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- EVALUATION OF WATER FLOW THROUGH PAVEMENT SYSTEMS
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Drainage water ( jstor ) Drains ( jstor ) Hydraulic conductivity ( jstor ) Material properties ( jstor ) Moisture content ( jstor ) Pavements ( jstor ) Soil water characteristic ( jstor ) Surgical suction ( jstor ) Water tables ( jstor )
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PAGE 1 EVALUATION OF WATER FLOW THOUGH PAVEMENT SYSTEMS By PAOLA ARIZA A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ENGINEERING UNIVERSITY OF FLORIDA 2002 PAGE 2 ACKNOWLEDGMENTS I would like to thank my advisor, Dr. Bjorn Birgisson, for his supervision, assistance and guidance throughout the project. Without his expertise, I would not have been able to accomplish this task. I would also like to thank Dr. Reynaldo Roque and Dr. Mang Tia for participating as members of my committee. I would also like to thank the Minnesota Department of Transportation for its financial and technical support. I would like to spend a special thanks to Ruth Roberson for her collaboration with this project. I would like to thank George Lopp for his valuable help in the laboratory, which helped me throughout my graduate studies. Thanks are also extended to many others for their collaboration and friendship: D.J. Swan, Tom Grant, and the rest of students in the Infrastructure Materials and Pavements Group. Finally, I would like to thank my parents, my brother, Oscar Garca, and also my friends back in Colombia for their permanent love, support, encouragement, and motivation during my stay in Gainesville, Florida. ii PAGE 3 TABLE OF CONTENTS page ACKNOWLEDGMENTS..................................................................................................ii LIST OF TABLES.............................................................................................................vi LIST OF FIGURES..........................................................................................................vii ABSTRACT.....................................................................................................................xiv CHAPTERS 1 INTRODUCTION...........................................................................................................1 1.1 Objectives.................................................................................................................3 1.2 Scope of Thesis.........................................................................................................3 2 LITERATURE REVIEW................................................................................................5 2.1 Current State-of-Practice..........................................................................................5 2.1.1 Effects of Drainage on Pavement Design Life................................................7 2.1.2 Summary of Current Practice..........................................................................9 2.2 Positive Drainage Systems........................................................................................9 2.2.1 Open Graded Base Course..............................................................................9 2.2.2 Edge Drains...................................................................................................10 2.2.3 Use of Geotextiles for Drainage Improvement.............................................11 2.3 Unsaturated Flow through Pavements....................................................................12 2.3.1 Soil Water Characteristic Curves..................................................................13 2.3.1.1 Brooks and Corey model (1966)..........................................................15 2.3.1.2 Van Genuchten model (1980)..............................................................16 2.3.1.3 Brutsaert model (1966)........................................................................17 2.3.1.4 Vauclin model (1979)..........................................................................18 2.3.1.5 Bear and Verruijt model (1990)...........................................................18 2.3.1.6 Gray and Hassanizadeh model (1991).................................................19 2.3.1.7 Mualen model (1973)...........................................................................20 2.3.1.8 Relative permeability models..............................................................20 2.3.2 Hydraulic Conductivity Curves Models.......................................................22 2.4 Effects of Layering on Unsaturated Flow of Water................................................25 iii PAGE 4 3 RESEARCH METHODOLOGY...................................................................................27 3.1 Analysis Tools Used...............................................................................................27 3.1.1 SEEP/W........................................................................................................27 3.1.2 DRIP..............................................................................................................28 3.2 Materials and Pavement Sections...........................................................................30 3.2.1 Pavement Sections........................................................................................30 3.2.2 Materials........................................................................................................31 3.2.2.1 Hot mix asphalt layers.........................................................................31 3.2.2.2 Base materials......................................................................................31 3.2.2.3 Subgrade material................................................................................33 3.3 Scope.......................................................................................................................34 4 VERIFICATION OF SEEP/W FOR PAVEMENT APPLICATION...........................36 4.1 Example 1...............................................................................................................36 4.2 Example 2...............................................................................................................41 4.3 Example 3...............................................................................................................46 4.4 Summary.................................................................................................................54 5 CALIBRATION OF RESULTS TO FIELD RESULTS FOR CELLS 33, 34, 35........55 5.1 Pavement System Description................................................................................55 5.2 Finite Element Model.............................................................................................56 5.2.1 Hot Mix Asphalt Layer.................................................................................57 5.2.2 Base Course...................................................................................................57 5.2.3 Subgrade........................................................................................................57 5.2.4 Initial and Boundary Conditions...................................................................57 5.2.5 FEM Analysis...............................................................................................58 5.2.6 Measured Volumetric Water Contents..........................................................59 5.3 Materials Characterization Adjustment..................................................................63 5.3.1 Initial Calibration Results.............................................................................64 5.3.2 Second Calibration Results...........................................................................66 5.3.3 Calibration due to Material Density..............................................................79 5.4 Cell 34.....................................................................................................................82 5.4.1 Calibration of Results at Locations 101 and 102..........................................84 5.4.2 Calibration to Location 103..........................................................................87 5.5 Cell 35.....................................................................................................................89 5.6 Summary.................................................................................................................92 6 PARAMETRIC STUDY...............................................................................................94 6.1 Initial Slope of the Base Material Soil Water Characteristic Curve.......................94 6.2 Air Entry Value of Base Material...........................................................................97 iv PAGE 5 6.3 K sat of Base Material...............................................................................................98 6.4 Air Entry Value of Subgrade Material..................................................................100 6.5 K sat at Subgrade Material......................................................................................101 6.6 Effects of the Type of Base Material....................................................................103 6.7 Infiltration Effects.................................................................................................106 6.8 Water Table Influence...........................................................................................106 6.9 Summary...............................................................................................................107 7 EFFECT OF EDGE AND UNDER DRAINS ON WATER FLOW THROUGH FLEXIBLE PAVEMENTS.........................................................................................109 7.1 Description of Case 1: Under Drain.....................................................................110 7.2 Description of Case 2: Under Drains with Collector Pipes..................................112 7.3 Description of Case 3: Edge Drains.....................................................................113 7.3 Description of Case 4: Combination....................................................................115 7.4 Drainage Systems Comparison.............................................................................115 8 CONCLUSIONS AND RECOMMENDATIONS......................................................118 APPENDIX EVALUATION OF TIME TO DRAIN CALCULATIONS FOR PAVEMENTS.........122 A.1 Time to Drain from Unsaturated Flow Theory....................................................122 A.2 Time to Drain from Saturated Flow Theory........................................................131 A.3 Comparison Applied to a Real Example..............................................................133 A.4 Sensitivity to Gradation.......................................................................................136 A.5 Summary..............................................................................................................143 LIST OF REFERENCES.................................................................................................144 BIOGRAPHICAL SKETCH...........................................................................................148 v PAGE 6 LIST OF TABLES Table page 2.1: Classification of 50% of drainage.................................................................................8 2.2: Recommended m values for modifying structural layer coefficients of untreated base and subbase materials in flexible pavements...........................................................8 3.1: Asphalt layer description............................................................................................31 4.1: Soil hydraulic parameters...........................................................................................37 5.1: Cell 33 â€“ Calibration for base layer (Class 6 special).................................................82 5.2: Cell 33 â€“ Calibration for subgrade (R-70 Silty clay)..................................................82 5.3: Cell 34 â€“ Calibration for base layer (Class 6 special).................................................88 5.4: Cell 35 â€“ Calibration for base layer (Class 6 special).................................................91 6.1: Maximum drainage for different base materials.......................................................105 A.1: Comparison of drainage times under unsaturated flow conditions..........................129 A.2: Saturated case â€“ Model parameters..........................................................................131 A.3: Comparison of drainage times under saturated flow conditions..............................132 A.4: Geometry and material parameters for saturated case.............................................134 A.5: Time to drain â€“ Saturated vs. unsaturated conditions for a geometry closer to pavement conditions............................................................................................134 A.6: Gradation limits for different base materials...........................................................137 A.7: Percentages of sand for different base materials......................................................137 A.8: Time to drain for lower and upper limit â€“ Brooks and Corey (1966) model...........142 A.9: Time to drain for lower and upper limit â€“ Van Genuchten (1980) model...............142 vi PAGE 7 LIST OF FIGURES Figure page 2.1: Typical soil water characteristic curve.......................................................................14 2.2: Typical values for the Brooks and Corey model for water retention..........................16 2.3: Typical values for the Van Genuchten model for water retention..............................17 2.4: Hysteresis effects â€“ Main drainage and wetting curves..............................................19 2.5: Variation of the air-water interface due to raindrop effect (Bear, 1972)....................19 3.1: Thickness of base and hot mix asphalt layers for Mn/ROAD Cells 33-35.................30 3.2: Pavement geometry and dimensions...........................................................................30 3.3: Grain size distribution for Mn/DOT Class 6 special..................................................31 3.4: Soil water characteristic curve â€“ Base material (Class 6 special)...............................32 3.5: Hydraulic conductivity curve â€“ Base material (Class 6 special)................................32 3.6: Soil water characteristic curve â€“ Subgrade material (R-70 Silty clay).......................33 3.7: Hydraulic conductivity curve â€“ Subgrade material (R-70 Silty clay)........................34 4.1: Example 1 â€“ Geometry and boundary conditions.......................................................36 4.2: Soil water characteristic curve (Brutsaert model).......................................................37 4.3: Hydraulic conductivity curve (Gardner model)..........................................................38 4.4: Example 1 â€“ FEM.......................................................................................................38 4.5: Comparison between measured and predicted water table at 2 hours........................39 4.6: Comparison between measured and predicted water table at 3 hours........................39 4.7: Comparison between measured and predicted water table at 4 hours........................40 4.8: Comparison between measured and predicted water table at 8 hours........................40 vii PAGE 8 4.9: Example 2 â€“ Geometry and boundary conditions.......................................................41 4.10: Soil water characteristic curve (Brooks and Corey model)......................................42 4.11: Hydraulic conductivity curve (Brooks and Corey model)........................................42 4.12: Example 2 â€“ FEM.....................................................................................................43 4.13: Comparison between measured and predicted volumetric water content at 1.5 h....44 4.14: Comparison between measured and predicted volumetric water content at 3 h.......44 4.15: Comparison between measured and predicted volumetric water content at 4.5 h....45 4.16: Comparison between measured and predicted volumetric water content at 6 h.......45 4.17: Example 3 â€“ Geometry and boundary conditions.....................................................46 4.18: Soil water characteristic curve for base and subbase (Brooks and Corey model)....47 4.19: Hydraulic conductivity curve â€“ Base (Brooks and Corey model)............................47 4.20: Hydraulic conductivity curve â€“ Subbase (Brooks and Corey model)......................48 4.21: Example 3 â€“ FEM.....................................................................................................48 4.22: Comparison between measured and predicted volumetric water content in base material at 1.5 hours...............................................................................................49 4.23: Comparison between measured and predicted volumetric water content in base material at 3 hours..................................................................................................49 4.24: Comparison between measured and predicted volumetric water content in base material at 4.5 hours...............................................................................................50 4.25: Comparison between measured and predicted volumetric water content in base material at 6 hours..................................................................................................50 4.26: Comparison between measured and predicted volumetric water content in subbase material at 1.5 hours...............................................................................................51 4.27: Comparison between measured and predicted volumetric water content in subbase material at 3 hours..................................................................................................51 4.28: Comparison between measured and predicted volumetric water content in subbase material at 4.5 hours...............................................................................................52 4.29: Comparison between measured and predicted volumetric water content in subbase material at 6 hours..................................................................................................52 viii PAGE 9 4.30: Comparison of measured volumetric water content in base material at 6 hours for Examples 2 and 3...................................................................................................53 4.31: Comparison of predicted volumetric water content in base material at 6 hours for Examples 2 and 3...................................................................................................53 5.1: Layer thicknesses for Mn/ROAD Cells 33, 34, and 35..............................................55 5.2: Pavement geometry and dimensions for Cells 33, 34, and 35....................................56 5.3: Section of the FEM used to represent Cell 33, 34 and 35..........................................56 5.4: FEM used to represent Cells 33, 34, and 35...............................................................58 5.5: Precipitation events for Cells 33, 34, and 35..............................................................59 5.6: TDR installation at Mn/DOT Cells 33, 34 and 35......................................................60 5.7: TDR location within FEM for Cells 33, 34, and 35...................................................60 5.8: Measured data for different TDR locations at Cell 33................................................61 5.9: Measured data for different TDR locations at Cell 34................................................62 5.10: Measured data for different TDR locations at Cell 35..............................................62 5.11: Volumetric water content at Cell 33 â€“ Location 101................................................65 5.12: Volumetric water content at Cell 33 â€“ Location 102................................................65 5.13: Volumetric water content at Cell 33 â€“ Location 103................................................66 5.14: Soil water characteristic curve (air entry = 3 kPa) â€“ Base material (Class 6 sp.).....67 5.15: Estimated hydraulic conductivity curve â€“ Base material (Class 6 special)..............67 5.16: Final soil water characteristic curve â€“ Base material (Class 6 special)....................68 5.17: Estimated hydraulic conductivity curve â€“ Base material (Class 6 special)..............69 5.18: Volumetric water content at Cell 33 â€“ Location 101................................................70 5.19: Volumetric water content at Cell 33 â€“ Location 102................................................70 5.20: Volumetric water content at Cell 33 â€“ Location 103................................................71 5.21: Modified hydraulic conductivity curve: 10 times K sat â€“ Subgrade material (R-70 Silty clay)...............................................................................................................72 ix PAGE 10 5.22: Volumetric water content at Cell 33 â€“ Location 101................................................73 5.23: Volumetric water content at Cell 33 â€“ Location 102................................................73 5.24: Volumetric water content at Cell 33 â€“ Location 103................................................74 5.25: Final hydraulic conductivity curve: K sat = 2.7535E-06 m/s â€“ Subgrade material (R-70 Silty clay)..........................................................................................................74 5.26: Volumetric water content at Cell 33 â€“ Location 101................................................75 5.27: Volumetric water content at Cell 33 â€“ Location 102................................................76 5.28: Volumetric water content at Cell 33 â€“ Location 103................................................76 5.29: Volumetric water content at Cell 33 â€“ Location 101................................................77 5.30: Volumetric water content at Cell 33 â€“ Location 102................................................78 5.31: Volumetric water content at Cell 33 â€“ Location 103................................................78 5.32: Final soil water characteristic curve for Location 102 â€“ Base material (Class 6 special)...................................................................................................................79 5.33: Volumetric water content at Cell 33 â€“ Location 102................................................80 5.34: Final soil water characteristic curve for Location 103 â€“ Base material (Class 6 special)...................................................................................................................81 5.35: Volumetric water content at Cell 33 â€“ Location 103................................................81 5.36: Volumetric water content at Cell 34 â€“ Location 101................................................83 5.37: Volumetric water content at Cell 34 â€“ Location 102................................................83 5.38: Volumetric water content at Cell 34 â€“ Location 103................................................84 5.39: Final soil water characteristic curve for Location 101 and 102 at Cell 34 â€“ Base material (Class 6 special).......................................................................................85 5.40: Volumetric water content at Cell 34 â€“ Location 101................................................86 5.41: Volumetric water content at Cell 34 â€“ Location 102................................................86 5.42: Final soil water characteristic curve for Location 103 Cell 34 â€“ Base material (Class 6 special)................................................................................................................87 5.43: Volumetric water content at Cell 34 â€“ Location 103................................................88 x PAGE 11 5.44: Volumetric water content at Cell 35 â€“ Location 101................................................89 5.45: Volumetric water content at Cell 35 â€“ Location 103................................................90 5.46: Final soil water characteristic curve for Location 102 Cell 35 â€“ Base material (Class 6 special)................................................................................................................90 5.47: Volumetric water content at Cell 35 â€“ Location 102................................................91 6.1: Soil water characteristic curves for initial slope cases...............................................95 6.2: Hydraulic conductivity curves for initial slope cases.................................................96 6.3: Results for initial slope cases......................................................................................96 6.4: Base soil water characteristic curves for air entry value cases...................................97 6.5: Results for air entry value cases at base layer............................................................98 6.6: Hydraulic conductivity curves for K sat cases at base material....................................99 6.7: Results for K sat cases at base layer............................................................................100 6.8: Results for air entry values at subgrade layer...........................................................101 6.9: Hydraulic conductivity curves for K sat cases at subgrade material...........................102 6.10: Results for K sat cases at subgrade layer..................................................................102 6.11: Soil water characteristic curves for base materials.................................................103 6.12: Soil water characteristic curves (air entry = 3kPa) for base materials....................104 6.13: Estimated hydraulic conductivity curves for base materials..................................104 6.14: Results for different types of base materials...........................................................105 6.15: Results for different rain events..............................................................................106 6.16: Results for different water table positions..............................................................107 7.1: Underdrain location for Case 1 in the pavement system..........................................110 7.2: Soil water characteristic curve for under drain material...........................................111 7.3: Estimated hydraulic conductivity curve for under drain material............................111 7.4: FEM for Case 1 (Under drain system)......................................................................112 7.5: Underdrain and collector pipes location for Case 2 in the pavement system...........113 xi PAGE 12 7.6: FEM for Case 2 (Under drain with collector pipes).................................................113 7.7: Edge drain location for Case 3 in the pavement system...........................................114 7.8: FEM for Case 3 (Edgedrain).....................................................................................114 7.9: FEM for Case 3 (Combination of drain systems).....................................................115 7.10: Results comparison for drainage systems...............................................................116 A.1: Finite element model â€“ Geometry and boundary conditions...................................123 A.2: Class 3 special â€“ Soil water characteristic curve.....................................................123 A.3: Class 4 special â€“ Soil water characteristic curve.....................................................124 A.4: Class 5 special â€“ Soil water characteristic curve.....................................................124 A.5: Class 6 special â€“ Soil water characteristic curve.....................................................125 A.6: Comparison of Hydraulic Conductivity Models in Class 3 Special........................125 A.7: Comparison of Hydraulic Conductivity Models in Class 4 Special........................126 A.8: Comparison of hydraulic conductivity models in Class 5 special...........................126 A.9: Comparison of hydraulic conductivity models in Class 6 special...........................127 A.10: Class 3 special â€“ Evolution of volumetric water content with time at the top of the soil column...........................................................................................................127 A.11: Class 4 special â€“ Evolution of volumetric water content with time at the top of the soil column...........................................................................................................128 A.12: Class 5 special â€“ Evolution of volumetric water content with time at the top of the soil column...........................................................................................................128 A.13: Class 6 special â€“ Evolution of volumetric water content with time at the top of the soil column...........................................................................................................129 A.14: Example â€“ Geometry and boundary conditions.....................................................133 A.15: Class 4 special â€“ Air entry potential at soil water characteristic curve.................135 A.16: Class 4 special â€“ Air entry potential at hydraulic conductivity curve...................136 A.17: Class 3 special â€“ Comparison upper and lower limit â€“ Brooks and Corey (1966) model....................................................................................................................138 xii PAGE 13 A.18: Class 4 special â€“ Comparison upper and lower limit â€“Brooks and Corey (1966) model....................................................................................................................138 A.19: Class 5 special â€“ Comparison upper and lower limit â€“ Brooks and Corey (1966) model....................................................................................................................139 A.20: Class 6 special â€“ Comparison upper and lower limit â€“ Brooks and Corey (1966) model....................................................................................................................139 A.21: Class 3 special â€“ Comparison upper and lower limit â€“ Van Genuchten (1980) model....................................................................................................................140 A.22: Class 4 special â€“ Comparison upper and lower limit â€“ Van Genuchten (1980) model....................................................................................................................140 A.23: Class 5 special â€“ Comparison upper and lower limit â€“ Van Genuchten (1980) model....................................................................................................................141 A.24: Class 6 special â€“ Comparison upper and lower limit â€“ Van Genuchten (1980) model....................................................................................................................141 xiii PAGE 14 Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Engineering EVALUATION OF WATER FLOW THROUGH PAVEMENT SYSTEMS By Paola Ariza May 2002 Chair: Bjorn Birgisson Major Department: Civil and Coastal Engineering Water in the pavement system can lead to moisture damage, modulus reduction, and loss of strength. By preventing water from entering the pavement, providing adequate drainage to remove it quickly, or building the pavement strong enough to resist the combined effect of load and water, the detrimental effects can be reduced. However, complete prevention is not possible during the useful life of a pavement; therefore the quick removal of the water should be enhanced before any damage can be initiated. Most of the current drainage criteria have been developed on the basis of experimental field results and theoretical analyses of infiltration under saturated conditions. This fact makes worse the lack of knowledge in this field. The purpose of this thesis is to focus on the modeling of unsaturated flow through pavement systems to represent 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. xiv PAGE 15 CHAPTER 1 INTRODUCTION It is a well-known fact that water in pavement systems is one of the principal causes of premature pavement failure. 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 by 30 percent or more and the base and subbase modulus by 50 percent or more (American Association of State Highway and Transportation Officials [AASHTO], 1998). Similarly, modulus reduction of up to 30 percent can be expected for asphalt-treated bases, with saturated fine-grained subgrade soils experiencing modulus reductions of over 50 percent (AASHTO, 1998). By preventing water from entering the pavement, providing adequate drainage to remove it quickly, or building the pavement strong enough to resist the combined effect of load and water, the detrimental effects can be reduced. Complete prevention is not possible during the useful life of a pavement, therefore the quick removal of the water should be enhanced before any damage can be initiated. Pavement service life can be increased by 50% if infiltrated water can be drained without delay (Forsyth, 1987). Similarly, pavement systems incorporating good drainage can be expected to have a design life of two to three times that of undrained pavement sections (Cedergren, 1987; Cedergren, 1989). The AASHTO pavement design guide (AASHTO, 1998) and the US Army Corps of Engineers Pavement Design Guide (1992) both account for the positive effects of drainage through the use of drainage factors. 1 PAGE 16 2 The magnitude of these factors is directly related to the length of the time that excess moisture remains in the pavement. With the new 2002 AASHTO mechanistic-empirical pavement design procedure, 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 decrease in modulus with water content. A drainability criterion based on actual field performance needs to be developed and incorporated into guidelines for pavement design. This criterion may be in the form of a specification of a given reduction of the degree of saturation to be achieved in a certain amount of time. Most of the current drainage criteria have been developed on the basis of experimental field results and theoretical analyses of infiltration under saturated conditions. This fact makes worse the lack of knowledge in this field. Full saturation of pavement systems can occur only under very specific circumstances. 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 infiltrate within the soil is a function of permeability and gravity forces, as well as material matric suction (Philip, 1969). Moreover, the permeability of a porous medium may also vary significantly with the degree of saturation. A degree of saturation of 80 percent may result in a soil with a permeability of only half its saturated value. Hence, the models that use only fully saturated approach are not adequate for pavement infiltration. Finally, recent studies by Minnesota Road Research Project (Mn/ROAD) pavement researchers (E.g. Ruth and Birgisson, 1998; Birgisson and Ruth, 2000) have shown that most dense graded bases 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 PAGE 17 3 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) modeling of the movement of water through flexible 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. 1.2 Scope of Thesis The study addresses the following: 1) verification of SEEP/W for modeling unsaturated flow of water through pavements, 2) modeling of the movement of water through flexible pavement systems that are unsaturated and 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. PAGE 18 4 Chapter 2 provides a detailed literature overview of both the current state-of-practice in drainage design, as well as the current-state-of-art. Chapter 3 details the research methodology used in this study. Chapter 4 evaluates the use of SEEP/W for simulating the flow of water 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 some parameters on water flow under unsaturated conditions. Chapter 7 presents the effects of edge and under drains in a typical flexible pavement system. Chapter 8 presents summary, conclusions, and recommendations based on the analyses presented in this study. PAGE 19 CHAPTER 2 LITERATURE REVIEW In this Chapter, the basics of pavement drainage will be reviewed. First the current assumptions used by AASHTO (1998) in dealing with pavement drainage and drainage design will be reviewed. An example of the effects on pavement thickness design of poor drainage for flexible pavements will be provided. Second, some of the more common positive pavement drainage systems will be reviewed, including edge drains, the use of open graded base courses, and the use of geotextiles for drainage improvement. Third, the effects of unsaturated pavement material properties on pavement drainage will be discussed. 2.1 Current State-of-Practice There are two different types of fluid flow, saturated and unsaturated. In the saturated flow all the soil voids are filled with water, therefore the volumetric water content is equal to the soil porosity. This type of flow occurs below the water table, so the pore suction is greater than the atmospheric pressure or the air point pressure, which is the point where air will begin to enter the pores. The hydraulic conductivity is not a function of the pore suction; hence K is considered as a constant value. Under saturated conditions, the discharge is proportional to the sample cross-section area, the length of the sample and the total hydraulic head loss across the sample length (Darcyâ€™s Law). The driving forces that cause saturated flow are gravitational and pressure-potential gradients (Tindall and Kunkel, 1999). 5 PAGE 20 6 Based on saturated flow conditions, there are two different approaches to have into consideration for the hydraulic design of a permeable base. The first one is the Steady-state flow, which assumes uniform flow conditions. The permeable base should carry the design flows that infiltrate the pavement surface. However, the difficulty to estimate the proper precipitation frequency and duration makes it not convenient. Here the second approach, Time-to drain, offers a more practical solution. Time-to drain is a parameter that allows to determine the performance of a permeable base. This approach is based on flow entering the pavement until the permeable base is saturated. Excess runoff will not enter the pavement section after is saturated; this flow will simply run off on the pavement surface. After the precipitation event, the base will drain to the drainage system. Casagrande and Shannon (1952) showed that the time for 50% degree of drainage can be calculated as follows: SL)2k(HLnt2e50 (2.1) where t 50 is time for 50% drainage. n e 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. PAGE 21 7 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 enable the design of pavement drainage systems. Following an assessment of excess moisture in the pavement system, the pavement subdrainage system should be designed using materials that have enough permeability. Cedergren (1988) 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, proper understanding of the factors that most influence the flow of water through pavements is required to fully realize these savings. Currently, the FHWA promotes the use of free draining materials in base and subbase construction. The AASHTO (1998) 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. As discussed previously, for a pavement to have good drainability characteristics according to AASHTO (1998), 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 PAGE 22 8 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 from the pavement structure, according to AASHTO (1998), 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 (1998) uses a m layer coefficient 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. 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 PAGE 23 9 2.1.2 Summary of Current Practice Unfortunately, the current drainage criteria used by the FHWA and AASHTO (1998), despite having been developed on the basis of experimental field results and theoretical analyzes of infiltration, have all been performed under the assumption of saturated conditions (Casagrande & Shannon, 1952; Cedergren, 1956 and 1972; Liu et al., 1983; Carpenter, 1990; Pufahl et al., 1990). In these previous works, material permeability and gravity action 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 infiltrates the base and subgrade is not only a function of permeability and the gravitational forces, it is also the function of matric suction of the material (Phillip, 1969). Permeability of a porous medium varies with its degree of saturation. Hence, it is not justified to consider fully saturated condition for study of pavement infiltration. 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. In summary, 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. 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 PAGE 24 10 should be protected from clogging by the use of filters. In order to have a good permeability, the fine portion should be eliminated from the gradation of this course (Huang, 1993). However, this results in the decrement of the drainage layer stability. To compensate for this, a small amount of asphalt or Portland cement is introduced into the base for stability. The material will have only a slightly reduced permeability 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 (Betram, 1940). 2.2.2 Edge Drains Design of subsurface drainage systems involve the consideration of many details, such as material type, separation layer type, edge drain location, and outlet design. Proper functioning of subsurface drainage system depends mainly on proper design and construction. The pipes to be used for subdrainage may be made of concrete, clay, bituminized fiber, metal, or various plastics with smooth or corrugated surfaces (Huang, 1993). Suitable aggregates or fabrics as filter materials to prevent the openings from clogging must surround them. The material 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 construction. The drainage trench should not be placed in the trackline of paver or in the wheelpath. 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 PAGE 25 11 to the permeable base should be left open to allow a direct path for the water into the drainage pipe. The drainage pipes are usually placed at a constant depth below the pavement surface. Longitudinal slope of the edge drain has a significant effect on flow capacity of pipe edge drains (FHWA, 1992). The backfill material for the trench should be at least as permeable as the permeable base material. Proper compaction of the backfill material is important to avoid settlement over the edge drain. 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 (Huang, 1993). They must be made from strong, tough, rot-proof polymer fibers formed into a fabric of the woven or nonwoven type. According to the Geotextile Engineering Manual (FHWA, 1989), the filter criteria depends of the hydraulic loadings and the importance of the performance of the drainage system. If the hydraulic loadings are severe, the use of more stringent criteria should be made. 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 (ASTM, 1989) specifies the method for determining AOS, as well as the retention, permeability and clogging criteria. Geotextiles are used for subsurface drainage as envelope of trench drains, a wrapping of pipe drains, or a filter of drainage layers. Although it is a system more ease to install, it is more cost effective. PAGE 26 12 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 voids are taken up by air. Therefore, 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 suction pressures are developed. In addition, in this zone both the volumetric water content and the hydraulic conductivity are function of this suction pressure. The soil volumetric water content is held between the soil grains under surface-tension forces that are reflected in the radius of curvature of each meniscus. The higher the volumetric water content, the larger the radii of curvature and the lower the tension heads. And due to the change in volumetric water content, the hydraulic conductivity is not constant. The hydraulic conductivity content increases with increasing the volumetric water content (Freeze and Cherry, 1979). Most water in pavements is introduced to the pavement system through the process of infiltration 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 atmospheresoil interface is known as infiltration rate. The total volume of liquid crossing the interface over a given period of time is known as cumulative infiltration. Infiltration also signifies soil sorptivity. 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 (Tindall and James, 1999). PAGE 27 13 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 as well as transverse construction joints and pavement cracks. Similarly, seasonal increase in ground water table elevation, along with a rise in the associated capillary fringe may allow near saturation of pavement components at various times. 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, root activity, and other physical properties determine the magnitude of the porosity of a given soil (Tindall and James, 1999). 2.3.1 Soil Water Characteristic Curves Water flow in the unsaturated zone primarily is due to volumetric water content, soil suction, and gravitational potential (Tindall and Kunkel, 1999). Due to the presence of air within part of the pore channels, water movement is obstructed and it only flows through the finer pores or in films around the soil particles. Hence, the drainage characteristics of unsaturated soil depend on the volumetric moisture content in soils and the fact that a volumetric moisture content less than the saturated value leads to: 1) development of suction within the soil mass, and 2) 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 that are either subject to infiltration or drainage, 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 PAGE 28 14 generally referred to as the â€œsoil water characteristic curveâ€ and the second one is called the â€œhydraulic conductivity curve.â€ Figure 2.1 (Fredlund and Xing, 1994) shows a typical soil water characteristic curve, displaying the relationship between volumetric water content and soil suction. The air-entry value of the soil is the matric suction at which air starts entering the largest pores in the soil. Residual water content is the water content of the soil when 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. 01020304050600.11101001000100001000001000000Soil Suction (KPa) Air-Entry Values Desorption Curve Residual Water Content, 'r Adsorption Curve 's Residual air content Figure 2.1: Typical soil water characteristic curve Soil Water Characteristic curves can be represented generally with the following relationship between the degree of saturation and the volumetric water content: rrsrrreSSSS1 (2.2) where S is the degree of saturation. PAGE 29 15 S r is the residual saturation corresponding to the value of r . is the volumetric water content. r is the residual water content. s is the volumetric water content at saturation There are primarily two ways of obtaining hydraulic conductivity curves for soil â€“ 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, some of the more popular models for both soil water characteristic curves and hydraulic conductivity curves will be described. 2.3.1.1 Brooks and Corey model (1966) This model proposed a relationship between the degree of saturation and the matric suction based on experimental data: 1PBSe for PB (2.3) 1eS for < PB where S e is the effective degree of saturation. PB is the bubbling pressure of the soil, which is the height of the capillary fringe. is the pore size distribution index parameter, a measure of the soil grain uniformity. PAGE 30 16 Based on Bearâ€™s (1972) definition of the water capacity (equation 2.4) and equations (2.2) and (2.3), a new expression for this water capacity can be obtained (2.5): wwC (2.4) ewSC (2.5) Figure 2.2 shows the influence of the parameter on the S e response. Figure 2.2: Typical values for the Brooks and Corey model for water retention 2.3.1.2 Van Genuchten model (1980) Van Genuchten proposed an empirical equation to relate the matric suction and the water content: 11eS (2.6) 1eS for < 0 where and are dimensionless coefficients, and = 1-1/ is a coefficient that has the dimension of the inverse of the piezometric head. PAGE 31 17 For limited cases, Brooks and Coreyâ€™s parameters can be related to those used in Van Genuchtenâ€™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: 1111ewSC (2.7) Figure 2.3 shows the variation of the matric suction for a range of b values. Figure 2.3: Typical values for the Van Genuchten model for water retention 2.3.1.3 Brutsaert model (1966) Brutsaert 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: eS for >0 (2.8) 1eS for < 0 where depends on the suction units. PAGE 32 18 is dimensionless. The water capacity equation for the Brutsaertâ€™s model is given by: 1221ewSC (2.9) Where and are empirical coefficients. 2.3.1.4 Vauclin model (1979) Similar to that proposed by Brutsaert, Vauclin et al. (1979) introduced another empirical equation relating the degree of saturation and the matric suction: )ln(eS for >1 (2.10) 1eS for 1 cm The water capacity equation for this model is given by: 1221)(ln)(ln)ln(ewSC for 1 cm (2.11) Where and are fitting coefficients. 2.3.1.5 Bear and Verruijt model (1990) The relationship between the degree of saturation and the suction is not unique and depends on whether wetting or drainage is taking place. 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 (1990) model states 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. PAGE 33 19 Figure 2.4: Hysteresis effects â€“ Main drainage and wetting curves Figure 2.5: Variation of the air-water interface due to raindrop effect (Bear, 1972) 2.3.1.6 Gray and Hassanizadeh model (1991) Based on the thermodynamic principles and momentum balance equations, Gray and Hassanizadeh 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. PAGE 34 20 2.3.1.7 Mualen model (1973) Mualen presented a model based on the independent domain theory, 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: dwdwddf, (2.12) where w and d are independent variables representing the suction on the main wetting and drying curves. w being always greater that or equal to d . f is a bivariate probability distribution function 2.3.1.8 Relative permeability models In unsaturated conditions, the total permeability is reduced due to the presence or air 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: KSKSkeer)()( (2.13) where k r 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 accounted for (Brutsaert, 1968). PAGE 35 21 Burdine (1953). Burdine used the series-parallel model and related the permeability to the soil water characteristic curves. By using the definition of the relative permeability (equation 2.13), he obtained: 102022)()()(eeSeeeerSdSSdSSSke (2.14) Where S e (r) = dS e /dr is the effective pore size density function. Mualen (1976). Mualen derived an analytical expression in which the hydraulic conductivity is not controlled by the radius of the narrower element: 2100)()()(eeSeeneerSdSSdSSSke (2.15) For an n equal to 0.5, equation 2.15 predicts reasonably well most hydraulic conductivity curves obtained in the laboratory. Falling and constant test permeameter. In order to determine the saturated permeability of the soil, the falling and constant test permeameter 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 can be used in permeameters. The consolidation test can also be used to determine the hydraulic conductivity of soils of low permeability (Richards, 1973). Other techniques. For 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. PAGE 36 22 2.3.2 Hydraulic Conductivity Curves Models In 1957, Gardner developed one of the first interpolation functions for the hydraulic conductivity curve, namely: ksAkk1 (2.16) where k S is the saturated hydraulic conductivity. is the pore suction. A k , 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 (1966) suggested a hydraulic conductivity relationship that relates hydraulic conductivity values on the effective saturation of a soil, as follows: nrsrskk (2.17) where k S is the saturated hydraulic conductivity. is the volumetric water content. s is the saturated volumetric water content. r is the residual volumetric water content. n = 3 + 2/, and is based on the pore size index (). 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. PAGE 37 23 Brooks and Coreyâ€™s relationship is based on the analysis performed by Burdine (1953), who applied theories of fluid flow through porous material to develop a relationship that produces the relative hydraulic conductivity (k r ) from the soil-water characteristic curve. The formulation proposed by Brooks and Corey (1966) is simply a reduced form of Burdineâ€™s equation (1953), including an assumed interpolation equation for the soil-water characteristic curve. Although the Brooks and Corey (1966) 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 (Forsyth, 1987), critical for pavement applications. Finally, as it can be seen from equation 2.17 that Brooks and Corey function requires a pore size distribution value () to characterize the material. The value can be calculated using a regression function from Rawls (1992). The regression relationship is based upon the percent sand, the percent clay, the soil porosity, and cross product of these values. Green and Corey (1971), based on Childs and Collis-George (1950), proposed a more refined equation to model the hydraulic conductivity, resulting in the following interpolation function: mjjpscsiijngnkkk122221230 (2.18) for i = 1, 2, , m where k() i is the calculated conductivity for a specified water content. is the volumetric water content. PAGE 38 24 i denotes the last water content class on wet end, e.g. i=1 identifies the pore class corresponding to the lowest water content for which the conductivity is calculated. k s / k sc is a matching factor. is the surface tension. is the density of water. g is the gravitational constant ( cm/sec2) is the viscosity of water ( g/cm/sec-1) 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 = 0 and s . j is the pore pressure for a given class of water filled pores. 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. (1994). Van Genuchten (1980) used a method similar to Brooks and Coreyâ€™s (1966) model to describe the hydraulic conductivity at low suction values, resulting in the following relationship: 212111mmrsrrsrskk (2.19) where k s is the saturated hydraulic conductivity. is the volumetric water content. s is the saturated volumetric water content. r is the residual volumetric water content. PAGE 39 25 m = / (1 +), and is based on the pore size index (). Unfortunately, just like the Brooks and Corey model (1966), Van Genuchtenâ€™s approach also relies on the pore size index discussed previously. However, the difference is that instead of basing his work on Burdineâ€™s equation (1953), Van Genuchten used Mualenâ€™s model (1976). In summary, the comparison of these four models indicated that Gardnerâ€™s model is merely empirical and it is sensitive to its coefficients. The Brooks and Corey model does not perform well at low suction values and relies on a difficult to obtain l value. This difficulty also applies to Van Genuchtenâ€™s model. Green and Coreyâ€™s model is simplest to calculate with the least amount of experience. 2.4 Effects of Layering on Unsaturated Flow of Water When a fine material is laid onto a coarser material and there is a combination of unsaturated effects, a flow reduction is experimented in the coarse material. In coarse materials the soil water characteristic curve shows that almost all the volumetric water content held in the pore space is removed at low suction values. These results are reasonable because of the low capillary effects in materials of this size. Conversely, in fine materials the soil water characteristic curve shows that that much of the water is held in the soil at higher suctions. These features determine where the majority of the volumetric water content is stored in the infiltration system. The other important factor of unsaturated flow is the hydraulic conductivity function. Due to the increased difficulty of flow and the longer path of flow, the hydraulic conductivity decreases with suction. Although the coarse material starts with a higher hydraulic conductivity, the larger pore size and reduced surface tension effects cause the hydraulic conductivity to drop PAGE 40 26 rapidly at lower pore suction levels. The fine material however tends to not decrease nearly as rapidly and hence the hydraulic conductivity can actually become lower in the coarse material. 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 material where the hydraulic conductivity is much higher at the crossover suction. Therefore, the water tends to flow primarily through the fine material. However, this only happens if the pore suction values are higher than the suction at which there are equivalent hydraulic conductivities. When using this capillary barrier effect in multiple layer systems, it can be effective in reducing the amount of seepage. However, in pavement systems, the capillary barrier effect it may result in adverse conditions for a proper drainage, if not accounted for properly in the drainage design. PAGE 41 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, scope of study, and research approach. 3.1 Analysis Tools Used 3.1.1 SEEP/W The finite element-based groundwater modeling software, SEEP/W, can simulate both saturated and unsaturated flow. For these two conditions, the program applies the overall principle that the flow of water through soil follows Darcyâ€™s law. However, the governing equation for all the calculations is Richardsâ€™ equation, shown below, which represents in a more suitable form the unsaturated flow: tQyHkyxHkxyx (3.1) where H is total head. k x is hydraulic conductivity in the x-direction. k y is hydraulic conductivity in the y-direction. Q is the applied boundary flux. is volumetric water content. t is time. 27 PAGE 42 28 This fundamental partial differential equation 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. As it can be seen, Richardsâ€™ equation can be used for saturated and unsaturated conditions. The right part of the equation would become zero when the first case is applied or in steady-state conditions. 3.1.2 DRIP The microcomputer program Drainage Requirements In Pavements (DRIP) 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 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 (1952) and Casagrande and Shannon method (1952). The Barber and Sawyer (1952) equations are: khLTnt2Re (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. n e is the effective porosity of the drainage layer. L R is the resultant length of the drainage path. It is a function of the width longitudinal slope and resultant slope (S R ) 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: PAGE 43 29 4.2SU-12.1USSlogS15.1S4.21logS48.0S5.0TRRRRR2RR (3.2a) for U>0.5 R2RRSU8.41logS48.0UST (3.2b) for U 0.5 Casagrande and Shannonâ€™s method (1952) is based on the same equation (3.2), but T factor is determined by: RR2RRRRRRS1SlnS1SU221US2S2lnSS2c T ( 3.3a) for U>0.5 RR2RRSU2SlnS2US2cT (3.3b) for U 0.5, 31RS0.84.2c (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 â€œTime to drainâ€ 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. PAGE 44 30 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 base material (Class 6 Special), and a subgrade. Figure 3.1 shows the thickness of each of base and hot mix asphalt layers for Cells 33-35. 12â€™â€™ 12â€™â€™ 12â€™â€™ Base Layer 3.96â€™â€™ Cell 35 3.92â€™â€™ Cell 34 4.04â€™â€™ Cell 33 Asphalt Layer 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. Subgrade Hot Mix As p hal t Base CL 4.53 m 4.27 m 4.27 m 3.43 m 4.53 m Figure 3.2: Pavement geometry and dimensions PAGE 45 31 3.2.2 Materials 3.2.2.1 Hot mix asphalt layers For this study the 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 base course for Cells 33-35 consisted of Class 6 Special, dense graded base material, consisting of 4 percent fines passing the 0.075 mm (No. 200) sieve, 57 percent gravel, and 39 percent sand. The grain-size distribution curve is shown in Figure 3.3. 01020304050607080901000.1110100Grain Size (mm) Figure 3.3: Grain size distribution for Mn/DOT Class 6 special According to the soil water characteristic curve, it is not possible to clearly identify the air entry value for the Class 6 material. Therefore, the change from saturated to PAGE 46 32 unsaturated behavior cannot be appreciated. Furthermore, the initial slope of the curve is really steep. This means that its volumetric water content drops down really quickly. For example, within the zero to one kPa range, the volumetric water content drops from 32.02 percent to 8.44 percent. Mn/DOT performed suction plate testing to obtain soil-water characteristic curve (SWCC) and hydraulic conductivity curves. Figures 3.4 and 3.5 show the different curves. 0.05.010.015.020.025.030.035.0051015202530Suction (kPa)Volumetric Water Content (%) Figure 3.4: Soil water characteristic curve â€“ Base material (Class 6 special) 1.0E-151.0E-131.0E-111.0E-091.0E-071.0E-050510152025Suction (kPa)k (m/s) Figure 3.5: Hydraulic conductivity curve â€“ Base material (Class 6 special) PAGE 47 33 The hydraulic conductivity curve shows that Class 6 Special is a material with a K sat value equal to 1.54E-06 m/s. This corresponds to fine sand. However, within the first 10 kPa the K value has dropped close to 1E-13 m/s. 3.2.2.3 Subgrade material The subgrade layer can be characterized as sandy clayey silt material. Figures 3.6 and 3.7 show the soil water characteristic curve and the hydraulic conductivity curve for the subgrade. Figure 3.6 shows that this sandy clayey silt material 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 is really slow. 20.025.030.035.040.045.050.055.00.0010.010.1110100100010000Suction (kPa) Figure 3.6: Soil water characteristic curve â€“ Subgrade material (R-70 Silty clay) PAGE 48 34 1.0E-151.0E-141.0E-131.0E-121.0E-111.0E-101.0E-091.0E-081.0E-070.002.004.006.008.0010.0012.0014.0016.00Suction (kPa) Figure 3.7: Hydraulic conductivity curve â€“ Subgrade material (R-70 Silty clay) As well as the soil water characteristic curve, the hydraulic conductivity curve also presents the subgrade material with 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. 3.3 Scope The study addresses the following: 1) verification of SEEP/W for modeling unsaturated flow of water through pavements, 2) modeling of the movement of water through flexible pavement systems that are unsaturated and 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. The following analyses were performed: â€¢ Comparison between saturated and unsaturated flow conditions in flexible pavements. â€¢ Parameters that have an effect on drainage performance. â€¢ Performance of drainage systems under unsaturated conditions. PAGE 49 35 The research approach essentially involved evaluating the effects of unsaturated conditions on pavement drainage due to â€¢ Pavement materials characterization â€¢ Pavement configuration (geometry, layers, drainage systems) â€¢ Pavement boundary conditions (ground water table, rain events) PAGE 50 CHAPTER 4 VERIFICATION OF SEEP/W FOR PAVEMENT APPLICATION In this Chapter, the use of SEEP/W is evaluated for simulating the flow of water through simplified pavement systems. SEEP/W predictions are compared against results obtained from three different infiltration examples from the published literature. 4.1 Example 1 The first example is based on an experimental setup performed by Vauclin (1979) in the laboratory with a 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 H o = 1.35 m. There was no flow through the vertical left hand side of the slab. A constant flux corresponding to q o = 4.1111 E-5 m/s was applied on the soil surface over a width L o = 0.50 m. Figure 4.1 describes the geometry and conditions for this example. 0.65 m 3 m 2 m qo = 4.1111 E -5 m/s 0.0 5 m Figure 4.1: Example 1 â€“ Geometry and boundary conditions 36 PAGE 51 37 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 (1966) and Gardner (1956) models respectively. Table 4.1 shows the parameters obtained with the mentioned regression analysis. Table 4.1: Soil hydraulic parameters Brutsaert Gardner s A K s (m/s) 40,000 2.9 0.30 2.99E+06 5.0 9.72E-05 Based on these hydraulic parameters (table 4.1) and the two previously mentioned models, the Soil Water Characteristic and the Hydraulic Conductivity Curves were obtained (Figures 4.2 and 4.3). 0.05.010.015.020.025.030.035.00.010.101.0010.00100.00Suction (kPa) Figure 4.2: Soil water characteristic curve (Brutsaert model) PAGE 52 38 1.0E-121.0E-101.0E-081.0E-061.0E-040.0010.0020.0030.0040.0050.00Suction (kPa) Figure 4.3: Hydraulic conductivity curve (Gardner model) The finite element mesh (FEM) used in SEEP/W to simulate this experiment is presented in figure 4.4. The mesh is composed of 0.1 x 0.1 m quadrilateral elements. q boundary conditions 1.35 m 0.65 m Water table 3.0 m Figure 4.4: Example 1 â€“ FEM A comparison between the measured data (Vauclin, 1979) and the predicted results (SEEP/W) is presented from Figures 4.5 to 4.8. As can be seen, the variation in the water PAGE 53 39 table with time obtained from the SEEP/W model follows the same trend as the measured data. 0.000.100.200.300.400.500.600.700.800.900.000.501.001.502.002.503.00Distance (m) Measured Predicted Figure 4.5: Comparison between measured and predicted water table at 2 hours 0.000.200.400.600.801.001.200.000.501.001.502.002.503.00Distance (m) Measured Predicted Figure 4.6: Comparison between measured and predicted water table at 3 hours PAGE 54 40 0.000.200.400.600.801.001.200.000.501.001.502.002.503.00Distance (m) Measured Predicted Figure 4.7: Comparison between measured and predicted water table at 4 hours 0.000.200.400.600.801.001.201.400.000.501.001.502.002.503.00Distance (m) Measured Predicted Figure 4.8: Comparison between measured and predicted water table at 8 hours The SEEP/W simulations showed 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. PAGE 55 41 4.2 Example 2 The second example is based on a modification of Vauclinâ€™s (1979) experiment, where base material is used to simulate the infiltration process that pavement structures may go through during rainfall events (Espinoza et al., 1993). This case is represented by two-dimensional infiltration into a simplified pavement structure. The simplified pavement system consists of a wearing course overlaying homogeneous base material (Figure 4.9). The bottom and lateral boundaries were impermeable, as well as the wearing course. Therefore, the only source of water was the shoulder. As an initial condition, the effective degree of saturation was specified as 50%. A rainfall of constant intensity was applied (q o = 2.7778 E-06 m/s). qo = 2.7778 E-06 0.0 5 m 2 m 0.20 m 0.025 m Kh=3.50 E-05 m/s Kv=3.50 E-06 m/s o=0.005, =0.382 Si=0.5 (initial saturation) Figure 4.9: Example 2 â€“ Geometry and boundary conditions The base material was characterized as an anisotropic material. The horizontal conductivity was 10 times greater than the vertical. The soil water characteristic curve and hydraulic conductivity curve were calculated using only the horizontal conductivity. The vertical value was taking into account in SEEP/W by using the ration between both values. PAGE 56 42 Brooks and Corey models (1966) were used to calculate the soil water characteristic curve and hydraulic conductivity curve (Figures 4.10 and 4.11). 0.05.010.015.020.025.030.035.040.045.00.010.101.0010.00Suction (kPa) Figure 4.10: Soil water characteristic curve (Brooks and Corey model) 1.0E-101.0E-091.0E-081.0E-071.0E-061.0E-051.0E-040.001.002.003.004.005.006.00Suction (kPa) Figure 4.11: Hydraulic conductivity curve (Brooks and Corey model) This example was modeled in SEEP/W, using the finite element mesh shown in Figure 4.12, with 0.025 x 0.025 m quadrilateral elements. Due to the fact that the initial degree PAGE 57 43 of saturation is 50%, an equivalent water table was set. Above it the maximum achievable suction pressure was 2.12 kPa, which is the suction required to have an effective saturation (S e ) of 50%. q boundary conditions 0.2 m Wearing course 2.0 m Base course 0.5 m Assumed Water table Figure 4.12: Example 2 â€“ FEM Figures 4.13 through 4.16 show the variation of the volumetric water content with the distance 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 () changes most rapidly in the transition zone between the shoulder and the edge of the wearing course. Also, as expected, the variation of is higher in the horizontal direction than in the vertical one, due to the anisotropic hydraulic conductivity conditions. PAGE 58 44 0.05.010.015.020.025.030.00.000.400.801.201.602.00Distance (m) Measured Predicted Figure 4.13: Comparison between measured and predicted volumetric water content at 1.5 hours 0.05.010.015.020.025.030.035.040.00.000.400.801.201.602.00Distance (m) Measured Predicted Figure 4.14: Comparison between measured and predicted volumetric water content at 3 hours PAGE 59 45 0.05.010.015.020.025.030.035.040.045.00.000.400.801.201.602.00Distance (m) Measured Predicted Figure 4.15: Comparison between measured and predicted volumetric water content at 4.5 hours 0.05.010.015.020.025.030.035.040.045.00.000.400.801.201.602.00Distance (m) Measured Predicted Figure 4.16: Comparison between measured and predicted volumetric water content at 6 hours PAGE 60 46 4.3 Example 3 The last example is based on a modification of Example 2. To simulate the case of a subdrainage layer with high permeability (Espinoza et al., 1993), base and subbase layers are introduced, as shown in Figure 4.17. As in the previous case, the pavement slab, both lateral boundaries, and the bottom boundary were assumed to be impervious. The subbase was considered to be 100 times more permeable as the base course. The initial moisture conditions were defined by assuming 50% saturation. The only source of infiltration was the shoulder, with a rate q o equal to 2.7778 E-06 m/s. 2 m qo = 2.7778 E-06 0.0 5 m o=0.005, =0.382 Si=0.5 (initial saturation) 0.10 m Kh=Kv=3.50 E-04 m/s Kh=Kv=3.50 E-06 m/s 0.025 m 0.20m Figure 4.17: Example 3 â€“ Geometry and boundary conditions The characterization of base and subbase materials was made based upon Brooks and Corey model (1966). Figures 4.18 to 4.20 present this characterization. The subbase layer was 100 times more permeable than the base layer. PAGE 61 47 0.05.010.015.020.025.030.035.040.045.00.010.101.0010.00Suction (kPa) Figure 4.18: Soil water characteristic curve for base and subbase (Brooks and Corey model) 1.0E-121.0E-111.0E-101.0E-091.0E-081.0E-071.0E-061.0E-050.001.002.003.004.005.006.00Suction (kPa) Figure 4.19: Hydraulic conductivity curve â€“ Base (Brooks and Corey model) PAGE 62 48 1.0E-101.0E-091.0E-081.0E-071.0E-061.0E-051.0E-041.0E-030.001.002.003.004.005.006.00Suction (kPa) Figure 4.20: Hydraulic conductivity curve â€“ Subbase (Brooks and Corey model) Figure 4.21 presents the FEM for this example, which has 0.025 x 0.025 m quadrilateral elements to represent both layers. As well as in example 2, a water table was assumed to simulate the initial 50% of saturation. q boundary conditions 0.2 m Wearing course 2.0 m Base course 0.5 m Assumed Water table Figure 4.21: Example 3 â€“ FEM PAGE 63 49 The resulted variation of volumetric water content with distance is presented in figures 4.22 through 4.29, at 1.5, 3, 4.5 and 6 hours for the base and subbase materials. 0.05.010.015.020.025.030.035.040.00.000.400.801.201.602.00Distance (m) Measured Predicted Figure 4.22: Comparison between measured and predicted volumetric water content in base material at 1.5 hours 0.05.010.015.020.025.030.035.040.00.000.400.801.201.602.00Distance (m) Measured Predicted Figure 4.23: Comparison between measured and predicted volumetric water content in base material at 3 hours PAGE 64 50 0.05.010.015.020.025.030.035.040.00.00.40.81.21.62.0Distance (m) Measured Predicted Figure 4.24: Comparison between measured and predicted volumetric water content in base material at 4.5 hours 0.05.010.015.020.025.030.035.040.00.00.40.81.21.62.0Distance (m) Measured Predicted Figure 4.25: Comparison between measured and predicted volumetric water content in base material at 6 hours PAGE 65 51 5.010.015.020.025.00.00.40.81.21.62.0Distance (m) Measured Predicted Figure 4.26: Comparison between measured and predicted volumetric water content in subbase material at 1.5 hours 5.010.015.020.025.030.035.00.00.40.81.21.62.0Distance (m) Measured Predicted Figure 4.27: Comparison between measured and predicted volumetric water content in subbase material at 3 hours PAGE 66 52 0.05.010.015.020.025.030.035.00.00.40.81.21.62.0Distance (m) Measured Predicted Figure 4.28: Comparison between measured and predicted volumetric water content in subbase material at 4.5 hours 0.05.010.015.020.025.030.035.00.00.40.81.21.62.0Distance (m) Measured Predicted Figure 4.29: Comparison between measured and predicted volumetric water content in subbase material at 6 hours PAGE 67 53 The effect of the subbase layer can be appreciated by comparing the change in volumetric water content of the base for Example 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. 0.05.010.015.020.025.030.035.040.045.00.000.400.801.201.602.00Distance (m) Example 2 Measured Example 3 Measured Figure 4.30: Comparison of measured volumetric water content in base material at 6 hours for Examples 2 and 3 0.05.010.015.020.025.030.035.040.045.00.000.400.801.201.602.00Distance (m) Example 2 Predicted Example 3 Predicted Figure 4.31: Comparison of predicted volumetric water content in base material at 6 hours for Examples 2 and 3 PAGE 68 54 4.4 Summary SEEP/W is a useful tool to simulate water flow through layering structures (i.e. pavement systems, base drainage layers, subgrades). It helps to predict water movement in a precise way for specific conditions. However, it is significant to know all the boundary conditions in order to have an accurate simulation of field scenery. Therefore, material characterization (soil water characteristic curve and hydraulic conductivity curve), initial water table position, and geometry, are some important key conditions to obtain predictions that in fact describe what it is happening on field. PAGE 69 CHAPTER 5 CALIBRATION OF RESULTS TO FIELD RESULTS FOR CELLS 33, 34, 35 In order to develop and understanding of the behavior of flow of water through flexible pavements under unsaturated conditions, a finite element based numerical model of flow through flexible pavements was developed 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. In the following, the finite element model will be described, followed by the calibration of the predicted results to measured field results. 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 base material (Class 6 Special), and an R-70 silty clay subgrade. Figure 5.1 shows the depth of each layer for these sections. Class 6 S p ecial HMA 3.96â€™â€™ Cell 35 12â€™â€™ 3.92â€™â€™ Cell 34 12â€™â€™ 4.04â€™â€™ Cell 33 12â€™â€™ Figure 5.1: Layer thicknesses for Mn/ROAD Cells 33, 34, and 35 55 PAGE 70 56 5.2 Finite Element Model Based on Figure 5.2, finite element-based cross sections of Mn/ROAD cells 33, 34, and 35 were constructed using SEEP/W. In the following an overview will be provided of the construction of the FEM mesh. Figure 5.3 presents a section of the mesh utilized to model Cell 33, 34 and 35. 16.5 m 4.0 m 4:1 4:1 R-70 silty clay 0.1 m Hot Mix As p hal t 0.3 m Class 6 S p ecial CL 3.05 m 4.27 m 4.27 m 1.83 m Figure 5.2: Pavement geometry and dimensions for Cells 33, 34, and 35 Base Finite Elements Hot Mix As p halt Subgrade Finite Elements Figure 5.3: Section of the FEM used to represent Cell 33, 34 and 35 PAGE 71 57 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 FEM. This layer was not represented with finite elements. Only its geometry was taking 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 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 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-70, 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 that replicated measured rain events simulated infiltration due to precipitation. The event selected for this simulation is presented later in the final element analysis. PAGE 72 58 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 FEM model. Extended Subgrade H = 0 m H = 0 m 36.5 m Extended Subgrade 4.0 m Figure 5.4: FEM used to represent Cells 33, 34, and 35 5.2.5 FEM 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 â€œrain event,â€ resulting in time-dependent changes in the volumetric moisture content throughout the pavement system. However, before starting the transient analysis, a steady-state analysis was performed to obtain the initial head conditions for the system. A steady-state analysis permits the determination of more rigorous head conditions to represent the water table. Therefore, total heads equal to 3.82 m were applied at both ends PAGE 73 59 of the subgrade to obtain a water table at 3.2 m of elevation, approximately. The suction corresponding to this depth of the water table resulted in a match with the initial volumetric water contents of the measured data. 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. -5.0E-080.0E+005.0E-081.0E-071.5E-072.0E-072.5E-073.0E-073.5E-07190200210220230240250260270Time (Julian day) Figure 5.5: Precipitation events for Cells 33, 34, and 35 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 different depths (Figure 5.6), at 1.83 m from PAGE 74 60 the centerline. They are designated as locations 101, 102, and 103, respectively for all the Cells. The corresponding locations of the TDRs in the FEM model are shown in Figure 5.7. R-70 silty clay Class 6 Special HM A Automated *TDR 3.6 m 0.30 m 0.10 m 0.38m 0.25 m 0.13 m Centerline Offset (-1.83 m) Figure 5.6: TDR installation at Mn/DOT Cells 33, 34 and 35 Hot Mix As p halt CL Base Subgrade Finite Elements Figure 5.7: TDR location within FEM for Cells 33, 34, and 35 PAGE 75 61 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. 2.04.06.08.010.012.014.016.018.020.0210220230240250260270Time (Julian day) TDR Location 101 TDR Location 102 TDR Location 103 Figure 5.8: Measured data for different TDR locations at Cell 33 PAGE 76 62 0.05.010.015.020.025.0210220230240250260270Time (Julian day) TDR Location101 TDR Location102 TDR L o catio n Figure 5.9: Measured data for different TDR locations at Cell 34 0.05.010.015.020.025.0210220230240250260270Time ( Julian day) TDR Location 101 TDR Location 102 TDR Location 103 Figure 5.10: Measured data for different TDR locations at Cell 35 PAGE 77 63 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 K sat 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. The subgrade characterization is presented in Figures 3.6 and 3.7. The soil water characteristic curve shows that this silty clay material has little variation of volumetric water content. For example, there is only 9% drop for the first 10 kPa of suction. The total change is 15% over the range of measured suction. This means that the subgrade has the capacity to hold water for a long time, therefore its drainage is likely really slow. The hydraulic conductivity curve for the subgrade 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 soil water characteristic curve results tend to be sensitive to density and gradation. Since the gradation is the same between the field and the laboratory, the density may be slightly different. In particular, the density around the TDR probes in the field is likely different from that in the laboratory. These differences can result in variations in both the air entry value and the slope of the soil water characteristic curve in the unsaturated region. Therefore, it was necessary to â€œtuneâ€ the measured soil water characteristic curves to fit the measured TDR data from the field. In addition, the TDR volumetric moisture contents may have a range of up 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. PAGE 78 64 In the following, the results from the original TDR data are shown, followed by calibration to field results. The calibration to field results was easily achieved by adjusting the air entry values slightly and changing the slope of the soil water characteristic curves to reflect more closely the field density conditions around the TDR probes. Finally, the saturated volumetric water content was adjusted slightly to reflect the variability in the TDR results, due to their limits of accuracy (plus or minus two (2) percent variations in volumetric water content are common). Once calibrated, soil water characteristic curves were obtained, and SEEP/W was used to generate the appropriate hydraulic conductivity curves, using the Green and Corey (1971) approach. Since the geometry and material properties were the same for Cells 33, 34, and 35, Cell 33 was chosen for the calibration (â€œtuningâ€) 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 curves were â€œtuned,â€ the infiltration rate was decreased to a percentage of the measured precipitation 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 characteristic 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 PAGE 79 65 volumetric water content remained constant at 32 percent, as shown in Figures 5.11 through 5.13. 0.04.08.012.016.020.024.028.032.036.0210220230240250260270Time (Julian day) Measured Predicted Figure 5.11: Volumetric water content at Cell 33 â€“ Location 101 4.08.012.016.020.024.028.032.036.0210220230240250260270Time (Julian day) Measured Predicted Figure 5.12: Volumetric water content at Cell 33 â€“ Location 102 PAGE 80 66 4.08.012.016.020.024.028.032.036.0210220230240250260270Time (Julian day) Measured Predicted Figure 5.13: Volumetric water content at Cell 33 â€“ Location 103 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 conditions. Since the density around the TDR probes in the field is likely to be different from that in the laboratory, a slight variation in both the air entry value and the slope of the soil water characteristic curve in the unsaturated region can be assumed. Based on a recommendation from Mn/DOT (Roberson, 2002), a new air entry value of 3kPa was used. Subsequently, SEEP/W was used to obtain a corresponding hydraulic conductivity curve. The K sat 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. PAGE 81 67 0.05.010.015.020.025.030.035.00.005.0010.0015.0020.0025.0030.0035.00Suction (kPa) Figure 5.14: Soil water characteristic curve (air entry = 3 kPa) â€“ Base material (Class 6 special) 1.0E-121.0E-101.0E-081.0E-060.05.010.015.020.025.030.035.0Suction (kPa) Figure 5.15: Estimated hydraulic conductivity curve â€“ Base material (Class 6 special) PAGE 82 68 The modifications didnâ€™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) was changed slightly to represent better the likely lower density conditions around the TDR probes in the field. 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 ( sat ) of 2 percent. Subsequently, SEEP/W was used to estimate the corresponding hydraulic conductivity curve, shown in Figure 5.17. 0.05.010.015.020.025.030.035.00.005.0010.0015.0020.0025.00Suction (kPa) Figure 5.16: Final soil water characteristic curve â€“ Base material (Class 6 special) PAGE 83 69 1.0E-151.0E-131.0E-111.0E-091.0E-071.0E-050.05.010.015.020.025.030.035.0Suction (kPa) Figure 5.17: Estimated hydraulic conductivity curve â€“ Base material (Class 6 special) Figures 5.18 to 5.20 show the resulting FEM 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. PAGE 84 70 0.04.08.012.016.020.024.028.032.0210220230240250260270Time (Julian day) Measured Predicted Figure 5.18: Volumetric water content at Cell 33 â€“ Location 101 6.010.014.018.022.026.030.034.0210220230240250260270Time (Julian day) Measured Predicted Figure 5.19: Volumetric water content at Cell 33 â€“ Location 102 PAGE 85 71 6.010.014.018.022.026.030.0210220230240250260270Time (days) Measured Predicted Figure 5.20: Volumetric water content at Cell 33 â€“ Location 103 The resistance to vertical flow is heavily determined by the properties of the subgrade. Hence, the K sat 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 K sat value (Figure 5.21). PAGE 86 72 1.0E-121.0E-101.0E-081.0E-060.005.0010.0015.0020.0025.0030.0035.00Suction (kPa) Figure 5.21: Modified hydraulic conductivity curve: 10 times K sat â€“ Subgrade material (R-70 Silty clay) Figures 5.22 through 5.24 show the resulting FEM predictions for TDR 101, 102, and 103. Subsequently, the process was repeated, until correspondence with field results was achieved. PAGE 87 73 0.04.08.012.016.020.024.028.032.0210220230240250260270Time (Julain day) Measured Predicted Figure 5.22: Volumetric water content at Cell 33 â€“ Location 101 6.010.014.018.022.026.030.0210220230240250260270Time (Julian day) Measured Predicted Figure 5.23: Volumetric water content at Cell 33 â€“ Location 102 PAGE 88 74 6.010.014.018.022.026.030.0210220230240250260270Time (Julian day) Measured Predicted Figure 5.24: Volumetric water content at Cell 33 â€“ Location 103 The final K sat value for the subgrade was taken as K sat = 2.7535E-6 m/s (Figure 5.25). 1.0E-151.0E-131.0E-111.0E-091.0E-071.0E-050.005.0010.0015.0020.0025.0030.0035.00Suction (kPa) Figure 5.25: Final hydraulic conductivity curve: K sat = 2.7535E-06 m/s â€“ Subgrade material (R-70 Silty clay) PAGE 89 75 Figures 5.26 through 5.28 show the predicted FEM 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 FEM predictions for TDR location 102 (Figure 5.27) are still slightly different from the field results. 6.07.08.09.010.011.012.013.014.0210220230240250260270Time (Julian day) Measured Predicted Figure 5.26: Volumetric water content at Cell 33 â€“ Location 101 PAGE 90 76 6.08.010.012.014.016.018.020.022.024.026.0210220230240250260270Time (Julian day) Measured Predicted Figure 5.27: Volumetric water content at Cell 33 â€“ Location 102 6.010.014.018.022.026.030.0210220230240250260270Time (Julian day) Measured Predicted Figure 5.28: Volumetric water content at Cell 33 â€“ Location 103 PAGE 91 77 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 FEM. 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 FEM results now follows that of the measured data. In particular, TDR location 101 predicted FEM volumetric moisture content values correspond closely with the field data. 6.07.08.09.010.011.012.0210220230240250260270Time (Julian day) Measured Predicted Figure 5.29: Volumetric water content at Cell 33 â€“ Location 101 PAGE 92 78 6.08.010.012.014.016.018.020.0210220230240250260270Time (Julian day) Measured Predicted Figure 5.30: Volumetric water content at Cell 33 â€“ Location 102 8.012.016.020.024.028.0210220230240250260270Time (Julian day) Measured Predicted Figure 5.31: Volumetric water content at Cell 33 â€“ Location 103 PAGE 93 79 5.3.3 Calibration due to Material Density The TDRs are installed into the base material after the construction process of the pavement is performed, thus likely affecting the density of the material around the TDR points. Any variation in density has a direct effect on the soil water characteristic curve. For example, if the density decreases, the volumetric water content at saturation will be higher. Assuming that density around TDR location 102 is slightly lower than in the rest of the base, 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. 0.010.020.030.040.00.005.0010.0015.0020.0025.00Suction (kPa) Figure 5.32: Final soil water characteristic curve for Location 102 â€“ Base material (Class 6 special) PAGE 94 80 As expected, the change in density improved the correspondence between the predicted FEM 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. 6.08.010.012.014.016.018.020.022.024.0210220230240250260270Time (Julian day) Measured Predicted Figure 5.33: Volumetric water content at Cell 33 â€“ Location 102 PAGE 95 81 0.05.010.015.020.025.030.00.005.0010.0015.0020.0025.00Suction (kPa) Figure 5.34: Final soil water characteristic curve for Location 103 â€“ Base material (Class 6 special) The resulting FEM prediction shown in Figure 5.35 now shows a close match with the field results. 8.010.012.014.016.018.020.022.024.0210220230240250260270Time (Julian day) Measured Predicted Figure 5.35: Volumetric water content at Cell 33 â€“ Location 103 PAGE 96 82 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. In perspective, since the actual density conditions around the TDRs are not well known, and the variability in TDR readings may be result in differences of up to plus or minus 6 percent volumetric moisture content, it has to be concluded that only minor changes in the volumetric moisture contents were needed to match field data. Similarly, since the actual densities in the upper layer of the subgrade are only approximate, it is not unlikely that the hydraulic conductivity may be slightly different from that measured in the laboratory. In summary, it has to be concluded that the field results were matched through fairly small adjustments in the soil water characteristic curve and hydraulic conductivity curves. Table 5.1: Cell 33 â€“ Calibration for base layer (Class 6 special) Final calibration Parameters Initial data Location 101 Location 102 Location 103 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 â€“ Calibration for subgrade (R-70 Silty clay) Parameters Initial data Final Calibration sat (%) 49 49 k sat (m/s) 2.7535E-08 2.7535E-06 5.4 Cell 34 The calibrations used 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 FEM results match the shape for the measured field volumetric moisture contents well. PAGE 97 83 6.07.08.09.010.011.012.013.014.0210220230240250260270Time (Julian day) Measured Predicted Figure 5.36: Volumetric water content at Cell 34 â€“ Location 101 4.06.08.010.012.014.016.018.020.0210220230240250260270Time (Julian day) Measured Predicted Figure 5.37: Volumetric water content at Cell 34 â€“ Location 102 PAGE 98 84 8.012.016.020.024.028.032.036.0210220230240250260270Time (Julian day) Measured Predicted Figure 5.38: Volumetric water content at Cell 34 â€“ Location 103 5.4.1 Calibration of Results at Locations 101 and 102 Due to likely density variations around TDR locations 101 and 102, 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. It is likely that slight variations in the construction process between Cells 33 and 34, as well as the subsequent densities achieved around each of the TDRs might explain these differences. PAGE 99 85 0.05.010.015.020.025.030.035.00.005.0010.0015.0020.00Suction (kPa) Figure 5.39: Final soil water characteristic curve for Location 101 and 102 at Cell 34 â€“ Base material (Class 6 special) The resulting comparison between the predicted FEM 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. PAGE 100 86 11.011.512.012.513.0210220230240250260270Time (Julian day) Measured Predicted Figure 5.40: Volumetric water content at Cell 34 â€“ Location 101 10.012.014.016.018.0210220230240250260270Time (Julian day) Measured Predicted Figure 5.41: Volumetric water content at Cell 34 â€“ Location 102 PAGE 101 87 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. Figure 5.42 shows the new soil water characteristic curve for this location at cell 34, and Figure 5.43 shows the resulting overall close comparison between the predicted and measured moisture contents for TDR location 103. 0.05.010.015.020.025.030.035.00.005.0010.0015.0020.00Suction (kPa) Figure 5.42: Final soil water characteristic curve for Location 103 Cell 34 â€“ Base material (Class 6 special) PAGE 102 88 8.012.016.020.024.028.032.036.0210220230240250260270Time (Julian day) Measured Predicted Figure 5.43: Volumetric water content at Cell 34 â€“ Location 103 However, small abnormalities at days 231, 249, and 266 in the measured TDR data were not captured in the FEM 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 5.3 summarizes the modifications made to the base material to achieve calibration for Cell 34. Table 5.3: Cell 34 â€“ Calibration for base layer (Class 6 special) Final calibration Parameters Initial data Location 101 Location 102 Location 103 q 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 PAGE 103 89 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 characteristic curve and hydraulic conductivity curve) that were used for Cell 34 resulted in reasonable comparisons of predicted and measured volumetric moisture contents for TDR locations 101 and 103, as shown in Figures 5.44 and 5.45. 8.09.010.011.012.013.014.015.016.017.0210220230240250260270Time (Julian day) Measured Predicted Figure 5.44: Volumetric water content at Cell 35 â€“ Location 101 PAGE 104 90 6.08.010.012.014.016.018.020.022.024.026.0210220230240250260270Time (Julian day) Measured Predicted Figure 5.45: Volumetric water content at Cell 35 â€“ Location 103 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. 0.05.010.015.020.025.030.035.00.005.0010.0015.0020.00Suction (kPa)Volumetric Water Content (%) s Figure 5.46: Final soil water characteristic curve for Location 102 Cell 35 â€“ Base material (Class 6 special) PAGE 105 91 The predictions obtained using calibrated data for TDR location 102 are shown in Figure 5.47. 6.08.010.012.014.016.018.020.0210220230240250260270Time (Julian day) Measured Predicted Figure 5.47: Volumetric water content at Cell 35 â€“ Location 102 Tables 5.4 summarizes the modifications made to the base material for Cell 35 to calibrate the predicted FEM results to the observed TDR volumetric moisture contents. Table 5.4: Cell 35 â€“ 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 PAGE 106 92 5.6 Summary The soil water characteristic curve tends to be sensitive to density and gradation. These differences can result in a variation in both the air entry value and the slope of the soil water characteristic curve in the unsaturated region. For example, if the density decreases, the volumetric water content at saturation will be higher. The TDRs are installed into the base material after the construction process of the pavement is performed, thus likely affecting the density of the material around the TDR points Therefore, if the density around the TDR probes in the field is likely different from that in the laboratory, the results obtained with FEM will be affected. Since the actual density conditions around the TDRs are not well known, and the variability in TDR readings may be result in differences of up to plus or minus 6 percent volumetric moisture content, it has to be concluded that only minor changes in the volumetric moisture contents were needed to match field data. Similarly, since the actual densities in the upper layer of the subgrade are only approximate, it is not unlikely that the hydraulic conductivity may be slightly different from that measured in the laboratory. In summary, it has to be concluded that the field results were matched through fairly small adjustments in the soil water characteristic curve and hydraulic conductivity curve. The resistance to vertical flow is heavily determined by the properties of the subgrade. Hence, the characterization (specially the K sat value) of this material has a significant effect in the upper layer drainage performance. Among the boundary conditions is important to consider that 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 FEM. Importantly, based on the calibration results, it appears that about 30 percent of the precipitation made PAGE 107 93 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. PAGE 108 CHAPTER 6 PARAMETRIC STUDY The purpose of this parametric study is to identify the effects of variations in the soil water characteristic curves and hydraulic characteristic curves, as well as variations in the ground water table on the water flow through typical flexible pavement configurations, represented by Cells 33-35 under unsaturated conditions. Since Cells 33-35 are similar, except for 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 material. 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 volumetric 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 sat = 30.19% and a drop of 4.6% up to the air entry value (3 kPa), 2) considering 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 94 PAGE 109 95 as that for Case 1, resulting in 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. 0.010.020.030.040.00.005.0010.0015.0020.00Suction (kPa) Case 1 Case 2 Case 3 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 conductivity 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. PAGE 110 96 1.0E-141.0E-121.0E-101.0E-081.0E-060.05.010.015.020.025.030.035.0Suction (kPa) Case 1 Case 2 Case 3 Figure 6.2: Hydraulic conductivity curves for initial slope cases The resulting FEM predictions are shown in Figure 6.3. It is apparent from the results that the initial slope of the soil water characteristic curve effects 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%. The fastest one corresponds to case 2, which had the highest hydraulic conductivity values among the three cases. 8.99.09.19.29.39.49.59.69.79.8210220230240250260270Time (Julian day) Predicted Case 1 Predicted Case 2 Predicted Case 3 Figure 6.3: Results for initial slope cases PAGE 111 97 6.2 Air Entry Value of Base Material Another important parameter to evaluate is the air entry value. It represents the transition suction value between unsaturated and saturated conditions. Figure 6.4 presents three cases considered for the soil water characteristic curve with different air entry values: 3 kPa, which is the original case, 4 kPa, and 5 kPa. 0.05.010.015.020.025.030.035.00.005.0010.0015.0020.0025.00Suction (kPa) Case 1 Case 2 Case 3 Figure 6.4: Base soil water characteristic curves for air entry value cases 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. PAGE 112 98 2.06.010.014.018.022.0210220230240250260270Time (Julian day) Predicted Case 1 Predicted Case 2 Predicted Case 3 Figure 6.5: Results for air entry value cases at base layer 6.3 K sat of Base Material Another important parameter is the saturated hydraulic conductivity of the base material (K sat ). Three different cases were considered: 1) K sat = 1.55E-6 m/s (original case), 2) a K sat which was 10 times larger than the original value (1.55E-5 m/s), and 3) a K sat 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 K sat values studies using SEEP/W. PAGE 113 99 1.0E-131.0E-111.0E-091.0E-071.0E-051.0E-030.05.010.015.020.025.030.035.0Suction (kPa) Case 1 Case 2 Case 3 Figure 6.6: Hydraulic conductivity curves for K sat cases at base material Figure 6.7 shows the resulting FEM predictions. The higher the hydraulic conductivity the faster the material will drain. Also, case 3 with the highest K sat value, results in much more abrupt changes in the predicted volumetric moisture content than for the other two cases with lower K sat values. PAGE 114 100 9.209.259.309.359.409.459.509.559.609.659.709.759.809.859.90210220230240250260270Time (Julian day) Predicted Case 1 Predicted Case 2 Predicted Case 3 Figure 6.7: Results for K sat cases at base layer 6.4 Air Entry Value of Subgrade Material Again, three distinct air entry values were considered: 1) 0 kPa, which is the original case, 2) 5 kPa, and 3) 10 kPa. Figure 6.8 shows the resulting FEM predictions. Interestingly, the base material drainage wouldnâ€™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. PAGE 115 101 9.09.19.29.39.49.59.69.79.8210220230240250260270Time (days) Predicted Case 1 Predicted Case 2 Predicted Case 3 Figure 6.8: Results for air entry values at subgrade layer 6.5 K sat at Subgrade Material In order to evaluate the effects of resistance to drainage through the base/subgrade interface and into the subgrade interface, the effects of the subgrade K sat were evaluated. Figure 6.9 presents the hydraulic conductivity curves considered for the three cases studied: 1) K sat = 2.7535E-8 m/s, 2) K sat = 2.7535E-7 m/s, and 3) K sat = 2.7535E-6 m/s (original case). PAGE 116 102 1.0E-131.0E-111.0E-091.0E-071.0E-050.005.0010.0015.0020.0025.0030.00Suction (kPa) Case 1 Case 2 Case 3 Figure 6.9: Hydraulic conductivity curves for K sat cases at subgrade material Figure 6.10 shows the resulting finite element predictions. As expected, the results show that the higher the subgrade K sat value, the faster the drainage. This means that the characterization of the subgrade material is key in determining representative drainage properties of pavement systems. 6.06.57.07.58.08.59.09.510.010.511.011.512.0210220230240250260270Time ( Julian day) Predicted Case 1 Predicted Case 2 Predicted Case 3 Figure 6.10: Results for K sat cases at subgrade layer PAGE 117 103 6.6 Effects of the Type of Base Material To evaluate the effects of the type and gradation of base material, FEM predictions using 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. Since the air entry value for these materials was unknown, they were all assigned the same air entry value as the Class 6 Special, namely 3.0 kPa. SEEP/W was used to estimate the hydraulic conductivity curves for all the base materials. Figures 6.12 and 6.13 show the resulting soil water characteristic curve and hydraulic conductivity curves for the Cl. 3 Sp., 4 Sp., 5 Sp. base materials. 0.05.010.015.020.025.0050100150200250300350Suction (kPa) Class 3 special Class 4 special Class 5 s p ecial Figure 6.11: Soil water characteristic curves for base materials PAGE 118 104 0.05.010.015.020.025.030.005101520253035Suction (kPa) Class 3 special Class 4 special Class 5 s p ecial Figure 6.12: Soil water characteristic curves (air entry = 3kPa) for base materials 1.0E-131.0E-111.0E-091.0E-070.005.0010.0015.0020.0025.0030.0035.00Suction (kPa) Class 3 special Class 4 special Class 5 s p ecial Figure 6.13: Estimated hydraulic conductivity curves for base materials Figure 6.14 shows the resulting FEM predictions. The Cl. 3 Sp, Cl 4 Sp, and Cl 5 Sp. base materials show little drainage. 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. PAGE 119 105 2.04.06.08.010.012.014.016.018.020.022.024.0210220230240250260270Time (Julian day) Predicted Class 6 Predicted Class 3 Predicted Class 4 Predicted Class 5 Figure 6.14: Results for different types of base materials Interestingly, although class 4 has the highest k sat value, it results in the highest volumetric water contents, since its saturated volumetric water content sat (24.45 %) is the highest one. The three evaluated materials remain close to its sat value. On the other hand, class 6 starts with a sat of 30% and reaches values around 9%, at later times after the rain event. This means that focusing solely on K sat may be completely misleading in evaluating the drainage response of base materials. Table 6.1 shows the maximum change (drainage) of volumetric water content obtained for each material. Table 6.1: Maximum drainage for different base materials Material Class 3 Special Class 4 Special Class 5 Special Class 6 Special sat (%) 14.07 24.45 18.97 30.19 Max. Difference (%) 1.17 2.14 1.38 20.95 PAGE 120 106 6.7 Infiltration Effects In order to evaluate the effects of infiltration on the drainage of base materials, three different cases are considered: 1) infiltration is equal to the total precipitation measurements (100%), 2) infiltration is 70 percent of the total precipitation, and 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. 8.08.59.09.510.010.511.011.512.012.5210220230240250260270Time (Julian day) Predicted Case 1 Predicted Case 2 Predicted Case 3 Figure 6.15: Results for different rain events Figure 6.15 shows the resulting FEM 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. 6.8 Water Table Influence The initial position of the water table in the FEM 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. Again, three cases were evaluated: 1) the PAGE 121 107 water table is at 3.20 m, which corresponds to the original case, 2) the water table is dropped by 0.20 m down to 3.0 m, and 3) the water table is at 2.85 m. 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 means that since the soil water characteristic curve control the unsaturated moisture conditions that when the suction increases the volumetric water content decreases. Figure 6.16 presents the results of the FEM simulations for the different water table positions. 4.04.55.05.56.06.57.07.58.08.59.09.510.0210220230240250260270Time (Julian day)Volumetric Water Content (%) f Predicted Case 1 Predicted Case 2 Predicted Case 3 Figure 6.16: Results for different water table positions 6.9 Summary Since the air entry potential determines the transition of a material from saturated to unsaturated conditions, the higher the air entry value the longer the material will retain water. For example, a material with an air entry value of 3 kPa would need less time to drain than if its air entry potential was reached at 5 kPa. PAGE 122 108 The higher the hydraulic conductivity the faster the material will drain. A material with a high K sat value has much more abrupt changes in the predicted volumetric moisture content than for other material with lower K sat value. The base material drainage would not be affected significantly by shifting the air entry values of the subgrade. However, the higher the subgrade Ksat value, the faster the drainage of the base. This means that the characterization of the subgrade material is key in determining representative drainage properties of pavement systems. The initial position of the water table in the FEM 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. When the water table is lowered, the suction increases for the points above the water table. Therefore, the lower the water table, the lower the volumetric water content. This means that since the soil water characteristic curve controls the unsaturated moisture conditions, if the suction increases the volumetric water content decreases. A material with a soil water characteristic curve that does not have slopes steep enough to induce quick change in the volumetric water content, will not drain for a small range of suction values. Since the greater the volume of infiltrated water, the more time is needed to drain the water, provided that everything else is constant, it is important to have data related to more accurate infiltration events. PAGE 123 CHAPTER 7 EFFECT OF EDGE AND UNDER DRAINS ON WATER FLOW THROUGH FLEXIBLE PAVEMENTS This chapter evaluates the relative benefits of a couple of different positive drainage systems: edge drains and under drains using geotextiles. The pavement system described previously in Chapter 5 for Cell 33 was used as a baseline for comparisons. Four positive drainage cases were considered. Case 1 consists of the original pavement section for Cell 33, but now with a 0.02 m thick geotextile underdrain located between the base and subgrade. Case 2 is a modification of Case 1, in which collector pipes were included 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. The biggest 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. 109 PAGE 124 110 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. 0.02 m Geotextile 16.5 m 4.0 m 4:1 4:1 R-70 silty clay 0.1 m Hot Mix As p hal t 0.3 m Class 6 S p ecial CL 3.05 m 4.27 m 4.27 m 1.83 m Figure 7.1: Underdrain location for Case 1 in the pavement system The saturated hydraulic conductivity K sat of the underdrain was assumed to be 1.0 E-3 m/s, which is an order of magnitude higher than the K sat value for the base material. A hydraulic conductivity of 1.0 E-3 m/s corresponds to that for uniform sand (Freeze and Cherry, 1979). 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 Coreyâ€™s approach (Green and Corey, 1971). PAGE 125 111 0.005.0010.0015.0020.0025.0030.000.005.0010.0015.0020.00Suction (kPa) Figure 7.2: Soil water characteristic curve for under drain material 1.00E-081.00E-061.00E-041.00E-020.005.0010.0015.0020.0025.0030.00Suction (kPa) Figure 7.3: Estimated hydraulic conductivity curve for under drain material PAGE 126 112 As can be seen from Figure 7.2, the volumetric water content 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. Hot Mix Asphalt Base Layer Subgrade Layer UNDER Figure 7.4: FEM 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 location 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 0.1m diameter. 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 circumference as a boundary condition. PAGE 127 113 Collector Pi p e 0.02 m Geotextile 16.5 m 4.0 m 4:1 4:1 R-70 silty clay 0.1 m Hot Mix As p hal t 0.3 m Class 6 S p ecial CL 3.05 m 4.27 m 4.27 m 1.83 m Figure 7.5: Underdrain and collector pipes location for Case 2 in the pavement system Hot Mix Asphalt Base Layer GEOTEXTILE Subgrade Layer Collector Pipe Figure 7.6: FEM for Case 2 (Under drain with collector pipes) 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. PAGE 128 114 Ed g e Drain Drainage Material 16.5 m 4.0 m 4:1 4:1 R-70 silty clay 0.1 m Hot Mix As p hal t 0.3 m Class 6 S p ecial CL 3.05 m 4.27 m 4.27 m 1.83 m 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 element 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 condition. Hot Mix Asphalt Base Finite Elements Ed g edrain Total head = 0 m Subgrade Finite Elements Figure 7.8: FEM for Case 3 (Edgedrain) PAGE 129 115 7.3 Description of Case 4: Combination 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. Hot Mix As p halt Base Finite Elements Uniform San d Geotextile Under Drain Subgrade Finite Elements Pressure head = 0 m Figure 7.9: FEM for Case 3 (Combination of drain systems) 7.4 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 may not be very effective in reducing the time to drain or the equilibrium moisture content in the base. PAGE 130 116 Case 2, under drains with collector pipes, shows a slightly faster drainage than Case 3 (edge drains only), since the increase in volumetric water content during the rain event at day 230 for Case 2 was not as significant as for Case 3. The likely reason for this difference is the shortened length in drainage path associated with the introduction of the under drain. 0.01.02.03.04.05.06.07.08.09.010.0210220230240250260270Time (Julian Day) No drainage system Case 1:Under Drain Case 2: Under Drain with Collector Pipes Case 3: Edge Drains Case 4: Combination Figure 7.10: Results comparison for drainage systems The combination of edge and under drains represented by Case 4 was shown to be the most effective in moving infiltrated water out of a pavement system, as evidenced by the reduced equilibrium water content and the negligible increase in water content during the rain event. PAGE 131 117 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 the base. This is 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. PAGE 132 CHAPTER 8 CONCLUSIONS AND RECOMMENDATIONS The results from this study showed that SEEP/W is a useful tool to simulate water flow through layering structures (i.e. pavement systems, base drainage layers, subgrades). It helps to predict water movement specific conditions. However, it is important to know all boundary and initial conditions in order to accurately simulate measured field results. Water flow through pavement systems is primarily governed by unsaturated conditions in the field, except for short periods of time when the pavement system may be saturated. Therefore, material characterization (soil water characteristic curve and hydraulic conductivity curve), initial water table position, knowledge of density variations and geometry, all play a central role in a successful computer simulation of flow trough pavement system. Saturated flow assumptions do not take into consideration the variation of the hydraulic conductivity with volumetric water content or suction, the time to drain evaluated on the basis of traditional â€œtime to drainâ€ equations (Equation 3.2) result in an unrealistically short time to drain compared to unsaturated conditions. In contrast the more realistic unsaturated flow theory considers the hydraulic conductivity as a function of the suction experienced in the material with drainage. Hence, the time to drain calculated based on unsaturated flow theory will be longer that that one evaluated under saturated flow assumptions. An accurate measurement and/or representation of the soil water characteristic curve and the hydraulic conductivity curve for each material are key in the successful modeling 118 PAGE 133 119 of flow through pavement systems. The air entry value from the soil water characteristic curve controls the amount of suction developed before a layer of material can be drained. The slopes of both the soil water characteristic curve and the hydraulic conductivity curve are also important in determining the drainage performance of pavement materials. The soil water characteristic curve tends to be sensitive to density and gradation. These differences can result in a variation in both the air entry value and the slope of the soil water characteristic curve in the unsaturated region. For example, if the density decreases, the volumetric water content at saturation will be higher. Therefore, it is even more important to have good knowledge of expected variations in density and gradation in the field. For example, the TDRs used to monitor the volumetric moisture content are installed into the base material after the construction of the pavement base layer, thus likely affecting the density of the material around the TDR points. Therefore, since the density around the TDR probes in the field is most likely slightly different from that in a laboratory suction plate test, the results obtained with FEM will be affected. Since the actual density conditions around the TDRs are not well known, and the variability in TDR readings may be result in differences of up to plus or minus 2 percent volumetric moisture content, it has to be concluded that only minor â€œtuningâ€ of the volumetric moisture contents was needed to match field data. Similarly, since the actual densities in the upper layer of the subgrade are only approximate, it is not unlikely that the hydraulic conductivity may be slightly different from that measured in the laboratory. In summary, it has to be concluded that the field results were matched through fairly small adjustments in the soil water characteristic curve and hydraulic conductivity curve. PAGE 134 120 The resistance to vertical flow is heavily determined by the properties of the subgrade. Hence, the characterization of the soil water characteristic curve and the hydraulic conductivity curve, and in particular the K sat value for subgrade materials has a significant effect on the predicted drainage performance of the overlying base layer. Among the boundary conditions is important to consider that 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 FEM. This study showed that an infiltration rate corresponding to about 30 percent of the rate of precipitation was needed to explain the measured changes in volumetric moisture contents within the base for Cells 33-35. As stated previously, the air entry potential determines the transition of a material from saturated to unsaturated conditions. This means that the higher the air entry value, the longer the material will retain water. For example, a material with an air entry value of 3 kPa would need less time to drain that if its air entry potential was reached at 5 kPa. The higher the hydraulic conductivity the faster the material will drain. A material with a high Ksat value tends to have much more abrupt changes in the predicted volumetric moisture content than a material with a low Ksat value. However, detailed knowledge of the soil water characteristic curve is needed to determine the amount of moisture at any given condition within the pavement system. This means that a material with a high porosity may possibly show a fast rate of drainage if it has a high Ksat value. However, at any given suction value there may still be a significant amount of moisture left in the system that saturated flow theory simply cannot account for adequately. For example, one implication with this observation is that in the determination of freeze thaw PAGE 135 121 effects it is very important to take the unsaturated flow properties of pavement materials into account. The drainage of the base materials in Cells 33-35 was not affected significantly by shifting the air entry values of the subgrade. However, the higher the subgrade Ksat value, the faster the drainage of the base layer. This means that the characterization of the subgrade material is key in determining representative drainage properties of pavement systems. The initial position of the water table in the FEM 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. When the water table is lowered, the suction increases for the points above it. Therefore, the lower the water table, the lower the volumetric water content. Hence, when suction increases the volumetric water content decreases. Similarly, a material with a soil water characteristic curve that does not have slopes steep enough to induce a quick change in the volumetric water content, will not drain for a small range of suction values. 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. An important aspect is the variation in 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. PAGE 136 APPENDIX 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. In the following, traditional time to drain calculations are performed using: 1) traditional formulations by Casagrande and Shannon (1952), and Barber and Sawyer (1952), 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 (reference), whereas the unsaturated flow calculations were obtained with SEEP/W. 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. 122 PAGE 137 123 Impervious 1.0 m P = 0 kPa 0.4 m Figure A.1: Finite element model â€“ Geometry and boundary conditions 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. 0.05.010.015.020.025.030.035.00.010.101.0010.00100.00Suction (kPa) Figure A.2: Class 3 special â€“ Soil water characteristic curve PAGE 138 124 0.05.010.015.020.00.010.101.0010.00100.001000.00Suction (kPa) Figure A.3: Class 4 special â€“ Soil water characteristic curve 0.05.010.015.020.025.030.035.040.045.00.010.101.0010.00100.001000.00Suction (kPa) Figure A.4: Class 5 special â€“ Soil water characteristic curve PAGE 139 125 0.010.020.030.040.050.060.00.010.101.0010.00100.00Suction (kPa) Figure A.5: Class 6 special â€“ Soil water characteristic curve For each material, five hydraulic conductivity models were applied. The hydraulic conductivity models used include models by Gardner (1958), Brooks and Corey (1966), Green and Corey (1971), Van Genuchten (1980), and Fredlund and Xing (1994). Figures A.6 to A.9 present the hydraulic conductivity for each material, based on the different models. 1.0E-371.0E-331.0E-291.0E-251.0E-211.0E-171.0E-131.0E-091.0E-050.010.101.0010.00100.00Suction (kPa) Brooks & Corey VanGenuchten Gardner Green & Corey Fredlund and Xin g Figure A.6: Comparison of Hydraulic Conductivity Models in Class 3 Special PAGE 140 126 1.0E-341.0E-311.0E-281.0E-251.0E-221.0E-191.0E-161.0E-131.0E-101.0E-071.0E-040.010.101.0010.00100.001000.00Suction (kPa) Brooks & Corey VanGenuchten Gardner Green & Corey Fredlund and Xin g Figure A.7: Comparison of Hydraulic Conductivity Models in Class 4 Special 1.0E-351.0E-321.0E-291.0E-261.0E-231.0E-201.0E-171.0E-141.0E-111.0E-081.0E-050.000.010.101.0010.00100.001000.00Suction (kPa) Brooks & Corey VanGenuchten Gardner Green & Corey Fredlund and Xin g Figure A.8: Comparison of hydraulic conductivity models in Class 5 special PAGE 141 127 1.0E-311.0E-271.0E-231.0E-191.0E-151.0E-111.0E-070.000.010.101.0010.00100.00Suction (kPa) Brooks & Corey VanGenuchten Gardner Green & Corey Fredlund and Xin g 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. 5.010.015.020.025.030.035.01.0E-051.0E-021.0E+011.0E+041.0E+071.0E+10Time (days) Brooks & Corey Van Genuchten Gardner Green & Corey Fredlund & Xin g Figure A.10: Class 3 special â€“ Evolution of volumetric water content with time at the top of the soil column PAGE 142 128 4.06.08.010.012.014.016.018.020.01.0E-051.0E-031.0E-011.0E+011.0E+03Time (days) Brooks & Corey Van Genuchten Gardner Green & Corey Fredlund & Xin g Figure A.11: Class 4 special â€“ Evolution of volumetric water content with time at the top of the soil column 15.020.025.030.035.040.045.01.0E-011.0E+011.0E+031.0E+051.0E+071.0E+09Time (days) Brooks & Corey Van Genuchten Gardner Green & Corey Fredlund & Xin g Figure A.12: Class 5 special â€“ Evolution of volumetric water content with time at the top of the soil column PAGE 143 129 0.05.010.015.020.025.030.035.040.045.050.055.01.0E-051.0E-021.0E+011.0E+041.0E+071.0E+10Time (days) Brooks & Corey Van Genuchten Gardner Green & Corey Fredlund & Xin g Figure A.13: Class 6 special â€“ 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. 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 (1966) 2.08 3.54E+04 Van Genuchten (1980) 7.64 1.04E+05 Gardner (1956) 0.42 5.21 Class 3 Special Green & Corey (1971) 7.64E+02 7.64E+04 Brooks & Corey (1966) Not reached Not reached Van Genuchten (1980) Not reached Not reached Gardner (1956) Not reached Not reached Class 4 Special Green & Corey (1971) Not reached Not reached Brooks & Corey (1966) 1.46 Not reached Van Genuchten (1980) 17.36 Not reached Gardner (1956) 0.42 Not reached Class 5 Special Green & Corey (1971) 2.64E+03 Not reached Brooks & Corey (1966) 2.22 1.94E+06 Van Genuchten (1980) 14.58 7.64E+06 Gardner (1956) 0.28 3.47 Class 6 Special Green & Corey (1971) 4.17E+03 2.78E+04 PAGE 144 130 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 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 Gardnerâ€™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 PAGE 145 131 hand, when using Green and Coreyâ€™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 k sat 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 (n e ) is determined because is the difference between sat and 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 (L R ) is 0.4 m. Table A.2: Saturated case â€“ Model parameters Material H (m) k (m/s) W (m) L R (m) sat (%) R (%) n e (%) 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 (1952) and the Casagrande and Shannon method (1952). These two procedures were applied to find time to drain at 50% and 90% of drainage. Table A.3 shows the results. PAGE 146 132 Table A.3: Comparison of drainage times under saturated flow conditions Method Barber and Sawyer (1952) Casagrande and Shannon (1952) 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 (1952) method (Equation 3.2) is about 50 percent of the time to drain obtained with Casagrande and Shannonâ€™s (1952) approach (Equation 3.2). 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 K sat 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 system, 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. PAGE 147 133 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 (1993). Geometry attributes of a drainage base layer were used to generate a FEM 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 FEM 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. Drainage base layer Im p ervious P = 0 kP a Figure A.14: Example â€“ Geometry and boundary conditions Class 3 Special, Class 4 Special, Class 5 Special, and Class 6 Special were used as base materials. The soil water characteristics curves were described at the beginning of the chapter. The hydraulic conductivity curves corresponded to Fredlund and Xing (1994) 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. PAGE 148 134 Table A.4: Geometry and material parameters for saturated case SOIL Class 3 Special Class 4 Special Class 5 Special Class 6 Special k (m/s) 2.20E-07 4.20E-06 3.80E-06 2.00E-06 max (%) 32.01 14.35 40.70 52.08 R (%) 16.97 11.28 16.09 5.92 n e (%) 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 â€“ Saturated vs. unsaturated conditions for a geometry closer to pavement conditions SOIL Class 3 Special Class 4 Special Class 5 Special Class 6 Special t 50 (days) Saturated conditions 597.03 6.39 56.56 201.53 t 50 (days) Unsaturated conditions Not reached Not reached Not reached Not reached 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 PAGE 149 135 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 example, 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). 0.05.010.015.020.00.010.101.0010.00100.001000.00Suction (kPa) Air entry = 10 kPa Saturated conditionUnsaturated condition Figure A.15: Class 4 special â€“ Air entry potential at soil water characteristic curve PAGE 150 136 1.0E-101.0E-081.0E-061.0E-040.010.101.0010.00100.001000.00Suction (kPa) Air entry = 10 kPa Saturated conditionUnsaturated condition Figure A.16: Class 4 special â€“ 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 FEM, 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. PAGE 151 137 Table A.6: Gradation limits for different base materials Material Class3 Special Class 4 Special Class 5 Special Class 6 Special Limit 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 % 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 Gardnerâ€™s model (1956) and Green and Coreyâ€™s model (1971) do not depend on the gradation of the material, the FEM was only run for Brooks and Coreyâ€™s model (1966) and Van Genuchtenâ€™s model (1980), 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. 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 Coreyâ€™s model (1966). When the upper limit of the specifications is used, the hydraulic conductivity is greater than in the lower limit, as PAGE 152 138 expected. Also, when the sand percentage is increased, the Brooks and Coreyâ€™s parameter n (n=3+2/l) decreases, resulting in an increase in hydraulic conductivity. 1.0E-341.0E-311.0E-281.0E-251.0E-221.0E-191.0E-161.0E-131.0E-101.0E-071.0E-040102030405Suction (kPa) 0 Lower Limit Upper Limit Figure A.17: Class 3 special â€“ Comparison upper and lower limit â€“ Brooks and Corey (1966) model 1.0E-341.0E-311.0E-281.0E-251.0E-221.0E-191.0E-161.0E-131.0E-101.0E-071.0E-04020406080100120140160180200220240260280300Suction (kPa) Lower Limit Upper Limit Figure A.18: Class 4 special â€“ Comparison upper and lower limit â€“Brooks and Corey (1966) model PAGE 153 139 1.0E-361.0E-331.0E-301.0E-271.0E-241.0E-211.0E-181.0E-151.0E-121.0E-091.0E-061.0E-03020406080100120140160180200220240260280300Suction (kPa) Lower Limit Upper Limit Figure A.19: Class 5 special â€“ Comparison upper and lower limit â€“ Brooks and Corey (1966) model 1.0E-311.0E-281.0E-251.0E-221.0E-191.0E-161.0E-131.0E-101.0E-071.0E-0405101520Suction (kPa) Lower Limit Upper Limit Figure A.20: Class 6 special â€“ Comparison upper and lower limit â€“ Brooks and Corey (1966) model Figures A.21 to A.24 show similar results for the Van Genuchten (1980) model. Again, when the sand content is increased (Upper limit applied), Van Genuchtenâ€™s parameter m (m= / ( + 1)) also increases, resulting in an increase in hydraulic conductivity. PAGE 154 140 1.0E-321.0E-291.0E-261.0E-231.0E-201.0E-171.0E-141.0E-111.0E-081.0E-050102030405Suction (kPa) 0 Lower Limit Upper Limit Figure A.21: Class 3 special â€“ Comparison upper and lower limit â€“ Van Genuchten (1980) model 1.0E-321.0E-291.0E-261.0E-231.0E-201.0E-171.0E-141.0E-111.0E-081.0E-05020406080100120140160180200220240260280300Suction (kPa) Lower Limit Upper Limit Figure A.22: Class 4 special â€“ Comparison upper and lower limit â€“ Van Genuchten (1980) model PAGE 155 141 1.0E-281.0E-251.0E-221.0E-191.0E-161.0E-131.0E-101.0E-071.0E-04020406080100120140160180200220240260280300Suction (kPa) Lower Limit Upper Limit Figure A.23: Class 5 special â€“ Comparison upper and lower limit â€“ Van Genuchten (1980) model 1.0E-311.0E-281.0E-251.0E-221.0E-191.0E-161.0E-131.0E-101.0E-071.0E-0405101520Suction (kPa) Lower Limit Upper Limit Figure A.24: Class 6 special â€“ Comparison upper and lower limit â€“ Van Genuchten (1980) model Using the Brooks and Corey (1966) and Van Genuchten (1980) 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 PAGE 156 142 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 â€“ Brooks and Corey (1966) 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 â€“ Van Genuchten (1980) 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 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, PAGE 157 143 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 conditions, 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. 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H., and A.T. Corey, â€œHydraulic Properties of Porous Media.â€ Hydrology Paper no. 3, Civil Engineering Dep., Colorado State Univ. Fort Collins, 1966. Brutsaert, W, â€œProbability Laws for Pore-size Distribution.â€ Soil Sci., 101, pp. 85-92, 1966. Brutsaert, W, â€œThe Permeability of a Porous Medium Determined from Certain Probability Lays for Pore Size Distribution.â€ Water Resources Research, Vol. 4, No. 2, 425-434, 1968. Burdine, N. T, â€œRelative Permeability Calculations from Pore Size Distribution Data.â€ Trans. AIME, Vol. 198, pp. 71-78, 1953. Carpenter, S.H, â€œHighway Subdrainage Design by Microcomputer (DAMP). Drainage Analysis and Modeling Programs.â€ Publication No. FHWA-IP-90-012. Washington, D.C., 1990. 144 PAGE 159 145 Casagrande, A. and W.L. Shannon, â€œBase Course Drainage for Airport Pavements.â€ Proceedings of the American Society of Civil Engineers, Vol. 77, pp 792-814, 1952. Cedergren, H.R., â€œSeepage Requirements of Filters and Pervious Bases.â€ Soil Mechanics and Foundation Division. ASCE, SM5, pp. 15-23, 1956. Cedergren, H.R., â€œWhy All Important Pavements Should be Well Drained.â€ Transportation Research Record 1188, Transportation Research Board, National Research Council. Washington, D.C., 1988. Cedergren, H.R, K.H. Oâ€™Brien, and J.A. Arman, â€œGuidelines for the Design of Subsurface Drainage Systems for Highway Structural Sections.â€ Publication No. FHWA-RD-72-30. Washington, D.C., 1972. Childs, E.C., and N. Collis-George, â€œThe Permeability of Porous Materials.â€ Proc. Roy. Soc. London Vol. 201 A, pp. 392-405, 1950. DRIP (Drainage Requirements in Pavements), Version 1.00. Federal Highway Administration. Washington, D.C., 1996. 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. 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Mualen, Y., â€œModified Approach to Capillary Hysteresis Based on a Similarity Hypothesis.â€ Water Resources Research, Vol. 9, No. 5, 1324-1331, 1973 Mualen, Y., â€œA New Model for Predicting the Hydraulic Conductivity of Unsaturated Porous Media.â€ Water Resources Research, Vol. 12, No. 3, 503-522, 1976. Philip, J.R., Theory of Infiltration. Advances in Hydroscience, Vol. 5, Academic Press. New York, 1969. Pufahl, D.E., R.L. Lytton, and H.S. Liang, â€œAn Integrated Computer Model to Estimate Moisture and Temperature Effects beneath Pavements.â€ Presented at the Annual Meeting of the Transportation Research Record. Washington D.C.,1990. Rawls, W. J., Infiltration and Soil Water Movement. Handbook of Hydrology, Editor in Chief D. R. Maidment. McGraw Hill. New York, 1992. Richards, B.G., Behavior of Unsaturated Soils. In Soil Mechanics-New Horizons, Ch. 4. American Elsevier Publishing Company Inc. New York, 1974. Richards, L.A., Capillary Conduction of Liquids Through Porous Mediums. Physics, Vol. 1, 318-333. American Physical Society. New York, 1931. Roberson, R and B.Birgisson, â€œEvaluation of Water Flow Through Pavement Systems.â€ International Symposium on Subdrainage in Roadway Pavements and Subgrades, pp. 295-302, 1998. SEEP /W, Version 4.24. GEO-SLOPE International Ltd. Calgary, 2001. PAGE 161 147 Tindall, J.A. and J.R. Kunkel, Unsaturated Zone Hydrology for Scientists and Engineers. Prentice Hall. New Jersey, 1999. 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. Vauclin, M., D. Khanji, and G. Vachaud, â€œExperimental and Numerical Study of a Transient Two Dimensional Unsaturated-Saturated Water Table Recharge Problem.â€ Water Resources Research, Vol. 15, No. 5, 1089-1101, 1979. PAGE 162 BIOGRAPHICAL SKETCH Paola Ariza was born on October 30, 1976, in Bogot, Colombia. Having completed her primary and secondary school education, she gained admission to Pontificia Universidad Javeriana, Bogot, Colombia, on January 1995 for an engineering career. As part of a co-operative education program she also spent time working for INVIAS (National Road Institute). Paola received a Bachelor of Science in Civil Engineering from the Pontificia Universidad Javeriana on May 2000. Immediately after her undergraduate studies she attended the University of Florida to pursue a Master of Engineering degree. 148 |