................... 28 3.2.2 Materials ................................................................................... 29 CHAPTER 4 EVALUATION OF SEEP/W FOR MODELING UNSATURATED FLOW. . . . 35 4.1 Example 1 ............................................................................................. 33 4.2 Example 2 ............................................................................................. 39 4.3 Example 3 ............................................................................................. 44 4.4 Summary ............................................................................................... 52 CHAPTER 5 VERIFICATION OF RESULTS TO FIELD RESULTS FOR CELLS 33, 34, 35......................................................................................... 54 5.1 Pavement System Description .............................................................. 54 5.2 Finite Element Model ........................................................................... 54 5.2.1 Hot mix asphalt layer ................................................................ 54 5.2.2 Base course ............................................................................... 56 5.2.3 Subgrade soil............................................................................. 56 5.2.4 Initial and boundary conditions ................................................ 57 5.2.5 Finite element model analysis................................................... 58 5.2.6 Measured volumetric water contents ........................................ 59
5.3 Materials Characterization Adjustment ................................................ 61 5.3.1 Initial calibration results ........................................................... 64 5.3.2 Second calibration results ......................................................... 64 5.3.3 Final matching of predicted and measured volumetric water contents ........................................................................... 76 5.4 Cell 34 ................................................................................................... 79 5.4.1 Calibration of results at locations 101 and 102......................... 82 5.4.2 Calibration to location 103 ....................................................... 82 5.5 Cell 35 ................................................................................................... 85 5.6 Summary ............................................................................................... 90 CHAPTER 6 PARAMETRIC STUDY.............................................................................. 91 6.1 Initial Slope of the Base Material Soil Water Characteristic Curve..... 91 6.2 Air Entry Value of Base Material ......................................................... 94 6.3 Effects of Ksat of Mn/DOT Class 6 Special Crushed Granite Base Material ........................................................................................ 96 6.4 Air Entry Value of Subgrade Material.................................................. 98 6.5 Ksat at Subgrade Material ..................................................................... 98 6.6 Effects of the Type of Base Material .................................................. 100 6.7 Infiltration Effects .............................................................................. 105 6.8 Water Table Influence......................................................................... 106 6.9 Summary ............................................................................................. 108 CHAPTER 7 EFFECT OF EDGE and UNDER DRAINS ON WATER FLOW THROUGH FLEXIBLE PAVEMENTS.................................................... 110 7.1 Description of Case 1: Under Drain ................................................... 111 7.2 Description of Case 2: Under Drains With Collector Pipes ............... 114 7.3 Description of Case 3: Edge Drains.................................................... 116 7.4 Description of Case 4: Combination of Edge and Under Drains........ 117 7.5 Drainage Systems Comparison ........................................................... 117 CHAPTER 8 SUMMARY, CONCLUSIONS, and RECOMMENDATIONS ................ 119 LIST OF REFERENCES…………………………………………………………………….122 APPENDIX A EVALUATION OF TIME TO DRAIN CALCULATIONS FOR PAVEMENTS…………………………………………………………….A-1 APPENDIX B DETERMINATION OF AIR ENTRY VALUE FOR CLASS 6 SPECIAL………………………………………………………………….B-1
List of Tables Page
Table 2.1 Classification of 50% of Drainage ................................................................. 6 Table 2.2 Recommended m Values for Modifying Structural Layer Coefficients of Untreated Base and Subbase Materials in Flexible Pavements ................. 7 Table 2.3 Soil Water Characteristic Models – Main Features, Advantages, and Disadvantages............................................................................................... 18 Table 2.4 Hydraulic Conductivity Models – Main Features, Advantages, and Disadvantages............................................................................................... 23 Table 3.1 Asphalt Layer Description............................................................................ 29 Table 4.1 Soil Hydraulic Parameters............................................................................ 34 Table 4.2 Maximum Difference Between Predicted and Measured Water Table Results in Figures 4.5 – 4.8 .......................................................................... 39 Table 5.1 Cell 33 – Calibration for Base Layer............................................................ 79 Table 5.2 Cell 33 – Calibration for Subgrade Soil ....................................................... 79 Table 5.3 Summary of SEEP/W Runs Performed to Adjust Predicted Volumetric Moisture Contents to TDR Measured Values at Cell 33.............................. 80 Table 5.4 Cell 34 – Calibration for Base Layer............................................................ 86 Table 5.5 Summary of Runs to Calibrate Cell 34 ........................................................ 86 Table 5.6 Cell 35 – Calibration for Base Layer............................................................ 89 Table 5.7 Summary of Runs to Calibrate Cell 35 ........................................................ 89 Table 6.1 Effects of the Initial Slope of the Base Material Soil Water Characteristic Curve on Maximum Predicted Volumetric Moisture Content ..................... 94 Table 6.2 Effects of Air Entry Value of Mn/DOT Class 6 Special Crushed Granite Base Material on Maximum Predicted Volumetric Moisture Content ........ 96 Table 6.3 Effects of Ksat of Mn/DOT Class 6 Special Crushed Granite Base Material on Maximum Predicted Volumetric Moisture Content ............................... 98
Table 6.4 Effects of Air Entry Value of R-12 Silty Clay Subgrade Soil on Maximum Predicted Volumetric Moisture Content ...................................................... 99 Table 6.5 Effects of Ksat of R-12 Silty Clay Subgrade Soil on Maximum Predicted Volumetric Moisture Content..................................................................... 101 Table 6.6 Maximum Difference Between Saturated Volumetric Water Content and Predicted Volumetric Water Content for Class 3 Special, Class 4 Special, Class 5 Special, and Class 6 Special Mn/DOT Granular Base Material.... 105 Table 6.7 Effects of Infiltration on the Maximum Predicted Volumetric Moisture Content at TDR Location 101 .................................................................... 106 Table 6.8 Water Table Positions – Effects Summary................................................. 108 Table 6.9 Summary of Evaluation of Effects of Unsaturated Soil Hydraulic Proper- ties and SEEP/W Input Parameters on the Sensitivity of Predicted Volu- metric Moisture Content at TDR Location 101.......................................... 109
List of Figures Page
Figure 2.1 Typical Soil Water Characteristic Curve ..................................................... 12 Figure 2.2 Typical Values for the Brooks and Corey Model for Water Retention........ 14 Figure 2.3 Typical Values for the Van Genuchten Model for Water Retention............ 15 Figure 2.4 Hysteresis Effects – Main Drainage and Wetting Curves............................ 17 Figure 2.5 Variation of the Air-Water Interface Due to Raindrop Effect...................... 17 Figure 3.1 Thickness of Base and Hot Mix Asphalt Layers for Mn/ROAD Cells 33-35. . ............................................................................................... 28 Figure 3.2 Pavement Geometry and Dimensions .......................................................... 29 Figure 3.3 Grain Size Distribution for Mn/DOT Class 6 Special.................................. 30 Figure 3.4 Soil Water Characteristic Curve – Base Material ........................................ 30 Figure 3.5 Hydraulic Conductivity Curve – Base Material ........................................... 31 Figure 3.6 Soil Water Characteristic Curve – Subgrade Material ................................. 32 Figure 3.7 Hydraulic Conductivity Curve – Subgrade Material.................................... 32 Figure 4.1 Example 1 – Geometry and Boundary Conditions....................................... 34 Figure 4.2 Soil Water Characteristic Curve for Example 1........................................... 35 Figure 4.3 Hydraulic Conductivity Curve for Example 1 ............................................. 35 Figure 4.4 Example 1 – Finite Element Model.............................................................. 36 Figure 4.5 Comparison Between Measured and Predicted Water Table at 2 Hours ..... 37 Figure 4.6 Comparison Between Measured and Predicted Water Table at 3 Hours ..... 37 Figure 4.7 Comparison Between Measured and Predicted Water Table at 4 Hours ..... 38 Figure 4.8 Comparison Between Measured and Predicted Water Table at 8 Hours ..... 38 Figure 4.9 Example 2 – Geometry and Boundary Conditions....................................... 40
Figure 4.10 Soil Water Characteristic Curve for Example 2........................................... 40 Figure 4.11 Hydraulic Conductivity Curve for Example 2 ............................................. 41 Figure 4.12 Example 2 – Finite Element Model.............................................................. 42 Figure 4.13 Comparison Between Measured and Predicted Volumetric Water Content at 1.5 Hours for Example 2 .......................................................................... 42 Figure 4.14 Comparison Between Measured and Predicted Volumetric Water Content at 3 Hours for Example 2 ............................................................................. 43 Figure 4.15 Comparison Between Measured and Predicted Volumetric Water Content at 4.5 Hours for Example 2 .......................................................................... 43 Figure 4.16 Comparison Between Measured and Predicted Volumetric Water Content at 6 Hours for Example 2 ............................................................................. 44 Figure 4.17 Example 3 – Geometry and Boundary Conditions....................................... 45 Figure 4.18 Soil Water Characteristic Curve for Base & Subbase for Example 3 .......... 46 Figure 4.19 Hydraulic Conductivity Curve for Base Material in Example 3 .................. 46 Figure 4.20 Hydraulic Conductivity Curve for Subbase Material in Example 3 ............ 47 Figure 4.21 Example 3 – Finite Element Model.............................................................. 47 Figure 4.22 Comparison Between Measured and Predicted Volumetric Water Content in Base Material at 1.5 Hours....................................................................... 48 Figure 4.23 Comparison Between Measured and Predicted Volumetric Water Content in Base Material at 3 Hours.......................................................................... 48 Figure 4.24 Comparison Between Measured and Predicted Volumetric Water Content in Base Material at 4.5 Hours....................................................................... 49 Figure 4.25 Comparison Between Measured and Predicted Volumetric Water Content in Base Material at 6 Hours.......................................................................... 49 Figure 4.26 Comparison Between Measured and Predicted Volumetric Water Content in Subbase Material at 1.5 Hours ................................................................. 50
Figure 4.27 Comparison Between Measured and Predicted Volumetric Water Content in Subbase Material at 3 Hours .................................................................... 50 Figure 4.28 Comparison Between Measured and Predicted Volumetric Water Content in Subbase Material at 4.5 Hours ................................................................. 51 Figure 4.29 Comparison Between Measured and Predicted Volumetric Water Content in Subbase Material at 6 Hours .................................................................... 51 Figure 4.30 Comparison of Measured Volumetric Water Content in Base Material at 6 Hours for Examples 2 and 3 .................................................................. 52 Figure 4.31 Comparison of Predicted Volumetric Water Content in Base Material at 6 Hours for Examples 2 and 3 .................................................................. 53 Figure 5.1 Layer Thicknesses for Mn/ROAD Cells 33, 34, and 35 .............................. 55 Figure 5.2 Pavement Geometry and Dimensions for Cells 33, 34, and 35.................... 55 Figure 5.3 Section of the Finite Element Model Used to Represent Cells 33, 34, and 35. . ................................................................................................. 56 Figure 5.4 Finite Element Model Used to Represent Cells 33, 34, and 35 ................... 57 Figure 5.5 Precipitation Events for Cells 33, 34, and 35............................................... 59 Figure 5.6 TDR Installation at Mn/DOT Cells 33, 34, and 35 ...................................... 60 Figure 5.7 TDR Location Within Finite Element Model for Cells 33, 34, and 35........ 60 Figure 5.8 Measured Data for Different TDR Locations at Cell 33 .............................. 61 Figure 5.9 Measured Data for Different TDR Locations at Cell 34 .............................. 62 Figure 5.10 Measured Data for Different TDR Locations at Cell 35 .............................. 62 Figure 5.11 Volumetric Water Content at Cell 33 – Location 101.................................. 64 Figure 5.12 Volumetric Water Content at Cell 33 – Location 102.................................. 65 Figure 5.13 Volumetric Water Content at Cell 33 – Location 103.................................. 65 Figure 5.14 Soil Water Characteristic Curve (Air Entry – 3 kPa) – Base Material ........ 66 Figure 5.15 Estimated Hydraulic Conductivity Curve – Base Material .......................... 67
Figure 5.16 Final Soil Water Characteristic Curve – Base Material ............................... 67 Figure 5.17 Estimated Hydraulic Conductivity Curve – Base Material .......................... 68 Figure 5.18 Volumetric Water Content at Cell 33 – Location 101.................................. 69 Figure 5.19 Volumetric Water Content at Cell 33 – Location 102.................................. 69 Figure 5.20 Volumetric Water Content at Cell 33 – Location 103.................................. 70 Figure 5.21 Modified Hydraulic Conductivity Curve: 10 Times Ksat - Subgrade Material ........................................................................................ 70 Figure 5.22 Volumetric Water Content at Cell 33 – Location 101.................................. 71 Figure 5.23 Volumetric Water Content at Cell 33 – Location 102.................................. 71 Figure 5.24 Volumetric Water Content at Cell 33 – Location 103.................................. 72 Figure 5.25 Final Hydraulic Conductivity Curve: Ksat = 2.7535E-06 m/s – Subgrade Material. . . .................................................................................................. 72 Figure 5.26 Volumetric Water Content at Cell 33 – Location 101.................................. 73 Figure 5.27 Volumetric Water Content at Cell 33 – Location 102.................................. 74 Figure 5.28 Volumetric Water Content at Cell 33 – Location 103.................................. 74 Figure 5.29 Volumetric Water Content at Cell 33 – Location 101.................................. 75 Figure 5.30 Volumetric Water Content at Cell 33 – Location 102.................................. 75 Figure 5.31 Volumetric Water Content at Cell 33 – Location 103.................................. 76 Figure 5.32 Final Soil Water Characteristic Curve for Location 102 – Base Material ... 77 Figure 5.33 Volumetric Water Content at Cell 33 – Location 102.................................. 77 Figure 5.34 Final Soil Water Characteristic Curve for Location 103 – Base Material ... 78 Figure 5.35 Volumetric Water Content at Cell 33 – Location 103.................................. 78 Figure 5.36 Volumetric Water Content at Cell 34 – Location 101.................................. 81
Figure 5.37 Volumetric Water Content at Cell 34 – Location 102.................................. 81 Figure 5.38 Volumetric Water Content at Cell 34 – Location 103.................................. 82 Figure 5.39 Final Soil Water Characteristic Curve for Locations 101 and 102 at Cell 34 – Base Material ............................................................................ 83 Figure 5.40 Volumetric Water Content at Cell 34 – Location 101.................................. 83 Figure 5.41 Volumetric Water Content at Cell 34 – Location 102.................................. 84 Figure 5.42 Final Soil Water Characteristic Curve for Location 203 Cell 34 – Base Material. . . .................................................................................................. 84 Figure 5.43 Volumetric Water Content at Cell 34 – Location 103.................................. 85 Figure 5.44 Volumetric Water Content at Cell 35 – Location 101.................................. 87 Figure 5.45 Volumetric Water Content at Cell 35 – Location 103.................................. 87 Figure 5.46 Final Soil Water Characteristic Curve for Location 102 Cell 35 – Base Material. . . . ................................................................................................. 88 Figure 5.47 Volumetric Water Content at Cell 35 – Location 102.................................. 88 Figure 6.1 Soil Water Characteristic Curves for Initial Slope Cases ............................ 92 Figure 6.2 Hydraulic Conductivity Curves for Initial Slope Cases ............................... 93 Figure 6.3 Results for Initial Slope Cases ..................................................................... 93 Figure 6.4 Base Soil Water Characteristic Curves for Air Entry Value Cases.............. 95 Figure 6.5 Results for Air Entry Value Cases at Base Layer ........................................ 95 Figure 6.6 Hydraulic Conductivity Curves for Ksat Cases at Base Material ................. 97 Figure 6.7 Results for Ksat Cases at Base Layer............................................................ 97 Figure 6.8 Results for Air Entry Values at Subgrade Layer.......................................... 99 Figure 6.9 Hydraulic Conductivity Curves for Ksat Cases at Subgrade Material........ 100 Figure 6.10 Results for Ksat Cases at Subgrade Layer .................................................. 101
Figure 6.11 Soil Water Characteristic Curves for Mn/DOT Aggregate Base Material.... 102 Figure 6.12 Soil Water Characteristic Curves (Air Entry = 3 kPa) for Base Material ..... 103 Figure 6.13 Estimated Hydraulic Conductivity Curves for Base Material....................... 103 Figure 6.14 Results for Different Types of Base Materials.............................................. 104 Figure 6.15 Results for Different Rain Events ................................................................. 106 Figure 6.16 Results for Different Water Table Positions ................................................. 107 Figure 7.1 Under Drain Location for Case 1 in the Pavement System........................... 111 Figure 7.2 Soil Water Characteristic Curve for Under Drain Material .......................... 112 Figure 7.3 Estimated Hydraulic Conductivity Curve for Under Drain Material ............ 113 Figure 7.4 Finite Element Model for Case 1 .................................................................. 114 Figure 7.5 Under Drain and Collector Pipes Location for Case 2 in the Pavement System .......................................................................................... 115 Figure 7.6 Finite Element Model for Case 2 .................................................................. 115 Figure 7.7 Edge Drain Location for Case 3 in the Pavement System ............................ 116 Figure 7.8 Finite Element Model for Case 3 .................................................................. 116 Figure 7.9 Finite Element Model for Case 4 .................................................................. 117 Figure 7.10 Results Comparison for Drainage Systems ................................................... 118
EXECUTIVE SUMMARY Water in the pavement system can lead to moisture damage, modulus reduction, and loss of
strength. In the past, the approach taken by state agencies has focused on preventing water from
entering the pavement, providing adequate drainage to remove it quickly, or building the pave-
ment strong enough to resist the combined effect of vehicle loads and water, thus presumably
reducing the detrimental effects of water on pavements. The drainage design criteria used in the
past have been based on the assumption that both the flow of water through pavements and the
drainage of pavement layers can be represented with saturated flow assumptions. However, full
saturation of pavement systems can occur only under very specific circumstances, when positive
total heads are present (e.g., surface ponding, etc.) and distributed in such a manner that
saturation of the pavement system is reached. In the absence of positive total heads, the
pavement system will remain unsaturated. When rain starts following a dry period, the system is
usually in an unsaturated state, and may remain in this condition even at the end of the rainfall.
The amount of water that can flow through the soil is primarily a function of matric suction and
gravity forces (7). For a given soil with a given gradation, the permeability is controlled by the
matric suction, which in turn is affected by the degree of saturation. A degree of saturation of 80
percent may result in heightened suction, and a resulting permeability of only half its saturated
value. Hence, the models that use only fully saturated approaches are not adequate for
representing the flow of water through pavements, and thus pavement drainage. Finally, recent
studies by Minnesota Road Research Project (Mn/ROAD) pavement researchers (8, 9) have
shown that most dense graded pavement base layers tend to be unsaturated most of the time, with
the exception of brief periods around major rain events.
This report focuses on the modeling of unsaturated flow through flexible pavement systems to
represent the first step in the development of a comprehensive approach to drainage and pave-
ment design that integrates the true effects of moisture on pavement moduli and mechanistic-
empirical pavement design. Three Mn/ROAD test cells are selected for the evaluation of water
flow through pavement systems, namely Cells 33 to 35. Volumetric moisture contents from
automated time domain reflectometry probes in the granular base courses at Cells 33 through 35,
in combination with measured rain events are used to back-calculate the likely infiltration and
drainage response of the pavement systems for Cells 33 through 35. The resulting unsaturated
flow patterns through these pavement sections are then used to evaluate how water moves
through pavements, how long the water stays in a pavement structure, what material properties
control how long water stays in a given structure, and what boundary conditions and structure
effects (water table, shoulder construction, edge drains, etc.) most affect the moisture conditions
in the pavement.
1
CHAPTER 1
INTRODUCTION It is a well-known fact that water in pavement systems is one of the principal causes of prema-ture pavement failure (1). Water in the pavement system can lead to moisture damage, modulus reduction, and loss of strength. Saturation can reduce the dry modulus of both the asphalt layer (30% or more) and the base and subbase modulus (50% or more) (2). Similarly, modulus reduction of up to 30 percent can be expected for asphalt-treated bases, and over 50 percent for saturated fine-grained subgrade soils (2). These detrimental effects can be reduced by preventing water from entering the pavement,
providing adequate drainage to remove infiltration, or building the pavement strong enough to
resist the combined effect of load and water. Pavement service life can be increased by 50% if
infiltrated water can be drained without delay (3). Similarly, pavement systems incorporating
good drainage can be expected to have a design life of two to three times that of undrained
pavement sections (4, 5). The AASHTO pavement design guide (2) and the US Army Corps of
Engineers Pavement Design Guide (6) both account for the positive effects of drainage through
the use of drainage factors.
The magnitude of these factors is directly related to the length of the time that excess moisture
remains in the pavement. With new mechanistic-empirical pavement design procedures be-
coming more common, there is a need to develop an improved understanding of the mechanics
of water flow through pavement systems, as well as the direct quantification of the effects of
modulus with varying water content. Current design criteria are based on only saturated flow
theory and on an over simplification of in situ conditions.
Full saturation of pavement systems can occur only when positive total heads are present (e.g.,
surface ponding, etc.) and distributed in such a manner that saturation of the pavement system
is
reached. In the absence of positive total heads, the pavement system will remain unsaturated.
When rain starts following a dry period, the system is usually in an unsaturated state, and may
remain in this condition even at the end of the rainfall. The amount of water that can flow
2
through the soil is a function of permeability and gravity forces, as well as material matric suc-
tion (7). For a given soil with a given gradation, the permeability is controlled by the matric
suction, which in turn is affected by the degree of saturation. A degree of saturation of 80 per-
cent may result in heightened suction, and a resulting permeability of only half its saturated
value. Hence, the models that use only fully saturated approaches are not adequate for repre-
senting the flow of water through pavements, and thus pavement drainage. Finally, recent
studies by Minnesota Road Research Project (Mn/ROAD) pavement researchers (8, 9) have
shown that most dense graded pavement base layers tend to be unsaturated most of the time,
with the exception of brief periods around major rain events. Hence, it is of extreme
importance to fully understand: 1) how water moves through pavements, 2) how long the water
stays in a pavement structure, 3) what material properties control how long water stays in a
given structure, and 4) what boundary conditions and structure effects (water table, shoulder
construction, edge drains, layering, etc.) most affect the moisture conditions in the pavement.
Knowledge of the relative effects of these factors should allow for the development and
integration of more direct measures of the effects of moisture in pavements into new pavement
mechanistic-empirical design procedures.
This research focuses on the modeling of unsaturated flow through pavement systems, and
therefore represents a first step in the development of a comprehensive approach to drainage
and pavement design that integrates the true effects of moisture on pavement moduli and
mechanistic-empirical pavement design.
1.1 OBJECTIVES
The objectives of this research include: 1) the modeling of the movement of water through flex-
ible pavement systems that are unsaturated, 2) evaluating which material properties most affect
how long water stays in a given pavement, and 3) evaluating the potential effects of water
table, shoulder construction, layering, edge drains, and open-graded bases on the drainage of
flexible pavement systems.
3
1.2 SCOPE OF REPORT
The study addresses the following: 1) verification of SEEP/W software for modeling unsatu-
rated flow of water through pavements, 2) modeling of the movement of water through flexible
pavement systems that are variably saturated, 3) identification of which material properties
most affect how long water stays in a given pavement, and 4) evaluating the potential effects of
water table, shoulder construction, layering, edge drains, and open-graded bases on the
drainage of flexible pavement systems.
Chapter 2 provides a literature overview of both the current state-of-the-practice in drainage
design, as well as the current-state-of-the-art. Chapter 3 details the research methodology used
in this study. Chapter 4 evaluates the use of SEEP/W for simulating the flow through
simplified pavement systems. Chapter 5 describes the calibration of predicted results to field
data for different pavement structures. Chapter 6 evaluates the effects of various parameters on
flow under unsaturated conditions. Chapter 7 presents the effects of edge and under drains in a
typical flexible pavement system. Chapter 8 presents conclusions and recommendations based
on the analyses presented in this study.
4
CHAPTER 2
LITERATURE REVIEW
Current assumptions (2) used in pavement drainage construction and design will be reviewed.
An example will be provided of the effects of poorly drained flexible pavements on pavement
thickness. Some of the more common positive pavement drainage systems will be reviewed,
including the use of open graded base courses, edge drains, and the use of geo-textiles for
drainage improvement. The effects of unsaturated pavement material properties and layering
on pavement drainage will also be discussed.
2.1 CURRENT STATE-OF-THE-PRACTICE
There are two different types of fluid flow, saturated and unsaturated. In general, the fluid flow
through porous soil is governed by the matric suction of the soil, which in turn controls the per-
meability of the soil. The matric suction is affected by the factors that affect how closely
packed the soil particles are, including gradation, density, and particle angularity (10). As any
given soil becomes less and less saturated, the matric suction will in turn increase and become
more and more negative. Similarly, in the extreme case when the soil is saturated, and all the
voids are filled with water, the matric suction is zero, and the hydraulic conductivity is
independent of the pore suction; hence Ksat is considered as a constant value. In this case,
positive total heads are required at every point in the pavement system to allow water to flow
into and through the system. Thus, the driving forces that are required for saturated flow are
gravitational and pressure-potential gradients (11). Under saturated conditions, the flow (flux)
is proportional to the length of the drainage path and the total hydraulic head loss between any
two points of interest, as well as the cross sectional area of flow (Darcy’s Law).
Based on saturated flow conditions, the two different cases that are typically considered for the
hydraulic design of pavement systems include steady-state flow conditions, and time-to-drain
conditions. Under steady state flow conditions, the permeable base should carry the design
flow that infiltrates the pavement surface. However, the difficulty in estimating the proper
5
precipitation frequency and duration makes the application of steady-state analyses tedious
under most circumstances, except where field measurements are available to determine all
input parameters and boundary conditions. Here the second approach, time-to drain, offers a
more practical solution.
According to the FHWA Pavement Subsurface Drainage Design Manual (12), the “time-to
drain” is a parameter that allows the determination of the drainage performance of pavements.
This approach is based on flow entering the pavement until the aggregate base course is satu-
rated. Excess runoff will not enter the pavement section after it is saturated; this flow will
simply run off on the pavement surface. After the precipitation event, the base will drain to a
drainage system.
Casagrande and Shannon (13) showed that the time for 50% drainage of a base layer can be
calculated as follows: (2.1) where t50 is time for 50% drainage, ne is the effective porosity, L is the length of the drainage layer, k is the permeability of the drainage layer, H is the thickness of the drainage layer, S is the slope of the drainage layer.
2.1.1 Effects of Drainage on Pavement Design Life
A good understanding of the flow of water in the subsurface of the pavement may improve the
design of pavement drainage systems. Cedergren (5) performed a study that shows that 15
billion dollars a year can be saved by designing and building pavements with good pavement
drainage and sub-drainage characteristics. However, a thorough understanding of the factors
influencing the flow of water through pavement systems is required to fully realize these
savings.
2e
50n Lt
2k(H SL)=
+
6
Currently, the FHWA promotes the use of free draining materials in base and subbase construc-
tion. Using the framework of time-to-drain, the AASHTO (2) pavement design equations show
that pavement performance can be greatly improved if free draining materials are used for base
and subbase construction. The effects of excess moisture and the length of time it is retained
within the pavement system are shown in the 1998 AASHTO Guide for pavement design. This
guide also contains specific structural requirements for pavements, which are weakened due to
effects of moisture. The magnitude of these structural factors is directly related to the length of
time that the moisture is retained in the structure. They apply not only to the design of new
pavements but also to the evaluation of existing pavements. For a pavement to have good
drainability characteristics according to AASHTO (2), the structural section of the pavement
should not be filled with excess water and it should not carry heavy wheel loads during periods
when there is excess moisture under the pavement. For this, the water should be able to flow
out of the pavement faster than it enters. The time required to drain at the end of the inflow
period must be short for the excess water not to remain in the structure long enough to freeze
(in cold places).
Table 2.1 presents the different drainage levels for a pavement structure, according to
AASHTO (2), for 50% of drainage.
Table 2.1 Classification of 50% of drainage
Quality of Drainage Water Removed Within
Excellent 2 hours Good 1 day Fair 1 week Poor 1 month Very poor (Water will not drain)
When calculating the adequate thickness for a layer within a pavement system, AASHTO (2)
uses a layer coefficient “m” to modify the structural number (SN). Table 2.2 presents the
recommended m values, as a function of the quality of drainage and the percent of time during
the year the pavement structure would normally be exposed to moisture levels approaching
saturation.
7
Table 2.2 Recommended m values for modifying structural layer coefficients of untreated base and subbase materials in flexible pavements
Percent of Time Pavement Structure is Exposed to Moisture
Levels Approaching Saturation Quality of Drainage Less Than 1% 1-5% 5-25% Greater Than 25%
Excellent 1.40-1.35 1.35-1.30 1.30-1.20 1.20 Good 1.35-1.25 1.25-1.15 1.15-1.00 1.00 Fair 1.25-1.15 1.15-1.05 1.00-0.80 0.80 Poor 1.15-1.05 1.05-0.80 0.80-0.60 0.60 Very poor 1.05-0.95 0.95-0.75 0.75-0.40 0.40
2.1.2 Summary of Current Practice
Unfortunately, the current drainage criteria used by the FHWA and AASHTO (2), have all
been performed under the assumption of saturated conditions (13, 14, 15, 16, 17, 18). In these
previous works, saturated permeability and gravity were identified as the controlling factors
for pavement drainability. However, most pavements stay unsaturated most of the time and it
is rare to have fully saturated conditions in pavements. When rain follows a dry period, the
base and the subbase are usually unsaturated. The amount of water that flows through the base
and subgrade is not only a function of gravitational forces, it is also the function of matric
suction of the material, which controls the permeability (7). Because of the relationship
between matric suction and permeability, it is not justified to consider fully saturated condition
for study of pavement drainage. Variation of time is another factor that should be considered in
addition to unsaturated zone. Transient flow problems are much more complex than the steady
state for which classical solutions are available.
The unsaturated characteristics of pavement materials, along with layering and geometry
dictate the flow of water through pavement systems. The next part of this chapter deals with an
overview of unsaturated flow studies.
8
2.2 POSITIVE DRAINAGE SYSTEMS
2.2.1 Open Graded Base Course
Perhaps the simplest drainage system is the inclusion of an open graded base course in the
pavement structure. This type of layer must consist of sound, clean and open-graded materials.
It must also have a high permeability to allow the free passage of water. It should be protected
from clogging by the use of filters. In order to have a high permeability, the fine portion
should be eliminated from the gradation (19). However, this results in the decrement of the
drainage layer stability. To compensate for this, small amounts of asphalt or Portland cement
are introduced into the base for stability. The material will have only a slightly reduced perme-
ability and be stable at the same time. A key issue in the design of open graded base courses, is
to design the underlying filter material to be fine enough to prevent the adjacent subgrade
(finer) material from piping into the filter material, and course enough to carry water without
any significant resistance (20).
2.2.2 Edge Drains
The design and functioning of subsurface drainage systems involves the consideration of many
details, such as material type, separation layer type, edge drain location, outlet design, and con-
struction. The pipes to be used for subdrainage may be made of concrete, clay, bituminized
fiber, metal, or various plastics with smooth or corrugated surfaces (19). Suitable aggregates or
fabrics as filter materials to prevent the openings from clogging must surround them. The mate-
rial in contact with the pipes must be coarse enough that no appreciable amount of this material
can enter into the pipes.
The edge drain must have the necessary hydraulic capacity to handle water being discharged
from the permeable base. The placement of the edge drain depends on the sequence of con-
struction. The drainage trench should not be placed in the trackline of the paver or in the wheel
path. It should be lined with the geotextile to prevent migration of fines from the surrounding
soil into the drainage trench, but the top of the trench adjacent to the permeable base should be
left open to allow a direct path for the water into the drainage pipe.
9
The drainage pipes are usually placed at a constant depth below the pavement surface. Longi-
tudinal slope of the edge drain has a significant effect on flow capacity of pipe edge drains
(12).
According to saturated flow theory, the one-dimensional flow of water from a high
permeability soil layer into a lower permeability soil layer can be represented by an effective
permeability for the two layers that is lower than the permeability of the high permeability soil
layer (10, 4). Therefore, the current practice has been to specify backfill material for the edge
drain trench with at least the permeability of the surrounding aggregate base material (19, 21).
The proper compaction of the backfill material is also important to avoid settlement over the
edge drain, as discussed by Birgisson and Roberson (9).
2.2.3 Use of Geotextiles for Drainage Improvement
Geotextiles are filter fabrics that not only retain the soil and allow water to flow, but also
protect the drainage layer from clogging (19). They are made from strong, tough, rot-proof
polymer fibers formed into a fabric of the woven or nonwoven type, and they must have
sufficient opening areas to prevent them from clogging.
The most important dimension of geotextiles is the apparent opening size (AOS), defined as the
size of glass beads when 5% pass through the geotextile. The American Society of Testing
Materials (22) specifies the method for determining AOS, as well as the retention, permeability
and clogging criteria.
Geotextiles are used in pavement subsurface drainage as an envelope around trench drains, a
wrapping of pipe drains, or a filter of drainage layers (23).
2.3 UNSATURATED FLOW THROUGH PAVEMENTS
The unsaturated zone is located above the water table. Within this zone, the pore spaces are
usually only partially filled with water, the reminder of the pores are taken up by air. There-
fore, the volumetric water content is lower than the soil porosity. Due to the fact that water in
this zone is held in the soil pores under surface-tension forces, negative pressures or matric
10
suction pressures are developed. In addition, in this zone both the volumetric water content
and the hydraulic conductivity are functions of this suction pressure (24, 25). Similarly,
changes in matric suction and volumetric water content, affect the hydraulic conductivity. The
hydraulic conductivity increases with increasing volumetric water content and decreasing
suction, as the matric suction becomes less and less negative (26).
Most water in pavements is introduced to the pavement system through the process of infiltra-
tion into unsaturated pavement layers. Infiltration is the process in which water moves across
the atmosphere-soil interface, i.e., water seeps from the pavement ground surface and enters the
base, subbase, and subgrade soils. The time rate at which water infiltrates across the atmo-
sphere-soil interface is known as infiltration rate (26). The total volume of liquid crossing the
interface over a given period of time is known as cumulative infiltration. Infiltration also signi-
fies soil sorptivity, which is the characteristic that determines how much of the incident rainfall
will run off and how much will enter the soil and either percolate downward or be evapo-trans-
ported (11). Under ponded conditions, infiltration into an initially dry soil profile has a high
rate early in time, decreasing rapidly and then more slowly settling down to nearly a constant
rate.
Water may infiltrate into the pavement from a number of sources, some of the most common
being surface water entering the pavement-shoulder joints, longitudinal and transverse
construction joints and pavement cracks, as well as from capillary rise of water above the water
table from below the pavement. Similarly, seasonal increases in ground water table elevation,
along with a rise in the associated capillary fringe may allow near saturation of pavement
components at various times (4).
Soil characteristics play an important role in the infiltration rate. Total infiltration of any layer
depends upon its porosity, thickness and quantity of water or other liquid present. Soil texture,
structure, organic matter, and other physical properties determine the magnitude of the porosity
of a given soil (11).
11
2.3.1 Soil Water Characteristic Curves
Water flow in the unsaturated zone primarily is due a gradient in total head potential, which is
dominated by differences in matric potential between one point and another (24). A volumetric
moisture content less than the saturated value leads to the development of suction within the
soil mass, which in turn causes a reduction of hydraulic conductivity. Hence, two material
properties are needed to describe the drainage behavior of soils at any given saturation level,
namely the suction present in the soil at a given saturation level, and the corresponding
hydraulic conductivity. To fully describe the unsaturated behavior of soils, it is necessary to
determine the suction present in the soil at all likely saturation levels, along with the hydraulic
conductivity as a function of the resulting soil suction. The first relationship is generally
referred to as the “soil water characteristic curve” and the second one is called the “hydraulic
conductivity curve.”
According to Gupta and Wang (27), the soil water characteristic curve describes the
relationship between the volume of water in the soil and the energy state of the water present in
the soil. The shape of the soil water characteristic curve is a function of the pore size
distribution, which is determined by the gradation of the soil, as well as the soil particle shape,
and the particle packing (27). Figure 2.1 shows a typical soil water characteristic curve,
displaying the relationship between volumetric water content and soil suction (28). The air-
entry value of the soil is the matric suction at which air starts entering the largest pores in the
soil. The residual water content is the water content of the soil at which a large amount of
suction pressure is required to remove the additional water from the initially saturated soil. The
desorption curve differs from the absorption curve due to hysteresis (26).
Since soil water characteristic curves are represented by relationships between volumetric
water content and suction and degree of saturation and suction, it is possible to also develop a
relationship between volumetric water content and the degree of saturation, which can be
expressed with the following relationship (29):
( )( )
( )( )
( )r r re
r s r
S SS
1 S− θ− θ θ− θ
= = =− θ − θ ∆θ
(2.2)
12
Figure 2.1 Typical soil water characteristic curve
where: S is the degree of saturation, Sr is the residual saturation corresponding to the value of θr , θ is the volumetric water content θr is the residual water content θs is the volumetric water content at saturation. There are primarily two ways of obtaining hydraulic conductivity curves for soil – either by
direct measurement or by estimation. Direct measurement of hydraulic conductivity curves is
tedious and time consuming. Therefore, hydraulic conductivity curves tend to be estimated
from soil-water characteristic curves, analytical models, and grain size curves. The hydraulic
conductivity models developed over the years vary in complexity from purely empirical
methods to more sophisticated closed-form solutions. Little work has been performed in
identifying appropriate hydraulic conductivity models for roadway materials. In the following
sections, some common models for both soil water characteristic curves and hydraulic
conductivity curves will be described.
0
10
20
30
40
50
60
0.1 1 10 100 1000 10000 100000 1000000
Soil Suction (KPa)
Vol
umet
ric
Wat
er C
onte
nt (%
) s Air-Entry Valueθs
Desorption Curve
Residual Water Content, θ'r
Adsorption Curve
θ's
Residual air content
13
2.3.1.1 Brooks and Corey model (30)
This model proposed a relationship between the degree of saturation and the matric suction
based on experimental data:
1
eSPB
−νΨ =
for Ψ ≥ PB (2.3)
eS 1= for Ψ< PB
where Se is the effective degree of saturation, Ψ is the matric suction, PB is the bubbling pressure of the soil, which is the height of the capillary fringe, ν is the pore size distribution index parameter, a measure of the soil grain uniformity. Based on Bear’s (31) definition of the water capacity:
wC ∂θ= −
∂ψ (2.4)
and Equations (2.2) and (2.3), a new expression for this water capacity can be obtained (2.5):
ew
SC ∆θ×=
νψ (2.5)
Figure 2.2 shows the influence of the parameter ν on the Se - Ψ response. 2.3.1.2 Van Genuchten model (32)
Van Genuchten proposed an empirical equation to relate the matric suction and the volumetric
water content:
(2.6) for Ψ< 0 where: β and γ are dimensionless coefficients, and γ = 1-1/β, α is a coefficient that has the dimension of the inverse of the piezometric head.
( )( )e1S
1γβ
=+ αΨ
eS 1=
14
Figure 2.2 Typical values for the Brooks and Corey model for water retention (33) For limited cases, Brooks and Corey’s parameters can be related to those used in Van
Genuchten’s model. However, this relation gets distorted when the water content approaches
saturation. As well as equation (2.5), an expression of the water capacity can be obtained based
on the Van Genuchten model:
( ) ( ) 1 1 1w eC 1 Sβ− + γ= α× ∆θ× β − × α× Ψ (2.7)
Figure 2.3 shows the variation of the matric suction for a range of b values.
2.3.1.3 Brutsaert model (34)
Brutsaert (34) proposed another relationship between the degree of saturation and the matric
suction. It is a relationship that combines the pore size distribution and statistical arguments
(34):
for Ψ>0 (2.8)
for Ψ< 0
( )eSβ
α=
α + Ψ
eS 1=
15
Figure 2.3 Typical values for the Van Genuchten model for water retention (29)
where α depends on the suction units, β is dimensionless.
The water capacity equation for the Brutsaert’s model is given by:
( )
12 1
w e2C Sβ−
β−
β
∆θ×α×β× Ψ ∆θ×β= = × Ψ
αα + Ψ (2.9)
where α and β are empirical coefficients.
2.3.1.4 Vauclin model (35)
Similar to the model proposed by Brutsaert (34), Vauclin (35) introduced another empirical
equation relating the degree of saturation and the matric suction: for Ψ>1 (2.10)
for Ψ≤ 1 cm
( )eSln( )β
α=
α + Ψ
eS 1=
16
The water capacity equation for this model is given by:
for Ψ≥1 cm (2.11) where α and β are fitting coefficients.
2.3.1.5 Bear and Verruijt model (36)
The relationship between the degree of saturation and the suction is not unique, but is charac-
terized by hysteresis between wetting and drying curves. Therefore, a value of suction during
drainage is greater than during wetting (Figure 2.4). This phenomenon, called hysteresis, has
been explained through several models. Bear and Verruijt (36) model states that the hysteresis
is due to the ink-bottle effect and the raindrop effect (Figure 2.5), which are related to the
variation of the meniscus radius in the capillary tube cross-section, and the variation of the
contact angle, respectively.
2.3.1.6 Gray and Hassanizadeh model (37)
Based on the thermodynamic principles and momentum balance equations, Gray and
Hassanizadeh (37) proposed a general expression for the capillarity. They also defined the
suction as net energy per unit volume of pore space that would be released per unit change in
saturation. Therefore, a unique suction curve is obtained as a function of water and air density,
temperature, degree of saturation, and area of air-water interface per unit of porous medium.
This allows obtaining the capillary pressure without taking into account the hysteresis effect.
However, the required parameters are not easy to obtain.
2.3.1.7 Mualen model (38)
Mualen presented a model based on the independent domain theory (38), which conceptualizes
the porous medium as a system of pore domains with characteristic wetting and drying pore
radii such that the pore volume can be expressed as: (2.12) where: Ψw and Ψd are independent variables representing the suction on the main wetting and
drying curves, Ψw being always greater that or equal to Ψd . f is a bivariate probability distribution function
( )1
2 1w e2
ln( )C S (ln )(ln )
β−β−
β
∆θ×α×β× Ψ ∆θ×β= = × × Ψ
α× ΨΨ α + Ψ
( )w d w df , d dθ = Ψ Ψ Ψ Ψ∫ ∫
17
Figure 2.4 Hysteresis effects – Main drainage and wetting curves (31)
Figure 2.5 Variation of the air-water interface due to raindrop effect (31)
18
2.3.1.8 Summary of soil water characteristic curve models
Table 2.3 summarizes the features of the soil water characteristic curve models discussed
previously.
Table 2.3 Soil water characteristic models – Main Features, Advantages, and
Disadvantages
Model Main Features Advantages Disadvantages Brooks and Corey (30)
Relates the degree of saturation and the matric suction
Based on substantial experimental data
Empirical method
Brutsaert (34) Relates the degree of saturation and the matric suction
Sensitive to suction values close to saturation
It has empirical coefficients
Mualen (38) Determines the volumetric water content as a function of the suc-tion on the main wetting and drying curves
Based on rigorous statistical considerations and hysteresis effect included
Requires wetting and drying test data
Vauclin (35) Relates the degree of saturation and the matric suction
Describes laboratory measurements at small suction well
It has empirical coefficients
Bear and Verruijt (36)
It takes into account the hysteresis phenomenon
Hysteresis effect included Requires wetting and drying data
Gray and Hassanizadeh (37)
Allows obtaining the capillary pressure without taking into account the hysteresis effect
Based on thermodynamic principles that allow for a unique relationship between a suction curve as a function of water and air density, temperature, degree of saturation, and area of air-water interface per unit of porous medium
The required parameters are tedious to obtain
2.3.1.9 Relative permeability models
Under unsaturated conditions, the total permeability is reduced due to the presence of matric
suction in the porous media. Therefore, the concept of relative permeability is used, and it is
the ratio between the unsaturated permeability and the saturated permeability:
er e
K (S )k (S )
K= (2.13)
19
where kr is the relative permeability ranging from 0 to 1, K is the saturated permeability.
Different models have been proposed to represent the relative permeability as a function of the
effective degree of saturation. Most of these models assume the porous medium is equivalent
to a set of tubes connected randomly in parallel-series, each tube having a different
permeability. As a result, the random variations of the pores sizes normal to and along the
direction of flow can be taken into account (39).
Burdine (40) used the series-parallel model and related the permeability to the soil water char-
acteristic curves. By using the definition of the relative permeability (Equation 2.13), he
obtained:
(2.14)
where Se(r) = dSe/dr is the effective pore size density function.
Mualen (41) derived an analytical expression in which the hydraulic conductivity is not
controlled by the radius of the narrower element:
(2.15) For an n equal to 0.5, Equation 2.15 predicts reasonably well most hydraulic conductivity
curves obtained in the laboratory (41).
In order to determine the saturated permeability of the soil, the falling and constant test perme-
ameter tests are commonly used for sandy soils. For lower hydraulic conductivities, larger
pressure differences need to be applied using pumps. Either flexible or rigid wall permeameters
eS2 ee 20
er e 1 e
20e
dSS(S )k (S ) dS
(S )
Ψ=
Ψ
∫
∫
e2
S e0
n er e e 1 e
0e
dS(S )k (S ) S dS(S )
Ψ = Ψ
∫
∫
20
can be used. The oedometer test can also be used to determine the hydraulic conductivity of
soils of low permeability (42).
For the determination of the unsaturated permeability of the soil, there are different techniques
such as transient flow in soil columns, pressure plate outflow technique, osmotic permeameter,
and permeameter apparatus (27, 31).
2.3.2 Hydraulic Conductivity Models
Gardner (43) developed one of the first interpolation functions for the hydraulic conductivity
curve, namely:
( ) ( )s
k
kk1 A β
ψ =+ ⋅ψ
(2.16)
where kS is the saturated hydraulic conductivity, ψ is the pore suction, Ak, β are empirical curve fitting coefficients. In order to use this method, the empirical curve-fitting coefficients must be acquired from
experimental hydraulic conductivity data.
Brooks and Corey (30) suggested a hydraulic conductivity relationship that relates hydraulic
conductivity values to the effective saturation of a soil, as follows:
( )n
rs
s r
k k θ − θ
θ = θ − θ (2.17)
where kS is the saturated hydraulic conductivity, θ is the volumetric water content, θs is the saturated volumetric water content, θr is the residual volumetric water content, n = 3 + 2/λ, and is based on the pore size index (λ).
This model allows the inclusion of the soil-water characteristic curve, in a direct way, due to
the defined equation was written in terms of the volumetric water content.
21
Brooks and Corey’s relationship is based on the analysis performed by Burdine (40), who
applied theories of fluid flow through porous material to develop a relationship that produces
the relative hydraulic conductivity (kr) from the soil-water characteristic curve. The
formulation proposed by Brooks and Corey (30) is simply a reduced form of Burdine’s
equation (40), including an assumed interpolation equation for the soil-water characteristic
curve. Although the Brooks and Corey (30) hydraulic conductivity model should apply nicely
to the coarse base materials, it loses some validity because it is not very efficient at low suction
values (3).
Finally, as can be seen from Equation 2.17, the Brooks and Corey function requires a pore size
distribution value (λ) to characterize the material. The λ value can be calculated using a
regression function from Rawls (44). The regression relationship is based upon the percent
sand, the percent clay, the soil porosity, and the cross product of these values.
Green and Corey (45), based on Childs and Collis-George (46), proposed a more refined
equation to model the hydraulic conductivity, resulting in the following interpolation function:
( ) ( )2 p m
2sj2i
j 1sc
k 30k 2j 1 2ik gn n
−
=
γ ε θ = ⋅ ⋅ + − ψ ρ ∑ (2.18)
for i = 1, 2, …, m where k(θ)i is the calculated conductivity for a specified water content, θ is the volumetric water content, i denotes the last water content class on the wet end, e.g. i = 1 identifies the pore class
corresponding to the lowest water content for which the conductivity is calculated, ks/ ksc is a matching factor, γ is the surface tension, ρ is the density of water, g is the gravitational constant (cm/sec2), η is the viscosity of water (g/cm/sec-1), ε is the soil porosity (cm3/cm3), p is a parameter that accounts for interaction of pore classes, n is the total number of pore classes between θ = 0 and θs, ψj is the pore pressure for a given class of water filled pores.
22
As can be seen from Equation (2.18), the range of validity for this relation is based on the use
of many soil and fluid properties. Also, it should be mentioned that with some manipulation,
this method provides the same results as the method outlined by Fredlund et al. (47).
Van Genuchten (32) used a method similar to Brooks and Corey’s (30) model to describe the
hydraulic conductivity at low suction values, resulting in the following relationship:
( )
2m1 12 m
r rs
s r s r
k k 1 1
θ − θ θ − θ θ = − − θ − θ θ − θ
(2.19)
where: ks is the saturated hydraulic conductivity, θ is the volumetric water content, θs is the saturated volumetric water content, θr is the residual volumetric water content, m = λ / (1 +λ), and is based on the pore size index (λ).
Unfortunately, just like the Brooks and Corey model (30), Van Genuchten’s approach also
relies on the pore size index discussed previously. However, the difference is that instead of
basing his work on Burdine’s equation (40), Van Genuchten used Mualen’s model (41).
Table 2.4 summarizes the key features of the hydraulic conductivity models presented.
2.3.3 Effects of Layering on Pavement Drainage
In coarse-grained materials the soil water characteristic curve shows that almost all the volu-
metric water content held in the pore space is removed at low suction values. These results are
reasonable because of the low capillary effects associated with large pores. Conversely, in
fine-grained materials the soil water characteristic curve shows that much of the water is held
in the soil at higher suction. These features determine where the majority of the volumetric
water content is stored in the infiltration system. The other important factor in unsaturated
flow behavior through layered systems is the hydraulic conductivity function for each material.
In general, due as matric suctions increase and become more negative, the hydraulic
conductivity decreases with
23
Table 2.4 Hydraulic conductivity models – Main Features, Advantages, and Disadvantages
Model Main Features Advantages Disadvantages
Gardner (43)
A two-parameter empirical model
Permeability is represented as a smooth function of suction instead of degree of saturation
Empirical curve-fitting coefficients must be acquired from experimental hydraulic conductivity data
Brooks and Corey (30)
Allows the inclusion of the soil-water characteristic curve in a direct way
Based on substantial experimental data
Empirical equation, not very efficient at low suction values, relies on a difficult to obtain λ value
Green and Corey (45)
Refined equation to model the hydraulic conductivity
Based on substantial experimental data
Use of many soil and fluid properties
Van Genuchten (32)
Equation based on the volumetric water content
Based on substantial experimental hydraulic conductivity data at low suction values
Relies on a difficult to obtain λ value
suction. Due to these effects, when a fine material is overlying a coarser material under
unsaturated conditions, the effect is a reduction in flow in the coarse-grained material.
Although the coarse-grained material starts with a higher hydraulic conductivity, the larger
pore size and reduced surface tension effects cause the hydraulic conductivity to drop rapidly at
lower pore suction levels. The hydraulic conductivity of the fine-grained material however
tends to not decrease nearly as rapidly and hence the hydraulic conductivity can actually
become lower in the coarse-grained material, resulting in a capillary barrier between the two
different materials. The intersection of these two curves represents the matric suction that
causes equivalent hydraulic conductivities.
A combination of these two effects causes the majority of the water to remain in the fine-
grained material where the hydraulic conductivity is much higher at the crossover suction.
Therefore, the water tends to flow primarily through the fine-grained material. However, this
only happens if the pore suction values are higher than the suction at which there are equivalent
hydraulic conductivities.
24
A proper understanding and use of the capillary barrier effect in multiple layer systems can be
effective in reducing the amount of flow through the system. Similarly, the capillary barrier
effect may result in adverse drainage conditions if not accounted for properly in the design of
pavements.
25
CHAPTER 3
RESEARCH METHODOLOGY In this Chapter, the research methodology used in this study will be discussed. First, the
analysis tools used will be described, followed by a description of pavement sections and
materials, and scope of study.
3.1 SELECTION OF ANALYSIS TOOLS
Based on the established fact that drainage through pavements is generally governed by un-
saturated flow conditions, it was necessary to select a software analysis tool that could perform
unsaturated flow analysis. In addition, other desired properties included seamless transition
between unsaturated and saturated flow analysis, full transient analysis capabilities, user
friendly pre- and post-processor interfaces, established track record, user-friendliness,
flexibility in terms of changing unsaturated material properties, and solid user support. Almost
immediately, the software package that was identified as possible candidate was SEEP/W from
Geoslope International (48). The SEEP/W package is formulated to analyze both saturated and
unsaturated flow, and includes user-friendly pre- and post-processors. SEEP/W also contains
options for choosing and inputting soil water characteristic curves and hydraulic conductivity
curves. A database of typical unsaturated hydraulic properties is included, and soil water
characteristic curves can be predicted from grain size distribution curves. Similarly, Van
Genuchten (32) and Fredlund and Xing (28) type hydraulic conductivity curves can be
predicted from soil water characteristic curves. Therefore, it was decided to select SEEP/W as
the software analysis tool to be used for the rest of this study.
Finally, to provide a baseline comparison between time-to-drain using unsaturated flow theory
and SEEP/W and traditional saturated time-to-drain calculations, the FHWA computer program
entitled “Drainage Requirements in Pavements,” or DRIP, was selected (49)
26
3.1.1 SEEP/W
The finite element-based SEEP/W is formulated to analyze both saturated and unsaturated
flow. Flow in unsaturated soil follows Darcy's Law in a similar manner to flow in saturated
soil. The flow is proportional to the hydraulic gradient and the hydraulic conductivity
(coefficient of permeability). The major difference between saturated and unsaturated flow in
SEEP/W is that in a saturated soil, the hydraulic conductivity is insensitive to the pore-water
pressure, while in an unsaturated soil, the hydraulic conductivity varies greatly with changes in
pore-water pressure.
Although SEEP/W assumes that the flow of water follows Darcy’s law for both unsaturated and
saturated flow, the governing equation for all the calculations is Richards’ equation, shown
below, which represents in a more suitable form the unsaturated flow:
x yH Hk k Q
x x y y t ∂ ∂ ∂ ∂ ∂Θ + + = ∂ ∂ ∂ ∂ ∂
(3.1)
where H is total head, kx is hydraulic conductivity in the x-direction, ky is hydraulic conductivity in the y-direction, Q is the applied boundary flux, Θ is volumetric water content, t is time.
Richards’ equation (Eqn. 3.1) is based on the balance of flow into and out of an element
volume of soil. This fundamental partial differential equation simply states that the difference
between the flow entering and leaving an elemental volume at a point in time is equal to the
change in volumetric water content. Richards’ equation can be used for both saturated and
unsaturated conditions, since the right part of the equation becomes zero when the first case is
applied or in steady-state conditions.
3.1.2 DRIP
The microcomputer program Drainage Requirements In Pavements (50) can be used to design
subsurface drainage for highway pavements. Among the drainage design elements, DRIP
allows for the calculation of the time to drain in the drainage layer of a pavement system. This
27
program is based on simple analytical prediction methods, which assume that pavement
systems are only exposed to saturated conditions.
The calculations are based on two methods: Barber and Sawyer method (51) and Casagrande
and Shannon method (13).
The Barber and Sawyer (51) equations are:
kh
LTnt
2Re= (3.2)
where t is time required to drain U% of water from the drainage layer, U is the percent of water drained, and it is a function of the porosity, saturation and
effective porosity of the drainage layer, ne is the effective porosity of the drainage layer, LR is the resultant length of the drainage path. It is a function of the width longitudinal
slope and resultant slope (SR) of the drainage path, k is the permeability of the drainage layer, h is the thickness of the drainage layer, T is a factor determined by, (3.2a)
for U > 0.5 (3.2b) for U ≤ 0.5 Casagrande and Shannon’s method (13) is based on the same equation (3.2), but T factor is
determined by:
(3.3a)
for U>0.5
( )( )
++−
⋅+
+⋅−=
4.2SU-12.1USSlogS15.1
S4.21logS48.0S5.0T
R
RRR
R
2RR
+⋅−=
R
2RR S
U8.41logS48.0UST
( )( )2R R R
R R RR R
2S 2US 1 S 1cT S S ln S ln2 2 2U S 1 S
− + + = + ⋅ − ⋅ − +
28
(3.3b)
for U ≤ 0.5,
(3.3c)
The amount of water present in the drainage layer material as a percentage of the available
volume is defined by the percent of saturation. In the “Time to drain” method, DRIP assumes
that saturation is 100% because it is considered that the drainage layer is saturated at the time
to drain and that there is no additional inflow to this layer once the rainfall has ceased. Thus,
the hydraulic conductivity is considered as a constant value.
3.2 MATERIALS AND PAVEMENT SECTIONS
3.2.1 Pavement Sections
The pavement systems that were used for this study correspond to testing sections constructed
by Minnesota Department of Transportation (Mn/DOT) as a part of the Minnesota Road
Research Project (Mn/ROAD). These sections are denominated Mn/ROAD Cell 33, Cell 34,
and Cell 35. They consist of a layer of hot mix asphalt, a Mn/DOT Class 6 Special base
course, consisting of 100 percent crushed granite, an R-12 silty clay subgrade. Figure 3.1
shows the thickness of each of base and hot mix asphalt layers for Cells 33-35.
Figure 3.1 Thickness of base and hot mix asphalt layers for Mn/ROAD Cells 33-35 Figure 3.2 shows pavement geometry, materials and dimensions of the complete system used to
simulate Cells 33, 34, and 35.
Asphalt Layer
Cell 33
4.04 in
Cell 34
3.92 in
Cell 35
3.96 in
Base Layer
12 in 12 in 12 in
2 RR R
R
S 2UcT 2US S ln2 S
+ = − ⋅
1 3R
0.8c 2.4S
= −
29
Figure 3.2 Pavement geometry and dimensions
3.2.2 Materials
3.2.2.1 Hot mix asphalt layers
For this study the hot mix asphalt layer was considered as an impervious material, therefore its
properties were not taken into account for the material characterization for the different finite
element models. However, Table 3.1 presents the asphalt binder description and thickness for
each cell.
Table 3.1 Asphalt layer description
Cell Asphalt Binder Thickness (in)33 PG 58-28 4.04 34 PG 58-34 3.92 35 PG 58-40 3.96
3.2.2.2 Base materials
The granular base course material for Cells 33-35 consisted of Mn/DOT Class 6 Special
crushed granite aggregate base material. The grain-size distribution curve is shown in Figure
3.3.
4.53 m
3.43 m 4.27 m 4.27 m4.53 m
CLBase Hot Mix Asphalt
Subgrade
30405060708090
100
30
Figure 3.3 Grain size distribution for Mn/DOT Class 6 special
The soil water characteristic curve and the estimated hydraulic conductivity curve, shown in
Figures 3.4 and 3.5, respectively were obtained from suction plate measurements performed by
Mn/DOT. For modeling purposes, the air entry value for the soil water characteristic curve
was shifted to 3 kPa (52). The verification of the resulting soil water characteristic curve is
shown in Appendix B, along with a verification of the final air entry value to be used.
Figure 3.4 Soil water characteristic curve – Base material (Class 6 special)
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
0.01 0.1 1 10 100
Suction (kPa)
31
Figure 3.5 Hydraulic conductivity curve – Base material (Class 6 special)
A saturated hydraulic conductivity (Ksat) of 1.54E-6 m/s was obtained from the estimated
hydraulic conductivity curve (Figure 3.5) provided by Mn/DOT. In this case, the saturated
hydraulic conductivity was simply obtained as the hydraulic conductivity value at zero suction.
This saturated hydraulic conductivity corresponds to fine sand.
3.2.2.3 Subgrade soil
The subgrade soil can be characterized as an R-12 sandy clayey silty soil. Figures 3.6 and 3.7
show the soil water characteristic curve and the hydraulic conductivity curve for the subgrade,
obtained from Mn/DOT. Figure 3.6 shows that this sandy clayey silt has little variation of
volumetric water content. For example, there is only 9 percent drop for the first 10 kPa. The
total change is 15%. This means that the subgrade has the capacity to hold water for a long
time, implying that its drainage will be slow.
As well as the soil water characteristic curve, the hydraulic conductivity curve also implies that
the subgrade soil has a high resistance to drainage. Within the first 5 kPa, this material goes
from 2.75E-08 m/s to a value close to 2E-13 m/s.
1.0E-15
1.0E-13
1.0E-11
1.0E-09
1.0E-07
1.0E-05
0.01 0.1 1 10 100
Suction (kPa)
k (m
/s)
32
20.0
25.0
30.0
35.0
40.0
45.0
50.0
55.0
0.001 0.01 0.1 1 10 100 1000 10000
Suction (kPa)
Vol
umet
ric
Wat
er C
onte
nt (%
) s
Figure 3.6 Soil water characteristic curve – Subgrade material (R-12 Silty clay)
1.0E-15
1.0E-13
1.0E-11
1.0E-09
1.0E-07
0.01 0.10 1.00 10.00 100.00
Suction (kPa)
k (m
/s)
Figure 3.7 Hydraulic conductivity curve – Subgrade material (R-12 Silty clay)
33
CHAPTER 4
EVALUATION OF SEEP/W FOR MODELING UNSATURATED FLOW
In this Chapter, SEEP/W predictions are compared to a series of experimental and analytical
results reported in the literature to evaluate its use for modeling the flow of water through soils
and simplified pavement systems. Results from three laboratory and analytical experiments
reported in the literature are used to provide a comparison to SEEP/W predictions. The first
example is based on a laboratory experiment performed by Vauclin (35), in which unsaturated
soil is infiltrated with a constant flux, and the resulting changes in water table within the soil
are monitored. The second example is based on a modification of Vauclin’s (35) experiment,
where now the soil in Vauclin’s (35) experiment is replaced by a typical dense graded base
material and the flux is set to be representative of the infiltration process that pavement struc-
tures may go through during rainfall events (29). Similarly, the third example is based on a
modification of Example 2, in which materials corresponding to typical granular base and
subbase layers are introduced to simulate the case of a subdrainage layer with high
permeability (29).
4.1 EXAMPLE 1
The first example is based on an experimental setup performed by Vauclin (35) in the labora-
tory with a single layer of soil 3 m long, 2 m high and 0.05 m thick, in order to study the
changes of water content and water pressure occurring in the flow. The soil was packed as
homogeneously as possible between two walls supported by a frame resting on an impervious
horizontal boundary. One of the vertical ends of the slab was connected to a constant head
reservoir, and a water table was imposed at the depth of Ho = 1.35 m. There was no flow
through the vertical left hand side of the slab. A constant flux corresponding to qo = 4.1111 E-
5 m/s was applied on the soil surface over a width Lo = 0.50 m. Figure 4.1 describes the
geometry and conditions for this example.
34
Figure 4.1 Example 1 – Geometry and boundary conditions
As part of the experiment, suction and hydraulic conductivity curves for the soil material were
determined in the laboratory and fitted by regression analysis to the Brutsaert (34) and Gardner
(43) models, which are also presented in Equations 2.18 and 2.16, respectively. Table 4.1
shows the parameters obtained with the regression analysis.
Based on the hydraulic parameters in Table 4.1 for the Brutsaert (34) and Gardner (43) models,
the soil water characteristic and the hydraulic conductivity curves were obtained (Figures 4.2
and 4.3).
Table 4.1 Soil hydraulic parameters (35)
Soil Water
Characteristic
Curve Parameters
(Brutsaert,1966)
Hydraulic Conductivity
Curve Parameters
(Gardner, 1956)
α β θs A β Ks (m/s)
40,000 2.9 0.30 2.99E+06 5.0 9.72E-05
The finite element mesh used in SEEP/W to simulate this experiment is presented in Figure 4.4.
The mesh is composed of 601 uniformly sized 0.1 m by 0.1 m quadrilateral elements. As
shown previously in Figure 4.1, the boundary conditions are modeled as impervious at the left,
right,
qo = 4.1111 E-05 m/s
2 m
3 m
0.65 m
0.50 m
Impervious boundary
H = 0.65 m
Total Head (H)
35
Figure 4.2 Soil water characteristic curve for Example 1 (34)
Figure 4.3 Hydraulic conductivity curve for Example 1 (43)
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
0.01 0.10 1.00 10.00 100.00
Suction (kPa)
1.0E-12
1.0E-10
1.0E-08
1.0E-06
1.0E-04
0.01 0.10 1.00 10.00 100.00
Suction (kPa)
Hyd
raul
ic C
ondu
ctiv
ity (m
/s) s
36
Figure 4.4 Example 1 – Finite element model and bottom edges of the mesh, as well as the top 2.5 m portion of the boundary that is not sub-
jected to infiltration.
A comparison between the measured water table data (35) and the predicted water table results
(SEEP/W) is presented in Figures 4.5 to 4.8. A comparison of Figures 4.5 to 4.8 shows that the
variation in the water table elevation with time and elevation obtained from the SEEP/W model
follows the same trend as the measured data.
Table 4.2 summarizes the maximum and minimum differences between the measured and
predicted results in Figures 4.5 through 4.8.
The SEEP/W simulations resulted in a slightly higher water table position under the section
where the constant flux was applied. However, over time, the differences between the
measured and predicted water table are reduced, until the water table reached its steady state
position, after the 8th hour.
37
Figure 4.5 Comparison between measured and predicted water table at 2 hours
Figure 4.6 Comparison between measured and predicted water table at 3 hours
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
0.00 0.50 1.00 1.50 2.00 2.50 3.00
Distance (m)
Vauclin (1979)SEEP/W
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0.00 0.50 1.00 1.50 2.00 2.50 3.00
Distance (m)
Ele
vatio
n (m
)
Vauclin (1979)SEEP/W
38
Figure 4.7 Comparison between measured and predicted water table at 4 hours
Figure 4.8 Comparison between measured and predicted water table at 8 hours
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0.00 0.50 1.00 1.50 2.00 2.50 3.00
Distance (m)
Ele
vatio
n (m
)
Vauclin (1979)SEEP/W
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
0.00 0.50 1.00 1.50 2.00 2.50 3.00
Distance (m)
Vauclin (1979)SEEP/W
39
Table 4.2 Maximum difference between predicted and measured water table results in Figures 4.5 – 4.8
Time (h)
Minimum difference (percent)
Maximum difference (percent)
2 0 4.0 3 0 4.0 4 0 4.0 8 0 3.0
4.2 EXAMPLE 2
The second example is based on a modification of Vauclin’s (35) experiment (Example 1),
where now the soil in Vauclin’s (35) experiment is replaced by a typical dense graded granular
base material and the flux is set to be representative of the infiltration process that pavement
structures may go through during rainfall events (29). This case is represented by two-
dimensional infiltration into a simplified pavement structure.
The simplified pavement system consists of an impermeable wearing course overlaying homo-
geneous base material (Figure 4.9). The bottom and vertical boundaries were impermeable, as
well as the wearing course. Therefore, the only source of water was the “shoulder,” which was
modeled with as a 0.5 m wide strip, with a uniform infiltration rate to simulate rainfall. As an
initial condition, the effective degree of saturation was specified as 50%, and a “rainfall” of
constant intensity was applied (qo = 2.7778 E-06 m/s) on the “shoulder” area.
The granular base material was characterized as an anisotropic material. The horizontal
conductivity was 10 times greater than the vertical. The vertical value was taking into account
in SEEP/W by introducing a ratio of 10 between the horizontal and vertical hydraulic conduc-
tivities.
The Brooks and Corey models (30) were used to represent both the soil water characteristic
curve and hydraulic conductivity curve (Figures 4.10 and 4.11).
40
Figure 4.9 Example 2 – Geometry and boundary conditions
Figure 4.10 Soil water characteristic curve for Example 2 (30)
Kh=3.50 E-05 m/s Kv=3.50 E-06 m/s θo=0.005, ∆θ=0.382 Si=0.5 (initial saturation)
0.025 m
0.20 m
2 m
0.50 m
qo = 2.7778 E-06 m/s Impervious boundary
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
40.0
45.0
0.01 0.10 1.00 10.00
Suction (kPa)
41
Figure 4.11 Hydraulic conductivity curve for Example 2 (30)
This example was modeled in SEEP/W, using the finite element mesh shown in Figure 4.12,
with 580 0.025 m by 0.025 m uniformly sized quadrilateral elements. Due to the fact that the
initial degree of saturation was 50%, an equivalent water table was set, resulting in a maximum
achievable suction pressure of 2.12 kPa above the water table, which was the suction required
to have an effective saturation (Se) of 50%. The suction value of 2.12 kPa is developed for the
entire base layer to reproduce the desired effective saturation.
Figures 4.13 through 4.16 show the variation of the volumetric water content with the distance
at times 1.5 hour, 3 hours, 4.5 hours, and 6 hours, respectively, for different periods of time.
The areas of maximum volumetric water content are located under the pavement shoulder,
within the first 0.5 m away from the only source of water for the system. As expected, the
volumetric water content (θ) changes most rapidly in the transition zone between the shoulder
and the edge of the wearing course. Also, as expected, the variation of θ is higher in the hori-
zontal direction than in the vertical one, due to the anisotropic hydraulic conductivity
conditions. Finally, the SEEP/W predicted results at the first two points closest to the
infiltration zone are
1.0E-10
1.0E-09
1.0E-08
1.0E-07
1.0E-06
1.0E-05
1.0E-04
0.01 0.10 1.00 10.00
Suction (kPa)
42
Figure 4.12 Example 2 – Finite Element Model
Figure 4.13 Comparison between measured and predicted volumetric water content at 1.5 hours for Example 2
0.0
5.0
10.0
15.0
20.0
25.0
30.0
0.00 0.40 0.80 1.20 1.60 2.00
Distance (m)
Espinoza et al. (1993)SEEP/W
43
Figure 4.14 Comparison between measured and predicted volumetric water content at 3 hours for Example 2
Figure 4.15 Comparison between measured and predicted volumetric water content at 4.5 hours for Example 2
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
40.0
0.00 0.40 0.80 1.20 1.60 2.00
Distance (m)
Espinoza et al. (1993)SEEP/W
0.05.0
10.015.020.025.030.035.040.045.0
0.00 0.40 0.80 1.20 1.60 2.00
Distance (m)
Espinoza et al. (1993)SEEP/W
44
Figure 4.16 Comparison between measured and predicted volumetric water content
at 6 hours for Example 2 slightly lower than the solution obtained by Espinoza, et al. (29), which used a simple first
order finite difference scheme to simulate the infiltration response. Due to the limitations of
the finite difference scheme used by Espinoza et al. (29), it may not have adequately predicted
the response in the zone where the volumetric water content is changing most rapidly at early
times (Figure 4.13), hence resulting in slight differences from the SEEP/W predictions.
In summary, the results show that SEEP/W provides reasonable predictions of unsaturated flow
behavior under controlled conditions using materials that are typical for dense graded granular
base courses used in pavements.
4.3 EXAMPLE 3
The third Example is based on a modification of Example 2, in which materials corresponding
to typical granular base and subbase layers, shown in Figure 4.17, are introduced to simulate
the case of a subdrainage layer with high permeability (29) As in Example 2, the pavement
slab, both lateral boundaries, and the bottom boundary were assumed to be impervious. The
subbase was
0.05.0
10.015.020.025.030.035.040.045.0
0.00 0.40 0.80 1.20 1.60 2.00
Distance (m)
Espinoza et al. (1993)SEEP/W
45
Figure 4.17 Example 3 – Geometry and boundary conditions considered to be 100 times more permeable than the base course. Similar to Example 2, the ini-
tial moisture conditions were defined by assuming 50% saturation. The only source of infiltra-
tion was the shoulder, with a rate qo equal to 2.7778 E-06 m/s.
Espinoza, et al. (29) obtained the unsaturated soil properties for the base and subbase materials
from the Brooks and Corey model (30). Figures 4.18 to 4.20 show the resulting soil water
characteristic curve and the hydraulic conductivity curve.
Figure 4.21 presents the SEEP/W Finite Element Model for this example, which has 580
0.025 m by 0.025 m uniformly sized quadrilateral elements to represent both layers. As well as
in Example 2, the water table elevation was fixed at 0.7 m below the surface, to obtain suctions
that produced a state of initial saturation of 50%.
The resulting variation in volumetric water content with distance is presented in Figures 4.22
through 4.29, at times 1.5, 3, 4.5 and 6 hours for the granular base and subbase materials.
0.20m
0.025 m Kh=Kv=3.50 E-06 m/s
Kh=Kv=3.50 E-04 m/s 0.10 m
θo=0.005, ∆θ=0.382 Si=0.5 (initial saturation)
0.50 m qo = 2.7778 E-06 m/s
2 m Impervious Boundary
46
Figure 4.18 Soil water characteristic curve for base and subbase for Example 3 (30)
Figure 4.19 Hydraulic conductivity curve for base material in Example 3 (30)
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
40.0
45.0
0.01 0.10 1.00 10.00
Suction (kPa)
1.0E-12
1.0E-11
1.0E-10
1.0E-09
1.0E-08
1.0E-07
1.0E-06
1.0E-05
0.01 0.10 1.00 10.00
Suction (kPa)
47
Figure 4.20 Hydraulic conductivity curve for subbase material in Example 3 (30)
Figure 4.21 Example 3 – Finite Element Model
1.0E-10
1.0E-09
1.0E-08
1.0E-07
1.0E-06
1.0E-05
1.0E-04
1.0E-03
0.01 0.10 1.00 10.00
Suction (kPa)
48
Figure 4.22 Comparison between measured and predicted volumetric water content in base material at 1.5 hours
Figure 4.23 Comparison between measured and predicted volumetric water content in base material at 3 hours
0.05.0
10.0
15.0
20.0
25.0
30.0
35.040.0
0.00 0.40 0.80 1.20 1.60 2.00
Distance (m)
Espinoza et al. (1993)SEEP/W
0.05.0
10.015.020.025.030.035.040.0
0.00 0.40 0.80 1.20 1.60 2.00
Distance (m)
Espinoza et al. (1993)SEEP/W
30.0
35.0
40.0
onte
nt (%
) s
49
Figure 4.24 Comparison between measured and predicted volumetric water content in base material at 4.5 hours
Figure 4.25 Comparison between measured and predicted volumetric water content
in base material at 6 hours
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
40.0
0.0 0.4 0.8 1.2 1.6 2.0
Distance (m)
Espinoza et al. (1993)SEEP/W
50
Figure 4.26 Comparison between measured and predicted volumetric water content in subbase material at 1.5 hours
Figure 4.27 Comparison between measured and predicted volumetric water content in subbase material at 3 hours
5.0
10.0
15.0
20.0
25.0
0.0 0.4 0.8 1.2 1.6 2.0
Distance (m)
Espinoza et al. (1993)SEEP/W
5.0
10.0
15.0
20.0
25.0
30.0
35.0
0.0 0.4 0.8 1.2 1.6 2.0
Distance (m)
Espinoza et al. (1993)
SEEP/W
51
Figure 4.28 Comparison between measured and predicted volumetric water content in subbase material at 4.5 hours
Figure 4.29 Comparison between measured and predicted volumetric water content in subbase material at 6 hours
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
0.0 0.4 0.8 1.2 1.6 2.0
Distance (m)
Espinoza et al. (1993)
SEEP/W
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
0.0 0.4 0.8 1.2 1.6 2.0
Distance (m)
Espinoza et al. (1993)
SEEP/W
52
The effect of the subbase layer can be appreciated by comparing the changes in volumetric
water content in the base between Examples 2 and 3 (Figure 4.30 and 4.31). Due to the higher
hydraulic conductivity of the subbase, the base drains faster for the system described in
Example 3.
4.4 SUMMARY
In Example 1, SEEP/W predictions were compared to laboratory testing results to establish that SEEP/W could be used to model unsaturated flow under transient conditions. In Example 2, it was shown that SEEP/W could also be used to accurately model the infiltration process that pavement structures may go through during rainfall events. Finally, Example 3 showed that SEEP/W could also be used to model more complicated structures consisting of layers of soil. The SEEP/W results in Example 3 showed a good agreement with previous predictions by Espinoza et al. (29) using first order finite differences. The results from all three examples show that SEEP/W is a useful tool for the modeling of unsaturated flow through layered systems under complex boundary conditions and material characterization. However, it is important to correctly specify the initial and boundary condi-tions in order to accurately predict the unsaturated flow of water through materials. Therefore, material characterization (soil water characteristic curve and hydraulic conductivity curve), initial water table position, and geometry, are some important key conditions.
Figure 4.30 Comparison of measured volumetric water content in base material
at 6 hours for Examples 2 and 3
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
40.0
45.0
0.00 0.40 0.80 1.20 1.60 2.00Distance (m)
Vol
umet
ric
Wat
er C
onte
nt (%
)s
Example 2 -Espinoza et al. (1993)Example 3 - Espinoza et al. (1993)
53
Figure 4.31 Comparison of predicted volumetric water content in base material at 6 hours for Examples 2 and 3
0.05.0
10.015.020.025.030.035.040.045.0
0.00 0.40 0.80 1.20 1.60 2.00
Distance (m)
Example 2 - SEEP/WExample 3 -SEEP/W
54
CHAPTER 5
VERIFICATION OF RESULTS TO FIELD RESULTS FOR CELLS 33, 34, 35
In order to develop an understanding of the behavior of flow of water through flexible pave-
ments under unsaturated conditions, a finite element based numerical model of flow through
flexible pavements was constructed based on actual Mn/ROAD pavement geometries and
material characteristics, along with results from automated time domain reflectometry (TDR)
probes placed in the base layers of the sections studied. The measured TDR volumetric water
contents were used as benchmarks for adjusting laboratory-based unsaturated soil hydraulic
properties. The results show that measured field volumetric moisture contents can be matched
well with SEEP/W, through only minor adjustments in the unsaturated soil hydraulic
properties. In the following, the finite element model will be described, followed by a
discussion of the backcalculation of unsaturated soil hydraulic properties that finally resulted in
the matching of predicted and measured volumetric moisture contents.
5.1 PAVEMENT SYSTEM DESCRIPTION
The pavement systems that were used for this study are Mn/ROAD Cells 33, 34, 35. They all
consist of a layer of hot mix asphalt, a Mn/DOT Class 6 Special crushed granite base, and an
R-12 silty clay subgrade. Figure 5.1 shows the depth of each layer for these sections.
5.2 FINITE ELEMENT MODEL
Based on Figure 5.2, idealized finite element-based cross sections of Mn/ROAD cells 33, 34,
and 35 were constructed using SEEP/W. An overview will be provided of the construction of
the Finite Element Model. Figure 5.3 presents a section of the mesh utilized to model Cell 33,
34 and 35, that included 8046 quadrilateral and triangular elements.
5.2.1 Hot Mix Asphalt Layer
The hot mix asphalt layer was considered as an impervious material, therefore its
characteristics were not required as input for the Finite Element Model. This layer was not
55
represented with
56
Figure 5.1 Layer thicknesses for Mn/ROAD Cells 33, 34, and 35
Figure 5.2 Pavement geometry and dimensions for Cells 33, 34, and 35
12 in
Cell 33
4.04 in
12 in
Cell 34
3.92 in
12 in
Cell 35
3.96 in
HMA
Class 6 Special
1.83 m 4.27 m 4.27 m3.05 m
CL
0.3 m Class 6 Special 0.1 m Hot Mix Asphalt
R-12 silty clay
4:1 4:1
4.0 m
16.5 m
57
Figure 5.3 Section of the Finite Element Model used to represent Cell 33, 34 and 35 finite elements. Only its geometry was taken into account. This assumption was made in order
to simplify the modeling process, since field measurements of infiltration through the hot mix
asphalt layer were not provided.
5.2.2 Base Course
The base layer was represented with 1926 quadrilateral and triangular finite elements. The
material properties, including the soil-water characteristic curve and hydraulic conductivity
curve corresponded to Class 6 Special material, discussed in Chapter 3.
5.2.3 Subgrade Soil
The subgrade was represented with a coarser mesh of finite elements. The finite element model
is composed of 6120 quadrilateral and triangular elements. The subgrade was extended laterally
10 m beyond the area covered by the asphalt and base layer (Figure 5.4), on each side, in order
Hot Mix Asphalt Base Finite
Subgrade Finite Elements
58
Figure 5.4 Finite Element Model used to represent Cells 33, 34, and 35 to represent real conditions more accurately, and provide continuity to the extension of the
subgrade, for consistency with field conditions. The subgrade corresponds to silty clay,
classified as R-12, with the soil water characteristic curve and hydraulic conductivity curve
presented previously in Chapter 3.
5.2.4 Initial and Boundary Conditions
Applying a time-dependent flux boundary condition on the shoulder simulated infiltration due
to precipitation. The rain event selected for this simulation is presented later in the final
element analysis.
In Figure 5.3, the triangular nodes represent boundary conditions. The ones on top of the base
simulate rain events (time dependent flux conditions), and the ones underneath the hot mix
asphalt layer represent no infiltration through this material (q = 0).
An initial water table position was set as well, as part of the boundary conditions. The initial
water table was chosen so as to match the suction value in the pavement to obtain the initial
volumetric water contents of the measured data. In order to induce lateral and vertical drainage
in the system, points of total head equal to 0 m were applied at the bottom corners (subgrade
layer) of the model. Figure 5.4 shows the resulting Finite Element Model.
Extended Subgrade
H = 0 m
Extended Subgrade
H = 0 m
4.0 m
36.5 m
59
5.2.5 Finite Element Model Analysis
To adequately model the non-steady unsaturated flow of water through pavements, a transient
analysis was performed, in which the pavement system at initial equilibrium was subjected to a
transient “rain event,” resulting in time-dependent changes in the volumetric moisture content
throughout the pavement system. Ideally, a detailed set of water table measurements at discrete
well points throughout the pavement cross-section would provide the initial head conditions for
the system. However, the only water table measurements available at the time this study was
performed are in the unpaved shoulder area, which is at an offset from the paved central part of
the pavement. These water table measurements should be expected to be somewhat different
than those obtained under the paved part of the pavement, due to the impervious nature of the
hot mix asphalt layer. Therefore, before starting the transient analysis, a steady-state analysis
was performed to obtain the initial head conditions for the system.
For the steady-state analysis, an initial total head value was set on the vertical sides of the sub-
grade to obtain a water table elevation that provided the required suction values to match the
initial moisture contents measured in the field. Therefore, a total head of 3.82 m was used for
that purpose. Material characterization, boundary conditions (rain event), geometry and mesh
configuration were not different from those used later on the transient analysis. After running
the steady-state analysis, a water table at 0.76 m depth was obtained, as measured from the top
of the pavement at the centerline cross section. The suction corresponding to this depth of the
water table resulted in a match with the initial volumetric water contents of the measured data.
The water table obtained from the steady-state analysis under the impervious paved part of the
pavement is higher than the measured water table in the unpaved shoulder. The water table in
the shoulder was measured at 2.98 m and 3.00 m depths on 2 August 2001 and 7 August 2001,
respectively. Water table measurements using field pressure transducers at Cell 34 under the
centerline of the pavement resulted in water table measurements at a depth of 1.57 m in August
2000. However, a detailed cross section of water table measurements for Cell 33 was not
available at the time the analysis for this report was performed.
60
Finally, transient analysis was performed, in which actual rain events were infiltrated into the
pavement in a time-dependent fashion and the resulting time-dependent changes in heads and
volumetric water content were monitored throughout the pavement model.
The precipitation events input into the numerical model correspond to real measurements
gathered from July 9th through September 30th, 2000. The original data had units of inches per
day, but due to requirements of SEEP/W, it was converted to units of flux (m/s per m2), as
shown in Figure 5.5.
5.2.6 Measured Volumetric Water Contents
Automated TDR volumetric moisture content readings with time in the base material were
obtained at three different locations at each of the pavement sections studied. TDR probes are
located within the base layer at 0.13 m, 0.25 m, and 0.38 m depth (Figure 5.6), at a horizontal
offset of 1.83 m from the centerline. They are designated as locations 101, 102, and 103,
respectively for all the Cells. The corresponding locations of the TDRs in the Finite Element
Model are shown in Figure 5.7.
Figure 5.5 Precipitation events for Cells 33, 34, and 35
-5.0E-08
0.0E+00
5.0E-08
1.0E-07
1.5E-07
2.0E-07
2.5E-07
3.0E-07
3.5E-07
190 200 210 220 230 240 250 260 270
Time (Julian day)
Prec
ipita
tion
(m/s
)
61
Figure 5.6 TDR installation at Mn/DOT Cells 33, 34 and 35
Figure 5.7 TDR location within Finite Element Model for Cells 33, 34, and 35
Hot Mix AsphaltBase
Subgrade Finite Elements
CL
Offset (-1.83 m)
Centerline
0.13 m0.25m 0.38m
0.10 m
0.30 m
3.6 m
Automated *TDR
HMA
Class 6 Special R-12 silty clay
Location 101Location 102Location 103
62
To allow a more detailed and definitive comparison between measured and predicted results,
the span of time from July 31st to September 30th, 2000 was chosen for this study. This range
is 22 days shorter than the one used for the precipitation data. However, the first 22 days, from
July 9th to July 30th, were used to establish an initial volumetric water content baseline in the
model, similar to that observed in the field by July 31st, 2000.
Finally, Figures 5.8 to 5.10 show the measured TDR water contents for each cell.
5.3 MATERIALS CHARACTERIZATION ADJUSTMENT
As discussed, Figures 3.4 and 3.5 present the soil water characteristic curves and the hydraulic
conductivity curves for the base material. The hydraulic conductivity curve shows that Class 6
special is a material with a Ksat value equal to 1.54E-06 m/s. This corresponds to fine sand.
However, within the first 10 kPa the K value has dropped down to about 1E-13 m/s.
Figure 5.8 Measured data for different TDR locations at Cell 33
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
18.0
20.0
210 220 230 240 250 260 270
Time (Julian day)
Vol
umet
ric
Wat
er C
onte
nt (%
) s
TDR Location 101TDR Location 102TDR Location 103
63
Figure 5.9 Measured data for different TDR locations at Cell 34
Figure 5.10 Measured data for different TDR locations at Cell 35
0.0
5.0
10.0
15.0
20.0
25.0
210 220 230 240 250 260 270
Time (Julian day)
Vol
umet
ric
Wat
er C
onte
nt (%
) s
TDR Location 101TDR Location 102TDR Location 103
0.0
5.0
10.0
15.0
20.0
25.0
210 220 230 240 250 260 270
Time ( Julian day)
Vol
umet
ric
Wat
er C
onte
nt (%
) s
TDR Location 101TDR Location 102TDR Location 103
64
The subgrade characterization is presented in Figures 3.6 and 3.7. The soil water characteristic
curve shows that this silty clay subgrade has a high water holding capacity, with a total change
is 15% in the volumetric moisture content over the range of measured suction. The hydraulic
conductivity curve for the subgrade soil also shows that this material has a high resistance to
drainage. Within the first 5 kPa, this material goes from a permeability of 2.75E-08 m/s to a
value close to 2E-13 m/s.
The laboratory-based soil water characteristic curves resulted in predicted volumetric water
contents that were slightly different from the measured field volumetric moisture contents.
Therefore, it was necessary to adjust or “tune” the measured soil water characteristic curves to
fit the measured TDR data from the field. Another reason for the differences in predicted and
measured volumetric moisture contents may be that the TDR volumetric moisture contents may
have a plus or minus 1 to 2 percent differences in volumetric water contents for the same
material, simply due to the limitations of the TDR technology and the required empirical
calibration of results.
The results from the original TDR data are shown, followed by calibration to field results.
Adjusting the air entry values slightly and changing the slope of the soil water characteristic
curves easily achieved the calibration to field results. Finally, the saturated volumetric water
content was adjusted slightly to reflect the variability in the TDR results, due to their limits of
accuracy.
Once calibrated, soil water characteristic curves were obtained, and SEEP/W was used to gen-
erate the appropriate hydraulic conductivity curves, using the Green and Corey (45) approach.
Since the geometry and material properties were the same for Cells 33, 34, and 35, Cell 33 was
chosen for the “tuning” or backcalculation of the soil water characteristic curve and the
resulting hydraulic conductivity curves.
For simplicity during the initial calibration, the infiltration was assumed to be 100 percent of
the measured precipitation. Once the soil water characteristic curve and hydraulic conductivity
65
curves were “tuned,” the infiltration rate was decreased to a percentage of the measured pre-
cipitation as a part of the final calibration to field results. Since it is unlikely that all of the
measured precipitation will infiltrate into the pavement system, only a percentage of the total
infiltration was assumed to infiltrate the pavement.
5.3.1 Initial Calibration Results
The initial calibration results were obtained from the original (uncalibrated) soil water charac-
teristic curve and hydraulic conductivity curve results for Cell 33. Figures 5.11 through 5.13
show the predicted versus measured volumetric water content results. No change was observed
in the volumetric water content, not even during the application of the highest precipitation
events. For all three locations (101, 102, 103), the predicted volumetric water content remained
constant at 32 percent, as shown in Figures 5.11 through 5.13.
5.3.2 Second Calibration Results
In this part of the study, the air entry potential of the soil water characteristic curve for Cell 33
was adjusted to better represent likely field density conditions. Since the density in the field is
Figure 5.11 Volumetric water content at Cell 33 – Location 101
0.0
4.0
8.0
12.0
16.0
20.0
24.0
28.0
32.0
36.0
210 220 230 240 250 260 270
Time (Julian day)
Vol
umet
ric
Wat
er C
onte
nt (%
) s
MeasuredPredicted
24 0
28.0
32.0
36.0
onte
nt (%
) s
66
Figure 5.12 Volumetric water content at Cell 33 – Location 102
Figure 5.13 Volumetric water content at Cell 33 – Location 103
4.0
8.0
12.0
16.0
20.0
24.0
28.0
32.0
36.0
210 220 230 240 250 260 270
Time (Julian day)
Vol
umet
ric
Wat
er C
onte
nt (%
) s
Measured
Predicted
67
likely to be slightly different from that in the laboratory, due to the differences in compaction processes, a small variation in the air entry value of the soil water characteristic curve in the unsaturated region can be assumed (52). Based on a recommendation from Mn/DOT (52), a new air entry value of 3kPa was used. Subsequently, SEEP/W was used to obtain a corresponding hydraulic conductivity curve. The Ksat value used was the same as the original one, 1.54E-06 m/s. The new characterization curves are presented in Figures 5.14 and 5.15. The modifications didn’t change the initial results significantly. The volumetric water content stayed at 32%. Hence, it was decided that some more modifications were needed in order to see a predicted response with the same trends as the observed field response. For this reason, the slopes of the soil water characteristic curve for the Class 6 Special base material (Figure 5.16) were changed slightly. In order to maintain all other aspects of the soil water characteristic
curve, this change in slope resulted in a change in saturated volumetric moisture content (θsat)
of 2 percent. Subsequently, SEEP/W was used to estimate the corresponding hydraulic conduc-tivity curve, shown in Figure 5.17.
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
0.01 1.00 100.00
Suction (kPa)
Figure 5.14 Soil water characteristic curve (air entry = 3 kPa) – Base material (Class 6 special)
68
1.0E-12
1.0E-10
1.0E-08
1.0E-06
1.0E-04
0.0 1.0 100.0
Suction (kPa)
k (m
/s)
Figure 5.15 Estimated hydraulic conductivity curve – Base material (Class 6 special)
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
0.01 1.00 100.00
Suction (kPa)
Figure 5.16 Final soil water characteristic curve – Base material (Class 6 special)
69
Figure 5.17 Estimated hydraulic conductivity curve – Base material (Class 6 special)
Figures 5.18 to 5.20 show the resulting Finite Element Model predictions using the updated soil
water characteristic curve and hydraulic conductivity curve. The results now show a stronger
response that is more consistent with the observed field results. However, the post-rain event
part of the volumetric water content curves tends to be higher than the observed field response,
implying a resistance to drainage in the numerical model that is not present in the field.
The resistance to vertical flow is heavily determined by the properties of the subgrade soil.
Hence, the Ksat value for the subgrade was increased by one order of magnitude (i.e. 10 times),
and the hydraulic conductivity curve was re-estimated using SEEP/W with the existing soil
water characteristic curve and the new Ksat value (Figure 5.21).
Figures 5.22 through 5.24 show the resulting Finite Element Model predictions for TDR 101,
102, and 103. Subsequently, the process was repeated, until correspondence with field results
was achieved.
The final Ksat value for the subgrade was taken as Ksat = 2.7535E-6 m/s (Figure 5.25).
1.0E-11
1.0E-10
1.0E-09
1.0E-08
1.0E-07
1.0E-06
1.0E-05
0.0 1.0 100.0
Suction (kPa)
k (m
/s)
70
0.0
4.0
8.0
12.0
16.0
20.0
24.0
28.0
32.0
210 220 230 240 250 260 270
Time (Julian day)
Measured
Predicted
Figure 5.18 Volumetric water content at Cell 33 – Location 101
6.0
10.0
14.0
18.0
22.0
26.0
30.0
34.0
210 220 230 240 250 260 270
Time (Julian day)
Vol
umet
ric
Wat
er C
onte
nt (%
) f
Measured
Predicted
Figure 5.19 Volumetric water content at Cell 33 – Location 102
71
6.0
10.0
14.0
18.0
22.0
26.0
30.0
34.0
210 220 230 240 250 260 270
Time (days)
Vol
umet
ric
Wat
er C
onte
nt (%
) f
MeasuredPredicted
Figure 5.20 Volumetric water content at Cell 33 – Location 103
1.0E-10
1.0E-09
1.0E-08
1.0E-07
1.0E-06
0.01 1.00 100.00
Suction (kPa)
k (m
/s)
Figure 5.21 Modified hydraulic conductivity curve: 10 times Ksat – Subgrade material (R-12 Silty clay)
72
0.0
4.0
8.0
12.0
16.0
20.0
24.0
28.0
32.0
210 220 230 240 250 260 270
Time (Julian day)
Vol
umet
ric
Wat
er C
onte
nt (%
) f
MeasuredPredicted
Figure 5.22 Volumetric water content at Cell 33 – Location 101
6.0
10.0
14.0
18.0
22.0
26.0
30.0
34.0
210 220 230 240 250 260 270Time (Julian day)
Vol
umet
ric
Wat
er C
onte
nt (%
) f
Measured
Predicted
Figure 5.23 Volumetric water content at Cell 33 – Location 102
73
6.0
10.0
14.0
18.0
22.0
26.0
30.0
34.0
210 220 230 240 250 260 270
Time (Julian day)
Vol
umet
ric
Wat
er C
onte
nt (%
) f
Measured
Predicted
Figure 5.24 Volumetric water content at Cell 33 – Location 103
1.0E-10
1.0E-08
1.0E-06
1.0E-04
0.01 1.00 100.00
Suction (kPa)
Figure 5.25 Final hydraulic conductivity curve: Ksat = 2.7535E-06 m/s – Subgrade material
(R-12 Silty clay)
74
Figures 5.26 through 5.28 show the predicted Finite Element Model results. Now, the overall
shape of the trends in the predicted and measured results at TDR at locations 101 and 103
(Figures 5.26 and 5.28) show close correspondence with each other. It is important to keep in
mind that no attempt has still been made to adjust the actual infiltration rate, hence the
predicted results should show a large response due to a rain event. However, the Finite
Element Model predictions for TDR location 102 (Figure 5.27) are still slightly different from
the field results.
Finally, all the water coming from precipitation events is not going to infiltrate the soil. Hence,
an adjustment is needed for the infiltration function that represents these events in the Finite
Element Model. For the first 22 days, 70% of the precipitation was applied, simply to achieve
the initial measured field values within a reasonable amount of time. Subsequently, starting
with day 23, that percentage was reduced to 30 percent, which seemed to result in a good
correspondence with observed field values, as shown in Figures 5.29 through 5.31.
It can be see that for all three locations the trend in the predicted Finite Element Model results
now follows that of the measured data. In particular, TDR location 101 predicted Finite
Element Model volumetric moisture content values correspond closely with the field data.
6.0
7.0
8.0
9.0
10.0
11.0
12.0
13.0
14.0
210 220 230 240 250 260 270
Time (Julian day)
Vol
umet
ric
Wat
er C
onte
nt (%
) f
Measured
Predicted
Figure 5.26 Volumetric water content at Cell 33 – Location 101
75
6.0
8.0
10.0
12.0
14.0
16.0
18.0
20.0
22.0
24.0
26.0
210 220 230 240 250 260 270
Time (Julian day)
Vol
umet
ric
Wat
er C
onte
nt (%
) f
Measured
Predicted
Figure 5.27 Volumetric water content at Cell 33 – Location 102
6.0
10.0
14.0
18.0
22.0
26.0
30.0
210 220 230 240 250 260 270
Time (Julian day)
Vol
umet
ric
Wat
er C
onte
nt (%
) f
Measured
Predicted
Figure 5.28 Volumetric water content at Cell 33 – Location 103
76
6.0
7.0
8.0
9.0
10.0
11.0
12.0
210 220 230 240 250 260 270
Time (Julian day)
Vol
umet
ric
Wat
er C
onte
nt (%
) f
Measured
Predicted
Figure 5.29 Volumetric water content at Cell 33 – Location 101
6.0
8.0
10.0
12.0
14.0
16.0
18.0
20.0
210 220 230 240 250 260 270
Time (Julian day)
Measured
Predicted
Figure 5.30 Volumetric water content at Cell 33 – Location 102
77
8.0
12.0
16.0
20.0
24.0
28.0
210 220 230 240 250 260 270
Time (Julian day)
Measured
Predicted
Figure 5.31 Volumetric water content at Cell 33 – Location 103
5.3.3 Final Matching of Predicted and Measured Volumetric Water Contents
To obtain a final fit to measured TDR volumetric moisture contents for TDR location 102, the
saturated volumetric moisture content was increased by 3 percent (Figure 5.32), and the
hydraulic conductivity curve was re-estimated using the adjusted soil water characteristic
curve. Due to the small percentage change in the volumetric moisture content, the estimated
hydraulic conductivity curve did not change from the previous one.
As expected, the slight increase in volumetric water content improved the correspondence
between the predicted Finite Element Model and the measured volumetric moisture contents
for at TDR location 102 (Figure 5.33). Using the same approach, the saturated volumetric
moisture content for the Class 6 material around TDR location 103 was reduced, resulting in
the soil water characteristic curve shown in Figure 5.34.
The resulting Finite Element Model prediction shown in Figure 5.35 now shows a close match
with the field results.
78
0.0
10.0
20.0
30.0
40.0
0.01 1.00 100.00
Suction (kPa)
Figure 5.32 Final soil water characteristic curve for Location 102 – Base material
(Class 6 special)
6.0
8.0
10.0
12.0
14.0
16.0
18.0
20.0
22.0
24.0
210 220 230 240 250 260 270
Time (Julian day)
Measured
Predicted
Figure 5.33 Volumetric water content at Cell 33 – Location 102
79
0.0
5.0
10.0
15.0
20.0
25.0
30.0
0.01 1.00 100.00
Suction (kPa)
Figure 5.34 Final soil water characteristic curve for Location 103 – Base material
(Class 6 special)
8.0
10.0
12.0
14.0
16.0
18.0
20.0
22.0
24.0
210 220 230 240 250 260 270
Time (Julian day)
Vol
umet
ric
Wat
er C
onte
nt (%
) f
Measured
Predicted
Figure 5.35 Volumetric water content at Cell 33 – Location 103
80
Tables 5.1 and 5.2 summarize the changes made in the saturated volumetric water content and
the saturated hydraulic conductivity to match field conditions, and Table 5.3 summarizes the
changes made between SEEP/W runs for all cases studied. In summary, it has to be concluded
that minor changes in the volumetric moisture contents, saturated hydraulic conductivity of the
subgrade soil, air entry value and slope of the soil water characteristic curve, with subsequent
adjustments in the hydraulic conductivity curves were needed to match the field data.
5.4 CELL 34
The adjustments in the unsaturated hydraulic properties obtained for Cell 33 were applied for
TDR locations 101, 102, and 103 in Cell 34.
As expected, Figures 5.36 through 5.38 show that the predicted finite element model results
match the shape for the measured field volumetric moisture contents well.
Table 5.1 Cell 33 – Calibration for base layer (Class 6 special)
Final Adjusted Values Parameters Initial data
Location 101 Location 102 Location 103
θ sat (%) 32.02 30.19 33.37 26.97
k sat (m/s) 1.5479E-06 1.5479E-06 1.5479E-06 1.5479E-06
Table 5.2 Cell 33 – Calibration for subgrade soil (R-12 Silty clay)
Parameters Initial data Final Calibration
θ sat (%) 49 49
k sat (m/s) 2.7535E-08 2.7535E-06
81
Table 5.3 Summary of SEEP/W runs performed to adjust predicted volumetric moisture contents to TDR measured values at Cell 33
Parameter Baseline
Run 1 (Adjustment in Air Entry
Value)
Run 2 (Adjustment in Slope
of Soil Water Characteristic
Curve)
Run 3 (Adjustment in Subgrade
Ksat)
Run 4 (Adjustment in
Precipitation and Predictions at TDR Location
101)
Run 5 (Adjustment in Predictions at TDR Location
102)
Run 6 (Adjustment is Predictions
at TDR Location 103)
Base
Air entry
(kPa)
0 3 3 3 3 3 3
Initial Slope 0.24 0.24 0.08 0.08 0.08 0.08 0.08
Subgrade
Ksat (m/s) 2.75E-08 2.75E-08 2.75E-08 2.75E-06 2.75E-06 2.75E-06 2.75E-06
Precipitatio
n (%) 100 100 100 100 70 70 70
θ sat (%) 32.02 32.02 30.19 30.19 30.19 33.37 26.97
81
6.0
7.0
8.0
9.0
10.0
11.0
12.0
13.0
14.0
210 220 230 240 250 260 270
Time (Julian day)
Vol
umet
ric
Wat
er C
onte
nt (%
) f
Measured
Predicted
Figure 5.36 Volumetric water content at Cell 34 – Location 101
4.0
6.0
8.0
10.0
12.0
14.0
16.0
18.0
20.0
210 220 230 240 250 260 270
Time (Julian day)
Vol
umet
ric
Wat
er C
onte
nt (%
) f
Measured
Predicted
Figure 5.37 Volumetric water content at Cell 34 – Location 102
83
8.0
12.0
16.0
20.0
24.0
28.0
32.0
36.0
210 220 230 240 250 260 270
Time (Julian day)
Vol
umet
ric
Wat
er C
onte
nt (%
) f
Measured
Predicted
Figure 5.38 Volumetric water content at Cell 34 – Location 103
5.4.1 Calibration of Results at Locations 101 and 102
Similar to Cell 33, a slight shift in the predicted and measured volumetric water content trends
was observed, which was subsequently adjusted by shifting the soil water characteristic curve
by an increment of 3 percent in the same manner as described previously for Cell 33. Figure
5.39 shows the updated soil water characteristic curve. The hydraulic conductivity curve
stayed unchanged due to the small change in the soil water characteristic curve.
The resulting comparison between the predicted finite element model and measured volumetric
moisture contents for TDR locations 101 and 102 is shown in Figures 5.40 and 5.41. In both
cases, a good match between predicted and measured TDR moisture contents was obtained.
5.4.2 Calibration to Location 103
Finally, for TDR location 103, a nominal reduction of 0.5 percent in the soil water
characteristic curve saturated volumetric moisture content was needed to match the field data.
84
Figure 5.42 shows the new soil water characteristic curve for this location at cell 34, and Figure
5.43 shows
85
Figure 5.39 Final soil water characteristic curve for Location 101 and 102 at Cell 34 –
Base material (Class 6 special)
11.0
11.5
12.0
12.5
13.0
210 220 230 240 250 260 270
Time (Julian day)
Vol
umet
ric
Wat
er C
onte
nt (%
) f
Measured
Predicted
Figure 5.40 Volumetric water content at Cell 34 – Location 101
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
0.01 1.00 100.00
Suction (kPa)
86
10.0
12.0
14.0
16.0
18.0
210 220 230 240 250 260 270
Time (Julian day)
MeasuredPredicted
Figure 5.41 Volumetric water content at Cell 34 – Location 102
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
0.01 1.00 100.00Suction (kPa)
Figure 5.42 Final soil water characteristic curve for Location 103 Cell 34 – Base material (Class 6 special)
87
8.0
12.0
16.0
20.0
24.0
28.0
32.0
36.0
210 220 230 240 250 260 270
Time (Julian day)
Vol
umet
ric
Wat
er C
onte
nt (%
) f
Measured
Predicted
Figure 5.43 Volumetric water content at Cell 34 – Location 103
the resulting overall close comparison between the predicted and measured moisture contents
for TDR location 103.
However, small abnormalities at days 231, 249, and 266 in the measured TDR data were not
captured in the finite element model. These small variations in the measured TDR data might
be due to a problem with the TDRs or a transient problem with the automated data acquisition
system.
Tables 5.4 summarizes the modifications made to the base material to achieve calibration for
Cell 34, and Table 5.5 summarizes the changes made between SEEP/W runs for all cases
studied.
5.5 CELL 35
The same approach that was used for Cells 33 and 34 to calibrate the numerical model to the
field results was used for Cell 35. The same adjustments to material properties (soil water
char-
88
89
Table 5.4 Cell 34 – Calibration for base layer (Class 6 special)
Final calibration Parameters Initial data
Location 101 Location 102 Location 103
θ sat (%) 32.02 33.10 33.10 29.70
k sat (m/s) 1.5479E-06 1.5479E-06 1.5479E-06 1.5479E-06
Table 5.5 Summary of runs to calibrate Cell 34
Parameter Baseline
Run 1 (Unsaturated
Soil Hydraulic Properties
from Cell 33)
Run 2 (Adjustment in Predictions at TDR Location
102)
Run 3 (Adjustment in Predictions at TDR Location
103) Base
Air entry (kPa) 0 3 3 3
Initial Slope 0.24 0.08 0.08 0.08
Subgrade
Ksat (m/s) 2.75E-08 2.75E-06 2.75E-08 2.75E-06
Precipitation (%) 100 70 70 70
θ sat (%) 32.02 30.19 33.10 29.70
acteristic curve and hydraulic conductivity curve) that were used for Cell 34 resulted in rea-
sonable comparisons of predicted and measured volumetric moisture contents for TDR
locations 101 and 103, as shown in Figures 5.44 and 5.45.
For location 102 a small change (2 percent) in the saturated volumetric moisture content was
needed to adjust the results to density variations around the TDRs, with the resulting soil water
characteristic curve shown in Figure 5.46.
The predictions obtained using calibrated data for TDR location 102 are shown in Figure 5.47.
90
8.0
9.0
10.0
11.0
12.0
13.0
14.0
15.0
16.0
17.0
210 220 230 240 250 260 270
Time (Julian day)
Vol
umet
ric
Wat
er C
onte
nt (%
) s
Measured
Predicted
Figure 5.44 Volumetric water content at Cell 35 – Location 101
6.0
8.0
10.012.0
14.0
16.0
18.0
20.022.0
24.0
26.0
210 220 230 240 250 260 270
Time (Julian day)
Vol
umet
ric
Wat
er C
onte
nt (%
) f
Measured
Predicted
Figure 5.45 Volumetric water content at Cell 35 – Location 103
91
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
0.01 1.00 100.00Suction (kPa)
Figure 5.46 Final soil water characteristic curve for Location 102 Cell 35 – Base material (Class 6 special)
6.0
8.0
10.0
12.0
14.0
16.0
18.0
20.0
210 220 230 240 250 260 270
Time (Julian day)
Vol
umet
ric
Wat
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onte
nt (%
) F
Measured
Predicted
Figure 5.47 Volumetric water content at Cell 35 – Location 102
92
Table 5.6 summarizes the modifications made to the base material for Cell 35 to calibrate the
predicted Finite Element Model results to the observed TDR volumetric moisture contents, and
Table 5.7 summarizes the changes made between SEEP/W runs for all cases studied.
Table 5.6 Cell 35 – Calibration for base layer (Class 6 special)
Final calibration Parameters Initial data
Location 101 Location 102 Location 103
q sat (%) 32.02 33.10 32.32 29.70
k sat (m/s) 1.5479E-06 1.5479E-06 1.5479E-06 1.5479E-06
Table 5.7 Summary of runs to calibrate Cell 35
Parameter Baseline
Run 1 (Unsaturated Soil
Hydraulic Properties from Cell 33)
Run 2 (Adjustment in Predictions at
TDR Location 102) Base Air
Entry (kPa) 0 3 3
Initial Slope 0.24 0.08 0.08
Subgrade
Ksat (m/s) 2.75E-08 2.75E-06 2.75E-06
Precipitation
(%) 100 70 100
θ sat (%) 32.02 32.32 29.70
93
5.6 SUMMARY
In this Chapter, a finite element based numerical model of flow through flexible pavements was
constructed based on actual Mn/ROAD pavement geometries and material characteristics.
Measured TDR volumetric water contents in the Mn/DOT Class 6 Special crushed granite layer
were used as benchmarks for adjusting laboratory-based unsaturated soil hydraulic properties.
The results show that measured field volumetric moisture contents can be matched well with
SEEP/W, through only minor adjustments in the unsaturated soil hydraulic properties. In
particular, the results obtained show that SEEP/W is a valuable tool for modeling the
unsaturated flow of water through pavement systems, and can be used to predict results that
compare favorably to measured field results. It is not surprising that some adjustment in
unsaturated hydraulic soil properties was required to obtain a match between predicted and
measured TDR volumetric moisture contents. For example, the variability in TDR readings
alone may result in differences in volumetric moisture contents of up to plus or minus 1 to 2
percent. Other factors may also potentially influence the results. These factors include the
possibility of slight differences in the soil packing arrangement between the field and the
laboratory due to differences in field and laboratory compaction processes, and the potential
presence of residual stresses and anisotropic stress conditions in the field. However, due to
lack of data at this point in time, it is premature to speculate about the presence and effects of
these various on measured unsaturated hydraulic properties of granular base material.
The numerical results presented in this Chapter show the importance of considering that only a
part of the water coming from precipitation events is going to infiltrate the pavement. Hence,
an adjustment is needed for the infiltration function that represents these events in the finite
element model. Based on the adjusted numerical predictions and comparison to measured field
volumetric water contents, it appears that about 30 percent of the precipitation made its way
into the pavement system, meaning that the presence of a flexible impervious pavement surface
does not preclude water from entering into the base and possibly affecting the modulus and
strength of the base material.
94
CHAPTER 6
PARAMETRIC STUDY Chapters 4 and 5 showed that SEEP/W can be used to model unsaturated flow through layered
pavement systems under complex boundary conditions and material characterization. In this
Chapter, the sensitivity of predicted volumetric moisture contents due to variations in SEEP/W
input parameters and unsaturated soil hydraulic properties are evaluated. The key parameters
evaluated are: 1) the initial slope of the soil water characteristic curve, 2) the air entry value of
the Mn/DOT Class 6 Special crushed granite, 3) the saturated hydraulic conductivity of the
Mn/DOT Class 6 Special crushed granite, 4) the air entry value of the R-12 silty clay subgrade
soil, 5) the saturated hydraulic conductivity for the subgrade soil, 6) the type of granular base
material, 7) variations in infiltration characteristics, and 8) the water table location. Since Cells
33-35 are similar, except for the composition of the hot mix asphalt layer, Cell 33 was selected
as a representative pavement configuration, with TDR location 101 being typical for
unsaturated flow of water, due to its high elevation within the base material. The original
conditions for this system were presented in Chapters 3 and 5, Figures 5.16 and 5.17 for the
base layer, and Figures 3.6 and 5.25 for the subgrade.
6.1 INITIAL SLOPE OF THE BASE MATERIAL SOIL WATER CHARACTERISTIC CURVE
Variation of the characteristics of the soil water characteristic curve can lead to significant
variation in the predicted volumetric water content. The first characteristic to be studied was
the initial slope of the soil water characteristic curve. The slope dictates the rate at which volu-
metric water content can change during effective saturation conditions (i.e. before passing the
air entry potential). Three cases were considered: 1) no change, meaning that the original slope
is described by θ sat = 30.19% and a drop of 4.6% up to the air entry value (3 kPa), 2) con-
sidering the initial slope equal to zero (0), taking the air entry volumetric moisture content
(25.59 percent) as representative of all effectively saturated conditions (i.e. with suction values
lower than the 3 kPa air entry value), and 3) considering the slope as being twice as steep as
that for Case 1, resulting in θ sat = 34.79%, and a drop of 9% between 0 kPa and 3 kPa suction
values. Figure 6.1 shows the resulting soil water characteristic curves for the three cases.
95
Figure 6.1 Soil water characteristic curves for initial slope cases
Due to the changes applied to the soil water characteristic curve, the hydraulic conductivity
curve is also affected. Figure 6.2 presents the new curves for these cases, as estimated from
SEEP/W. Although faster drainage could be expected with steeper slopes, the hydraulic con-
ductivity also affects the water flow. The new estimated hydraulic conductivity curves show
that case 1 would likely drain quicker than case 3, which has a steeper slope at the soil water
characteristic curve.
The resulting Finite Element Model predictions are shown in Figure 6.3. It is apparent from
the results that the initial slope of the soil water characteristic curve effects only slightly how
fast the material can drain. Case 1 shows that the base would have a rate of drainage of 0.13 %
within the first 17 days, Case 2 a rate of 0.14%, and Case 3 a rate of 0.09%, showing that the
results are not significantly affected by the change in initial slope of the soil water
characteristic curve.
0.0
10.0
20.0
30.0
40.0
0.01 1.00 100.00
Suction (kPa)
Case 1 - Slope 4.6%Case 2 - Slope 0 %Case 3 - Slope 9 %
96
Figure 6.2 Hydraulic conductivity curves for initial slope cases
8.9
9.0
9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8
210 220 230 240 250 260 270
Time (Julian day)
Vol
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Wat
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nt (%
) f
Predicted - Case 1 (Slope = 4.6%)
Predicted - Case 2 (Slope = 0%)
Predicted - Case 3 (Slope = 9%)
Figure 6.3 Results for initial slope cases
1.0E-11
1.0E-09
1.0E-07
1.0E-05
0.0 1.0 100.0
Suction (kPa)
k (m
/s)
Case 1 - Slope 4.6%Case 2 - Slope 0 %Case 3 - Slope 9%
97
Table 6.1 summarizes the effects, in terms of the maximum volumetric water content, of the
change in the initial slope of the soil water characteristic curve for the base material. Overall it
can be concluded that the predicted volumetric moisture content is relatively insensitive to
changes in the in the initial slope of the soil water characteristic curve.
Table 6.1 Effects of the initial slope of the base material soil water characteristic curve on maximum predicted volumetric moisture content
Parameter Case 1 Case 2 Case 3
Initial slope – Base material (%)
4.6 0 9
Maximum volumetric water content (%)
9.67 9.69 9.65
6.2 AIR ENTRY VALUE OF BASE MATERIAL
Another important parameter to evaluate is the air entry value. It represents the transition suc-
tion value between unsaturated and saturated conditions. Figure 6.4 presents three cases consid-
ered for the soil water characteristic curve with different air entry values. In Case 1, the air
entry value is 3 kPa, which is the original case, in Case 2, the air entry value is 4 kPa, and
finally in Case 3, the air entry value is set to 5 kPa.
As expected, the higher the air entry value the longer the material will retain water. Therefore,
higher volumetric water contents are observed for Case 3 than for Cases 1 and 2, as shown in
Figure 6.5.
Table 6.2 summarizes the effects, in terms of the maximum volumetric water content, of the
change in the air entry value of the soil water characteristic curve for the base material. The
results show that the predicted volumetric moisture content is sensitive to changes in the air
entry value, resulting in almost a doubling of the predicted maximum volumetric water content
from 12.20 percent to 23.41 percent, as the air entry value is increased from 4 kPa to 5 kPa.
The results show the importance of an accurate determination of air entry values for modeling
purposes.
98
Figure 6.4 Base soil water characteristic curves for air entry value cases
0.0
4.0
8.0
12.0
16.0
20.0
24.0
210 220 230 240 250 260 270
Time (Julian day)
Vol
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ric
Wat
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nt (%
) f
Predicted - Case 1 (Air Entry = 3 kPa)Predicted - Case 2 (Air Entry = 4 kPa)Predicted - Case 3 (Air Entry = 5 kPa)
Figure 6.5 Results for air entry value cases at base layer
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
0.01 1.00 100.00Suction (kPa)
Case 1 - Air Entry = 3 kPaCase 2 - Air Entry = 4 kPaCase 3 - Air Entry = 5 kPa
99
Table 6.2 Effects of air entry value of Mn/DOT Class 6 special crushed granite base material on maximum predicted volumetric moisture content
Parameter Case 1 Case 2 Case 3
Air entry value – Base
material (kPa) 3 4 5
Maximum volumetric
water content (%) 9.67 12.20 23.41
6.3 EFFECTS OF KSAT OF Mn/DOT CLASS 6 SPECIAL CRUSHED GRANITE BASE MATERIAL Another important parameter is the saturated hydraulic conductivity of the base material (Ksat).
Three different cases were considered: 1) Ksat = 1.55E-6 m/s (original case), 2) a Ksat which
was 10 times larger than the original value (1.55E-5 m/s), and 3) a Ksat which was 100 times
larger than the original value (1.55E-4 m/s). Again, the resulting hydraulic conductivity curves
shown in Figure 6.6 were estimated from the existing soil water characteristic curve and the
Ksat values studies using SEEP/W.
Figure 6.7 shows the resulting Finite Element Model predictions. The higher the hydraulic
conductivity the faster the material will drain. Also, Case 3 with the highest Ksat value, results
in much more abrupt changes in the predicted volumetric moisture content than for the other
two cases with lower Ksat values. Table 6.3 summarizes the effects, in terms of the maximum
volumetric water content, of the change in the Ksat for the base material. The overall change in
the predicted volumetric moisture content from 9.67 percent to 9.87 percent as the hydraulic
conductivity is increased by two orders of magnitude is only about 2.1 percent, meaning that
overall the predicted volumetric moisture content is fairly insensitive to large variations in
saturated hydraulic conductivity.
100
Figure 6.6 Hydraulic conductivity curves for Ksat cases at base material
9.209.259.309.359.409.459.509.559.609.659.709.759.809.859.90
210 220 230 240 250 260 270
Time (Julian day)
Predicted - Case 1 ( Ksat = 1.55 E-06 m/s)
Predicted - Case 2 ( Ksat = 1.55 E-05 m/s)
Predicted - Case 3 ( Ksat = 1.55 E-04 m/s)
Figure 6.7 Results for Ksat cases at base layer
1.0E-11
1.0E-09
1.0E-07
1.0E-05
1.0E-03
0.0 1.0 100.0Suction (kPa)
Case 1 - Ksat = 1.55 E-06 m/sCase 2 - Ksat = 1.55 E-05 m/sCase 3 - Ksat = 1.55 E-04 m/s
101
Table 6.3 Effects of Ksat of Mn/DOT Class 6 special crushed granite base material on maximum predicted volumetric moisture content
Parameter Case 1 Case 2 Case 3
Ksat – Base material
(m/s) 1.55 E-06 1.55 E-05 1.55 E-04
Maximum volumetric
water content (%) 9.67 9.79 9.87
6.4 AIR ENTRY VALUE OF SUBGRADE MATERIAL
Three distinct air entry values for the R-12 silty clay subgrade soil were considered, namely
Case 1: 0 kPa, which is the original case, Case 2: 5 kPa, and Case 3: 10 kPa. Figure 6.8 shows
the resulting Finite Element Model predictions. Interestingly, the base material drainage
wouldn’t be affected significantly by shifting the air entry values of the soil water characteristic
curve. Case 2 and 3 resulted in only small changes in the volumetric water content.
Table 6.4 summarizes the effects, in terms of the maximum volumetric water content, of the
change in the air entry value of the soil water characteristic curve for the subgrade material. In
summary, the results show that the maximum predicted volumetric moisture content as TDR
location 101 is insensitive to variations in the air entry value of the R-12 silty clay subgrade
soil.
6.5 Ksat AT SUBGRADE MATERIAL
In order to evaluate the effects of resistance to drainage through the base/subgrade interface
and into the subgrade soil, the effects of the subgrade Ksat were evaluated. Figure 6.9 presents
the hydraulic conductivity curves considered for the three cases studied. In Case 1: Ksat =
2.7535E-8 m/s, in Case 2: Ksat = 2.7535E-7 m/s, and finally in Case 3: Ksat = 2.7535E-6 m/s
(original case).
102
9.0
9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8
210 220 230 240 250 260 270
Time (days)
Vol
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Wat
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onte
nt (%
) f
Predicted - Case 1 (Air Entry = 0 kPa)Predicted - Case 2 (Air Entry = 5 kPa)Predicted - Case 3 (Air Entry = 10 kPa)
Figure 6.8 Results for air entry values at subgrade layer
Table 6.4 Effects of air entry value of R-12 silty clay subgrade soil on maximum predicted volumetric moisture content
Parameter Case 1 Case 2 Case 3
Air entry value –
Subgrade (kPa) 0 5 10
Maximum volumetric
water content (%) 9.67 9.71 9.71
103
Figure 6.9 Hydraulic conductivity curves for Ksat cases at subgrade material
Figure 6.10 shows the resulting finite element predictions of volumetric water content at TDR
location 101. As expected, the results show that the higher the subgrade Ksat value, the faster
the drainage. Table 6.5 summarizes the effects, in terms of the maximum volumetric water
content, of the change in the Ksat for the subgrade. As the saturated hydraulic conductivity of
the subgrade soil is increased from 2.7535E-8 m/s in Case 1 to 2.7535E-6 m/s in Case 3, the
maximum predicted volumetric moisture contents at TDR location 101 changes from 10.25
percent to 9.67 percent, which corresponds to a change of about 5.6 percent. Hence, as the
Ksat for the subgrade soil is increased by two orders of magnitude, the resulting predicted
volumetric moisture content increases only by about 5.6 percent, implying a moderate
sensitivity to the Ksat of the subgrade soil.
6.6 EFFECTS OF THE TYPE OF BASE MATERIAL
To evaluate the effects of the type and gradation of granular base course material, Finite
Element Model predictions using Mn/DOT Class 3 Special, Class 4 Special, and Class 5
Special materials were compared to those for Class 6 Special. Figure 6.11 presents the soil
water characteristic curve for these new base materials.
1.0E-13
1.0E-11
1.0E-09
1.0E-07
1.0E-05
0.01 0.10 1.00 10.00 100.00Suction (kPa)
Case 1 - K sat = 2.75 E-08 m/sCase 2 - K sat = 2.75 E-07 m/sCase 3 - K sat = 2.75 E-06 m/s
104
6.06.57.07.58.08.59.09.5
10.010.511.011.512.0
210 220 230 240 250 260 270
Time ( Julian day)
Predicted - Case 1 (K sat = 2.75 E-08 m/s)Predicted - Case 2 (K sat = 2.75 E-07 m/s)Predicted - Case 3 (K sat = 2.75 E-06 m/s)
Figure 6.10 Results for Ksat cases at subgrade layer
Table 6.5 Effects of Ksat of R-12 silty clay subgrade soil on maximum predicted
volumetric moisture content
Parameter Case 1 Case 2 Case 3
Ksat – Subgrade
material (m/s) 2.75 E-08 2.75 E-07 2.75 E-06
Maximum volumetric
water content (%) 10.25 10.20 9.67
105
0.0
5.0
10.0
15.0
20.0
25.0
0.01 1 100 10000
Suction (kPa)
Class 3 specialClass 4 specialClass 5 special
Figure 6.11 Soil water characteristic curves for Mn/DOT aggregate base materials
Since the air entry value for these materials was unknown, they were all assigned the same air
entry value as the Mn/DOT Class 6 Special, namely 3.0 kPa. SEEP/W was used to estimate the
hydraulic conductivity curves for all the granular base course materials. Figures 6.12 and 6.13
show the resulting soil water characteristic curves and hydraulic conductivity curves for the Cl.
3 Sp., 4 Sp., and 5 Sp. base materials.
Figure 6.14 shows the resulting Finite Element Model predictions of the volumetric moisture
content at TDR location 101. The Cl 3 Sp, Cl 4 Sp, and Cl 5 Sp. base materials show higher
equilibrium water content than the Class 6 Special, and therefore less drainage than the Class 6
Special. This may be due to the fact that their soil water characteristic curves do not have
slopes that are steep enough to induce quick change in the volumetric water content for a small
range of suction values.
Interestingly, although Class 4 has the highest ksat value, it results in the highest volumetric
water contents, since its saturated volumetric water content θsat (24.45 %) is the highest one.
106
The Mn/DOT Cl. 3 Sp., Cl. 4 Sp., and Cl. 5 Sp. granular base materials all remain close to their
θsat
Figure 6.12 Soil water characteristic curves (air entry = 3 kPa) for base materials
Figure 6.13 Estimated hydraulic conductivity curves for base materials
0.0
5.0
10.0
15.0
20.0
25.0
30.0
0.01 1 100
Suction (kPa)
Class 3 specialClass 4 specialClass 5 special
1.0E-12
1.0E-10
1.0E-08
1.0E-06
0.01 1.00 100.00Suction (kPa)
Class 3 specialClass 4 specialClass 5 special
107
2.04.06.08.0
10.012.014.016.018.020.022.024.026.0
210 220 230 240 250 260 270
Time (Julian days)
Vol
umet
ric
Wat
er C
onte
nt (%
) f
Predicted - Class 6Predicted - Class 3Predicted - Class 4Predicted - Class 5
Figure 6.14 Results for different types of base materials
value. On the other hand, the Mn/DOT Class 6 Special drains fast enough to ensure that the
base course never reaches the θsat of 30%. Rather, the predicted saturated volumetric water
contents at location 101 stay around 9% equilibrium water content throughout the rain event, as
well as at later times after the rain event. This means that focusing solely on Ksat may be com-
pletely misleading in evaluating the drainage response of base materials. Table 6.6 shows the
maximum difference between saturated volumetric water content obtained from the soil water
characteristic curves in Figure 6.12 and the minimum predicted water content shown in Figure
6.14, reached after the rain event. Again, the results in Table 6.6 show that Cl. 3 Sp., Cl. 4 Sp.,
and the Cl. 5 Sp. do not result in significant drainage and tend to stay at elevated volumetric
water contents that are close to their saturated values, as compared to the Cl. 6 Sp., which
shows a maximum difference of 20.95 percent from its saturated volumetric water content.
This means that the Cl. 6 Sp. crushed granite is significantly more efficient in draining the
infiltrated water out of the base course than the Cl. 3 Sp., Cl. 4 Sp., or the Cl. 5 Sp. granular
materials.
108
Table 6.6 Maximum difference between saturated volumetric water content and predicted volumetric water content for Class 3 special, Class 4 special, Class 5 special, and Class 6 special Mn/DOT granular base materials
Material Class 3 Special
Class 4 Special
Class 5 Special
Class 6 Special
θsat (%) 14.07 24.45 18.97 30.19 Max.
Difference (%) 1.17 2.14 1.38 20.95
6.7 INFILTRATION EFFECTS
In order to evaluate the effects of infiltration on the drainage of base materials, three different
cases are considered, namely Case 1: infiltration is equal to the total precipitation
measurements (100%); Case 2: infiltration is 70 percent of the total precipitation, and Case 3:
initial infiltration is 70% of the total precipitation, followed by a reduction down to 30 percent
after the 22nd day. This last case was the final rain event function used in the numerical
simulations for Cells 33-35, discussed previously.
Figure 6.15 shows the resulting Finite Element Model predictions. As expected the volumetric
moisture content for Case 1 remained the highest, since the greater the volume of infiltrated
water, the more time is needed to drain the water.
Table 6.7 summarizes the effects of infiltration on predicted volumetric moisture contents in
terms of the maximum predicted volumetric water content at TRD location 101 As expected,
Case 1 resulted in the greatest predicted volumetric moisture content of 11.89 percent, as com-
pared to Case 3 (the baseline case) of 9.67 percent, which corresponds to a difference of about
23 percent, meaning that the predicted volumetric moisture content is moderately sensitive to
changes in infiltration.
109
8.0
8.5
9.0
9.5
10.0
10.5
11.0
11.5
12.0
12.5
210 220 230 240 250 260 270
Time (Julian day)
Predicted - Case 1 (100%)Predicted - Case 2 (70%)Predicted - Case 3 (70 and 30%)
Figure 6.15 Results for different rain events
Table 6.7 Effects of infiltration on the maximum predicted volumetric moisture content at TDR location 101
Parameter Case 1 Case 2 Case 3
Rain event (%) 100 70 70 and 30
Maximum volumetric
water content %) 11.89 10.27 9.67
6.8 WATER TABLE INFLUENCE
The initial position of the water table in the Finite Element Model is used to establish the
pressure head conditions for the system at the beginning of each simulation. Therefore, if the
water table is set at different elevations, the system will be under different initial suction and
volumetric moisture conditions.
110
Again, three cases were evaluated. In Case 1, the water table is set at a depth of 0.76 m below
the surface, which corresponds to the original case. In Case 2, the water table is dropped by
0.20 m down to 0.96 m, and in Case 3 the water table was set at a depth of 1.10 m, from the top
of the hot mix asphalt surface. In all cases, the water table depths were located at a horizontal
offset of 1.83 m from the centerline of the pavement, which is the same offset as for TDR loca-
tions 101, 102, and 103. Again, the predicted volumetric moisture content at TDR location 101
was used to compare results from the three different cases.
When the water table is lowered, the suction increased for the points above it. Therefore, the
lower the water table, the lower the volumetric water content. This effect is due to the fact that
the soil water characteristic curve controls the unsaturated moisture conditions, so that when
the suction increases the volumetric water content decreases. Figure 6.16 presents the results
of the Finite Element Model simulations for the different water table positions, and Table 6.8
summarizes the effects, in terms of the maximum volumetric water content, of the change in
water table position.
4.04.55.05.56.06.57.07.58.08.59.09.5
10.0
210 220 230 240 250 260 270
Time (Julian day)
Predicted - Case 1 (water table at 0.76 m)Predicted - Case 2 (water table at 0.96 m)Predicted - Case 3 (water table at 1.10 m)
Figure 6.16 Results for different water table positions
111
Table 6.8 Water table positions – Effects summary
Parameter Case 1 Case 2 Case 3
Water table position (m) 0.76 0.96 1.10
Maximum volumetric water
content (%) 9.67 7.68 6.08
In summary, as the water table is changed by 6.2 percent from 0.76 meters depth to 0.96 meters
depth, the resulting predicted maximum volumetric moisture content changes from 9.67 percent
to 7.68 percent, or by 20.6 percent. This means that the predicted volumetric moisture content
at TDR location 101 is sensitive to changes in water table, as expected.
6.9 SUMMARY
In this Chapter, the sensitivity of predicted volumetric moisture contents due to variations in
key unsaturated soil hydraulic properties and SEEP/W input parameters was evaluated. The
key parameters evaluated are: 1) the initial slope of the soil water characteristic curve, 2) the air
entry value of the Mn/DOT Class 6 Special crushed granite, 3) the saturated hydraulic conduc-
tivity of the Mn/DOT Class 6 Special crushed granite, 4) the air entry value of the R-12 silty
clay subgrade soil, 5) the saturated hydraulic conductivity for the subgrade soil, 6) the type of
granular base material, 7) variations in infiltration characteristics, and 8) the water table
location.
Overall, the most sensitive parameters were: 1) the air entry value of the granular base course
material, which if changed from 4 kPa to 5 kPa, changed the predicted volumetric moisture
content at TDR location 101 from 12.20 percent to 23.41 percent, and 2) water table location,
and 3) gradation and type of Mn/DOT Class granular base material, infiltration effects,
similarly, moderate sensitivity of the predicted volumetric moisture content at TDR location
101 was observed due to changes in: 1) the saturated hydraulic conductivity of the subgrade,
and 2) time history of infiltration. Finally, the predicted volumetric moisture content at TDR
location 101 was found to be relatively insensitive to changes in: 1) the initial slope of the soil
water characteristic curve, 2) the saturated hydraulic conductivity of the granular base material,
and 3) the air entry value for the subgrade soil. Table 6.9 provides a summary of the sensitivity
analysis.
112
Table 6.9 Summary of evaluation of effects of unsaturated soil hydraulic properties and SEEP/W input parameters on the sensitivity of predicted
volumetric moisture content at TDR location 101
Effect Degree of Sensitivity (Low, Moderate, High)
Initial slope of the soil water characteristic curve Low
Air entry value of the Mn/DOT Class 6 Special crushed granite High
Saturated hydraulic conductivity of the Mn/DOT Class 6 Special crushed granite
Low
Air entry value of the R-12 silty clay subgrade soil Low
Saturated hydraulic conductivity of the subgrade soil Moderate
Type of granular base material High
Variations in infiltration characteristics Moderate
Water table location High
The results of the sensitivity study show that it is important to establish good estimates of the
air entry value for granular base course materials, as the water table location throughout the
cross section to be analyzed. The sensitivity to material type (gradation) was expected.
However, the results imply the importance of obtaining actual measured soil water
characteristic curves.
Similarly, the other effects that should be considered important in unsaturated finite element
modeling of unsaturated flow through pavements include establishing the saturated hydraulic
conductivity of the subgrade, as well as a detailed time history of infiltration that not only
includes, but starts well before and extends beyond the rain event of interest.
Finally, the results show that it may be justified in the absence of detailed measurements to
evaluate the following effects: 1) initial slope of the soil water characteristic curve, 2) the
saturated hydraulic conductivity of the granular base course material, and 3) the air entry value
for the subgrade soil, if the soil is a silty clay soil, as evaluated in this study. Other subgrade
soil types would have to be evaluated in the same manner as presented in this Chapter.
110
CHAPTER 7
EFFECT OF EDGE AND UNDER DRAINS ON WATER FLOW THROUGH FLEXIBLE PAVEMENTS
Edge drains typically consist of a backfilled trench with a collector pipe that is placed longi-
tudinally next to the outer traffic lane, under the shoulder. The collector pipe is hooked up to
transverse drain pipes periodically along the highway. The backfill material used is typically
coarse graded gravel (9). Under drains simply consist of a layer of a woven or a non-woven
geotextile that extends all the way under the traffic lanes. The geotextile used is designed so as
to replace an equivalent sand drainage layer, and therefore the design of the geotextile system
is based on common drainage criteria. The FHWA Geotextile Engineering Manual (23)
provides a good overview of the design of geotextiles for drainage purposes. The main
advantage with an under drain is that the drainage path is significantly shortened. Another
feature of under drains is that they may provide a break in capillary suction. Finally, most
under drain systems today are designed to connect to longitudinal collector pipes, which may
also connect to transverse drainage pipes periodically along the highway. However, these
collector pipes are often embedded into the granular base material directly, rather than placed
in a trench, as in the case of edge drains.
In this Chapter, the relative benefits of edge drains and under drains using geotextiles are
evaluated. The pavement system described previously in Chapter 5 for Cell 33 was used as a
baseline for comparisons. Four different drainage designs were Case 1 consisted of the original
pavement section for Cell 33, but now with a 0.02 m thick geotextile underdrain located
between the Mn/DOT Class 6 Special crushed granite base course and the subgrade soil. Case
2 was a modification of Case 1, in which collector pipes were placed directly in the Mn/DOT
Class 6 Special crushed granite coarse base material under the shoulder. In Case 3, a typical
edge drain configuration from Cell 10 is introduced into the Cell 33 pavement system. Case 4
simply consists of a combination of an edge drain and a geotextile under drain system, in which
the under drain now connects to a backfilled trench containing a collector pipe. Thus, the main
111
difference between Case 2 and Case 4 is that the material around the collector pipe (Case 2) is
Class 6 Special crushed granite, whereas the material around the edge drain consists of well
draining gravel (pea gravel).
In all cases, the base and subgrade characterization remained unchanged from that presented in
Figures 5.16 and 5.17 for the base layer, and Figures 3.6 and 5.25 for the subgrade material.
Finally, for simplicity of presentation, the comparison between different drainage systems was
limited to an evaluation of the volumetric water content at TDR location 101.
7.1 DESCRIPTION OF CASE 1: UNDER DRAIN
Figure 7.1 shows the pavement system used in the finite element model, along with the location
of the under drain that was included in this part of the study. The thickness of the geotextile
under drain is 0.02 m.
Figure 7.1 Under drain location for Case 1 in the pavement system
1.83 m 4.27 m 4.27 m3.05 m
CL
0.3 m Class 6 Special 0.1 m Hot Mix Asphalt
R-12 silty clay
4:1 4:1
4.0 m
16.5 m
0.02 m Geotextile
112
The saturated hydraulic conductivity Ksat of the under drain was assumed to be 1.0 E-3 m/s,
which is an order of magnitude higher than the Ksat value for the base material. A hydraulic
conductivity of 1.0 E-3 m/s corresponds to that for uniform sand (26). The corresponding soil
water characteristic curve shown in Figure 7.2 for uniform sand was selected from the SEEP/W
database of soil water characteristic curves, Figure 7.3 shows the corresponding hydraulic
conductivity curve, which was again estimated with SEEP/W based on Green and Corey’s
approach (45).
0.00
5.00
10.00
15.00
20.00
25.00
30.00
0.01 1.00 100.00
Suction (kPa)
Figure 7.2 Soil water characteristic curve for under drain material
113
1.00E-08
1.00E-06
1.00E-04
1.00E-02
0.01 1.00 100.00
Suction (kPa)
Figure 7.3 Estimated hydraulic conductivity curve for under drain material
114
As shown in Figure 7.2, the volumetric water content for the under drain drops down to about
21 percent around 10 kPa suction.
The under drain geotextile layer was represented with a row of 304 quadrilateral elements.
Figure 7.4 shows a section of the left side of the system with this new layer.
Figure 7.4 Finite Element Model for Case 1 (Under drain system)
7.2 DESCRIPTION OF CASE 2: UNDER DRAINS WITH COLLECTOR PIPES
Figure 7.5 describes the pavement system used in the finite element model, along with the loca-
tion of the under drain and collector pipes that were used for this case. The thickness of the
geotextile under drain is 0.02 m and the collector pipes have a diameter of 0.1m.
The material characterization for the geotextile is the same as presented in Figures 7.2 and 7.3.
Figure 7.6 presents a section of the left side of the system with the underdrain and collector
pipes. The geotextile layer was represented with a row of 186 quadrilateral elements that is
extended along the Hot Mix Asphalt layer length up to 0.1 m diameter collector pipes. In order
to simulate the collector pipes, a total pressure head equal to 0 m is set around the pipe circum-
ference as a boundary condition.
115
Figure 7.5 Under drain and collector pipes location for Case 2 in the pavement system
Figure 7.6 Finite Element Model for Case 2 (Under drain with collector pipes)
1.83 m 4.27 m 4.27 m3.05 m
CL
0.3 m Class 6 Special 0.1 m Hot Mix Asphalt
R-12 silty clay
4:1 4:1
4.0 m
16.5 m
0.02 m Geotextile
Collector Pipe
116
7.3 DESCRIPTION OF CASE 3: EDGE DRAINS
The third case has edge drains at the ends of the asphalt layer. The drains were represented with
0.1 m diameter pipes, around which there was free draining material. The free draining
material was assumed to have the properties shown previously in Figures 7.2 and 7.3, which
correspond to uniform sand. The geometry is shown in Figure 7.7.
Figure 7.7 Edge drain location for Case 3 in the pavement system The material around the edge drain was represented with triangular elements in the finite ele-
ment model. Figure 7.8 shows the left side of the system. In order to simulate the drainage
pipes, a pressure head equal to 0 m is set around the pipe circumference as a boundary condi-
tion.
Figure 7.8 Finite Element Model for Case 3 (Edge drain)
1.83 m 4.27 m 4.27 m3.05 m
CL
0.3 m Class 6 Special 0.1 m Hot Mix Asphalt
R-12 silty clay
4:1 4:1
4.0 m
16.5 m
Drainage Material
Edge Drain
117
7.4 DESCRIPTION OF CASE 4: COMBINATION OF EDGE AND UNDER DRAINS
The last case consists of the combination of Cases 1 and 3, in which an edge drain system is
combined with an under drain system. The pavement system and materials are the same as in
Cases 1 and 3, with under drains connecting to an edge drain system surrounded by well
draining material, whose hydraulic properties can be represented with Figures 7.2 and 7.3.
Figure 7.9 presents a snapshot of the finite element mesh for this case.
Figure 7.9 Finite Element Model for Case 4 (Combination of drain systems)
7.5 DRAINAGE SYSTEMS COMPARISON
Figure 7.10 shows a comparison of volumetric water content versus time for the four drainage
schemes presented. Interestingly, although Case 1 had an under drain layer, the resulting
volumetric water content is about the same as the reference case without any positive drainage
systems, implying that the sole presence of under drains in combination with Mn/DOT Class 6
Special crushed granite aggregate base course material may not be very effective in reducing
the time to drain or the equilibrium moisture content in the base.
In Cases 2, 3 and 4, the equilibrium moisture contents as compared to Case 1 (no drainage sys-
tem) were lowered from about 9.0 to 9.5 percent down to about 5.0 percent at TDR location
101. However, Figure 7.10 also shows that Cases 2, 3, and 4 resulted in about the same rate of
drainage. This means that whether the under drain is drained into a collector pipe that is placed
118
0.01.0
2.03.04.05.0
6.07.08.0
9.010.0
210 220 230 240 250 260 270
Time (Julian Day)
No drainage systemCase 1:Under DrainCase 2: Under Drain with Collector PipesCase 3: Edge DrainsCase 4: Combination
Figure 7.10 Results comparison for drainage systems
in the granular base course, or to a backfilled trench with a collector pipe (edge drain), the
resulting drainage is about the same. Also, the benefits of under drains with a collector system
are about the same as those of a traditional edge drain system.
In summary, the results show that under drains by themselves do not significantly improve the
drainability of dense graded bases, whereas the introduction of either collector pipes or edge
drains in combination with under drains is very effective in reducing the amount of moisture in
a Mn/DOT Class 6 Special crushed granite base course material. These benefits are likely due
to the effects of zero head boundary conditions around the collector pipes and edge drains,
which in combination with the shortened drainage path due to the under drains affect the
distribution of suctions significantly throughout the base material, thus promoting better
drainage.
119
CHAPTER 8
SUMMARY, CONCLUSIONS AND RECOMMENDATIONS
With the evaluation of SEEP/W for modeling unsaturated flow (Chapter 4), it was possible to
conclude that this program can be used to model unsaturated flow under transient conditions
through layered systems under complex boundary conditions and material characterization.
However, it is important to correctly specify the initial and boundary conditions in order to
accurately predict the unsaturated flow of water through materials. Therefore, material charac-
terization (soil water characteristic curve and hydraulic conductivity curve), initial water table
position, and geometry, are some important key conditions. In addition, it was shown that
SEEP/W could also be used to accurately model the infiltration process that pavement
structures may go through during rainfall events. Finally, it was shown that SEEP/W could
also be used to model more complicated structures consisting of layers of soil.
The verification of results to field results for cells 33, 34, and 35 (Chapter 5) illustrated how it
is possible to match well with SEEP/W measured field volumetric moisture contents, through
only minor adjustments in the unsaturated soil hydraulic properties. The results obtained show
that SEEP/W is a valuable tool for modeling the unsaturated flow of water through pavement
systems, and can be used to predict results that compare favorably to measured field results.
It is not surprising that some adjustment in unsaturated hydraulic soil properties was required to
obtain a match between predicted and measured TDR volumetric moisture contents. Some fac-
tors that may influence the results include the possibility of slight differences in the soil
packing arrangement between the field and the laboratory due to differences in field and
laboratory compaction processes, and the potential presence of residual stresses and anisotropic
stress conditions in the field. However, due to lack of data at this point in time, it is premature
to speculate about the presence and effects of these various factors on measured unsaturated
hydraulic properties of granular base material.
120
In addition, the numerical results presented in Chapter 5 show the importance of considering
that only a part of the water coming from precipitation events is going to infiltrate the
pavement. Hence, an adjustment is needed for the infiltration function that represents these
events in the finite element model.
The parametric study presented in Chapter 6 showed the sensitivity of predicted volumetric
moisture contents due to variations in key unsaturated soil hydraulic properties and SEEP/W
input parameters was evaluated. The most sensitive parameters were: 1) the air entry value of
the granular base course material, which if changed from 4 kPa to 5 kPa, changed the predicted
volumetric moisture content at TDR location 101 from 12.20 percent to 23.41 percent, and 2)
water table location, and 3) gradation and type of Mn/DOT Class aggreagate base course
material. Similarly, moderate sensitivity of the predicted volumetric moisture content at TDR
location 101 was observed due to changes in: 1) the saturated hydraulic conductivity of the
subgrade, and 2) time history of infiltration. Finally, the predicted volumetric moisture content
at TDR location 101 was found to be relatively insensitive to changes in: 1) the initial slope of
the soil water characteristic curve, 2) the saturated hydraulic conductivity of the granular base
material, and 3) the air entry value for the subgrade soil.
The results of the sensitivity study show that it is important to establish good estimates of the
air entry value for granular base course materials, as the water table location throughout the
cross section to be analyzed. The sensitivity to material type (gradation) was expected. The
results imply the importance of obtaining actual measured soil water characteristic curves.
Similarly, the other effects that should be considered important in unsaturated finite element
modeling of unsaturated flow through pavements include establishing the saturated hydraulic
conductivity of the subgrade, as well as a detailed time history of infiltration that not only
includes, but starts well before and extends beyond the rain event of interest.
121
After the evaluation of the effect of edge and under drains on water flow through flexible pave-
ments (Chapter 7), the results show that under drains by themselves do not significantly
improve the drainability of dense graded bases, whereas the introduction of either collector
pipes or edge drains in combination with under drains is very effective in reducing the amount
of moisture in a Mn/DOT Class 6 Special crushed granite base course material. These benefits
are likely due to the effects of zero head boundary conditions around the collector pipes and
edge drains, which in combination with the shortened drainage path due to the under drains
affect the distribution of suctions significantly throughout the base material, thus promoting
better drainage.
The results in Appendix B show that saturated flow assumptions do not take into consideration
the variation of the hydraulic conductivity with volumetric water content or suction. This
means that the time to drain evaluated on the basis of traditional “time to drain” equations
(Equation 3.2) results in an unrealistically short time to drain compared to the more realistic
unsaturated conditions. The more realistic unsaturated flow theory considers the hydraulic
conductivity as a function of the matric suction experienced in the material with drainage.
Hence, the time to drain calculated based on unsaturated flow theory will generally be longer
that that one evaluated under saturated flow assumptions for dense graded granular base
materials.
In summary, the results obtained in this study show that pavement drainage should generally be
modeled using unsaturated flow theory. The quality of the predictions is heavily dependent
upon the accuracy of both the soil water characteristic curve and the hydraulic conductivity
curve obtained in the laboratory, as well as on having a detailed knowledge of field conditions.
In addition to having detailed water table measurements throughout the cross section to be
analyzed, it is also important to have knowledge of the variation of moisture contents in both
the vertical and horizontal plane. In particular, horizontal arrays of TDRs around key
interfaces could play a major role in furthering the understanding of unsaturated flow through
flexible pavements obtained in this project.
122
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2. American Association of State Highway and Transportation Officials, AASHTO Guide
for Design of Pavement Structures. Washington, D.C., 1998.
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4. Cedergren, H.R., Drainage of Highways and Airfield Pavements. Wiley Interscience
Publication. New York, 1974.
5. Cedergren, H.R., Why All Important Pavements Should be Well Drained. Transportation
Research Record 1188, Transportation Research Board, National Research Council.
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10. Lambe, R. and R. Whitman, Soil Mechanics, Wiley, New York, 1969.
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13. Casagrande, A. and W.L. Shannon, “Base Course Drainage for Airport Pavements.”
Proceedings of the American Society of Civil Engineers, Vol. 77, pp 792-814, 1952.
123
14. Cedergren, H.R., Seepage Requirements of Filters and Pervious Bases. Soil Mechanics
and Foundation Division. ASCE, SM5, pp. 15-23, 1956.
15. Cedergren, H.R, K.H. O’Brien, and J.A. Arman, “Guidelines for the Design of
Subsurface Drainage Systems for Highway Structural Sections.” Report No. FHWA-RD-
72-30. Washington, D.C., 1972.
16. Liu, S.J., J.K. Jeyapalan, and R.L. Lytton, Characteristics of Base and Subgrade Drain-
age of Pavements, Transportation Research Record 945, Transportation Research Board,
National Research Council. Washington, D.C., 1983.
17. Carpenter, S.H, “Highway Subdrainage Design by Microcomputer (DAMP). Drainage
Analysis and Modeling Programs.” Report No. FHWA-IP-90-012. Washington, D.C.,
1990.
18. Pufahl, D.E., R.L. Lytton, and H.S. Liang, An Integrated Computer Model to Estimate
Moisture and Temperature Effects beneath Pavements. Presented at the Annual Meeting
of the Transportation Research Record. Washington D.C.,1990.
19. Huang, Y.H., Pavement Analysis and Design. Prentice-Hall. New York, 1993.
20. Betram, G.E, An Experimental Investigation of Protective Filters. Publication No. 267,
Graduate School of Engineering, Harvard University. Cambridge, 1940.
21. Christopher, B.R. and V.C. McGuffey, Pavement Subsurface Drainage Systems.
National Cooperative Highway Research Program, Synthesis of Highway Practice 239,
National Academy Press, Washington, D.C., 1997.
22. American Society for Testing Materials (ASTM), Annual Book of ASTM Standards,
Concrete and Aggregates, Vol. 04.02. Philadelphia, 1989.
23. FHWA Geotextile Engineering Manual, Course Text. Report No. FHWA-HI-89-050,
Federal Highway Administration, 1989.
24. Fredlund, D.G. and H. Raharjo, Soil Mechanics for Unsaturated Soils. 1993 pp 30-31.
25. Hillel, D., Introduction to Soil Physics. 1980.
26. Freeze, R.A. and J.A. Cherry, Groundwater. Prentice-Hall. Englewood Cliffs, 1979.
27. Gupta, S.C. and D. Wang (2001). Soil Water Retention. In: R. Lal. Encyclopedia of Soil
Science. Marcel-Dekker (In print).
28. Fredlund, D.G. and A. Xing, Equations for the Soil-Water Characteristic Curve. Can.
Geotech J., Vol 31, pp. 521-532, 1994.
124
29. Espinoza, R.D., P.L. Bourdeau, and T.D. White, Pavement Drainage and Pavement
Shoulder Joint Evaluation and Rehabilitation. Numerical Analysis of Infiltration and
Drainage in Pavement Systems. Report. Purdue University, West Lafayette, 1993.
30. Brooks, R.H. and A.T. Corey, Hydraulic Properties of Porous Media. Hydrology Paper
No. 3, Civil Engineering Dep., Colorado State Univ. Fort Collins, 1966.
31. Bear, J., Dynamics of Porous Media. Dover Publications, Inc. New York, 1972.
32. Van Genuchten, M.A., Closed-form equation for predicting the hydraulic conductivity of
unsaturated soils. Soil Sci. Soc. Amer. Proc., Vol. 44, pp. 892-898, 1980.
33. Wallace, K.B. and F. Leonardi, The influence of soil properties on the wetting-up of
earth structures. ARRB Proceedings, Volume 8, session 18. 1976.
34. Brutsaert, W, Probability Laws for Pore-size Distribution. Soil Sci., 101, pp. 85-92,
1966.
35. Vauclin, M., D. Khanji, and G. Vachaud, Experimental and Numerical Study of a
Transient Two Dimensional Unsaturated-Saturated Water Table Recharge Problem.
Water Resources Research, Vol. 15, No. 5, 1089-1101, 1979.
36. Bear, J. and A.M. Verruijt, Modeling Groundwater Flow and Pollution. D. Reidel Pub-
lishing Company. Boston, 1990.
37. Gray, W.G. and S.M. Hassanizadeh, Unsaturated Flow Theory Including Interfacial
Phenomena. Water Resources Research, Vol. 27, No. 8, 1855-1863, 1991.
38. Mualen, Y., Modified Approach to Capillary Hysteresis Based on a Similarity Hypoth-
esis. Water Resources Research, Vol. 9, No. 5, 1324-1331, 1973.
39. Brutsaert, W., The Permeability of a Porous Medium Determined from Certain Proba-
bility Lays for Pore Size Distribution. Water Resources Research, Vol. 4, No. 2, 425-
434, 1968.
40. Burdine, N.T., Relative Permeability Calculations from Pore Size Distribution Data.
Trans. AIME, Vol. 198, pp. 71-78, 1953.
41. Mualen, Y., A New Model for Predicting the Hydraulic Conductivity of Unsaturated
Porous Media. Water Resources Research, Vol. 12, No. 3, 503-522, 1976.
42. Richards, B.G., Behavior of Unsaturated Soils. In Soil Mechanics-New Horizons, Ch. 4.
American Elsevier Publishing Company Inc. New York, 1974.
125
43. Gardner, W.R., Calculation of Capillary Conductivity from Pressure Plate Outflow
Data. Soil Sci. Soc. Am.J. 3, pp. 317-320, 1956.
44. Rawls, W. J., Infiltration and Soil Water Movement. Handbook of Hydrology, Editor in
Chief D. R. Maidment. McGraw Hill. New York, 1992.
45. Green, R.E. and J.C. Corey, Calculation of Hydraulic Conductivity: A Further Evalua-
tion of Some Predictive Methods. Soil Sci. Soc. Amer. Proc., Vol. 35, pp. 3-8, 1971.
46. Childs, E.C. and N. Collis-George, The Permeability of Porous Materials. Proc. Roy.
Soc. London Vol. 201 A, pp. 392-405, 1950.
47. Fredlund, D.G., A. Xing, and S. Huang, Predicting the Permeability Function for
Unsaturated Soils Using the Soil-Water Characteristic Curve. Can. Geotech. J., Vol. 31,
pp. 533-546, 1994.
48. SEEP /W Users Manual, Version 4.24. GEO-SLOPE International Ltd. Calgary, 2001.
49. NHI Course No. 130126 Pavement Subsurface Drainage Design, National Highway
Institute, Arlington, VA, April, 1999.
50. DRIP (Drainage Requirements in Pavements), Version 1.00. Federal Highway Adminis-
tration. Washington, D.C., 1996.
51. Barber, E.S. and C.L. Sawyer, Highway Subdrainage, Proceedings, Highway Research
Board, pp. 643-666, 1952.
52. Roberson, R., Personal Communication, 2002.
A - 1
APPENDIX A
EVALUATION OF TIME TO DRAIN
CALCULATIONS FOR PAVEMENTS
A - 2
APPENDIX A EVALUATION OF TIME TO DRAIN CALCULATIONS FOR PAVEMENTS
Drainage performance of base materials is often measured in terms of the time it takes to drain
a certain amount of water out of the paper. The two drainage levels that are most often used
are the time to drain either 50 percent or 90 percent of the water out of the pavement.
Traditional time to drain calculations are performed using: 1) traditional formulations by
Casagrande and Shannon (13), and Barber and Sawyer (51), discussed in Chapter 3, and 2)
from unsaturated flow theory. The differences in predicted time to drain for these two cases are
compared and discussed. The saturated time to drain calculations were performed using the
program DRIP (50), whereas the unsaturated flow calculations were obtained with SEEP/W
(48).
A.1 Time to Drain from Unsaturated Flow Theory
A one-dimensional finite element-based flow model was run under unsaturated conditions,
using SEEP/W. The finite element model consisted of a one m tall column that had a 0.4 m by
0.4 m cross section, with 0.05 x 0.05m quadrilateral elements (Figure A.1). The column was
setup so that the material was fully saturated initially; therefore no water table was set. Lateral
sides were considered impervious (q = 0 m/s per square meter). Subsequently, the bottom of
the column was subjected to atmospheric conditions, and the column was allowed to drain
freely.
Figure A.1 Finite element model – Geometry and boundary conditions
A - 3
The purpose of this finite element model is to observe how the flow behaves under unsaturated
conditions, with different material characterizations. Four different materials were used: Class
3 Special, Class 4 Special, Class 5 Special, and Class 6 Special. Figures A.2 to A.5 present the
different soil-water characteristic curves for these materials.
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
0.01 0.10 1.00 10.00 100.00
Suction (kPa)
Figure A.2 Class 3 special – Soil water characteristic curve
0.0
5.0
10.0
15.0
20.0
0.01 0.10 1.00 10.00 100.00 1000.00
Suction (kPa)
Figure A.3 Class 4 special – Soil water characteristic curve
A - 4
0.05.0
10.015.020.025.030.035.040.045.0
0.01 0.10 1.00 10.00 100.00 1000.00
Suction (kPa)
Figure A.4 Class 5 special – Soil water characteristic curve
0.0
10.0
20.0
30.0
40.0
50.0
60.0
0.01 0.10 1.00 10.00 100.00
Suction (kPa)
Figure A.5 Class 6 special – Soil water characteristic curve
For each material, five hydraulic conductivity models were applied. The hydraulic
conductivity models used include models by Gardner (43), Brooks and Corey (30), Green and
Corey (45), Van Genuchten (32), and Fredlund and Xing (28). Figures A.6 to A.9 present the
hydraulic conductivity for each material, based on the different models.
A - 5
1.0E-37
1.0E-33
1.0E-29
1.0E-25
1.0E-21
1.0E-17
1.0E-13
1.0E-09
1.0E-05
0.01 0.10 1.00 10.00 100.00Suction (kPa)
Brooks & CoreyVanGenuchtenGardnerGreen & CoreyFredlund and Xing
Figure A.6 Comparison of hydraulic conductivity models in Class 3 special
1.0E-341.0E-311.0E-281.0E-251.0E-221.0E-191.0E-161.0E-131.0E-101.0E-071.0E-04
0.01 0.10 1.00 10.00 100.00 1000.00Suction (kPa)
Brooks & CoreyVanGenuchtenGardnerGreen & CoreyFredlund and Xing
Figure A.7 Comparison of hydraulic conductivity models in Class 4 special
A - 6
1.0E-351.0E-321.0E-291.0E-261.0E-231.0E-201.0E-171.0E-141.0E-111.0E-081.0E-05
0.00 0.01 0.10 1.00 10.00 100.00 1000.00Suction (kPa)
Brooks & CoreyVanGenuchtenGardnerGreen & CoreyFredlund and Xing
Figure A.8 Comparison of hydraulic conductivity models in Class 5 special
1.0E-31
1.0E-27
1.0E-23
1.0E-19
1.0E-15
1.0E-11
1.0E-07
0.00 0.01 0.10 1.00 10.00 100.00Suction (kPa)
Brooks & CoreyVanGenuchtenGardnerGreen & CoreyFredlund and Xing
Figure A.9 Comparison of hydraulic conductivity models in Class 6 special
The evolution of the volumetric water content at the top of the soil column at selected times
during the experiment is shown in Figures A.10 to A.13.
A - 7
5.0
10.0
15.0
20.0
25.0
30.0
35.0
1.0E-05 1.0E-02 1.0E+01 1.0E+04 1.0E+07 1.0E+10
Time (days)
Vol
umet
ric
Wat
er C
onte
nt (
%)
s
Brooks & CoreyVan GenuchtenGardnerGreen & CoreyFredlund & Xing
Figure A.10 Class 3 special – Evolution of volumetric water content with time at the top of the soil column
4.0
6.0
8.0
10.0
12.0
14.0
16.0
18.0
20.0
1.0E-05 1.0E-03 1.0E-01 1.0E+01 1.0E+03Time (days)
Vol
umet
ric
Wat
er C
onte
nt (%
) s
Brooks & CoreyVan GenuchtenGardnerGreen & CoreyFredlund & Xing
Figure A.11 Class 4 special – Evolution of volumetric water content with time at the top of the soil column
A - 8
15.0
20.0
25.0
30.0
35.0
40.0
45.0
1.0E-01 1.0E+01 1.0E+03 1.0E+05 1.0E+07 1.0E+09
Time (days)
Vol
umet
ric
Wat
er C
onte
nt (%
) s
Brooks & CoreyVan GenuchtenGardnerGreen & CoreyFredlund & Xing
Figure A.12 Class 5 special – Evolution of volumetric water content with time
at the top of the soil column
0.05.0
10.015.020.025.030.035.040.045.050.055.0
1.0E-05 1.0E-02 1.0E+01 1.0E+04 1.0E+07 1.0E+10
Time (days)
Brooks & CoreyVan GenuchtenGardnerGreen & CoreyFredlund & Xing
Figure A.13 Class 6 special – Evolution of volumetric water content with time
at the top of the soil column
Based on the change in volumetric water content, the time to drain was determined (Table A.1)
for each combination of hydraulic conductivity model and material.
A - 9
Table A.1 Comparison of drainage times under unsaturated flow conditions
Material Hydraulic Conductivity
Model
Time for 50%
Drainage (days)
Time for 90%
Drainage (days)
Brooks & Corey (30) 2.08 3.54E+04
Van Genuchten (32) 7.64 1.04E+05
Gardner (43) 0.42 5.21
Class 3
Special
Green & Corey (45) 7.64E+02 7.64E+04
Brooks & Corey (30) Not reached Not reached
Van Genuchten (32) Not reached Not reached
Gardner (43) Not reached Not reached
Class 4
Special
Green & Corey (45) Not reached Not reached
Brooks & Corey (30) 1.46 Not reached
Van Genuchten (32) 17.36 Not reached
Gardner (43) 0.42 Not reached
Class 5
Special
Green & Corey (45) 2.64E+03 Not reached
Brooks & Corey (30) 2.22 1.94E+06
Van Genuchten (32) 14.58 7.64E+06
Gardner (43) 0.28 3.47
Class 6
Special
Green & Corey (45) 4.17E+03 2.78E+04
Due to the geometry of the finite element model (Figure A.1), the maximum suction that can be
achieved is 9.8 kPa. The total height of the mesh is 1 m, therefore, if the water table reaches
the bottom of the mesh, the pressure head created above the water table is equal to 1m. This
suction head corresponds to a suction pressure of 9.8 kPa. The materials will only show
significant drainage if the air entry potential is considerably less than the maximum suction
sustained by the height of the soil column. Hence, the results from the finite element analyses
for all four materials showed a negligible to small change in volumetric water content, meaning
that the times to drain to 50 and 90 percent were also affected greatly. For example, according
to the Class 4 Special soil water characteristic curve, a pressure higher than 10 kPa is needed to
have a reduction of volumetric water content. Because the system maximum developed suction
A - 10
is 9.8 kPa, this material never achieves 50 percent drainage, let alone 90 percent drainage. This
phenomenon was also observed with the Class 5 Special at about 90% drainage, meaning that
the Class 4 and Class 5 base materials never drain fully.
The results from the numerical simulations using SEEP/W and full-unsaturated conditions
show that the different hydraulic conductivity models all result in very different times to drain.
The time difference varies from a few hours to many days. Although all of the hydraulic
conductivity models follow the same general trend, the materials drain at dissimilar times. For
all the materials, the fastest time to drain is obtained when using Gardner’s model, for 50 and
90%. If this model is compared against the others (Figures 5.6 through 5.9), it is possible to
see that the slope of the hydraulic conductivity curve is more gradual than for the other models.
Therefore, the reduction in hydraulic conductivity is slower and the material could be drained
faster. On the other hand, when using Green and Corey’s model, the time to drain is really
long, due to the steep slope in the hydraulic conductivity curve, as well as the continuous
change in hydraulic conductivity starting at zero (0) kPa.
A.2 Time to Drain from Saturated Flow Theory
The parameters used to perform the calculations in DRIP are summarized in Table A.2. Due to
the saturated condition assumption, the hydraulic conductivity does not change. Therefore, a
ksat value is needed for each material. This value is the same for all the hydraulic conductivity
models used previously. From each soil water characteristic curve, the effective porosity (ne) is
determined because is the difference between θ sat and θ R.
The height (H) of the model is 1 m, the width of the drainage path (W) is 0.4 m, and the
resultant length of the drainage path (LR) is 0.4 m.
A - 11
Table A.2 Saturated case – Model parameters
Material H
(m)
k
(m/s)
W
(m)
LR
(m)
θ sat
(%)
θ R
(%)
ne
(%)
Class 3 Special 4.0 2.20E-07 0.4 0.40 32.01 16.97 15.04
Class 4 Special 4.0 4.20E-06 0.4 0.40 14.35 11.28 3.08
Class 5 Special 4.0 3.80E-06 0.4 0.40 40.70 16.09 24.61
Class 6 Special 4.0 2.00E-06 0.4 0.40 52.08 5.92 46.16
The calculations in DRIP of time-to-drain are based on two methods: the Barber and Sawyer
method (51) and the Casagrande and Shannon method (13). These two procedures were
applied to find time to drain at 50% and 90% of drainage. Table A.3 shows the results.
Table A.3 Comparison of drainage times under saturated flow conditions
Method
Barber and Sawyer (51) Casagrande and Shannon (13) Material
Time for 50%
Drainage (min)
Time for 90%
Drainage (min)
Time for 50%
Drainage (min)
Time for 90%
Drainage (min)
Class 3 Special 2.22 38.40 4.41 39.56
Class 4 Special 0.02 0.41 0.05 0.42
Class 5 Special 0.21 3.64 0.42 3.75
Class 6 Special 0.75 12.94 1.48 13.33
Interestingly, the time for 50% drainage based on the Barber and Sawyer (51) method (Equa-
tion 3.2) is about 50 percent of the time to drain obtained with Casagrande and Shannon’s (13)
approach (Equation 3.2).
A - 12
In stark contrast to the time to drain based on unsaturated conditions, the Class 4 Special material showed the quickest drainage time for 50% and 90%. This soil has the highest Ksat of all the materials used for the modeling, and subsequently shows faster drainage using saturated flow theory that ignores suction effects. Although saturated flow theory considers the material characterization and geometry of the sys-tem, it does not take into account the variation of the hydraulic conductivity with volumetric water content or suction that represents the true behavior of the material under field conditions. Therefore, by taking just the ksat value and using that throughout to characterize the drainage of base materials the time to drain will obviously be significantly shorter than for the more realistic unsaturated conditions, in which the hydraulic conductivity is a function of the suction experienced in the material with drainage. A comparison of Tables 5.1 and 5.3 shows that most materials would drain under saturated conditions in just a few minutes, while for unsaturated conditions it would take days or not be achieved.
A.3 Comparison Applied to a Real Example Based on the previous results, a more detailed comparison between saturated and unsaturated conditions was performed, using a SEEP/W finite element model based on a case proposed by Huang (19). Geometry attributes of a drainage base layer were used to generate a Finite Ele-ment Model system, 0.5 m tall and 6.5 m long, with a slope of 2%, and quadrilateral elements. Figure A.14 presents a section of the Finite Element Model left side for the unsaturated case. The layer was setup so that the material was fully saturated initially, the bottom was subjected to atmospheric conditions, and the layer was allowed to drain freely. The layer was considered impervious on right and left sides. Class 3 Special, Class 4 Special, Class 5 Special, and Class 6 Special were used as base mate-rials. The soil water characteristics curves were described at the beginning of the chapter. The hydraulic conductivity curves corresponded to Fredlund and Xing (28) model. The time to drain for the saturated case was obtained by applying Casagrande and Shannon method (Equation 2.1). Table A.4 summarizes the parameters used for this case.
A - 13
Figure A.14 Example – Geometry and boundary conditions
Table A.4 Geometry and material parameters for saturated case
SOIL Class 3 Special Class 4 Special Class 5 Special Class 6 Specialk (m/s) 2.20E-07 4.20E-06 3.80E-06 2.00E-06 θmax (%) 32.01 14.35 40.70 52.08
θR (%) 16.97 11.28 16.09 5.92 ne (%) 15.04 3.08 24.61 46.16 L (m) 6.5 6.5 6.5 6.5 H (m) 0.15 0.15 0.15 0.15 S (%) 2 2 2 2
As it can be seen from Table A.5, the saturated conditions approach (Casagrande and Shannon
method) results in a quicker time for 50% drainage. On the other hand, the more realistic
unsaturated conditions show that 50% drainage is never reached.
Table A.5 Time to drain – Saturated vs. unsaturated conditions for a geometry closer to
pavement conditions
SOIL Class 3 Special
Class 4 Special Class 5 Special Class 6 Special
t50 (days) Saturated conditions
597.03 6.39 56.56 201.53
t50 (days) Unsaturated conditions
Not reached Not reached Not reached Not reached
A - 14
Due to the geometry of the layer under unsaturated conditions, the maximum suction pressure
that can be obtained is approximately 1.5 kPa. When the water table reaches the layer bottom,
the maximum pressure head developed is 0.15 m. This is equivalent to 1.47 kPa of suction.
Therefore, only a small reduction in the volumetric water content will occur according to the
characterization of the base materials.
In conclusion, saturated flow conditions will result in a quicker drainage of soil materials.
However, in most cases, this does not represent real conditions. Unsaturated conditions result
in a more realistic behavior of the drainage flow, showing that the drainage depends on the
suction pressure, and therefore on the variability of the volumetric water content and hydraulic
conductivity.
Within unsaturated conditions is also important to take into account, the air entry potential for
the material. This value determines the suction at which the material starts to drain. For ex-
ample, by looking at the soil water characteristic curve for Class 4 Special (Figure A.15), this
soil is saturated before 10 kPa are reached. This suction value is its air entry potential. This
value can also be observed at the hydraulic conductivity curve (Figure A.16).
0.0
5.0
10.0
15.0
20.0
0.01 0.10 1.00 10.00 100.00 1000.00
Suction (kPa)
Air entry = 10 kPa
Saturated condition
Unsaturated condition
Figure A.15 Class 4 special – Air entry potential at soil water characteristic curve
A - 15
1.0E-10
1.0E-08
1.0E-06
1.0E-04
0.01 0.10 1.00 10.00 100.00 1000.00Suction (kPa)
Air entry = 10 kPa
Saturated conditionUnsaturated condition
Figure A.16 Class 4 special – Air entry potential at hydraulic conductivity curve
A.4 Sensitivity to Gradation
As a complementary component to the evaluation of the time to drain, the effects of variations
in material gradation on time to drain were estimated using SEEP/W. The one-dimensional
finite element-based flow model shown previously in Figure A.1 was used to evaluate the
sensitivity to gradation. Same Finite Element Model, geometry and boundary conditions were
applied.
Table A.6 describes the limits used for Class 3 Special, Class 4 Special, Class 5 Special, and
Class 6 Special. These materials were used as base layers. The upper and lower limits in Table
A.6 refer to the gradation specification limits used by Mn/DOT for these materials.
The soil water characteristic curves used to characterize the base materials are the same as
presented in Figures A.2 to A.5. Due to the fact that Gardner’s model (43) and Green and
Corey’s model (45) do not depend on the gradation of the material, the Finite Element Model
was only run for Brooks and Corey’s model (30) and Van Genuchten’s model (32), which
depend on the pore size index that is function of the percentage of sand. Table A.7 summarizes
the percentage of sand used for the different gradation limits.
A - 16
Table A.6 Gradation limits for different base materials
Material Class 3 Special Class 4 Special Class 5 Special Class 6 SpecialLimit Lower Upper Lower Upper Lower Upper Lower Upper
Passing 1" (25mm) 100 % 95 % 100 % 100 % 100 %
Passing 3/4" (19mm) - 90 % 100 % 90 % 100 % 85 % 100 %
Passing 3/8" (9.5mm) 95 % 100 % 80 % 95 % 70 % 85 % 50 % 70 %
Passing #4 (4.75mm) 85 % 100 % 70 % 85 % 55 % 70 % 30 % 50 %
Passing #10 (2mm) 65 % 90 % 55 % 70 % 35 % 55 % 15 % 30 %
Passing #20 (0.85mm) - - - -
Passing #40 (0.425mm) 30 % 50 % 15 % 30 % 15 % 30 % 5 % 15 %
Passing #60 (0.225mm) - - - -
Passing #100 (0.15mm) - - - -
Passing #200 (0.075mm) 8 % 15 % 5 % 10 % 3 % 8 % 0 % 5 %
Table A.7 Percentages of sand for different base materials
Limit Class3
Special
Class 4
Special
Class 5
Special
Class 6
Special
Lower 77 65 52 30
Upper 85 75 65 45
Figures A.17 to A.20 show predicted hydraulic conductivity with suction, as determined by
Brooks and Corey’s model (30). When the upper limit of the specifications is used, the
hydraulic conductivity is greater than in the lower limit, as expected. Also, when the sand
percentage is increased, the Brooks and Corey’s parameter n (n=3+2/l) decreases, resulting in
an increase in hydraulic conductivity.
A - 17
1.0E-341.0E-311.0E-281.0E-251.0E-221.0E-191.0E-161.0E-131.0E-101.0E-071.0E-04
0.01 1 100Suction (kPa)
Lower LimitUpper Limit
Figure A.17 Class 3 special – Comparison upper and lower limit –
Brooks and Corey (30) model
1.0E-341.0E-311.0E-281.0E-251.0E-221.0E-191.0E-161.0E-131.0E-101.0E-071.0E-04
0.01 1 100 10000Suction (kPa)
Lower Limit
Upper Limit
Figure A.18 Class 4 special – Comparison upper and lower limit –
Brooks and Corey (30) model
A - 18
1.0E-361.0E-331.0E-301.0E-271.0E-241.0E-211.0E-181.0E-151.0E-121.0E-091.0E-061.0E-03
0.01 1 100 10000
Suction (kPa)
Lower LimitUpper Limit
Figure A.19 Class 5 special – Comparison upper and lower limit –
Brooks and Corey (30) model
1.0E-31
1.0E-28
1.0E-25
1.0E-22
1.0E-19
1.0E-16
1.0E-13
1.0E-10
1.0E-07
1.0E-04
0.01 1 100
Suction (kPa)
Lower Limit
Upper Limit
Figure A.20 Class 6 special – Comparison upper and lower limit –
Brooks and Corey (30) model
Figures A.21 to A.24 show similar results for the Van Genuchten (32) model. Again, when the
sand content is increased (Upper limit applied), Van Genuchten’s parameter m (m=λ / (λ + 1))
also increases, resulting in an increase in hydraulic conductivity.
A - 19
1.0E-32
1.0E-29
1.0E-26
1.0E-23
1.0E-20
1.0E-17
1.0E-14
1.0E-11
1.0E-08
1.0E-05
0.01 1 100
Suction (kPa)
k (m
/s)
Lower LimitUpper Limit
Figure A.21 Class 3 special – Comparison upper and lower limit –
Van Genuchten (32) model
1.0E-32
1.0E-29
1.0E-26
1.0E-23
1.0E-20
1.0E-17
1.0E-14
1.0E-11
1.0E-08
1.0E-05
0.01 1 100 10000Suction (kPa)
Lower LimitUpper Limit
Figure A.22 Class 4 special – Comparison upper and lower limit –
Van Genuchten (32) model
A - 20
1.0E-28
1.0E-25
1.0E-22
1.0E-19
1.0E-16
1.0E-13
1.0E-10
1.0E-07
1.0E-04
0.01 1 100 10000
Suction (kPa)
k (m
/s)
Lower LimitUpper Limit
Figure A.23 Class 5 special – Comparison upper and lower limit – Van Genuchten (32) model
1.0E-31
1.0E-28
1.0E-25
1.0E-22
1.0E-19
1.0E-16
1.0E-13
1.0E-10
1.0E-07
1.0E-04
0.01 1 100
Suction (kPa)
k (m
/s)
Lower LimitUpper Limit
Figure A.24 Class 6 special – Comparison upper and lower limit – Van Genuchten (32) model
A - 21
Using the Brooks and Corey (30) and Van Genuchten (32) predictions, along with the Upper
and Lower limits on hydraulic conductivity, the time to drain to 50 and 90 percent was
obtained. Tables A.8 and A.9 summarize the results for Class 3, 4, 5, and 6 Special, in terms of
a decrease in volumetric water content. For the lower gradation limit, the results show that
more time is needed to drain 50% as well as 90% as compared to the results obtained for the
Upper limit.
Table A.8 Time to drain for lower and upper limit – Brooks and Corey (30) model
Time (days) Limit Material
50% Drainage 90% Drainage Lower Class 3 Special 2.20 4.79E+04 Upper Class 3 Special 2.08 4.10E+04 Lower Class 4 Special Not reached Not reached Upper Class 4 Special Not reached Not reached Lower Class 5 Special 1.53 Not reached Upper Class 5 Special 1.39 Not reached Lower Class 6 Special 2.01 2.43E+06 Upper Class 6 Special 1.74 1.46E+06
Table A.9 Time to drain for lower and upper limit – Van Genuchten (32) model
Time (days) Limit Material
50% Drainage 90% Drainage Lower Class 3 Special 7.90 1.32E+05 Upper Class 3 Special 7.64 1.04E+05 Lower Class 4 Special Not reached Not reached Upper Class 4 Special Not reached Not reached Lower Class 5 Special 18.06 Not reached Upper Class 5 Special 14.58 Not reached Lower Class 6 Special 13.89 1.25E+07 Upper Class 6 Special 13.19 6.60E+06
A - 22
In conclusion, the results clearly show that under unsaturated conditions the gradation of a
material has a strong effect on the time to drain. However, this is not the only factor to take
into account. The soil water characteristic curve of the material is also important, as well as the
data that is measured in field because it provides initial parameters as the hydraulic
conductivity when is saturated.
A.5 Summary
Time to drain is a variable that describes the drainage performance of a soil layer (i.e. base,
subbase, subgrade). It helps to understand how long takes the water to leave a specific system.
Evaluation of the reduction in water content of a material, under saturated or unsaturated con-
ditions, can be used to determine this parameter.
Due to the fact that saturated flow assumptions do not take into consideration the variation of
the hydraulic conductivity with volumetric water content or suction, the drainage performance
of a simulated system will result in a short time to drain compared to unsaturated conditions.
Therefore, true behavior of the material under field conditions are not being reproduced in a
realistic way. In contrast unsaturated flow theory considers the hydraulic conductivity as a
function of the suction experienced in the material with drainage. Hence, the time to drain the
system will be longer that that one evaluated under saturated flow assumptions.
As mentioned before, the material characterization is an important input to simulate the
drainage performance of a system. soil water characteristic curve and hydraulic conductivity
curve permit to evaluate when and how fast a material can drain under certain conditions.
Therefore, the trend and slope of the curves is really significant. Besides, knowing the point at
which the material will start to drain (i.e. air entry potential) helps to have a more complete
perspective of what it is taking place in the drainage of a material.
B - 1
APPENDIX B
DETERMINATION OF AIR ENTRY VALUE
FOR CLASS 6 SPECIAL
B - 2
APPENDIX B
DETERMINATION OF AIR ENTRY VALUE FOR CLASS 6 SPECIAL The air entry value for the Mn/DOT Class 6 Special aggregate course material was determined
by using two different methods. The first method consisted on plotting its soil water character-
istic curve (Figure 5.16) in a semi log scale and finding the air entry value as the intercept
between the tangents to the slopes of this curve. Figure B.1 presents this procedure.
According to this graph, the air entry value for the class 6 special material is 3 kPa.
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
0.01 0.10 1.00 10.00 100.00
Suction (kPa)
Air Entry = 3 kPa
Figure B.1 Air entry value determination for Class 6 special material – Semi log scale
In order to check the air entry value determined through the first method, a second method was
applied. This method consisted of plotting the soil water characteristic curve of the material in
a log-log scale and determining the air entry value from the intercept of the tangents to the
slopes of this curve. Figure B. 2 shows that the air entry value determined confirms the first
founded value.
B - 3
1.0
10.0
100.0
0.01 0.10 1.00 10.00 100.00Suction (kPa)
Air entry = 3 kPa
Figure B.2 Air entry value determination for Class 6 special material – Log-log scale