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Evaluation of Pore Presure and Aggregate Structural Effects on Water Damage in Hot Mix Asphalt

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Title:
Evaluation of Pore Presure and Aggregate Structural Effects on Water Damage in Hot Mix Asphalt
Creator:
LE, MINH H. ( Author, Primary )
Copyright Date:
2008

Subjects

Subjects / Keywords:
Asphalt ( jstor )
Bituminous concrete pavements ( jstor )
Construction aggregate ( jstor )
Flood damage ( jstor )
Image analysis ( jstor )
Pavements ( jstor )
Pressure ( jstor )
Specimens ( jstor )
Stress tests ( jstor )
Water pressure ( jstor )

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Source Institution:
University of Florida
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University of Florida
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Copyright Minh H. Le. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Embargo Date:
8/1/2004
Resource Identifier:
80211282 ( OCLC )

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EVALUATION OF PORE PRESSURE AND AGGREGATE STRUCTURAL EFFECTS ON WATER DAMAGE IN HOT MIX ASPHALT By MINH H. LE 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 2003

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Copyright 2003 by Minh H. Le

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TO MY FAMILY

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ACKNOWLEDGMENTS First, I would like to thank Dr. Bjorn Birgisson for his financial assistance and guidance throughout the project. Without his knowledge, I would not have been able to finish my project. I would like to thank Dr. Raynaldo Roque for the time spent with me and help with the project. I would like also to thank Dr. Michael McVay for helping me on finite element modeling and for providing such a great educational experience. I wish to extend my gratitude to Dr. Eyad Masad for his help on the tomographic imaging and to Dr. Frank Townsend for his expertise on the triaxial test. The implementation of the tests would not have been successful without the help of many students and staffs in both material and geotechnical group. I would like to thank George Lopp, Tait Karlson, Erkan Enkingen, Linh Pham, Tipakorn Samanrak. Lila Niraula. Special appreciation is expressed to Marc Novak for his consistent help on finite element modeling and to Jeff Frank for performing the heating and cooling tests. I would like to thank all my friends for their help and mostly for providing an unforgettable and enjoyable time during my two years of study in Gainesville, especially Thai Nguyen, Dinh Nguyen, Dhuruva Badri, Zhihong Hu, Maria Lucia, Arvind Varadhan, Parimala Rajan, Tung Thai, and Tung Khuc. Finally, I would like to thank my father, my mother and my sister for all the love and support they have for me. iv

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TABLE OF CONTENTS Page ACKNOWLEDGMENTS.................................................................................................iv LIST OF TABLES...............................................................................................................x LIST OF FIGURES...........................................................................................................xi ABSTRACT....................................................................................................................xvii CHAPTER 1 INTRODUCTION........................................................................................................1 Background...................................................................................................................1 Aggregate Structural Effects.................................................................................1 Triaxial Compression Test....................................................................................2 Objectives.....................................................................................................................3 Scope.............................................................................................................................3 2 MIXTURE PREPARATION AND TESTING EQUIPMENTS..................................5 Mixture Preparation......................................................................................................5 Materials................................................................................................................5 Aggregate Blend....................................................................................................6 Mixture Design......................................................................................................6 Apparatus......................................................................................................................8 MTS 810 System...................................................................................................8 Measurement System.............................................................................................8 Axial displacement.........................................................................................8 Axial force......................................................................................................8 Pressure..........................................................................................................8 Vacuum Chamber..................................................................................................9 Dry Chamber.........................................................................................................9 Triaxial Compression Chamber.............................................................................9 Triaxial Control Panel.........................................................................................11 Sample Saturation.......................................................................................................13 Sample Pre-saturation..........................................................................................13 Backpressure Saturation......................................................................................13 B Value Measurement................................................................................................14 Temperature Control System......................................................................................16 v

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3 TESTING PROCEDURES FOR EVALUATION OF PORE WATER PRESSURE EFFECT UNDER TRIAXIAL LOADING CONDITION.........................................18 The Complex Modulus Test.......................................................................................18 Background..........................................................................................................18 Apparatus.............................................................................................................20 Loading................................................................................................................20 Contact load..................................................................................................20 Haversine load..............................................................................................21 Testing Frequencies.............................................................................................21 Testing Temperature............................................................................................21 Procedure for Complex Modulus Test of Saturated Samples.............................21 Complex modulus test at 100C.....................................................................21 Complex modulus test at 400C.....................................................................22 Procedure for Complex Modulus Test of Dry Samples......................................23 Sample setup................................................................................................23 Complex modulus test at 100C.....................................................................24 Data Analysis.......................................................................................................24 The Static Triaxial Test..............................................................................................25 Test Specimen Preparation..................................................................................25 Procedures...........................................................................................................25 Prior to saturation.........................................................................................25 Saturation by vacuum...................................................................................26 Saturation by back pressure..........................................................................27 Prior to axial loading....................................................................................27 Axial loading................................................................................................27 Removing specimen.....................................................................................28 4 EVALUATION OF PORE WATER PRESSURE EFFECT UNDER TRIAXIAL LOADING CONDITION...........................................................................................29 Static Triaxial Loading...............................................................................................29 B value.................................................................................................................29 Static Triaxial Test of F1 at 250C........................................................................29 Initial conditions...........................................................................................29 Finial conditions...........................................................................................31 Results..........................................................................................................31 Static Triaxial Test of F1 at 400C........................................................................33 Initial conditions...........................................................................................33 Final conditions............................................................................................33 Results..........................................................................................................33 Static Triaxial Test of C1 at 250C........................................................................33 Initial conditions...........................................................................................33 Final conditions............................................................................................34 Results..........................................................................................................35 Static Triaxial Test of C3 at 400C........................................................................36 Initial conditions...........................................................................................36 vi

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Final conditions............................................................................................36 Results..........................................................................................................36 Result Comparison..............................................................................................37 Effect of temperature....................................................................................37 Effect of gradation........................................................................................37 A – value......................................................................................................38 Summary of the Static Triaxial Loading.............................................................41 Cyclic Axial Loading..................................................................................................41 Initial Conditions.................................................................................................41 Summary of the Cyclic Axial Loading................................................................44 Finite Element Modeling............................................................................................45 Element Type.......................................................................................................45 Element Material Properties................................................................................45 Modeling Results.................................................................................................46 Plane strain test.............................................................................................46 Static triaxial loading test.............................................................................49 Summary.....................................................................................................................51 5 DEVELOPMENT OF CAPABILITIES FOR THE INTERPRETATION OF DIGITAL X-RAY TOMOGRAPHIC IMAGES........................................................52 X-Ray Computed Tomography Imaging....................................................................52 Aggregate Orientation.........................................................................................54 Aggregate Segregation........................................................................................56 Surface Area Parameter.......................................................................................57 Air Void Distributions.........................................................................................58 Aggregate Contacts.............................................................................................58 Using Imagetool in Quantifying the Air Void Structure of Asphalt Concrete...........59 Converting Images...............................................................................................60 Thresholding Images...........................................................................................60 Summary.....................................................................................................................64 6 EVALUATION OF AGGREGATE STRUCTURAL EFFECTS ON WATER DAMAGE IN MIXTURES AND PAVEMENTS.....................................................65 Aggregate Structural Effects in Moisture Susceptibility............................................65 Mixture Preparation and Moisture Conditioning................................................67 Number of Air Void............................................................................................68 Air Void Radius...................................................................................................68 Surface Area Parameter.......................................................................................70 Percentage of Air Void........................................................................................71 Summary..............................................................................................................72 Effect of Air Void Distribution in Water Flow in Pavement......................................72 Air Void Distribution in Mixtures.......................................................................72 Water Flow Simulation Using Seep W...............................................................76 Summary.....................................................................................................................83 vii

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7 DEVELOPMENT OF METHODOLOGY FOR TRANSFERRING DIGITAL TOMOGRAPHIC IMAGES OF CORES INTO FINITE ELEMENT – BASED BOUNDARY VALUE PROBLEMS.........................................................................85 Background.................................................................................................................85 Adina FSI.............................................................................................................85 Adina Commands................................................................................................85 Adina Memory Allocation...................................................................................86 Converting X-Ray CT Image to Finite Element Model.............................................86 Simple Example..........................................................................................................87 Summary.....................................................................................................................90 8 CONCLUSIONS AND RECOMMENDATIONS.....................................................91 Pore Pressure Effect under Triaxial Loading Condition.............................................91 Aggregate Structural Effects on Water Damage and Fluid Flow in Asphalt Concrete......................................................................................................................92 Recommendations.......................................................................................................92 APPENDIX A MIX DESIGN.............................................................................................................94 B EVALUATION OF PORE WATER PRESSURE EFFECT UNDER TRIAXIAL LOADING CONDITION...........................................................................................98 Static Triaxial Tests....................................................................................................98 Complex Modulus Tests...........................................................................................101 Phase Angle.......................................................................................................101 Stress Amplitude...............................................................................................103 Strain Amplitude...............................................................................................105 Pore Pressure Measurement – C1 at 100C.........................................................107 Pore Pressure Measurement – C1 at 400C.........................................................109 Pore Pressure Measurement – F1 at 100C.........................................................111 Pore Pressure Measurement – F1 at 400C.........................................................113 Falling Head Test on Various Samples.............................................................115 C IMAGETOOL INSTRUCTIONS.............................................................................116 D FINITE ELEMENT SOURCE CODES...................................................................119 Converting Image File To Finite Element Program.................................................119 Input File Structure............................................................................................119 Image File in Text Format.................................................................................119 Header File........................................................................................................120 Main Program....................................................................................................122 The Dam Problem.....................................................................................................141 viii

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E AIR VOID DISTRIBUTION...................................................................................147 Fine Mix....................................................................................................................147 Coarse Mix................................................................................................................149 LIST OF REFERENCES.................................................................................................151 BIOGRAPHICAL SKETCH...........................................................................................154 ix

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LIST OF TABLES Table page 2-1. Material information.....................................................................................................5 2-2. Job mix formulas for the granite mixtures....................................................................6 2-3. B – value for different type of soil.............................................................................15 3-1. Time between recorded points....................................................................................22 4-1. Values of pressures for each step...............................................................................39 4-2. Testing modes.............................................................................................................41 4-3. Material properties......................................................................................................47 6-1. Average sublayer permeability for finite element simulation....................................77 A-1. Batch sheet for coarse material – C1.........................................................................94 A-2. Batch sheet for coarse material – C2.........................................................................94 A-3. Batch sheet for coarse material – C3.........................................................................95 A-4. Batch sheet for fine material – F1..............................................................................95 A-5. Batch sheet for fine material – F2..............................................................................96 A-6. Batch sheet for fine material – F3..............................................................................96 A-7. Sample properties......................................................................................................97 B-1. Samples and temperatures used in triaxial compression tests...................................98 B-2. Values of pressures applied in B-value measurement...............................................98 x

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LIST OF FIGURES Figure page 2-1. Gradation chart for coarse mixtures.............................................................................7 2-2. Gradation chart for fine mixtures.................................................................................7 2-3. MTS 810 system (from MTS.com)..............................................................................9 2-4. Vacuum chamber........................................................................................................10 2-5. Dry chamber for dry complex modulus testing..........................................................10 2-6. Trixial compression chamber.....................................................................................11 2-7. Trixial control panel. 1-8: valves, 9: burette..............................................................12 2-8. Back pressure required to attain various degrees of saturation..................................14 2-9. Time needed to saturate the sample using backpressure............................................15 2-10. Time vs. temperature specimen at 10C...................................................................17 2-12. Time vs. temperature specimen to 40C...................................................................17 3-1. Stress – Strain response of the complex modulus test................................................19 3-2. Stress state during the test..........................................................................................28 4-1. B – value during different times of the test – mixture F1...........................................30 4-2. B – value during different times of the test – mixture C1..........................................30 4-3. Typical final B-value for mixture F1 and C1.............................................................31 4-4. Stress-strain relationship-F1 at 250C..........................................................................32 4-5. Pore pressure -F1 at 250C...........................................................................................32 4-6. Stress-strain relationship-F1 at 400C..........................................................................34 4-7. Pore pressure -F1 at 400C...........................................................................................34 xi

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4-8. Stress-strain relationship – C1 at 250C.......................................................................35 4-9. Pore pressure -C1 at 250C...........................................................................................35 4-10. Stress-strain relationship – C3 at 400C.....................................................................36 4-11. Pore pressure -C3 at 400C.........................................................................................37 4-12. Pore pressure comparison of F1 at 400C and 100C...................................................38 4-13. Stress-strain relationship of F1 at 400C and 100C....................................................38 4-14. Stress path of F1 at 400C and 100C...........................................................................39 4-15. Stress path at 25C....................................................................................................39 4-16. Stress-strain relationship at 250C..............................................................................40 4-17. Pore pressure at 250C...............................................................................................40 4-18. Pore pressure development in 1Hz cyclic loading of F1 at 100C.............................42 4-19. Complex modulus at 100C of coarse mix (C1).........................................................43 4-20. Complex modulus at 400C of coarse mix (C1).........................................................43 4-21. Complex modulus at 100C of fine mix (F1).............................................................44 4-22. Complex modulus at 400C of fine mix (F1).............................................................44 4-23. Nine node axisymmetric element.............................................................................46 4-24. Boundary conditions and loads applied....................................................................47 4-25. Cell pressure (load applied) – C1 at 400C................................................................48 4-26. Pore pressure measured versus predicted by PlasFEM – C1 at 400C.......................48 4-27. Change in vertical load measured versus predicted by PlasFEM – C1 at 400C.......49 4-28. Effective stress paths between lab test and PlasFEM prediction – C1.....................50 4-29. Change in effective axial stress between lab test and PlasFEM prediction – C1.....50 4-30. Pore pressure results between lab test and PlasFEM prediction – C1......................51 5-1. Components of X-ray computed tomography system................................................53 5-2. Horizontal X-Ray CT image of asphalt concrete specimen.......................................53 xii

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5-3. Particle orientation......................................................................................................54 5-4. Vertical cuts of the specimen......................................................................................55 5-5. Image captured by digital camera...............................................................................55 5-6. Inner and outer regions for segregation analysis........................................................57 5-7. Illustration of the method for measuring aggregate contacts.....................................59 5-8. Thresholded X-Ray CT image of asphalt concrete specimen....................................61 6-1. Correlation between the number of air void and energy ratio – coarse mix..............68 6-2. Correlation between the number of air void and energy ratio – fine mix..................69 6-3. Correlation between the air void radius and energy ratio – coarse mix.....................69 6-4. Correlation between the air void radius and energy ratio – fine mix.........................70 6-5. Correlation between the surface area parameter and energy ratio – coarse mix........70 6-6. Correlation between the air void radius and energy ratio – fine mix.........................71 6-7. Correlation between the percentage of air void and energy ratio – coarse mix.........71 6-8. Correlation between the percentage of air void and energy ratio – fine mix.............72 6-9. Air void distribution for F1........................................................................................73 6-10. Air void distribution for F2......................................................................................73 6-11. Air void distribution for F3......................................................................................74 6-12. Air void distribution for C1......................................................................................74 6-13. Air void distribution for C2......................................................................................75 6-14. Air void distribution for C3......................................................................................75 6-15. Air void distribution for field core...........................................................................76 6-16. Illustration of the finite element model...................................................................78 6-17. Total head versus distance in HMA pavement layer................................................81 6-18. Predicted flow vectors near centerline for projects A and B...................................82 6-19. Predicted fluid flow for uniform hydraulic conductivity in asphalt concrete layers..................................................................................................................................83 xiii

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6-20. Predicted fluid flow for project a with an increased base permeability...................83 7-1. Mesh of solid elements...............................................................................................88 7-2. Mesh of fluid elements...............................................................................................88 7-3. Velocity vector...........................................................................................................89 7-4. Nodal pressure – fluid elements.................................................................................89 7-5. Nodal pressure – solid elements.................................................................................90 B-1. Effective stress path-F1 at 250C.................................................................................99 B-2. Effective stress path-F1 at 400C.................................................................................99 B-3. Stress path – C1 at 250C...........................................................................................100 B-4. Stress path – C3 at 400C...........................................................................................100 B-5. Phase angle at 100C of coarse mix (C1)...................................................................101 B-6. Phase angle at 400C of coarse mix (C1)...................................................................101 B-7. Phase angle at 100C of fine mix (F1).......................................................................102 B-8. Phase angle at 400C of fine mix (F1).......................................................................102 B-9. Stress amplitude at 100C of coarse mix (C1)...........................................................103 B-10. Stress amplitude at 400C of coarse mix (C1).........................................................103 B-11. Stress amplitude at 100C of fine mix (F1).............................................................104 B-12. Stress amplitude at 400C of fine mix (F1).............................................................104 B-13. Strain amplitude at 100C of coarse mix (C1).........................................................105 B-14. Strain amplitude at 400C of coarse mix (C1).........................................................105 B-15. Strain amplitude at 100C of fine mix (F1).............................................................106 B-16. Strain amplitude at 400C of fine mix (F1).............................................................106 B-17. Pore pressure of complex modulus test at frequency 16Hz, temperature 100C of coarse mix (C1)................................................................................................................107 B-18. Pore pressure of complex modulus test at frequency 10Hz, temperature 100C of coarse mix (C1)................................................................................................................107 xiv

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B-19. Pore pressure of complex modulus test at frequency 4Hz, temperature 100C of coarse mix (C1)................................................................................................................108 B-20. Pore pressure of complex modulus test at frequency 1Hz, temperature 100C of coarse mix (C1)................................................................................................................108 B-21. Pore pressure of complex modulus test at frequency 16Hz, temperature 400C of coarse mix (C1)................................................................................................................109 B-22. Pore pressure of complex modulus test at frequency 10Hz, temperature 400C of coarse mix (C1)................................................................................................................109 B-23. Pore pressure of complex modulus test at frequency 4Hz, temperature 400C of coarse mix (C1)................................................................................................................110 B-24. Pore pressure of complex modulus test at frequency 1Hz, temperature 400C of coarse mix (C1)................................................................................................................110 B-25. Pore pressure of complex modulus test at frequency 16Hz, temperature 100C of fine mix (F1)....................................................................................................................111 B-26. Pore pressure of complex modulus test at frequency 10Hz, temperature 100C of fine mix (F1)....................................................................................................................111 B-27. Pore pressure of complex modulus test at frequency 4Hz, temperature 100C of fine mix (F1)...........................................................................................................................112 B-28. Pore pressure of complex modulus test at frequency 1Hz, temperature 100C of fine mix (F1)...........................................................................................................................112 B-29. Pore pressure of complex modulus test at frequency 16Hz, temperature 400C of fine mix (F1)....................................................................................................................113 B-30. Pore pressure of complex modulus test at frequency 10Hz, temperature 400C of fine mix (F1)....................................................................................................................113 B-31. Pore pressure of complex modulus test at frequency 4Hz, temperature 400C of fine mix (F1)...........................................................................................................................114 B-32. Pore pressure of complex modulus test at frequency 1Hz, temperature 400C of fine mix (F1)...........................................................................................................................114 B-33. Falling head results of permeability test on samples.............................................115 D-1. Import file in Scion image.......................................................................................116 D-2. Manually threshold the image.................................................................................117 D-3. Finding object..........................................................................................................117 xv

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D-4. Analyze menu..........................................................................................................118 xvi

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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 PORE PRESSURE AND AGGREGATE STRUCTURAL EFFECTS ON WATER DAMAGE IN HOT MIX ASPHALT By Minh H. Le December 2003 Chair: Dr. Bjorn Birgisson Major Department: Civil and Coastal Engineering Asphalt concrete material is distinctly heterogeneous and consists of aggregates, air voids, and asphalt binder. The internal structure of asphalt concrete material plays an important role in the resistance of asphalt concrete pavements to major pavement distresses including rutting, fatigue cracking, thermal cracking, and low temperature cracking. Most current investigations are confined to comparisons of performance based on macroscopic behavior due to the difficulty associated with the quantitative measurement of the internal structure of asphalt concrete and the random nature of aggregate distribution. The internal structure has thus been largely ignored. One of the purposes of this thesis is to provide measurements based on digital image processing to quantify the internal structure of asphalt concrete, and correlate these measurements to the behavior of asphalt concrete, particularly asphalt concrete moisture susceptibility. The thesis will also investigate the effects of pore water pressure on the triaxial loading condition on asphalt concrete. xvii

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The results have shown that for the comparable range of air voids, the moisture damage increases with the amount of surface area of aggregate exposed to water. The associated moisture related damage would thus depend not only on the average permeability in an asphalt mix but also on the percent air voids and the direction of the developed flow patterns. The pore pressure also has many effects on the triaxial compression tests. xviii

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CHAPTER 1 INTRODUCTION Background Aggregate Structural Effects The response of asphalt pavements subjected to wheel loads is predicted in pavement engineering by the asphalt concrete stiffness. Asphalt concrete stiffness is often described using parameters such as the resilient, dynamic, and relaxation moduli. The dynamic modulus is currently proposed as the primary Standard Performance Testing for permanent deformation and fracture distresses of pavement (Witczak et al. 2002). All available stiffness testing procedures assume the asphalt mixture to exhibit isotropic properties. However, asphalt concrete material is distinctly heterogeneous and consists of aggregates, air voids, and asphalt binder. The internal structure of asphalt concrete material is therefore influenced by many factors, including asphalt binder, aggregate gradation and shape, and degree of compaction. Monismith (1992) has proved that the internal structure plays an important role in the resistant of asphalt concrete pavements to major pavement distresses including rutting, fatigue cracking, thermal cracking, and low temperature cracking. Most of the current investigations are confined to comparisons of the performance based on macroscopic behavior because the difficulty associated with the quantitative measurement of the internal structure of asphalt concrete and the random nature of aggregate distribution. The difference in macroscopic properties including bulk specific 1

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2 gravity, indirect tensile strength, and resilient modulus of the same mix design of asphalt concrete compacted using different methods has been attributed mainly to the difference in the internal structure of the compacted mix, in particular, the distribution and orientation of coarse aggregates (Yue et al. 1995). In addition, most of the mechanistic models assume asphalt concrete to be a homogeneous and isotropic composite material, and its internal structure is largely ignored. One of the purposes of this thesis is to provide measures based on digital image processing to quantify the internal structure of asphalt concrete, and correlate it to the behavior of asphalt concrete on water damage. Triaxial Compression Test The triaxial compressive strength test has been used in evaluating a hot mix asphalt mixture’s susceptibility to permanent deformation compared with the dynamic modulus and repeated load test. From the triaxial test, the shear strength of an HMA mixture is developed based on two components: cohesion and friction angle. These parameters are obtained from Mohr-Coulomb plots. Wissa and Blouin (1968) have performed a study of strength behavior of selected asphalt-aggregate system in triaxial compression. The study was conducted on asphalt mixtures with uniform spherical sand-sized aggregate. The aggregate sizes ranged from 1.19 mm (No. 16 US standard sieve) to less than 0.105 mm (No. 140 and finer). Their observations showed that the effective stress rather than the total stress control the strength behavior of asphalt concrete. The research, however, has not been completed with tests on actual asphalt concrete aggregate specimens. This research will study the pore pressure effect on triaxial compression test including the static triaxial and dynamic triaxial test.

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3 Objectives The objectives of this thesis are to Develop the capability for the interpretation of digital X-Ray tomographic imaging of hot mix asphalt samples Evaluate the effects of internal structural properties obtained from tomographic images on water damage in mixtures and pavements Develop a framework for fully coupled microstructure fluid-flow in pavement The methods for obtaining aggregate structural properties from X-Ray Computed Tomography image will be reviewed, and developed. These aggregate structural properties will be used for evaluating the water damage. The flow of water in pavement will be also simulated to see the effect of the gradient of base course permeability. The testing procedures for triaxial loading tests including triaxial compression and complex modulus test for saturated samples will be developed. Theses test will help in evaluating the pore pressure effects. The modeling of these conditions is also developed to capture these effects. Scope Chapter 2 will present the mixture preparations and testing equipments that will be used for the complex modulus and triaxial compression tests. In chapter 3, the complex modulus will be reviewed and the procedures of the complex modulus and triaxial compression tests used for this research will be described in detail. Chapter 4 will present the results of the complex modulus and triaxial compression tests and pore pressure prediction from the modeling. Chapter 5 will describe the use of X-Ray Computed (CT) image analysis in evaluating internal structure of asphalt concrete. These internal structure properties will be used in evaluating the water damage in chapter 6. Chapter 7

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4 will propose a methodology for the finite element analysis based on X-Ray images. Chapter 8 will summarize the results and provide recommendations for future research.

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CHAPTER 2 MIXTURE PREPARATION AND TESTING EQUIPMENTS This chapter discusses the procedure and the materials required to prepare mixtures and equipments used in all the complex modulus, triaxial, plain strain tests. Mixture Preparation Six granite mixtures were used for these above tests. All of these mixtures were developed according to Superpave mix design method. A detailed description of Superpave mix design method can be found in FHWA report number FHWA-SA-95-003, 1995. All the mixtures were designed for traffic level 5 (<30 million ESALs). The air void at N – initial (Ni) , N – design (Nd), and N – maximum (Nm) were recorded to check the quality of the mixture. The mixture should have a minimum air void of 11% at Ni, 4% at Nd and 2% at Nm. Materials Table 2-1 shows the aggregate types used for this research. Table 2-1. Material information Material No. Material Type Material Source Gsb 1 Granite No. 7 stone Pit No. GA-185 2.693 2 Granite No. 89 stone Pit No. GA-185 2.689 3 W-10 Screen Pit No. GA-185 2.682 4 Granite Filler Pit No. Ga-185 2.710 The materials were selected based on the guidance of Superpave mix design method. The consensus aggregate properties are the coarse and fine aggregate angularity, flat and elongated particles, and sand equivalent results. Some of these additional 5

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6 properties to ensure the quality of the aggregate include L.A abrasion, sulfate soundness and absorption. Aggregate Blend The gradation of the aggregate is important to ensure 1) the maximum aggregate size is not too large or too small, 2) VMA requirements are met, and 3) a satisfactory aggregate skeleton is obtained. Table 2-2 shows the aggregate blend used for this research. The 0.45 power gradation charts for these mixtures are shown in Figure 2-1, Figure 2-2. Table 2-2. Job mix formulas for the granite mixtures Percent Material Passing each Sieve Size Sieve Size (mm) GAC1 GAC2 GAC3 GAF1 GAF2 GAF3 19 100.0 100.0 100.0 100.0 100.0 100.0 12.5 97.4 90.9 97.3 94.7 90.5 94.6 9.5 89.0 72.9 89.5 84.0 77.4 85.1 4.75 55.5 45.9 55.4 66.4 60.3 65.1 2.36 29.6 28.1 33.9 49.2 43.2 34.8 1.18 19.2 18.9 23.0 32.7 34.0 26.0 0.60 13.3 13.2 16.0 21.0 23.0 18.1 0.30 9.3 9.2 11.2 12.9 15.3 12.5 0.15 5.4 5.6 6.8 5.9 8.7 7.7 0.075 3.5 3.9 4.7 3.3 5.4 5.8 Mixture Design The mixtures use AC-30 as asphalt concrete with anti-stripping agent (AS). The samples were aged in accordance with the short-term over aging procedure as in AASHTO PP2. The samples were then compacted to 7%.5% using Superpave Gyratory compacter.

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7 After the samples were compacted and cooled down, the buck specific gravity was performed to check the air void content of the samples. Finally, the samples were cut to the desired height (6 inches-150 mm) using a wet saw. 0102030405060708090100Sieve size (mm) ^ 0.45% Passing 4.75 0.0750.150.300.601.182.369.512.519.0 C2C3C1 Figure 2-1. Gradation chart for coarse mixtures 0102030405060708090100Sieve size (mm) ^ 0.45% Passing 4.75 0.0750.150.300.601.182.369.512.519 F1F2F3 Figure 2-2. Gradation chart for fine mixtures

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8 The samples were stored at temperature 250 C (room temperature) and were wrapped with plastic bag prior to use. For complete information about mixture design, please refer to Appendix A. Apparatus MTS 810 System All the tests used the MTS 810 hydraulic system for the axial load. This system has the maximum capacity of 100 kN (22 Kip) of applying load. It is capable of applying load with a range of frequencies from 0.1 to 30Hz. The axial load can be controlled by either force mode or displacement load. Measurement System Axial displacement The MTS system can record the axial displacement of the transferring rod without any additional equipment. However, to be accurate, two LVDTs were installed on the sample to measure axial displacement. These LVDTs has a working range from -3 mm to +2 mm. This working range was found to be sufficient for the complex modulus test. The LVDTs were connected to the GCTS before connecting to the MTS acquisition system. Axial force The amount of load applied was recorded and controlled by a load cell connected to the top actuator. Pressure The cell pressure and the pore water pressure at top and bottom of the sample can be recorded using the triaxial compression chamber.

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9 Figure 2-3. MTS 810 system (from MTS.com) Vacuum Chamber The vacuum chamber and the vacuum device were used to pre-saturated the samples. The maximum amount of vacuum that can be created is 30 mm Hg. Dry Chamber The dry chamber (Figure 2-5) was used for dry complex modulus. It has the capacity to control the temperature and allows the LVDTs to be connected to the data acquisition system Triaxial Compression Chamber The triaxial compression chamber was used for the triaxial test, the plain strain test, and the saturated complex modulus test. Like the dry chamber, it has the capacity to control the sample at desired temperature. The pressure can be applied to top, bottom, and side of the sample contained in the chamber through the three pipelines. The

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10 pressures of these lines were measured by three pressure transducers connected to the data acquisition system. Figure 2-4. Vacuum chamber Figure 2-5. Dry chamber for dry complex modulus testing

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11 Figure 2-6. Trixial compression chamber Triaxial Control Panel The control panel (Figure 2-7) was used in the triaxial test and the saturated complex modulus. It controls the pressure applied to the sample. The burette can be used to measure the change in volume. During the vacuum process, the bubble leaves the sample to the burette. This is the list of the valves in the control panel and their uses: Valve 1: Controlling the connection between the top of the burette and the atmosphere or valve 2 Valve 2: Controlling the connection between valve 1 and the vacuum source or the pressure source from the GCTS Valve 3: Controlling the connection between the top of the sample and the burette Valve 4: Not used in the current tests Valve 5: Controlling the connection between the bottom of the sample and the hydraulic pump

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12 Valve 6: Not used in the current tests Valve 7: Controlling the connection between the burette or the annulus to valve 3 (top of the sample) Valve 8: Controlling the drainage of the burette 123457869 Figure 2-7. Trixial control panel. 1-8: valves, 9: burette

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13 Sample Saturation Sample Pre-saturation The sample is pre-saturated in the vacuum chamber before introducing in to the triaxial compression chamber. The pre-conditioned uses a normal vacuum chamber (Figure 2-4). The sample is first put in to the chamber. The chamber is then filled with water so that the specimen has at least one inch of water above their surfaces. A vacuum of 20 mm Hg is applied for 15 minutes. The vacuum is then removed and the sample is at rest in the water for 20 minutes. This step allows the water to fill the void that has been vacuumed. These steps were repeated until there was not substantial air bubble coming out of the samples. This procedure is usually repeated three times. The sample pre-saturation helps increase the degree of saturation, thou reduces the amount of time and value of the back pressure saturation. Backpressure Saturation In order to fully saturate the sample, the back pressure saturation should be used. The purpose of this method is to dissolve air in the sample into the water under high pressure. To minimize the effect of high pore water pressure, the confining pressure was increased simultaneously with the pore pressure and always kept 5 psi higher than the pore water pressure. The magnitude of the required back pressure can be found by using Figure 2-8. Assuming a initial degree of saturation of 92%, the sample needs a back pressure of 60 psi to get to 100% of saturation. The time required to get to different degrees of saturation is shown on Figure 2-9. For the purpose of triaxial test, the time for back pressure saturation was taken as 24 hours.

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14 Figure 2-8. Back pressure required to attain various degrees of saturation (Black, D. K. 1970). B Value Measurement The B parameter is the ratio of the change in pore pressure over the total stress for a three-dimensional loading in undrained condition. B = u/3 where u: change in back pressure and : change in cell pressure The B parameter has been shown by various authors to be a function of material’s porosity, the compressibility of water, the absolute pressure existing in the fluid, the

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15 degree of saturation, and stiffness of the samples. Table 2-3 presents typical B value for soil depending on various soil stiffness and degree of saturation. Figure 2-9. Time needed to saturate the sample using backpressure (Black, D. K. 1970). Table 2-3. B – value for different type of soil (Black, D. K. 1970)

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16 Chaney et al. (1979) has suggested a method for measuring B value for dense cohesionless soil or overconsolidated stiff clay. The B value is measured with different back pressure and is plotted on the graph. A constant B value with increasing value of back pressure is the criterion for full saturation (Sr = 100%). This method will be used in this research as a criterion for saturation of the samples. Temperature Control System The complex modulus and triaxial tests were performed at two temperatures: 100C and 400C. The following procedures were tested and were used to get the specimens to the desired temperature. The prescribed protocol for cooling the specimen to 10C is summarized as: 1. Set chiller to 7C and run for 40 minutes 2. Change chiller set temperature to 8C and run for 50 minutes 3. Discontinue conditioning and allow a maximum of 30 minutes for off-line testing 4. If additional testing time is required, reinitiate the conditioning process with the chiller set temperature to 8C and run for 30 minutes The prescribed protocol for cooling the specimen to 40C is summarized as: 1. Set heater to 45C and run for 55 minutes 2. Change heater set temperature to 40C and run for 35 minutes 3. Discontinue conditioning and allow a maximum of 30 minutes for off-line testing 4. If additional testing time is required, reinitiate the conditioning process with the heater set temperature to 40C and run for 30 minutes Temperatures tests were performed following the heating and cooling protocols. The water and chamber temperatures were monitored by two thermocouples, one in the triaxial base chamber and one in the core of the sample. Figure 2-10 shows how the temperature changed during the 100C test. The sample temperature got to 100C degree after the first 60 minutes. The last 30 minutes allows the sample to stabilize.

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17 Figure 2-11 represents the change of sample temperature during the heating protocol. The sample temperature starts with 100C degree and it reaches 600 C after 65 minutes. The last 30 minutes allows the sample to stabilize. Specimen to 100C0.05.010.015.020.025.030.00102030405060708090100Time (min)Temperature (C) Chiller @ 7Deg C Chiller @ 8Deg C Specimen Core Figure 2-10. Time vs. temperature specimen at 10C Specimen to 400C0.010.020.030.040.050.00102030405060708090100Time (min)Temperature (C) Heater @ 45DegC Heater @ 40DegC Specimen Core Figure 2-11. Time vs. temperature specimen to 40C

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CHAPTER 3 TESTING PROCEDURES FOR EVALUATION OF PORE WATER PRESSURE EFFECT UNDER TRIAXIAL LOADING CONDITION This chapter describes the background as well as the procedures for the tests on asphalt concrete used to evaluate the pore water pressure effect. The test includes static triaxial tests and complex modulus tests. The triaxial compression tests were performed following the guide of ASTM standard. A B–value measurement was checked to ensure the saturation of the sample. The dry and the saturated complex modulus tests were performed in each sample to compare the effects of pore water pressure. The load applied of the saturated complex modulus test is similar to the dry one except that the sample is saturated before testing. The Complex Modulus Test Background The dynamic complex modulus test is standardized by ASTM D3497. It is implemented by applying a uniaxial haversine load to a confined or unconfined HMA cylindrical sample. The relationship between the applied stress and the responded strain is called “Dynamic Complex Modulus” (E*). Viscoelastic theory showed that the modulus can be separated into a viscous portion and an elastic portion (Findley et al., 1976). The complex modulus is written as |E*| = 0 0 18

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19 The phase angle is the angle by which the strain is lag behind the stress Figure 3-1. The phase angle is calculated as: = tlag . f * 360 where f: the frequency of the dynamic load (in Hz) tlag: is the time difference between the signals (in seconds) A f of zero indicates a purely elastic material and a f of 90 indicates a purely viscous material. The viscous portion and the elastic portion of E* can be calculated as: E’ = |E* | cos E” = |E* | sin where E’: elastic modulus or storage modulus E”: viscous modulus or lost modulus sin t) tlag t sin t Figure 3-1. Stress – Strain response of the complex modulus test The Complex modulus is known to be related to pavement distress that includes the accumulation of damage (cracking of material). Research at University of Florida has

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20 shown that an asphalt mixture’s resistance to crack growth is related to its creep rate at short loading times (Zhang, 2001), which can be most accurately obtained through complex modulus testing. Witczak et al (2002) has suggested that complex modulus values can be used as performance criteria for permanent deformation resistant and fatigue cracking of the asphalt concrete mixture. Apparatus All the test apparatus was described in chapter 2. The following equipments were used: MTS 810 system and data acquisition system Triaxial compression chamber for saturated complex modulus test (black chamber) Dry chamber for dry complex modulus test (white chamber) Vacuum chamber Heating unit to get the sample temperature to 400C Cooling unit to get the sample temperature to 100C Loading Contact load The contact load is the load applied before the haversine load. It helps stabilizing the system and preventing any sudden impact to the sample caused by the haversine load. In the test, the time for applying the contact load is 60 seconds. Witczak et al (2002) has recommended the value of contact load (seating load) as 5% of the dynamic load. It was found that a higher contact load is needed to maintain the stabilization of the test. Pham (2003) use the value of contact load around 10% of the harversine load. In all these tests, the seating loads were used as 10% of the applied load.

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21 Haversine load The magnitude of the haversine load is varied from 500 N to 8000 N depending on the testing frequency and testing temperature since the axial strain should be kept between 50 to 150 strain Witczak et al (2002). Refer to Appendix B for the details use of the harversine load and the contact load. Testing Frequencies The specimen was then loaded with the following consecutive frequency: 16Hz, 10Hz, 4Hz, 1Hz. The order of the frequency is from higher value to lower value in order to minimize the damage to specimen. There is a rest time of 10 minutes after each frequency allowing the sample to be recovered. Swan (2002) has performed an evaluation of the effect of the complex modulus to the samples. The tests shown that the difference between results from a sample without prior testing and a samples with prior testing were not significant. Testing Temperature The tests were performed in two temperatures: 100C and 400C. The temperature of samples was first reduced to 100C using the cooling unit. The complex modulus at 100 was performed. After that, the heater unit was used to elevate the sample temperature to 400C and the complex modulus test at 400C was performed. Procedure for Complex Modulus Test of Saturated Samples The procedure for saturated complex modulus followed the same step of the triaxial test in chapter 4 including: prior to saturation, saturation by vacuum, saturation by back pressure. The different steps were ‘prior to axial loading’ and ‘axial loading’. Complex modulus test at 100C Prior to axial loading. The following steps were used

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22 The cooling protocol in chapter 2 was used to get the sample to 100C. The contact load of 800 N (180 lbf) was applied to the samples. A haversine load at 16Hz was applied to the specimen and the axial deformation is recorded. The magnitude of the load is taken in the range from 5000 N (1124 lbf) to 8000 N (1798 lbf). The haversine loading was adjusted to obtain axial strains between 50 and 150 strains. Undrained axial loading. The adjusted haversine loading from the previous step was used. This load was put on the sample for 16Hz, 10Hz, 4Hz, and 1Hz frequencies consecutively. Each frequency was tested for 200 cycles. There is a rest period of 10 minutes between each frequency. The time, axial displacement, and applied force were recorded with a frequency of 50 points per cycle. Table 3-1 shows the time between two neighbor data. Table 3-1 Time between recorded points Frequency (Hz) Time between recorded points (sec) 16 0.00125 10 0.002 4 0.005 1 0.02 The bottom valve, top valve, and cell valve were closed during the undrained axial loading. Drained axial loading. The bottom valve, top valve, and cell valve were let open for 5 minutes. After that, all the steps in undrained axial loading was applied. Complex modulus test at 400C Prior to axial loading. The following steps were used The heating protocol in chapter 2 was used to get the sample to 400C. The contact load of 200 N (45 lbf) was applied to the samples.

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23 A haversine load at 16Hz was applied to the specimen and the axial deformation is recorded. The magnitude of the load is taken in the range from 2000 N (450 lbf) to 3000 N (674 lbf). The haversine loading was adjusted to obtain axial strains between 50 and 150 strains. Axial loading. The adjusted haversine loading from the previous step was used. This load was put on the sample for 16Hz, 10Hz, 4Hz, and 1Hz frequencies consecutively. Each frequency was tested for 200 cycles. There is a rest period of 10 minutes between each frequency. The time, axial displacement, and applied force were recorded with a frequency of 50 points per cycle. Table 3-1 shows the time between two neighbor data. The above steps were first applied when the bottom, top, and cell valve were closed. These valves were then opened. After 5 minutes, the steps were performed again for the drained complex modulus test. Procedure for Complex Modulus Test of Dry Samples Sample setup The MTS 810 system was turn on. The dry chamber was placed in position. The pressure transducers and LVDTs were connected to the data acquisition system. Vacuum grease was filled on O-ring track to keep the chamber sealed at later steps. The membrane was inspected for flaws, holes, and leaks. It is recommended to check the edge of the sample and reduce its sharpness before putting the membrane on because the edge of the sample can cause damage to the membrane. The O-rings and the latex membrane were then put in the sample. Later, the samples were placed in the dry chamber between the bottom and the top plate. Using O-ring, the membrane was attached to these plates. This step helped sealing samples from water of the dry chamber.

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24 The LVDTs were mounted to the sample by the LVDT holders. The ranges of LVDTs were adjusted to be in the linear range to be available for the accumulation of the permanent deformation. A small test was performed to ensure the balance of the LVDTs. This test applied a haversine loading to the specimen and the axial deformations from the two LVDTs were recorded. The difference of recorded data between two LVDTs should be tolerable. The dry chamber was adjusted to the right position. It was then sealed and filled with water. Complex modulus test at 100C Prior to axial loading. The following steps were used The cooling protocol in chapter 2 was used to get the sample to 100C. The contact load of 700 N (180 lbf) was applied to the samples. A haversine load at 16Hz was applied to the specimen and the axial deformation is recorded. The magnitude of the load is taken in the range from 4000 N (1124 lbf) to 7000 N (1798 lbf). The haversine loading was adjusted to obtain axial strains between 50 and 150 strains. Axial loading. The adjusted haversine loading from the previous step was used. This load was put on the sample for 16Hz, 10Hz, 4Hz, and 1Hz frequencies consecutively. Each frequency was tested for 200 cycles. There is a rest period of 10 minutes between each frequency. The time, axial displacement, and applied force were recorded with a frequency of 50 points per cycle. Table 3-1 shows the time between two neighbor data. Data Analysis There are many available methods for data analysis: hand calculations, the iterative curve fit method, the linear regression method, the peak-valley method, the DFT method,

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25 and the dissipated energy method. A comparison made by Swan (2002) and Pham (2003) has shown that the linear regression method is one of the best methods to analyze data. This method was selected for the research tests. All the data were analyzed using “Complex Modlus Macro V3.xls”, a spreadsheet developed by Swan (2002) using the linear regression methods. The Static Triaxial Test Test Specimen Preparation The samples were prepared as describe in chapter 2. The samples were tested at two temperatures: 250C and 400C. Different temperatures were used in order to have the effect of temperature on triaxial compression tests. Procedures Prior to saturation The MTS 810 system was turned on. The triaxial compression chamber was placed in position. The pressure transducers and LVDTs were connected to the data acquisition system. The bottom specimen line was filled with water. Vacuum grease was filled on O-ring track to keep the chamber sealed at later steps. The samples were pre-saturated using the vacuum chamber before installed into the testing position. The purpose of pre-saturation is to expedite the saturation process and reduce the required back pressure of the samples. The membrane was inspected for flaws, holes, and leaks. It is recommended to check the edge of the sample and reduce its sharpness before putting the membrane since the edge of the sample can cause damage to the membrane.

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26 The O-rings and the latex membrane were now put in the sample. The samples were then placed in the triaxial compression chamber between the bottom and the top plate. Using O-ring, the membrane was attached to these plates. This step helped sealing samples from water of the triaxial compression chamber. The LVDTs were mounted to the sample by the LVDT holders. The ranges of LVDTs were adjusted to be in the linear range to be available for the accumulation of the permanent deformation. A small test was performed to ensure the balance of the LVDTs. This test applied an increasing loading to the specimen and the axial deformations from the two LVDTs were recorded. The difference of recorded data between two LVDTs should be tolerable. The triaxial chamber was adjusted to the right position. It was then sealed and filled with water. Saturation by vacuum Step 1-Using the control panel, mm Hg of vacuum pressure was applied on the top of the samples. The bottom valve is closed to maintain vacuum. Step 2-After 10 minutes, the water percolated from the bottom to the top of the sample using the pressure created from the hydraulic pump. A pressure of 3 psi was used to keep the water flowing. A cell pressure of 5 psi was maintained at this time to protect the membrane from expanding. This step helps filling the void with water These steps were repeated until there is no substantial void bubble coming out of the sample. For all the tests, a value of five times was found to be enough.

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27 Saturation by back pressure The back pressure was applied in order to fully saturate the samples. A B – value check was performed before and during the back pressure saturation process. The back pressure saturation process is stopped when the sample is fully saturated. Prior to axial loading If the desired temperature of the specimen is 400C, the heating protocol in chapter 2 will be used. Since 250C is the room temperature, there this no action required if the sample is tested in this temperature. Using the GCTS control system and the manual control of MTS 810, the cell pressure and the total axial stress were increased to 55 psi. The pore pressure was increased to 50 psi. These pressures were increased by step of 5 psi each time as shown on the following table. By increasing the stress gradually and keeping the sample in the isotropic stress state, the sample is submitted an effective stress of only 5 psi. Axial loading In the test, the control program specified a maximum load of 2003 lbf (1500 psi). The loading process will be stopped once the maximum load or the maximum strain is reached. The maximum strain was used as 4%-5%. The axial load was applied to the specimen using a rate of 0.5 minute/1% strain (1 psi/sec). This rate was found to be small enough to allow the pore pressure to stabilize through out the specimen. All the axial load, axial deformation, bottom, top, and cell pressures were recorded for every 0.5 sec.

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28 Before applying the axial loading to the failure of the sample, the sample was fixed at the top and the bottom. An increase in cell pressure was then applied to the sample. This test was done to see the pore water effect when there is no volume change. Removing specimen When the shear test was completed, the load was removed to the previous isotropic stress state. From the isotropic stress state, the axial pressure, the cell pressure and the pore water pressure were reduced gradually. The triaxial compression chamber was drained. After a complete drainage of the chamber, the cover was taken out. The LVDTs and LVDTs holders were remove from the sample and the sample was taken out. c c c c c + c c + a) b)c) c Figure 3-2. Stress state during the test. a) initial condition, b) isotropic stress, c) during loading

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CHAPTER 4 EVALUATION OF PORE WATER PRESSURE EFFECT UNDER TRIAXIAL LOADING CONDITION The chapter will present the development of pore water pressure of a cylindrical asphalt concrete sample during a triaxial test in static and cyclic load condition. The finite element modelings also were used to predict the development of pore water pressure. Static Triaxial Loading B Value The B – Value were recorded at different times during the test to check the degree of saturation. During all the test the back saturation were stopped only when the degree of saturation was attained. Figure 4-1 and Figure 4-2 show the B – value for different mixtures F1 & C1. The F1 mixture got saturated at the third B – value check. The C1 mixture got saturated after the forth B – value check. Figure 4-3 shows a comparison of B – value between C1 and F1. Even though these two sample were fully saturated, the B – value of F1 is always smaller than C1 with the same back pressure. This difference can be due to stiffness of the samples. Static Triaxial Test of F1 at 250C Initial conditions The test was started with temperature of 250C. This is a room temperature so no heating or cooling procedure was needed. The applied back pressure was 13 psi and the cell pressure was kept at 40 psi 29

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30 The procedure for performing the test was described in chapter 3. 00.20.40.60.810204060801Back pressure (psi)B value 00 1 st time 2nd time 3rd time Figure 4-1. B – value during different times of the test – mixture F1 0.30.40.50.60.70.80.910204060801Back pressure (psi)B value 00 4th time 3rd time 2nd time 1st time Figure 4-2. B – value during different times of the test – mixture C1

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31 0.40.50.60.70.80.91020406080100Back pressure (psi)B value Mixture F1 Mixture C1 Figure 4-3. Typical final B-value for mixture F1 and C1 Finial conditions After the test, the cell pressure is still remained the same while the back pressure (pore pressure) was dropped to 7 psi. Results The strain is corrected by using the corrected area formula Ac = A/(1-e) The test was stopped at a failure strain of 4%. The load at 4% strain is 647 psi. Figure 4-5 represents the development of pore water pressure during the test. Its behavior is very similar to that of the triaxial test on dense sand or heavily over consolidated clay. The pore pressure increased with the load in the first part. The pore pressure started to decrease when the strain of the sample reached about 0.45%. The pore pressure changed from positive to negative.

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32 0100200300400500600700012345Axial Strain (%)Principal Stress Difference (3) (psi) Figure 4-4. Stress-strain relationship-F1 at 250C -12-10-8-6-4-20246012345Axial Strain (%)Change in Pore Pressure (psi) Figure 4-5. Pore pressure -F1 at 250C This can be explaneed by looking at the micro mechanics of the mixtures. At a very dense state, the sample tends to dilate with increase in loads. Because the sample dilates, there is an increase in volume of the mix. This reduces the value of the pore water pressure.

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33 The A-value was determined as 0.044 for the first loading part and .041 at failure. Static Triaxial Test of F1 at 400C Initial conditions The test was started with temperature of 400C. The heating procedure in chapter 2 was used to get the temperature of the specimen to 400. The applied back pressure was 70 psi and the cell pressure was kept at 80 psi. The applied back pressure was change to see different effect of back pressure on the sample. The procedure for performing the test was described in chapter 3. Final conditions After the test, the cell pressure is still remained the same while the back pressure (pore pressure) was dropped to 19 psi. Results The test was stopped at a failure strain of 6%. The load at 6% strain is 530 psi. The development of the pore water pressure was similar to that of F1 at 250(Figure 4-7). The pore pressure reduced when the strain reached 0.3%. Noticed that the threshold strain for the pore pressure started to reduce at 250C is 0.45%, the threshold strain at 400C is considerably smaller. The A-value was determined as 0.051 for the first loading part and .113 at failure. Static Triaxial Test of C1 at 250C Initial conditions The test was started with temperature of 250C. The applied back pressure was 50 psi and the cell pressure was kept at 75 psi

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34 The procedure for performing the test was described in chapter 3. 010020030040050060001234567Axial strain (%)Principal Stress Difference (1 3) (psi) Figure 4-6. Stress-strain relationship-F1 at 400C -50-40-30-20-1001001234567Axial strain (%)Change in pore pressure (psi) Figure 4-7. Pore pressure -F1 at 400C Final conditions After the test, the cell pressure is still remained the same while the back pressure (pore pressure) was dropped to 31 psi.

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35 Results The test was stopped at a failure strain of 3.7%. The load at 3.7% strain is 546 psi. The A-value was determined as 0.087 for the first loading part and .129 at failure. The threshold strain at which the pore water pressure starts reducing is 0.24%. 010020030040050060001234Axial Strain (%)Principal Stress Difference (1 3) (psi) Figure 4-8. Stress-strain relationship – C1 at 250C -350-300-250-200-150-100-5005010001234Axial Strain (%)Principal Stress Difference (1 3) (psi) Figure 4-9. Pore pressure -C1 at 250C

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36 Static Triaxial Test of C3 at 400C Initial conditions The test was started with temperature of 400C. The heating procedure in chapter 2 was used to get the temperature of the specimen to 400. The applied back pressure was 10 psi and the cell pressure was kept at 20 psi. The applied back pressure was change to see different effect of back pressure on the sample. The procedure for performing the test was described in chapter 3. Final conditions After the test, the cell pressure is still remained the same while the back pressure (pore pressure) was first increased and then dropped to 20 psi. Results 02040608010000.10.20.30.40.5Axial Strain (%)Principal Stress Difference (1-3) (psi) Figure 4-10. Stress-strain relationship – C3 at 400C Even though this sample was not loaded to failure, the trend of pore pressure was clearly shown, and is similar to the previously mentioned tests. The threshold strain for which the pore water pressure starts reducing is 0.17%.

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37 00.40.81.21.600.10.20.30.40.Axial Strain (%)Change in pore water pressure (psi) 5 Figure 4-11. Pore pressure -C3 at 400C Result Comparison Effect of temperature To see the effect of temperature in the triaxial test, the results of F1 at 250C and at 400C degree were compared. These tests have similar stress paths; however, because asphalt concrete becomes softer with increase in temperature, the failure stress of the test at 400C is smaller than that of the test at 250C. Figure 4-12 shows that at higher temperature, the pore water pressure of the specimen started to reduce at a lower value of strain. Also, the A –value at failure was higher with higher temperature. This value indicates that the sample tends to dilate more when heated. Effect of gradation To see the effect of gradation, the results of F1 and C1 at 250C degree were compared. These tests also has similar stress path. C1 reached failure (4% of strain) with a lower axial stress than F1 (Figure 4-16) and has a bigger A-value at failure than F1.

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38 -45-40-35-30-25-20-15-10-50501234Axial strain (%)Change in Pore Pressure (psi) F1 40C F1 25C Figure 4-12. Pore pressure comparison of F1 at 400C and 100C 010020030040050060070001234Axial strain (%)Principal Stress Difference ( 13) (psi) F1 40C F1 25C Figure 4-13. Stress-strain relationship of F1 at 400C and 100C A – value The A – value was calculated at two different times: at the initial loading and at failure. The result is represented in the following table:

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39 Table 4-1. Values of pressures for each step A-value Mix Temperature At loading At failure F1 40 0.051 -0.113 F1 25 0.044 -0.041 C3 40 0.041 C1 25 0.028 -0.98 0100200300400500600700050100150200250p' (psi)q' (psi) F1 40C F1 25C Figure 4-14. Stress path of F1 at 400C and 100C 0100200300400500600700050100150200250p' (psi)q' (psi) C1 25C F1 25C Figure 4-15. Stress path at 25C

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40 01002003004005006007000123Axial strain (%)Principal Stress Difference ( 4 13) (psi) C1 25C F1 25C Figure 4-16. Stress-strain relationship at 250C -20-15-10-5050123Axial strain (%)Change in pore pressure (psi) 4 C1 25C F1 25C Figure 4-17. Pore pressure at 250C

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41 Summary of the Static Triaxial Loading The B-value results has suggested that an HMA sample can be fully saturated by using a back pressure saturation of 60 psi for a period of 24 hours. The B-value varies with the value of back pressure. In all the tests, the behavior of the pore water pressure has shown that specimens were dilated during the test. This can be explaneed by the interlocking of the particle in the specimen. Once the particle reached the densest state, it expanded when more load was applied. The plastic volumetric expansion then caused the reduction of the pore water pressure A-value depends largely on the stiffness of the samples. Because of that, the gradation or temperature can affect this value. Cyclic Axial Loading The complex modulus tests were used to evaluate the pore water pressure effect in cyclic loading condition. The tests were performed on two sample types: F1 and C1 with two samples for each type. E. The test temperatures are represented in Table 4-2 Table 4-2. Testing modes Sample Dry Undrained Drained Sample 1 F1 Sample 2 100C 400C 100C 400C 100C 400C Sample 1 C1 Sample 2 100C 400C 100C 400C 100C 400C Initial Conditions For all the complex modulus tests, the back pressure of the sample was kept at 0. The cell pressure was kept at 5 psi so that the pore pressure can be developed. Since the applied loads were cyclic these conditions remained until the tests were finished.

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42 F1 at 100C at 1Hz00.511.522.53110764211096441111646111364811156501117652Time (msec)Change in pore pressure (psi)-1001020304050607080Principal Stress Difference ( 1 3) (psi) Pore pressure Principal stress difference Figure 4-18. Pore pressure development in 1Hz cyclic loading of F1 at 100C Figure 4-18 shows a typical measured pore pressure from cyclic loading. The load is applied at a rate of 1Hz.Appendix B shows more of the measured pore pressure in the complex moduIt can be seen that the measured pore pressure has the same cyclic form as the applied load but with different magnitude. There is a time lag between the pore pressure and the applied load. This is similar to the time lag between the response strain and the applied load. The Complex Modulus results are shown from Figure 4-19 to Figure 4-22. The dynamic modulus appears to be increasing with frequency. This trend is predictable, since the work by (Sousa, 1987) confirmed that asphalt concrete gets stiffer with an increased loading rate. For coarse mix C1 (Figure 4-19, Figure 4-20), there is a considerable increase in complex modulus value when the condition of the sample changed from dry mode to saturated mode. The trend is even clearer when the sample is tested at 400C.

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43 For fine mix (Figure 4-21, Figure 4-22), the complex moduli do not differ between dry and saturated mode at 100C. The difference is increasing with temperature. In all test, there is not much difference between the drained and undrained complex modulus. This can be explained because the tests happen in such a short time that there is no drainage of water. C1 at 10C010002000300040005000600070008000161041Frequency (Hz)Dynamic Modulus (|E*|) (MPa) Undrained Drained Dry Figure 4-19. Complex modulus at 100C of coarse mix (C1) C1 at 40C02004006008001000120014001600161041Frequency (Hz)Dynamic Modulus C1 (MPa) Undrained Drained Dry Figure 4-20. Complex modulus at 400C of coarse mix (C1)

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44 F1 at 10C010002000300040005000600070008000161041Frequency (Hz)Dynamic Modulus (|E*|) (MPa) Undrained Drained Dry Figure 4-21. Complex modulus at 100C of fine mix (F1) F1 at 40C05001000150020002500161041Frequency (Hz)Dynamic Modulus (|E*|) (MPa) Undrained Drained Dry Figure 4-22. Complex modulus at 400C of fine mix (F1) Summary of the Cyclic Axial Loading The effect of water to the complex modulus is significant, especially at higher temperature where the complex modulus is lower.

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45 For coarse mix C1 (Figure 4-19, Figure 4-20), there is a considerable increase in complex modulus value when the condition of the sample changed from dry mode to saturated mode. The trend is even clearer when the sample was tested at 400C. For fine mix (Figure 4-21, Figure 4-22), the complex moduli do not differ much between dry and saturated mode at 100C. The difference is increasing with temperature. In all test, there is almost no difference between the drained and undrained complex modulus. Finite Element Modeling In order to develop and understanding the behavior of pore pressure in a saturated asphalt concrete sample, finite element models were developed. The modeling also helped in the prediction of pore water pressure in asphalt concrete. The modeling was implemented using PlasFEM, a program developed at the University of Florida (McVay 2000). PlasFEM is capable of modeling in one, two or three dimensions both the solid phase and fluid phase under both static and dynamic loading (Pinto 1997). The plane strain test was modeled using linear elastic material and the triaxial loading was modeled using the modified Cam-Clay material. Element Type The element used for the modeling is nine-node axisymmetric element. The nodes, when analyzed in a dynamic saturated state, have four degrees of freedom corresponding to fluid and solid displacements in the X and Y directions. Only the four corner nodes of each element have the 5th additional pore pressure degrees of freedom (node 1, 2, 3, 4). Element Material Properties The properties of the sample were mostly taken from the lab results. The permeability is taken as the average of the results of the falling head tests on various

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46 samples. The Young’s modulus is taken in reference to the range of complex modulus test results. 12345678 9 Figure 4-23. Nine node axisymmetric element Modeling Results In this part, the modeling results of the plane strain test and the static triaxial compression were plotted against the lab results. Plane strain test The test used in this chapter is the test where the top and the bottom of the sample were fixed. The test was performed to investigate the pore pressure when the dilative volume is restricted. The load was applied to the side of the sample. The sample was fully saturated. The test was started from the isotropic condition where the cell pressure equal to 60 psi. The 9 node plane strain elements with 4 pore pressure nodes were used for the plane strain modeling. The modeling mesh was 12x4 elements. The total degrees of freedom for this problem is 152.

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47 From Figure 4 – 25 and 4 , the ratio of the vertical load and horizontal load: K0 = 1. Table 4-3. Material properties Es1106kNm2 Young's modulus0.4Value is taken for 40 celcious degreeN0.07Initial porositys2.0Mgm2 Mass density of the solidMass density of the fluidf1Mgm3 Bulk modulus of the fluid, use incompressible fluidKf1011kNm2 PermeabilitykD + c c + Figure 4-24. Boundary conditions and loads applied Figure 4-25 shows the applied load for both the lab test and the model. Figure 4-26 presents the pore pressure results from the lab test and from the prediction. There is not much different between the predicted pore pressure and the measured one, although the

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48 pore pressure from the lab has the lower value. This was confirmed by the B – value. With the back pressure of 60 psi, the B – value from the test was observed to have the approximate value of 0.97.Figure 4 – 26 shows the change in vertical load needed to keep the top of the sample constant. 05101520250100200300400500600Time (sec)Change in cell pressure (psi) Lab test Applied load Figure 4-25. Cell pressure (load applied) – C1 at 400C 05101520250100200300400500600Time (sec)Change in pore pressure(psi) Lab test PlasFEM Figure 4-26. Pore pressure measured versus predicted by PlasFEM – C1 at 400C

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49 05101520250100200300400500600Time (sec)Change in vertical load applied(psi) Lab test PlasFEM Figure 4-27. Change in vertical load measured versus predicted by PlasFEM – C1 at 400C Static triaxial loading test The modified Cam-clay was used to model the static triaxial loading test. The following parameters were used for the modified cam-clay model to simulate the static triaxial test on C1 at 250. Bulk modulus: K = 7E+05 kN/m2 Poisson's ratio: = 0.35 Initial void ratio: e0 = 7% Critical state slope: M = 1 Recompression / swell index: rkappa = 0.46 Compression index: rlambda= 0.04 Preconsolidation pressure: pc0 = 6000 kN/m2 Unit weight: row = 0 Initial stress in elements: sig0 = 200 kN/m2 Ratio of initial horizontal stress / initial vertical stress: k0 = 1 The total stress path of the PlasFEM model was made identical to that of the lab test. Figure 4-28 to Figure 4-30 shows the comparison between the lab test result and PlasFEM prediction. The pore pressure result of the lab test was multiplied by 15 times

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50 for the shape comparison purpose. The PlasFEM model shows a similar response of the pore pressure. The pore pressure was first go up when the loading is in linear range. There was no change in mean effective stress. The yielding with stress ratio > M induced the shrinking of the yield locus and increase in mean effective stress. The pore pressure reduced from its maximum value. 01002003004005006000100200300400500p' (psi)q' (psi) Lab result PlasFEM Figure 4-28. Effective stress paths between lab test and PlasFEM prediction – C1 01002003004005006000123Axial Strain (%)Principal Stress Difference (1 3) (psi) 4 Lab test PlasFEM Figure 4-29. Change in effective axial stress between lab test and PlasFEM prediction – C1

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51 -350-300-250-200-150-100-500501000123Axial Strain (%)Change in pore pressure (psi) 4 Lab test x 15 PlasFEM Figure 4-30. Pore pressure results between lab test and PlasFEM prediction – C1 Summary The chapter has presented the results from the triaxial loading for both static and dynamic condition. Finite element modeling was also used to predict the pore water pressure development in asphalt concrete. Based on the results, the following observation was made: Mixtures are dilative materials. The pore pressure can be predicted with poroelasticity if dilative volume changed is minimized. A small amount of negative pore pressure was induced by shear stresses due to dilation Temperature has large effect on the stiffness of the sample, hence, it affects the development of pore water pressure. The higher temperature, the greater the effect of dilation on pore pressure. There was not much different in pore pressure effect between the undrained and drained cyclic loading.

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CHAPTER 5 DEVELOPMENT OF CAPABILITIES FOR THE INTERPRETATION OF DIGITAL X-RAY TOMOGRAPHIC IMAGES This chapter will describe the use of X-Ray Computed (CT) image analysis in evaluating internal structure of asphalt concrete. The internal structure includes air void distribution, aggregate orientation, aggregate contact, and aggregate segregation. Monismith (1992) has proved that the internal structure plays an important role in the resistant of asphalt concrete pavements to major pavement distresses including rutting, fatigue cracking, thermal cracking, and low temperature cracking. X-Ray Computed Tomography Imaging X-ray computed tomography imaging is a complete non-destructive technique to obtain digital information on 3D geometry and properties of an opaque solid object (Denison et al. 1997). The components of X-ray CT are shown on Figure 5-1. The X-ray is passing through the specimen in different paths and different direction. The intensity of the X-ray is measured before it enters the specimen and after it passes through it. After measuring the X-ray for the full rotation of the specimen, the specimen is shifted vertically by a fixed amount and the procedure is continued. The difference in intensity represents the density of the specimen. Therefore, X-ray CT of the specimen results in images that display the density at every point in two-dimensional slices (Masad et al. 2002a). 52

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53 Figure 5-1. Components of X-ray computed tomography system (Masad et al., 2002a) Figure 5-2. Horizontal X-Ray CT image of asphalt concrete specimen Figure 5-2 shows a typical X-Ray CT image of a horizontal cut of an asphalt concrete specimen with a diameter of 150 mm. The image is grayscale (256 levels of

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54 intensity) with dimensions of 512 x 512 pixels, which means each pixel in the image represent a point with a size of 0.195 mm in a horizontal section. The dark colors represent the air voids and the bright colors represent the aggregates. Aggregate Orientation The orientation of an aggregate can be measured by the angle between its longest axis and a horizontal line on the scanned image. The longest axis is defined as the greatest distance between two pixels of an aggregate boundary contour. Using the orientation of individual aggregates, statistical parameters can be calculated to quantify the directional distribution of aggregates. n+ nx1 x2 p article orientation Figure 5-3. Particle orientation The vector magnitude and the average angle of inclination from the horizontal line were defined by Curray (1956) as: 222cos2sin100kkN Nk k: The angle from the major axis to the horizontal line of individual aggregate.

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55 : the vector magnitude, varies from 0% to 100%. Complete random distribution of aggregate orientation will give the value of %0. Value of 100% means all the aggregate has the same direction. 110 140 mm 50 mm Figure 5-4. Vertical cuts of the specimen. The method to get the aggregate orientation was described by Masad et al. (1999), (2002a), (2002b). The samples were first cut into vertical sections. The images of these vertical sections were captured by digital camera connected to a computer. Using image analysis software ImageTools (1997), the aggregate orientation on two dimensions was calculated. Figure 5-5. Image captured by digital camera (Masad et al. 2002a)

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56 To describe the three-dimensional distribution of aggregate orientation, Oda and Nakayama (1989) has proposed the following tensor: 310003100031Mij The tensor was made with two assumptions, proven applicable to HMA specimens by Masad et al (2002a): The specimen aggregate are axial symmetry with a symmetry axial parallel to the vertical direction The major and minor axes of the aggregate distribution correspond to horizontal and vertical directions. The aggregate orientation has been used successfully by Masad et al. (1999), (2002b) to evaluate the development of the internal structure of AC mixes during laboratory compaction by the Superpave Gyratory Compactor and in the field. Aggregate Segregation The aggregate segregation was defined after Stroup-Gardiner and Brown (1998) as the heterogeneous of the asphalt mix constituents, in such a manner that there is a considerable accelerate pavement distress. The segregation can cause poor performance of the HMA. Masad et al. (2002b) has proposed a method to evaluate the segregation of HMA specimens. The image captured from the sample was divided in two parts, the inner part, and the outer part. The average diameter of each part was calculated. After this method, the segregation is calculated as:

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57 100%1regioninnertheinaggregatesofdiameterAverageregionoutertheinaggregatesofdiameterAverageSL SL indicated the lateral segregation. There is no segregation if SL = 0%. Outer Region Inner Region Figure 5-6. Inner and outer regions for segregation analysis (Masad 2002a) The segregation was used by Masad et al. (2002a) to evaluate the effect of field and Superpave Gyratory Compaction effect to HMA specimens. Surface Area Parameter The surface area parameter is defined as the ratio of total surface area of the void-solid phase interface, to the total volume of porous material. The specific surface area of aggregates is a comprehensive measurement of size, shape and roughness (Wang and Lai, 1998). It also represents the gradation: fine aggregates have a larger specific surface area. In asphalt mixtures, the specific surface area of aggregate can be directly related to the asphalt binder thickness and therefore related to the rutting and fatigue performance of asphalt concrete. In this research, the surface area parameter was estimated using X-Ray CT image analysis method as described by Al-Omari et al. (2002). It is calculated for each slice of the horizontal cut of the sample and assembled for the whole mix.

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58 Air Void Distributions Air void distribution controls the permeability and aging characteristics of asphalt mixes. Tashman et al. (2001) has conducted a study to characterize the air void distribution in superpave gyratory specimens and filed cores using X-ray computed tomography system. Masad et al. (1999) has described the procedure for quantifying air void distribution. In the image, the air voids are shown on dark color. A threshold intensity will be chosen. The gray intensity lower than the threshold intensity can be considered as air void. Using the threshold value, the original image is transformed to a binary image of black (air voids) and white (solid). Image analysis software (UTHCSA image tool) was used to capture the size of all air voids existed on each image. The ratio of air void area over the total area of each image give at the air void at the point where the image was taken. The stack of these values will give us the air void distribution. Aggregate Contacts Masad et al. (2002) and Tashman et al. (2001) have described the use of Image Pro Plus to determine the aggregate contacts. The main stress transfer mechanism among the particles is assumed being through the stiffness of mastic. Contact domain has the same thickness as the image resolution. The contact domains were captured by first converting the gray image to a binary image (Figure 6-7a). Then the aggregates in contact are separated using the “Watershed filter” (Figure 6-7 b). The image is then inverted in color and a “Thinning filter” is applied (Figure 6-7c). This image is combined with the original binary image using “AND” logic operator. With this operator, two image a and c are compared and which pixels that have the same black color (mastic) remain (Figure 6-7d). The resultant image consists of segments of lines representing the region of contact of aggregates.

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59 Work by Masad et al. (2002a) has shown that the aggregate orientation has better correlation to the mixture stiffness anisotropy, although the aggregate contact has been considered by several authors as a criterion for asphalt concrete anisotropy. Contact Direction N ormal to Contact b) a ) Contact Direction N ormal to Contact c ) d ) Figure 5-7. Illustration of the method for measuring aggregate contacts Using Imagetool in Quantifying the Air Void Structure of Asphalt Concrete This part will describe in details the use of the image software ImageTool (1997) in quantifying the air void structure of asphalt concrete based on the method and suggestion of Masad et al. (2002b), Tashman et al. (2001), and Al-Omari et al. (2002). The images were obtained from X-Ray CT image system.

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60 Converting Images All the images used for ImageTool should be 8 bits in order to do the image analysis. All the 16 bits images should be converted to 8 bits prior to use. The software Scion image was used for this purpose. The image was first opened on Scion image. The import menu was used with the calibrate unchecked (Figure D1 Appendix). After these steps, the image will become eight bits which means the intensity of each pixel ranges from 0 to 255. If the image will be used for air void analysis, the intensity of the particle is saved such that the air voids were represented by the darker colors; the aggregates were represented by the brighter color. On the other hand, if the image will be used for aggregate analysis (Aggregate orientation), the colors will be inversed so that the air voids were represented by the brighter colors; the aggregates were represented by the darker colors. Thresholding Images The 8 bits image was now opened in ImageTool. To separate the air void from solid part in Figure 6 – 2, a threshold value of intensity must be chosen. This threshold value will define the type of the image pixels. Using this threshold value, the image is transferred to a black and white image (Figure 6-3). In case of air void analysis, the pixels that have the intensity larger than the threshold will be air void. The others pixels will be solid particle. In case of aggregate analysis, the colors of air void and aggregate will be inversed. After the image was thresholded, the feature “Find object” in Object Analysis menu was used. This feature will allocate all the black objects in the black and white objects.

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61 The black boundary part of the image (the outside part) was excluded and not considered as an object for air void analysis. Figure 5-8. Thresholded X-Ray CT image of asphalt concrete specimen After all objects (air voids) in the image were recognized, the “Analyze” feature in menu “Analysis” was used. This will calculate the following properties of the black objects, which can be either air void or aggregate depending on which image was using. From ImageTool help: Area: The area of the object, measured as the number of pixels in the polygon. This measurement tends to produce a slight over-estimate of the object's area . If spatial measurements have been calibrated for the image, then the measurement will be in the units of that calibration; otherwise, it will be in square pixels.

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62 Perimeter: The length of the outside boundary of the object, again taking the spatial calibration into account. The method used will tend to over-estimate the perimeter for convex objects. Roundness: Computed as: (4 x PI x area) / perimeter2. The result give a value between 0 and 1. The greater the value, the rounder the object. If the ratio is equal to 1, the object is a perfect circle, as the ratio decreases from 1, the object departs from a circular form. Elongation: The ratio of the length of the major axis to the length of the minor axis. The result is a value between 0 and 1. If the elongation is 1, the object is roughly circular or square. As the ratio decreases from 1, the object becomes more elongated. Feret Diameter: The diameter of a circle having the same area as the object, it is computed as: sqrt(4 x area / PI). Compactness: Computed as: sqrt(4 x area / PI) / major axis length this provides a measure of the object's circleness. Basically the ratio of the feret diameter to the object's length, it will range between 0 and 1. At 1, the object is roughly circular. As the ratio decreases from 1, the object becomes less circular. Major Axis Length: The length of the longest line that can be drawn through the object. The result will be in the units of the image's spatial calibration. Major Axis Angle: The angle between the horizontal axis and the major axis, in degrees.

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63 Minor Axis Length: The length of the longest line that can be drawn though the object perpendicular to the major axis, in the units of the image's spatial calibration. Minor Axis Angle: The angle between the horizontal axis and the minor axis, in degrees. Centroid: The center point (center of mass) of the object. It is computed as the average of the x and y coordinates of all of the pixels in the object. Gray Centroid: Also called the brightness-weighted center of mass, this is the point in the object having equal brightness levels above, below, and to both sides of the point. It is computed as a weighted average of the x and y coordinates and the pixel brightness for all pixels in the object. If the image has been density calibrated, then the pixel brightnesses will be in these units. Integrated Density. Computed as the product of the mean gray level and the number of pixels in the image. If the image has been density calibrated, then the mean gray level will be in these units. Min/Mean/Median/Mode/Max Gray Level, Std. Dev.: Computes the given statistic for the pixels in the object, taking density calibration into account. Measurement Precision: The number of decimal places that should be used in the measurements sent to the results window. The ratio of area of air void over the area of the horizontal section gives us the percentage of air void. To get the surface area parameter, the image should be changed in the way that the aggregate has darker color and the air void has the lighter color. When thresholded and

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64 analyzed, the objects will be then the aggregate. The ratio of the perimeter over the area of the aggregate will give us the surface area parameter. If the image used was that of a vertical cut, the major axis angle was the aggregate orientation. The average ferret diameter over all the captured images will give us the average air void radius of the sample. The number of air void is taken as the ratio of total area of air void for a horizontal section and the average air void area. Summary This chapter summarized the current practice of image analysis in quantifying the internal structure of asphalt concrete. It also describes in detail the use of ImageTool in obtaining the internal structure properties. In the next two chapters, these properties and the X-Ray CT image will be used to evaluating the water damage susceptibility and the evaluation of water flow through the aggregate using finite element program.

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CHAPTER 6 EVALUATION OF AGGREGATE STRUCTURAL EFFECTS ON WATER DAMAGE IN MIXTURES AND PAVEMENTS This chapter will discuss the use of HMA properties obtained from CT X-Ray tomography imaging for evaluating the moisture susceptibility. The research will use the new performance-based fracture parameter, the Energy Ratio as the parameter in quantifying the moisture damage on the fracture resistance of mixtures. The simulation of water flow through asphalt concrete will also developed using on the permeability obtained from air void distribution from X-Ray tomography analysis. Aggregate Structural Effects in Moisture Susceptibility The research used the new fracture performance-based criterion, the energy ratio to evaluate the moisture damage on mixtures containing aggregates of known stripping performance. This parameter has shown to be not only capable of detecting the effects of moisture damage on the fracture resistance of the mixtures but also shown to detect the presence of anti stripping agent in the mixture (Birgisson, Roque, Page 2003). The energy ratio was calculated based on the results of the Superpave Indirect Tension Test (IDT) fracture parameters as described by e.g. Zhang, et al. (2001). The key Superpave IDT fracture parameters monitored include creep properties, resilient modulus, tensile strength, fracture energy limit, and dissipated creep strain energy limit. Based on detailed forensic investigations of 36 field pavement sections of known cracking performance in Florida, a HMA fracture mechanics-based performance specification criterion, termed the “Energy Ratio” (ER), was developed by Jailiardo 65

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66 (2003). This parameter is a measure of the fracture resistance of mixtures, and is expressed by: 198.2minDmDCSEaDCSEDCSEERff where 81.31046.236.60299.0tSa = tensile stress of asphalt layer (in psi), St = tensile strength (in MPa), DCSEf = Dissipated Creep Strain Energy (in KJ/m3), DCSEmin = Minimum Dissipated Creep Strain Energy for adequate cracking performance (in KJ/m3), and D1 and m are creep parameters in 1/psi. Based on the observed pavement performance from these 36 field sections, Jailiardo (2003) was able to determine a minimum DCSE for adequate cracking performance for the mixtures used. Jailiardo (2003) also recommended a minimum required ER (ERmin) for various traffic levels. For 3 million ESAL, the recommended ERmin is 1.1, for 10 million ESAL, ERmin is 1.3, and for 30 million ESAL, ERmin is 1.7. Hence, ER forms the basis for a performance-based fracture criterion for flexible pavements. Since it is known that the fracture resistance of mixtures is strongly affected by moisture damage (Birgisson 2003), in this research ER was evaluated as a mechanics-based criterion for evaluating the moisture sensitivity of mixtures. To allow for

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67 consistent comparisons of the mixtures studied, the tensile stress of the asphalt layer was taken to be a constant 120 psi. This part will compare the parameters taken from air void analysis to the ratio of the energy ratio of conditioned sample over unconditioned samples. The results were separated for coarse mix and fine mix. Mixture Preparation and Moisture Conditioning All mixtures were produced in the laboratory following the procedure outlined in AASHTO T-283. First, the aggregates and asphalt binder were heated to 150 C (300 F) for three hours prior to mixing. Once the mixing was completed, the mixture was allowed to cool to room temperature for two hours. After the cooling period, the loose mixture was long-term conditioned for 16 hours at 60 C (140 F). After the mixture was conditioned for 16 hours, it was reheated to 135 C (275 F) for two hours before compaction. The specimens were then compacted on the IPC Servopac SuperPaveTM gyratory compactor to 7 0.5 percent air voids. Six samples of each mix was prepared. For each mixture, three samples were then subjected to saturation according to the AASHTO T-283 procedure. Throughout the testing, a target saturation level of 65 and 80 percent was maintained. After the target saturation level was achieved, the specimens were placed in a 60 C (140 F) hot water bath for 24 hours. Once the moisture conditioning was completed, the conditioned mixtures were allowed to drain for 36 hours. Then, conditioned and unconditioned specimens were cut, by a wet saw, into 2-inch thick specimens. The specimens were placed in a dehumidifier chamber for 48 hours. The SuperPaveTM IDT test was used to perform Resilient Modulus (MR), Creep Compliance, and Strength tests (17,18,19) from which the

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68 following properties were determined: tensile strength, resilient modulus, fracture energy limit (FE), dissipated creep strain energy limit (DCSE), and creep properties. Using these mixture properties and the fracture mechanics-based Energy Ratio fracture performance specification criterion developed at the University of Florida, the effects of moisture damage on the fracture resistance of the mixtures was calculated. Number of Air Void The number of air void and the energy ratio were plotted on Figure 7-1 and Figure 7-2. Based on these figures, the number of air voids is inversely proportional to the water damage susceptibility. The larger the number of air void, the more the water damage affects the specimens. 0.0000.1000.2000.3000.4000.5000.600GA-C1GA-C2GA-C3GA-C4/F3ERConditioned/ERUnconditioned050100150200250300350400 W/O Antistrip Antistrip Number of air void Figure 6-1. Correlation between the number of air void and energy ratio – coarse mix Air Void Radius The average air void radius and the energy ratio were plotted on Figure 7-3 and Figure 7-4. The decrease in the average air void radius leads to the increase in water damage.

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69 Because the air void of all the specimens were aimed to be 7%0.5, the decrease in air void radius will lead to an increase in the number of air void as shown earlier. 0.0000.1000.2000.3000.4000.5000.6000.700GA-F1GA-F2ERConditioned/ERUnconditioned0100200300400500600Air void radius (mm) W/O Antistrip Antistrip Number of air void Figure 6-2. Correlation between the number of air void and energy ratio – fine mix 0.0000.1000.2000.3000.4000.5000.600GA-C1GA-C2GA-C3GA-C4/F3ERConditioned/ERUnconditione d 00.20.40.60.811.2Air void radius (mm) W/O Antistrip Antistrip Air void Radius Figure 6-3. Correlation between the air void radius and energy ratio – coarse mix

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70 0.0000.1000.2000.3000.4000.5000.6000.700GA-F1GA-F2ERConditioned/ERUnconditione d 0.570.580.590.60.610.620.630.640.650.66Air void radius (mm) W/O Antistrip Antistrip Air void Radius Figure 6-4. Correlation between the air void radius and energy ratio – fine mix Surface Area Parameter There is a general trend of the relation between the surface area parameter and water damage. The water damage increases with the surface area parameter except for sample C1. 0.0000.1000.2000.3000.4000.5000.600GA-C1GA-C2GA-C3GA-C4/F3ERConditioned/ERUnconditione d 00.020.040.060.080.10.120.140.160.180.2Surface area parameter (1/mm-1) W/O Antistrip Antistrip Surface area parameter Figure 6-5. Correlation between the surface area parameter and energy ratio – coarse mix

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71 0.0000.1000.2000.3000.4000.5000.6000.700GA-F1GA-F2ERConditioned/ERUnconditioned0.170.180.190.20.210.220.23Surface area parameter (1/mm-1) W/O Antistrip Antistrip Surface area parameter Figure 6-6. Correlation between the air void radius and energy ratio – fine mix Percentage of Air Void Figure 6-7 and figure 6-8 show the air void used for the specimen. 0.0000.1000.2000.3000.4000.5000.600GA-C1GA-C2GA-C3GA-C4/F3ERConditioned/ERUnconditioned6.4%6.6%6.8%7.0%7.2%7.4%7.6%7.8%8.0%8.2% W/O Antistrip Antistrip Percentage of air void Figure 6-7. Correlation between the percentage of air void and energy ratio – coarse mix

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72 0.0000.1000.2000.3000.4000.5000.6000.700GA-F1GA-F2ERConditioned/ERUnconditione d 7.1%7.2%7.3%7.4%7.5%7.6%7.7%7.8%7.9%8.0%8.1% W/O Antistrip Antistrip Percentage of air void Figure 6-8. Correlation between the percentage of air void and energy ratio – fine mix Summary The HMA properties obtained from image analysis were used to evaluate the moisture susceptibility. The moisture damage was represented by the new performance-based fracture, the energy ratio. The results show that for the same air void, the moisture damage increases with the increase of the number of air void and with the decreases of the air void radius. Effect of Air Void Distribution in Water Flow in Pavement Air Void Distribution in Mixtures By using the X-Ray image analysis described in chapter 5, the air void distribution of the mix was captured. Figure 6-9 to Figure 6-14 show us the air void distribution of all the mixtures. To perform the fluid flow, the actual field core used in the study study by Al-Omari et al. (2002) was chosen. It can be seen that there are vertical gradients in the percentage of air void in all the mixtures but with a different extend. These gradients are expected to affect the flow of water in the pavement. To simulate the effect, two mixtures with

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73 smallest and largest gradient on air void were chosen. F1 was chosen as the largest gradient (called as project A) and C2 was chosen as the smallest gradient (project B) on air void. The effect of air void distribution to the flow of water in pavement was simulate by using Seep W. Air Void Distribution through the thickness of (GA-F1-6)0204060801004%6%8%10%12%14%16%18%AV, %Thickness, mm Figure 6-9. Air void distribution for F1 Air Void Distribution through the thickness of (GA-F2-16)0204060801004%6%8%10%12%14%16%18%AV, %Thickness, mm Figure 6-10. Air void distribution for F2

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74 Air Void Distribution through the thickness of (GA-F3-5)0204060801004%5%6%7%8%9%10%11%AV, %Thickness, mm Figure 6-11. Air void distribution for F3 Air Void Distribution through the thickness of (GA-C1-6)0204060801004%6%8%10%12%14%16%AV, %Thickness, mm Figure 6-12. Air void distribution for C1

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75 Air Void Distribution through the thickness of (GA-C2-5)0204060801004%5%6%7%8%9%10%11%AV, %Thickness, mm Figure 6-13. Air void distribution for C2 Air Void Distribution through the thickness of (GA-C3-17)0204060801003%5%7%9%11%13%15%AV, %Thickness, mm Figure 6-14. Air void distribution for C3

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76 01020304050600510152025% Air VoidsDepth(mm) Figure 6-15. Air void distribution for field core. Water Flow Simulation Using Seep W The cores were divided into sublayers of 10.4 mm thickness (13 X-ray CT slices). The cores varied in their thickness between 52 mm to 60 mm. Therefore, each core consisted of at least 4 sublayers. The percent air voids of the X-ray CT slices were averaged for each sublayer of the cores. Then, the percent air voids was determined for the corresponding sublayers of the cores that belong to the same project. It is noted that only the top four layers were included here in order to be able to compare the results of the two projects. The flow of water through flexible pavements was modeled using the idealized cross section of a typical flexible pavement as shown in Figure 6-16a. A SEEP/W finite element model was developed based on this cross section (Walsh and 2001). Figure 6

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77 16b shows the resulting finite element mesh. The mesh included 11,422 quadrilateral and triangular elements. Table 6-1. Average sublayer permeability for finite element simulation Project Sublayer thickness (mm) Permeability (10-5 cm/sec) 25 3837.69 25 579.5 25 547.95 A 25 826.99 25 592.64 25 544.87 25 165.00 B 25 328.55 Each sublayer of the asphalt mix was assigned a permeability value as given in table 6 – 1. These permeability values were calculated using the following empirical formula (Masad et al., in press): taggmaScVk. where k is the coefficient of permeability in m/sec. is the unit weight of the fluid = 9.79 kN/m3. is fluid viscosity and is equal to 10-3 kg/(m.sec) for water. Va is the total percent air voids in an asphalt mix. The c, m and t values are obatined through statistical data fitting to the permeability values expressed in the units of 10-5 cm/sec. The base course layer was represented with 3062 quadrilateral and triangular finite elements. The granular aggregate base material was assumed to have a saturated

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78 permeability of 15.410-5 cm/s. This value was selected to represent a dense graded crushed granite aggregate base (Ariza and Birgisson, in press). The subgrade soil permeability was taken as 0.27510-5 cm/s to represent a sandy clayey silty soil (Ariza and Birgisson, in press). The subgrade was represented with a coarser mesh of finite element, consisting of 6120 quadrilateral and triangular elements. The subgrade was extended laterally 10 m beyond the area covered by the asphalt and base layer (Figure 13b), on each side, in order to represent real conditions more accurately, and provide continuity to the extension of the subgrade. (a) Pavement Geometry and Dimensions 1.83 m 4.27 m 4.27 m 3.05 m C 03 3 – 03 5m B a s e 00 5 0 075 m H ot Mix Subgrade 4:1 4:1 16.5 m 4.0 36.5 m Extended Extended 4.0 m (b) Finite Element Model Figure 6-16. Illustration of the finite element model

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79 To adequately model the transient flow of water through the pavement system, a transient finite element analysis was performed. A pavement system at initial equilibrium, defined by a water table, was subjected to a transient “rain event,” resulting in time-dependent changes in the volumetric moisture content throughout the pavement system. The water table was set at a depth of 0.76 m from the top of the pavement at the centerline cross section. The precipitation events input into the numerical model correspond to real precipitation measurements gathered at the Mn/ROAD project site (Ariza and Birgisson, in press). Figure 6-17 shows the variation in total heads for projects A and B at the peak of the rain event for the four HMA sub-layers. In order for water to flow under saturated conditions from one location to another, a positive difference in total heads has to be present. From Figure 6-17, it is clear that the total heads throughout the four asphalt layers analyzed do not differ significantly across the thickness of the HMA layer, meaning that only a small amount of water is flowing in the vertical direction. In contrast, a significant gradient in total heads away from the centerline is present for both cases, meaning that water is primarily flowing horizontally away from the centerline in the hot mix asphalt layer. It should be noted that Figure 6-17 is related to the flow over a large distance horizontally, and may therefore not depict the more detailed flow patterns over a smaller area in the HMA layer. Figure 6-18 presents a closer look of the flow vectors in the area near the centerline of pavement. In Project A, which has the largest gradient in permeability from the top to the bottom of the HMA layer, the flow is primarily in the horizontal direction away from the centerline, with a small vertical flow component. In addition, most of the flow is

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80 concentrated in the top two HMA sub-layers. Similarly, in Project B, which has the smallest gradient in permeability from the top to the bottom of the HMA layer, the water flows primarily in the horizontal direction away from the centerline. However, the flow vectors for Project B (Figure 6-18) have a slightly larger vertical component of flow, as compared to Project A. The lower two HMA sub-layers in Project B now show noticeable flow, even though the flow vectors are smaller than for the top two HMA sub-layers. It is noted that different scales are used in Figure 6-18 to illustrate the flow vectors for Projects A&B due to the difference in the measured permeability and flow amount in these two projects. The fluid flow patterns for an idealized pavement layer with uniform air void distribution are simulated by assuming the permeability to be uniform throughout the HMA layer, with a saturated permeability (ksat) of 500.010-5 cm/s, which is the average permeability of the samples from Projects A and B. Figure 6-19 shows the flow vectors for this case. As expected, the flow is mainly vertical which is different from the cases where nonuniform air void distribution is present in the HMA layer. The effects of base permeability on the flow pattern through the HMA layer were evaluated, by increasing the saturated base permeability (ksat) by 100 times to 1540.010-5 cm/s for project A. Figure 6-20 shows the flow vectors in the area near the centerline of pavement. The flow now has a stronger vertical gradient than in the case of a lower base permeability (Figure 6-18), meaning that more of the water is now flowing vertically through the pavement. However, interestingly, Figure 6-20 shows that the high permeability top layer in the HMA layer still has a significant horizontal flow component, despite the high base permeability value.

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81 44.054.14.154.200.511.522.533.544.5Distance from center line (m)Total head (m) Project A Sublayer 1 Project A Sublayer 2 Project A Sublayer 3 Project A Sublayer 4 (a) Project A 3.43.423.443.463.483.500.511.522.533.544.5Distance from center line (m)Total head (m) Project B Sublayer 1 Project B Sublayer 2 Project B Sublayer 3 Project B Sublayer 4 (b) Project B Figure 6-17. Total head versus distance in HMA pavement layer

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82 0.80 m Centerline (a) Project A 0.38 m Centerline (b) Project B Figure 6-18. Predicted flow vectors near centerline for projects A and B. The variation in permeability through typical HMA layers from higher at the surface to lower at the bottom of the HMA layer will encourage lateral flow in the more permeable part of the HMA layer, and discourage vertical flow into the underlying base course material. Consequently, the associated moisture related damage would depend not only in the average permeability in an asphalt mix, but on the percent air voids and the direction of the developed flow patterns.

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83 Center line 0.416 m Figure 6-19. Predicted fluid flow for uniform hydraulic conductivity in asphalt concrete layers Centerline 0.416 m Figure 6-20. Predicted fluid flow for project a with an increased base permeability Summary This chapter has presented the application of X-Ray tomography image on water damage and water flow through pavement. For the moisture damage, the results have

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84 shown that for the same air void, the moisture damage increase with the increase of the number of air void and with the decrease of the air void radius. The air void distribution obtained from X-Ray Image analysis help us to predict the fluid flow in the pavement. The variation in permeability through typical HMA layers from higher at the surface to lower at the bottom of the HMA layer will encourage lateral flow in the more permeable part of the HMA layer, and discourage vertical flow into the underlying base course material. Consequently, the associated moisture related damage would depend not only in the average permeability in an asphalt mix, but on the direction of the developed flow patterns.

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CHAPTER 7 DEVELOPMENT OF METHODOLOGY FOR TRANSFERRING DIGITAL TOMOGRAPHIC IMAGES OF CORES INTO FINITE ELEMENT – BASED BOUNDARY VALUE PROBLEMS This chapter discusses the idea of using X-ray computed tomography (CT) images of asphalt mixes for the modeling of fluid flow through HMA samples. From the X-Ray CT images, the air voids particle will be transferred to fluid elements and the aggregate particle will be transferred to solid elements in Adina. Having these two model coupled, the fluid flow through the asphalt concrete will be simulated. Background Adina FSI To model the effect of water flow in the structure, Adina fluid – structure interaction (FSI) analysis was used. The solid is elastic and the fluid is incompressible. The fluid force is applied to the structure domain. The change of structure domain affects the boundary of the fluid. The problem was divided into fluid and solid domain. Each domain was model separately with boundary condition, load, fluid – structure interface, etc. The interaction between fluid and structure happens at the interface. Having two domains coupled, the simulation of fluid flow through HMA samples can be performed (Adina 2001a). Adina Commands The Adina model can be constructed by using Adina commands. The commands can be input directly into the user interface or can be read from a batch file (Adina 2001b). In this research, they were written in a text file. A small program was 85

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86 implemented for converting the image into command files hence. After the batch file the image was then transferred into finite element mesh (Appendix D). Adina Memory Allocation The instruction for memory allocation is in Adina Manual (Adina 2001a). For the big problem, the sparse solver memory should be used. It can distribute the memory between the needed of the program. The model use 100 MW (400 Mb) as the amount of memory (MTOT) and 300 MW as the sparse solver memory. Converting X-Ray CT Image to Finite Element Model In order to convert the X-ray CT image to finite element model, the same steps were performed as in the estimating percentage of air void part. That included converting the image into eight bits, choosing the threshold value. With the aid of image software, the following steps were performed in order to convert the X-Ray CT in to finite element model Threshold X-ray tomography image in order to identify mastic, aggregate and air void. Figure 1 shows a typical X-ray CT image. In an X-ray CT image, the intensity of the pixel represents the density of materials. The dark colors correspond to the air voids and the bright colors correspond to the aggregate. The intensity of the mastic is in between that of these two colors. By thresholding the image, ranges of intensity of the aggregate and air void is recorded. Export the image into a text file. The image is in gray mode so each pixel in the image can be represented by a number ranging from 1 to 255 corresponding to the intensity of the image. A program was written to read the text file and transformed it to an Adina finite element input file. Each pixel in the image is corresponded to an element in Adina. With

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87 a large image, this will lead to a large mesh. The image therefore has to be reduced in to an appropriate size before transforming. Because each X-ray CT image represent a horizontal slice of the HMA sample, Stacking these images will have the complete 3-D image of the sample. The mastic and aggregate particles will be modeled by the solid elements in Adina, and the air void particles will be modeled by fluid elements in Adina-F. These elements will be combined together in Adina-FSI for the fully coupled analysis. Summary of the procedure to convert an X-ray CT image in to finite element model: 1. Obtain the X-ray Computed Tomography image of HMA samples. 2. Using image free software such as Image tools, Scion Image or commercial software such as Image pro, threshold intensity of the images was determined. One threshold value was used to all the images of the same sample. 3. Ten images were chosen for the modeling purpose. These images should be consecutive. An area is chosen. The area was then rescale to 15x15. These steps were repeated for 10 images. 4. The images were converted to text format. To have a consistency for the transfer process from , all the images were converted to 8 bytes before converting to text format. 5. A C++ program was written to transfer these text files in to Adina solid and Adina Fluid input file. Since each image represent two dimensions of the sample, the stack of all the images gave us a 3D of the HMA samples. The size of the problems were 15x15x10 elements. It was limited by the maximum the memory that Adina can allocated. 6. The input files was opened in Adina and analyzed in Adina FSI Simple Example A simple problem was implemented and analyzed by Adina FSI. It compose of two vertical connected air void. These air voids was model by fluid element. The normal traction was applied in one end of the void. The analysis gave us the velocity and the stress that was applied to the solid model from the fluid. The mesh of model is 5x5x5. The total degrees of freedom for this problem is 3375.

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88 Figure 7-1. Mesh of solid elements Figure 7-2. Mesh of fluid elements

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89 Figure 7-3. Velocity vector Figure 7-4. Nodal pressure – fluid elements

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90 Figure 7-5. Nodal pressure – solid elements Summary The aggregate structural of asphalt concrete was captured by using X-Ray computed tomographic image system. A threshold value for image intensity was chosen so that the aggregate and the air void can be distinguished. The image was then transferred to solid and fluid models. The models were coupled in Adina to analyze the fluid flow in asphalt concrete.

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CHAPTER 8 CONCLUSIONS AND RECOMMENDATIONS Pore Pressure Effect under Triaxial Loading Condition The effects of pore water pressure were investigated using triaxial compression tests including static triaxial compression and dynamic traixial compression tests. The B-value results has suggested that the HMA samples used in the test can be fully saturated by using a back pressure saturation of 60 psi for a period of 24 hours. The B-value varies with the value of back pressure. In all the static triaxial tests, the behavior of the pore water pressure has shown that a small decrease in volume occurred during the initial stage of the test. Additional loading caused a volume increase and hence a drop in pore water pressure. The initial reduction of volume could be due to: 1, a recovery of expansion that occurred upon release of compression pressures applied during sample fabrication. 2, an elastic compression of the specimens under confining pressures. 3, plastic deformation of the bitumen. The dilation of the volume could be due to the fact that the grains were force to moved apart to ride over one another in the shear test. The effects of pore pressure to the complex modulus are significant, especially at higher temperature where the complex modulus is lower. This is expected because the pore pressure is dependence partly of the stiffness of the samples. Under a dynamic loading condition, there is not much different in the complex modulus between the undrained and drained condition. 91

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92 Aggregate Structural Effects on Water Damage and Fluid Flow in Asphalt Concrete Capabilities were developed for the interpretation of digital X-Ray tomographic images. The framework for translating digital tomographic images into finite element input files was also developed. The aggregate structural properties of asphalt concrete obtained from X-Ray tomography image are useful on evaluating water damage and water flow through pavement. For the moisture damage, the results have shown that for the comparable range of air void, the moisture damage increase with the amount of aggregate surface areas exposed to water. The air void distribution obtained from X-Ray Image analysis help us to predict the fluid flow in the pavement. The variation in permeability through typical HMA layers from higher at the surface to lower at the bottom of the HMA layer will encourage lateral flow in the more permeable part of the HMA layer, and discourage vertical flow into the underlying base course material. Consequently, the associated moisture related damage would depend not only in the average permeability in an asphalt mix, but on the percent air voids and the direction of the developed flow patterns. Recommendations Due to time limitation, this research cannot be carried out to completion. Further study on the pore pressure effect is suggested. The further triaxial tests should include the environmental effects such as rate of strain, temperature, and percentage of air void as well as the influence of various asphalt contents and asphalts. Aggregate structural properties should be studied more to evaluate asphalt concrete behavior. The study should include the influence of anisotropy on the non-linearities and instabilities of asphalt mixtures.

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93 Pore pressure conditioning should be considered when evaluating the potential for water damage in mixtures The development of coupled micro-structural modeling approaches for mixtures are needed

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APPENDIX A MIX DESIGN Table A-1. Batch sheet for coarse material – C1 Sieve #7 stone # 89 stone W-10 scr Filler Size "3/4 0.0 318.8 1289.9 2794.2 12.5(1/2) 75.6 318.8 1289.9 2794.2 9.5(3/8) 318.8 318.8 1289.9 2794.2 4.75(#4) 318.8 1289.9 1289.9 2794.2 2.36(#8) 318.8 1289.9 2037.7 2794.2 1.18(#16) 318.8 1289.9 2338.8 2794.2 600(#30) 318.8 1289.9 2510.1 2794.2 300(#50) 318.8 1289.9 2626.7 2794.2 150(#100) 318.8 1289.9 2740.8 2794.2 75(#200) 318.8 1289.9 2794.2 2794.2 <75(#200) 318.8 1289.9 2794.2 2896.1 Table A-2. Batch sheet for coarse material – C2 Sieve #7 stone # 89 stone W-10 scr Filler Size "3/4 0.0 811.4 1617.7 2873.3 12.5(1/2) 271.1 811.4 1617.7 2873.3 9.5(3/8) 811.4 811.4 1617.7 2873.3 4.75(#4) 811.4 1617.7 1617.7 2873.3 2.36(#8) 811.4 1617.7 2149.5 2873.3 1.18(#16) 811.4 1617.7 2425.5 2873.3 600(#30) 811.4 1617.7 2596.8 2873.3 300(#50) 811.4 1617.7 2714.6 2873.3 150(#100) 811.4 1617.7 2824.7 2873.3 75(#200) 811.4 1617.7 2873.3 2873.3 <75(#200) 811.4 1617.7 2873.3 2991.3 94

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95 Table A-3. Batch sheet for coarse material – C3 Sieve #7 stone # 89 stone W-10 scr Filler Size "3/4 0.0 313.5 1333.2 2851.4 12.5(1/2) 82.1 313.5 1333.2 2851.4 9.5(3/8) 313.5 313.5 1333.2 2851.4 4.75(#4) 313.5 1333.2 1333.2 2851.4 2.36(#8) 313.5 1333.2 1977.5 2851.4 1.18(#16) 313.5 1333.2 2303.5 2851.4 600(#30) 313.5 1333.2 2511.8 2851.4 300(#50) 313.5 1333.2 2655.4 2851.4 150(#100) 313.5 1333.2 2786.9 2851.4 75(#200) 313.5 1333.2 2851.4 2851.4 <75(#200) 313.5 1333.2 2851.4 2991.3 Table A-4. Batch sheet for fine material – F1 Sieve #7 stone # 89 stone W-10 scr Filler Size "3/4 0.0 478.1 1004.2 2894.5 12.5(1/2) 157.4 478.1 1004.2 2894.5 9.5(3/8) 478.1 478.1 1004.2 2894.5 4.75(#4) 478.1 1004.2 1004.2 2894.5 2.36(#8) 478.1 1004.2 1519.1 2894.5 1.18(#16) 478.1 1004.2 2014.7 2894.5 600(#30) 478.1 1004.2 2363.6 2894.5 300(#50) 478.1 1004.2 2606.9 2894.5 150(#100) 478.1 1004.2 2817.0 2894.5 75(#200) 478.1 1004.2 2894.5 2894.5 <75(#200) 478.1 1004.2 2894.5 2992.9

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96 Table A-5. Batch sheet for fine material – F2 Sieve #7 stone # 89 stone W-10 scr Filler Size "3/4 0.0 696.3 1224.6 2918.1 12.5(1/2) 292.4 696.3 1224.6 2918.1 9.5(3/8) 696.3 696.3 1224.6 2918.1 4.75(#4) 696.3 1224.6 1224.6 2918.1 2.36(#8) 696.3 1224.6 1750.5 2918.1 1.18(#16) 696.3 1224.6 2035.4 2918.1 600(#30) 696.3 1224.6 2373.0 2918.1 300(#50) 696.3 1224.6 2612.6 2918.1 150(#100) 696.3 1224.6 2813.5 2918.1 75(#200) 696.3 1224.6 2918.1 2918.1 <75(#200) 696.3 1224.6 2918.1 3083.2 Table A-6. Batch sheet for fine material – F3 Sieve #7 stone # 89 stone W-10 scr Filler Size "3/4 0.0 449.5 1053.6 2841.6 12.5(1/2) 161.7 449.5 1053.6 2841.6 9.5(3/8) 449.5 449.5 1053.6 2841.6 4.75(#4) 449.5 1053.6 1053.6 2841.6 2.36(#8) 449.5 1053.6 1966.0 2841.6 1.18(#16) 449.5 1053.6 2231.3 2841.6 600(#30) 449.5 1053.6 2469.6 2841.6 300(#50) 449.5 1053.6 2640.1 2841.6 150(#100) 449.5 1053.6 2784.4 2841.6 75(#200) 449.5 1053.6 2841.6 2841.6 <75(#200) 449.5 1053.6 2841.6 3016.9

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Table A-7. Sample properties Mixture Sample # A (g) B (g) C (g) T (oC) Corr. Fac. Gmb Gmm AV H V Gmb Diff %Diff 1-1 3056 3087.4 1735.8 27.6 0.999299 2.259 2.442 7.5 177.0 1390.7 2.197 0.062 2.744 1-2 3017.4 3043.1 1706.8 27.2 0.99941 2.257 2.442 7.6 173.5 1363.1 2.214 0.043 1.911 2-1 3007.6 3026.8 1697.9 25.1 0.999974 2.263 2.442 7.3 172.9 1358.7 2.214 0.050 2.188 GAA-C1 2-2 3146.8 3167.4 1816.1 27.2 0.99941 2.327 2.500 6.9 177.0 1390.7 2.263 0.065 2.777 1-1 2968.3 2973.2 1686.8 25.1 0.999974 2.307 2.473 6.7 166.4 1307.4 2.270 0.037 1.606 1-2 3199.3 3211.8 1844.7 27.2 0.99941 2.339 2.532 7.6 177.0 1390.7 2.300 0.038 1.640 2-1 2922.6 2928.3 1684.4 27.2 0.99941 2.348 2.532 7.3 161.0 1264.6 2.311 0.037 1.579 GAA-F1 2-2 3172.5 3199.7 1838.2 27.2 0.99941 2.329 2.505 7.0 177.0 1390.7 2.281 0.048 2.043 97

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APPENDIX B EVALUATION OF PORE WATER PRESSURE EFFECT UNDER TRIAXIAL LOADING CONDITION Static Triaxial Tests Table B-1. Samples and temperatures used in triaxial compression tests. Samples Test temperature F1 250C 400C C3 400C C1 250C Table B-2. Values of pressures applied in B-value measurement Cell pressure Back pressure Axial pressure Axial load Axial load (relative change) Steps (psi) (psi) (psi) (N) (N) 1 5 0 5 271 194 2 10 5 10 541 -76 3 15 10 15 812 -347 4 20 15 20 1082 -617 5 25 20 25 1353 -888 6 30 25 30 1624 -1159 7 35 30 35 1894 -1429 8 40 35 40 2165 -1700 9 45 40 45 2436 -1971 10 50 45 50 2706 -2241 11 55 50 55 2977 -2512 98

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99 q'0100200300400500600700050100150200250300p' (psi)q' (psi) Figure B-1. Effective stress path-F1 at 250C 0100200300400500600050100150200250300p' (psi)q' (psi) Figure B-2. Effective stress path-F1 at 400C

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100 0100200300400500600050100150200250p' (psi)q' (psi) Figure B-3. Stress path – C1 at 250C 0204060801000102030p' (psi)q' (psi) 40 Figure B-4. Stress path – C3 at 400C

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101 Complex Modulus Tests Phase Angle C1 at 10C0.05.010.015.020.025.030.035.040.045.050.0161041Frequency (Hz)Phase Angle (degrees) Undrained Drained Dry Figure B-5. Phase angle at 100C of coarse mix (C1) C1 at 40C0102030405060161041Frequency (Hz)Phase Angle (degrees) Undrained Drained Dry Figure B-6. Phase angle at 400C of coarse mix (C1)

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102 F1 at 10C0.010.020.030.040.050.060.0161041Frequency (Hz)Phase Angle (degrees) Undrained Drained Dry Figure B-7. Phase angle at 100C of fine mix (F1) F1 at 40C0.010.020.030.040.050.060.070.0161041Frequency (Hz)Phase Angle (degrees) Undrained Drained Dry Figure B-8. Phase angle at 400C of fine mix (F1)

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103 Stress Amplitude C1 at 10C00.10.20.30.40.50.60.7161041Frequency (Hz)Stress Amplitude Undrained Drained Dry Figure B-9. Stress amplitude at 100C of coarse mix (C1) C1 at 40C00.050.10.150.20.25161041Frequency (Hz)Stress Amplitude Undrained Drained Dry Figure B-10. Stress amplitude at 400C of coarse mix (C1)

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104 F1 at 10C00.20.40.60.811.2161041Frequency (Hz)Stress Amplitude Undrained Drained Dry Figure B-11. Stress amplitude at 100C of fine mix (F1) F1 at 40C00.050.10.150.20.250.30.35161041Frequency (Hz)Stress Amplitude Undrained Drained Dry Figure B-12. Stress amplitude at 400C of fine mix (F1)

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105 Strain Amplitude C1 at 10C0.00E+002.00E-054.00E-056.00E-058.00E-051.00E-041.20E-041.40E-041.60E-041.80E-042.00E-04161041Frequency (Hz)Strain Amplitude Undrained Drained Dry Figure B-13. Strain amplitude at 100C of coarse mix (C1) C1 at 40C0.00E+005.00E-051.00E-041.50E-042.00E-042.50E-04161041Frequency (Hz)Strain Amplitude Undrained Drained Dry Figure B-14. Strain amplitude at 400C of coarse mix (C1)

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106 F1 at 10C0.00E+002.00E-054.00E-056.00E-058.00E-051.00E-041.20E-041.40E-041.60E-041.80E-042.00E-04161041Frequency (Hz)Strain Amplitude Undrained Drained Dry Figure B-15. Strain amplitude at 100C of fine mix (F1) F1 at 40C0.00E+002.00E-054.00E-056.00E-058.00E-051.00E-041.20E-041.40E-041.60E-041.80E-04161041Frequency (Hz)Strain Amplitude Undrained Drained Dry Figure B-16. Strain amplitude at 400C of fine mix (F1)

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107 Pore Pressure Measurement – C1 at 100C C1 at 100C at 16Hz00.050.10.150.20.250.3121313351458158017021824Time (msec)Change in pore pressure (psi)0102030405060708090100Principal Stress Difference ( 1 3) (psi) Pore pressure Principal stress difference Figure B-17. Pore pressure of complex modulus test at frequency 16Hz, temperature 100C of coarse mix (C1) C1 at 100C at 10Hz00.050.10.150.20.250.30.350.4381805382000382196382391382586382782Time (msec)Change in pore pressure (psi)0102030405060708090100Principal Stress Difference ( 1 3) (psi) Pore pressure Principal stress difference Figure B-18. Pore pressure of complex modulus test at frequency 10Hz, temperature 100C of coarse mix (C1)

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108 C1 at 100C at 4Hz00.10.20.30.40.50.60.70.80.9774555775044775532776020776509776997Time (msec)Change in pore pressure (psi)0102030405060708090100Principal Stress Difference ( 1 3) (psi) Pore pressure Principal stress difference Figure B-19. Pore pressure of complex modulus test at frequency 4Hz, temperature 100C of coarse mix (C1) C1 at 100C at 1Hz00.050.10.150.20.250.30.350.40.450.5116776911697711171772117377411757761177778Time (msec)Change in pore pressure (psi)0102030405060Principal Stress Difference ( 1 3) (psi) Pore pressure Principal stress difference Figure B-20. Pore pressure of complex modulus test at frequency 1Hz, temperature 100C of coarse mix (C1)

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109 Pore Pressure Measurement – C1 at 400C C1 at 400C at 16Hz-0.15-0.1-0.0500.050.10.150.20.250.3121313351458158017021824Time (msec)Change in pore pressure (psi)-5051015202530354045Principal Stress Difference (1 3) (psi) Pore pressure Principal stress difference Figure B-21. Pore pressure of complex modulus test at frequency 16Hz, temperature 400C of coarse mix (C1) C1 at 400C at 10Hz-0.15-0.1-0.0500.050.10.150.20.250.30.350.4381805382000382195382391382586382781Time (msec)Change in pore pressure (psi)-20-10010203040Principal Stress Difference (1 3) (psi) Pore pressure Principal stress difference Figure B-22. Pore pressure of complex modulus test at frequency 10Hz, temperature 400C of coarse mix (C1)

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110 C1 at 400C at 4Hz00.10.20.30.40.50.60.70.80.9774542775031775519776007776496776984Time (msec)Change in pore pressure (psi)-20-1001020304050Principal Stress Difference ( 1 3) (psi) Pore pressure Principal stress difference Figure B-23. Pore pressure of complex modulus test at frequency 4Hz, temperature 400C of coarse mix (C1) C1 at 400C at 1Hz00.10.20.30.40.50.6116771211697141171716117371811757201177722Time (msec)Change in pore pressure (psi)-15-10-5051015202530Principal Stress Difference ( 1 3) (psi) Pore pressure Principal stress difference Figure B-24. Pore pressure of complex modulus test at frequency 1Hz, temperature 400C of coarse mix (C1)

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111 Pore Pressure Measurement – F1 at 100C F1 at 100C at 16Hz1.11.151.21.251.31.351.41.451.51.55121313351458158017021824Time (msec)Change in pore pressure (psi)020406080100120140160Principal Stress Difference ( 1 3) (psi) Pore pressure Principal stress difference Figure B-25. Pore pressure of complex modulus test at frequency 16Hz, temperature 100C of fine mix (F1) F1 at 100C at 10Hz00.050.10.150.20.250.30.350.4361806362002362197362392362588362783Time (msec)Change in pore pressure (psi)020406080100120140Principal Stress Difference ( 1 3) (psi) Pore pressure Principal stress difference Figure B-26. Pore pressure of complex modulus test at frequency 10Hz, temperature 100C of fine mix (F1)

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112 F1 at 100C at 4Hz00.20.40.60.811.2734534735023735511735999736488736976Time (msec)Change in pore pressure (psi)020406080100120Principal Stress Difference ( 1 3) (psi) Pore pressure Principal stress difference Figure B-27. Pore pressure of complex modulus test at frequency 4Hz, temperature 100C of fine mix (F1) F1 at 100C at 1Hz00.511.522.53110764211096441111646111364811156501117652Time (msec)Change in pore pressure (psi)-1001020304050607080Principal Stress Difference ( 1 3) (psi) Pore pressure Principal stress difference Figure B-28. Pore pressure of complex modulus test at frequency 1Hz, temperature 100C of fine mix (F1)

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113 Pore Pressure Measurement – F1 at 400C F1 at 400C at 16Hz00.050.10.150.20.250.3121313351458158017021824Time (msec)Change in pore pressure (psi)010203040506070Principal Stress Difference ( 1 3) (psi) Pore pressure Principal stress difference Figure B-29. Pore pressure of complex modulus test at frequency 16Hz, temperature 400C of fine mix (F1) F1 at 400C at 10Hz00.050.10.150.20.250.30.35361809362004362200362395362590362786Time (msec)Change in pore pressure (psi)010203040506070Principal Stress Difference ( 1 3) (psi) Pore pressure Principal stress difference Figure B-30. Pore pressure of complex modulus test at frequency 10Hz, temperature 400C of fine mix (F1)

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114 F1 at 400C at 4Hz00.050.10.150.20.250.30.35734550735039735527736015736503736992Time (msec)Change in pore pressure (psi)05101520253035404550Principal Stress Difference ( 1 3) (psi) Pore pressure Principal stress difference Figure B-31. Pore pressure of complex modulus test at frequency 4Hz, temperature 400C of fine mix (F1) F1 at 400C at 1Hz00.10.20.30.40.50.60.70.80.91109598010979821099984110198611039881105990Time (msec)Change in pore pressure (psi)05101520253035Principal Stress Difference ( 1 3) (psi) Pore pressure Principal stress difference Figure B-32. Pore pressure of complex modulus test at frequency 1Hz, temperature 400C of fine mix (F1)

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115 Falling Head Test on Various Samples Falling Head Permeability Test1.500E-043.500E-045.500E-047.500E-049.500E-041.150E-031.350E-03234567891Average Gradient Across SamplePermeability (cm/s) 0 J8 J14 J15 J18 Figure B-33. Falling head results of permeability test on samples

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APPENDIX C IMAGETOOL INSTRUCTIONS Figure D-1. Import file in Scion image 116

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117 Figure D-2. Manually threshold the image Figure D-3. Finding object

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118 Figure D-4. Analyze menu

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APPENDIX E FINITE ELEMENT SOURCE CODES Converting Image File To Finite Element Program Input File Structure The input file structure has the following format: B; // Number of element in x dimension L; // Number of element in y dimension H; // Number of element in z dimension e_depth; // Element depth-element length in X direction e_width; // Element width-element length in y direction e_height; // Element height-element length in z direction mesh_x = 2; // Number of mesh in x direction. Default value is 2 mesh_y = 2; // Number of mesh in z direction. Default value is 2 mesh_z = 2; // Number of mesh in z direction. Default value is 2 intens_A_M; //Intensity between aggregate and mastic intens_M_V; // Intensity between mastic and Airvoid intenFname // List of file names from 1 to H layer Image File in Text Format The image files in text format were created using Scion Image software. The images were imported in tiff format and exported to text format. 119

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120 Header File The header file includes all the global variants used in the programs and two main structures: class Element and class Surface. The class Element describes all the name of the surfaces needed to construct the volumes for Adina solid and Adina fluid input file. The class Surface contains the types of surfaces: Air void – air void surface, air void – structure surface, air void – air void surface, and structure – structure surface. #include #include #include #include #include #include int B; // Number of element in x dimension int L; // Number of element in y dimension int H; // Number of element in z dimension int mesh_x = 2; // Number of mesh in x direction int mesh_y = 2; // Number of mesh in z direction int mesh_z = 2; // Number of mesh in z direction const int SOLID = 1; // Constant value const int MASTIC = 2; const int AIR_VOID = 3; const int AirB = 1; // Airvoid boundary -value 1 * AirB const int AirS = 4;// Airvoid-structure surface-value 4* AirS const int StructureS = 6; // Structure-structure surface-value 6 * StructureS const int AirA = 2; // Airvoid-airvoid surface-2 *AirA // Structure boundary-Value 3 * StructureB double Hor_spacing = 0.25; // Distance between pixels is 0.25 mm double Ver_spacing = 0.25; int intens_A_M; //Intensity between aggregate and mastic int intens_M_V; // Intensity between mastic and Airvoid char program_ver[80] = "AdinaGEN version 1.0"; char intenFname[20][80]; double e_depth; // Element depth-element length in X direction double e_width; // Element width-element length in y direction double e_height; // Element height-element length in z direction void start(); void readfile(); void createAdinaA(); void createAdinaF(); voidcreateS(); // Creating surface type class Element { private : int type; // Solid, air void or mastic. Solid = 1, air void = 2, mastic = 3

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121 int surf_bottom; int surf_top; int surf_left; int surf_right; int surf_front; int surf_back; public: void setsurf_top(int n); void setsurf_bott(int); om n void setsurf_left(int n); void setsurf_right(int n); void setsurf_front(int n); void setsurf_back(int n); void settype(int n); int get_Sbot(); tom int get_Stop(); int get_Sfront(); int get_Sleft(); int get_Sright(); int get_Sback(); int get_type(); Element(); Element(int bottom, int front, int left, int back, int right, int p, int ntype); to}; // Surface is the type of data that contain the type of the surface, either structure-structure, air void-air void // or structure-air void class Surface { private: int type; // Will have the following value: 1, 2, 3, 4, 6 public : int get_type() { return type; }; void set_type(int n) { type = n; }; Surface() { set_type(0); }; Surface(int n) { set_type(n); }; }; //Stack of element // Egroup[k][j][i]: // k element in z direction // j element in y direction // i element in x direction Element Egroup[100][100][100]; Surface Sgroup[5000000];

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122 Main Program The main program compose of four main procedures: 1. start(): This procedure reads the input file specified in file structures 2. readfile(): This procedure reads the image input file and separate the particle in to fluid and solid element and stack all the 2D images to get the 3D model. 3. creatS(): This procedure creates the surface number for the volumes of both the solid and the fluid model. The surface number is stored in Element database. 4. createAdinaA(): Creat the input for Adina solid input file. 5. createAdinaF(): Creat the input for Adina fluid input file. /*********************************************************************/ /* This program will transfer images file in to 3D Adina-Fluid and Adina solid file*/ // Output compatible with Adia 7.5 */ #include "AdinaGEN.hpp" //Header file int main() { start(); // Reading input parameter file readfile(); // Reading image file createS(); createAdinaA(); createAdinaF(); cout << "Press any key to finish ..." << endl; while( !_kbhit() ); return 0; } // Creating Adina solid file void createAdinaA() { int i, j, k; int point_number; int e_number; double x; // X coordinate double y; // X coordinate double z; // X coordinate int SFP; // Number of point in a surface int RP; // Number of point in a row SFP = (B+1)*(L+1); RP = B + 1; //****************************************************************************** // Make output file // Command file created from session file information stored within AUI database ofstream resultFile("result.out", ios::out); if (!resultFile)

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123 { cerr << "File can not be created" << endl; exit(1); } resultFile << " Element's surface:" << endl; for (k = 1; k<=H; k++) { for (j = 1; j<=L; j++) { for (i = 1; i<=B; i++) { int point_1 = SFP * (k-1)+ (j-1)*RP + i; resultFile << " Volume [" << k << "][" << j << "][" << i << "] = " << Egroup[k][j][i].get_Sbottom() << ", " << Egroup[k][j][i].get_Sfront() <<", " << Egroup[][j][i].get_Sleft() <<", " << k Egroup[k][j][i].get_Sback() <<", " << Egroup[k][j][i].get_Sright() <<", " << Egroup[k][j][i].get_Stop() << " Type =" << Egroup[k][j][i].get_type(); resultFile << " Point = "<< point_1 << ", " << point_1 + 1 << ", "; resultFile << point_1 + B + 2 << ", " << point_1 + B + RP << ", " << point_1 + SFP << ", " ; resultFile << point_1 + SFP +1 << ", " << point_1 + SFP + 1 + RP << ", " << point_1 + SFP + RP << endl; } } } resultFile << "****************************************************************"<< endl; resultFile << "Image files"<< endl; for (k = 1; k<=H; k++) { for (j = 1; j<=L; j++) { for (i = 1; i<=B; i++) { if (Egroup[k][j][i].get_type() == AIR_VOID) { resultFile << " 0 "; } else { resultFile << " x "; } } resultFile << endl; } resultFile << endl; resultFile << "****************************************************************"<< endl; }

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124 ofstream outFile("AdinaA.in", ios::out); if (!outFile) { cerr << "File AdinaA.in can not be created" << endl; exit(1); } outFile << "* Command file created from: 'Fluid flow program'" << endl; outFile << "*--by " << program_ver << "---*" << endl; outFile << "DATABASE NEW SAVE=NO PROMPT=NO" <
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125 outFile << "COORDINATES POINT SYSTEM=0"<< endl; for (k = 1; k <= H+1; k++) { for (j = 1; j <= L+1; j++) { for ( i = 1; i <= B+1; i++) { point_number = (k-1)* SFP + (j-1)* RP + i; x = (1) e_width; i* y = (j -1) * e_depth; z = (k -1) * e_height; outFile << setiosflags (ios::left) << setw(10) << point_number; outFile << setiosflags (ios::fixed | ios::showpoint) << setw(10) << setprecision(3) x; //x coordinate << outFile << setiosflags (ios::fixed | ios::showpoint) << setw(10) << setprecision(3) << y; //y coordinate outFile << setiosflags (ios::fixed | ios::showpoint) << setw(10) << setprecision(3) << z; //z coordinate outFile << " " << 0 << endl; } } } outFile <<"*" << endl; // End writing coordinate //Writing volume resultFile << "****************************************************************"<< endl; resultFile << "Volume point:"<< endl; for (k = 1; k <= H; k++) { for (j = 1; j <= L; j++) { for ( i = 1; i <= B; i++) { e_number = (k-1)*L*B + (j-1)*B + i; int point_1 = SFP * (k-1)+ (j-1)*RP + i; outFile << "VOLUME VERTEX NAME=" << e_number <<" " << "SHAPE=HEX VERTEX1="<< point_1 << " " << "VERTEX2=" << point_1 + 1 << " " << "VERTEX3=" << point_1 + B + 2 <<"," << endl; outFile << "VERTEX4=" << point_1 + RP << " " << "VERTEX5=" << point_1+SFP << " " << "VERTEX6=" << point_1 + SFP +1 << " " << "VERTEX7=" << point_1 + SFP +1 + RP << " " << "VERTEX8=" << point_1 + SFP + RP << endl; outFile << "*" << endl; } } } // Define the mesh for the forum.

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126 // Only divide the mesh in the z direction // Writing sub volume // SUBDIVIDE VOLUME NAME MODE SIZE NDIV1 NDIV2 NDIV3 RATIO1, // RATIO2 RATIO3 PROGRESSION CBIAS1 CBIAS2 CBIAS3 //Assigns mesh subdivision data to a set of geometry volumes. The data can be in the form of a //specified element size, or the number of divisions along the edges of the geometry volume. //The subdivision data is actually assigned to the geometry lines which comprise the edges of //the geometry volumes. k = 0; i = 0; int ok = 1; while ((ok !=0) & (k < H)) { k++; j; = 0 while ((ok !=0) & (j < L)) { j++; i = 0; while ((ok !=0) & (i < B)) { i++; if (Egroup[k][j][i].get_type() == SOLID) ok = 0; } } } outFile << "SUBDIVIDE VOLUME NAME="<< (k-1)*(B*L) + (j-1)*B + i <<" MODE=DIVISIONS NDIV1=" << mesh_x <<" NDIV2=" << mesh_y <<" NDIV3="<< mesh_z <<" ," << endl; outFile << " RATIO1=1.00000000000000 RATIO2=1.00000000000000," << endl; outFile << " RATIO3=1.00000000000000 PROGRESS=GEOMETRIC EXTEND=NONE CBIAS1=NO," << endl; outFile << " CBIAS2=NO CBIAS3=NO" << endl; outFile << <
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127 outFile << " DENSITY=0.00000000000000 ALPHA=0.00000000000000" << endl; outFile <<"*" << endl; outFile << "*" << endl; outFile << "EGROUP THREEDSOLID NAME=1 DISPLACE=DEFAULT STRAINS=DEFAULT MATERIAL=1," << endl; outFile << " RSINT=DEFAULT TINT=DEFAULT RESULTS=STRESSES DEGEN=NO FORMULAT=0," << endl; outFile << " STRESSRE=GLOBAL INITIALS=NONE FRACTUR=NO CMASS=DEFAULT," << endl; outFile << " STRAIN-F=0 UL-FORMU=DEFAULT LVUS1=0 LVUS2=0 SED=NO RUPTURE=ADINA," << endl; outFile << " INCOMPAT=DEFAULT TIME-OFF=0.00000000000000 POROUS=NO," << endl; outFile << " WTMC=1.00000000000000" << endl; outFile << "*" << endl; // *********************************** //Meshing the file outFile << "GVOLUME NODES=27 PATTERN=0 NCOINCID=BOUNDARIES NCFACE=123456 NCEDGE=," << endl; outFile << "'123456789ABC' NCVERTEX=12345678 NCTOLERA=1.00000000000000E-05," << endl; outFile << " SUBSTRUC=0 GROUP=1 MESHING=MAPPED PREFSHAP=AUTOMATIC," << endl; outFile << " DEGENERA=YES COLLAPSE=NO MIDNODES=CURVED METHOD=DELAUNAY" << endl; outFile << "@CLEAR" << endl; for (k = 1; k<= H; k++) { for (j = 1; j <= L; j++) { for (i = 1; i <= B; i++) { if ((Egroup[k][j][i].get_type() == SOLID) || (Egroup[k][j][i].get_type() == MASTIC)) { outFile << (k-1)*(B*L) + (j-1)*B + i << endl; } } } } outFile << "@" << endl; // End meshing file // *********************************** // Start creating boundary for the file outFile << "FIXBOUNDARY SURFACES FIXITY=ALL" << endl; outFile << "@CLEAR" << endl; for (j=1; j<= L; j++) { for (i=1; i<=B; i++) { outFile << Egroup[1][j][i].get_Sbottom() << endl; } }

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128 outFile << "@" << endl; // *********************************** // Begin creating FSI boundary int n; int count; n = Egroup[H][L][B].get_Stop(); // The number of surface count = 0; for (i=1; i<= n; i++) { resultFile << " Sgroup[" << i << "]= " << Sgroup[i].get_type() << endl; if (Sgroup[i].get_type() == 4) // FSI interface { count += 1; outFile << "FSBOUNDARY SURFACES NAME=" << count << endl; outFile << "@CLEAR" << endl; outFile << i << endl; outFile << "@" << endl; // End of surface } } } // evoid Element::setsurf_top(int n) nd creating file { surf_top = n; } void Element::setsurf_bottom(int n) { } surf_bottom = n; void Element::setsurf_left(int n) { surf_left = n; } void Element::setsurf_right(int n) { surf_right = n; } void Element::setsurf_front(int n) { } surf_front = n; void Element::setsurf_back(int n) { surf_back = n; } void Element::settype(int n) { type = n; } int Element::get_Sbottom() { return surf_bottom; } int Element::get_Stop() {

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129 return surf_top; } int Element::get_Sfront() { return surf_front; } int Element::get_Sleft() { return surf_left; } int Element::get_Sright() { return surf_right; } int Element::get_Sback() { return surf_back; } int Element::get_type() { return type; } Element::Element() { surf_top = 0; surf_bottom = 0; surf_left = 0; surf_right = 0; surf_front = 0; surf_back = 0; type = 0; } Element::Element(int top, int bottom, int front, int back, int left, int right, int ntype) { setsurf_fron(fro); tnt setsurf_back(back); setsurf_left(left); setsurf_right(right); setsurf_top(top); setsurf_bottom(bottom); } settype(ntype); void readfile() { int intens; // intesity of the pixel int k, i, j; i = 1; j = 1; // From the current image, may be changed if the image scaned is different. 0 is white // From the current image, may be changed if the image scaned is different. 255 is black for (k = 1; k<= H; k++) { ifstream inImageFile(intenFname[k], ios::in); if (!inImageFile)

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130 { cerr << "File can not be opened" << endl; exit(1); } for (j = 1; j<= L; j++) { for (i = 1; i<=B; i++) { inImageFile >> intens; // cout << intens << " "; if ((intens >= 0) && (intens <= intens_A_M)) // Aggregate { Egroup[k][j][i].settype(SOLID); } else if ((intens >= intens_A_M) && (intens <= intens_M_V)) // Mastic { Egroup[k][j][i].settype(MASTIC); } else if ((intens >= intens_M_V) && (intens <= 255)) // Air void { Egroup[k][j][i].settype(AIR_VOID); } else { cout << "Intesity in position: " << i << " " << j << "is invalided"; while(bhit()); !k exit (1); } } } } } void start() { char filename[80]; int i, j, k; int surf_bottom; int surf_top; int surf_left; int surf_right; int surf_fron; t int surf_back; int nOuterSurf; // Number of surface in the outer layer int nInnerSurf; // Number of surface in inner layer int nInnerLine2; // Number of lines in inner layer second line int nOuterLine2; // Number of lines in outer layer second line int nInnerLine1; // Number of lines in inner layer first line int nOuterLine1; // Number of lines in outer layer first line // The structure of single file // The file will content all the input for the problem.

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131 cout << " **************************************************" << endl; cout << " * AdinaGEN *" << endl; cout << " * Version 1.0 *" << endl; cout << " * *" << endl; cout << " * Output files compatible with Adina 7.5 *" << endl; cout << " * *" << endl; cout << " * *" << endl; cout << " * Department of Civil Engineering *" << endl; cout << " * University of Florida *" << endl; cout << " **************************************************" << endl; cout << endl; cout << endl; cout << endl; cout << "Enter text input filename: "; cin >> filename; ifstream inFile(filename, ios::in); if (!inFile) { cerr << "File can not be opened" << endl; exit(1); } inFile >> B; // "Number of element in X direction: "; inFile >> L; //"Number of element in L direction: "; inFile >> H; //"Number of element in H direction: "; inFile >> e_depth; inFile >> e_width; inFile >> e_height; inFile >> mesh_x; inFile >> mesh_y; inFile >> mesh_z; inFile >> intens_A_M; //"Intensity limit between aggregate and mastic // cout << "Intensity limit between mastic and air void: "; inFile >> intens_M_V; for (k = 1; k <= H; k++) { inFile >> intenFname[k]; } nInnerLine1 = 5 + 4 * (B-1); // Number of lines in inner layer first line nOuterLine1 = 6 + 5 * (B-1); // Number of lines in outer layer first line nInnerLine2 = 4 + 3 * (B-1); // Number of lines in inner layer second line

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132 nOuterLine2 = 5 + 4 * (B-1); // Number of lines in outer layer second line nOuterSurf = nOuterLine1 + (L-1)*nOuterLine2; // Number of surface in the outer layer nInnerSurf = nInnerLine1 + (L-1)*nInnerLine2; // Number of surface in inner layer // Create surface for element for (k = 1; k<= H; k++) { cout << "k = " << k; for (j = 1; j<=L; j++) { cout << " j = " << j; for (i = 1; i <=B; i++) { cout << " i = " << i << endl; if (k == 1) { if (j == 1) { if (i == 1) //k = 1, j = 1, i = 1 { surf_bottom = 1; surf_front = ; 2 surf_left = 3; surf_back = 4; surf_right =; 5 surf_top = 6; } else //k = 1, j = 1, i # 1 { surf_bottom = 6 + 5*(i-2) + 1; surf_front = surf_bottom + 1; surf_left = Egroup[k][j][i-1].get_Sright(); surf_back = 6 + 5*(i-2) + 3; surf_right = 6 + 5*(i-2) + 4; surf_top = 6 + 5*(i-2) + 5; }; } else //k = 1, j # 1 { surf_front = Egroup[k][j-1][i].get_Sback(); // The same for both i if (i == 1) //k = 1, j # 1, i = 1 { surf_bottom = nOuterLine1 + (j-2) * nOuterLine2 + 1; surf_left = surf_bottom + 1; surf_back = surf_bottom + 2; surf_right =surf_bottom + 3; surf_top = surf_bottom + 4; } else //k = 1, j # 1, i #1; {

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133 surf_bottom = nOuterLine1 + (j-2) * nOuterLine2 + 5 + 4* (i-2)+1; surf_left = Egroup[k][j][i-1].get_Sright(); surf_back = surf_bottom + 1; surf_right =surf_bottom + 2; surf_top = surf_bottom + 3; } } } else //k > 1 { surf_bottom = Egroup[k-1][j][i].get_Stop(); // Doesn't depend on i and j if (j == 1) { if (i == 1) //k > 1, j = 1, i = 1 { surf_front = Egroup[k-1][L][B].get_Stop() + 1; surf_left = surf_front + 1; surf_back = surf_front + 2; surf_right = surf_front + 3; surf_top = surf_front + 4; } else //k > 1, j = 1, i > 1 { surf_front = Egroup[k][j][i-1].get_Stop() + 1; surf_left = Egroup[k][j][i-1].get_Sright(); surf_back = surf_front + 1; surf_right = surf_front +; 2 surf_top = surf_front + 3; } } else //k > 1, j > 1 { if (i == 1) //k > 1, j > 1, i = 1 { surf_front = Egroup[k][j-1][i].get_Sback(); surf_left = Egroup[k][j-1][B].get_Stop() + 1; surf_back = surf_left + 1; surf_right = surf_left + 2; surf_top = surf_left + 3; } else //k # 1, j # 1, i #1; { surf_front = Egroup[k][j-1][i].get_Sback(); surf_left = Egroup[k][j][i-1].get_Sright(); surf_back = Egroup[k][j][i-1].get_Stop() + 1; surf_right = surf_back + 1;

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134 surf_top = surf_back + 2; } } } Egroup[k][j][i].setsurf_bottom(surf_bottom); Egroup[k][j][i].setsurf_front(surf_front); Egroup[k][j][i].setsurf_left(surf_left); Egroup[k][j][i].setsurf_back(surf_back); Egroup[][j][i].setsurf_right(surf_right); k Egroup[k][j][i].setsurf_top(surf_top); } } } } //******************************************** // This procedure will create the type of surface that is neccessary for creating FSI surface // Run after Start() (after creating element) // Run after readfile() (after knowing the type of element) void createS() { int k, j, i; for (k=1; k<=H; k++) { for (j=1; j<=L; j++) { for (i=1; i<=B; i++) { int n; intdd; A if ((Egroup[k][j][i].get_type() == SOLID) || (Egroup[k][j][i].get_type() == MASTIC)) { Add = 3; } else { Add = 1; } n = Egroup[k][j][i].get_Stop(); Sgroup[n].set_type(Sgroup[n].get_type() + Add); n = Eg[k][j][i].get_Sbottom(); roup Sgroup[n].set_type(Sgroup[n].get_type() + Add); n = Egroup[k][j][i].get_Sfront(); Sgroup[n].set_type(Sgroup[n].get_type() + Add); n = Egroup[k][j][i].get_Sback(); Sgroup[n].set_type(Sgroup[n].get_type() + Add); n = Eg[k][j][i].get_S(); roupleft Sgroup[n].set_type(Sgroup[n].get_type() + Add); n = Egroup[k][j][i].get_Sright(); Sgroup[n].set_type(Sgroup[n].get_type() + Add); } } } } // Creating AdinaF file void createAdinaF()

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135 { int i, j, k; int point_number; int e_number; double x; // X coordinate double y; // X coordinate double z; // X coordinate int SFP; // Number of point in a surface int RP; // Number of point in a row SFP = (B+1)*(L+1); RP = B + 1; ofstream outFile("AdinaF.in", ios::out); if (!outFile) { cerr "File AdinaF.in can not be created" << endl; << exit(1); } outFile << "* Command file created from image files" < endl; < outFile << "*--by " << program_ver << "---*" << endl; outFile << "DATABASE NEW SAVE=NO PROMPT=NO" <
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136 outFile << "20.0000000000000 1.00000000000000" << endl; outFile << "@" << endl; outFile << "*" << endl; outFile << "COORDINATES POINT SYSTEM=0" << endl; // Use global Cartesian // (ENTRIES NAME X Y Z SYSTEM) // Writing coordinate for (k = 1; k <= H+1; k++) { for (j = 1; j <= L+1; j++) { for ( i = 1; i <= B+1; i++) { point_number = (k-1)* SFP + (j-1)* RP + i; x = (1) e_width; i* y = (j -1) * e_depth; z = (k -1) * e_height; outFile << setiosflags (ios::left) << setw(10) << point_number; outFile << setiosflags (ios::fixed | ios::showpoint) << setw(10) << setprecision(3) x; //x coordinate << outFile << setiosflags (ios::fixed | ios::showpoint) << setw(10) << setprecision(3) << y; //y coordinate outFile << setiosflags (ios::fixed | ios::showpoint) << setw(10) << setprecision(3) << z; //z coordinate outFile << " " << 0 << endl; } } } outFile <<"*" << endl; // End writing coordinate // Writing volume for (k = 1; k <= H; k++) { for (j = 1; j <= L; j++) { for ( i = 1; i <= B; i++) { e_number = (k-1)*L*B (1)B ; +j-*+ i int point_1 = SFP * (k-1)+ (j-1)*RP + i; outFile << "VOLUME VERTEX NAME=" << e_number <<" " << "SHAPE=HEX VERTEX1="<< point_1 << " " << "VERTEX2=" << point_1 + 1 << " " << "VERTEX3=" << point_1 + B + 2 <<"," << endl; outFile << "VERTEX4=" << point_1 + RP << " " << "VERTEX5=" << point_1+SFP << " " << "VERTEX6=" << point_1 + SFP +1 << " " << "VERTEX7=" << point_1 + SFP +1 + RP << " " << "VERTEX8=" << point_1 + SFP + RP << endl; outFile << "*" << endl; } } }

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137 // Writing sub volume // SUBDIVIDE VOLUME NAME MODE SIZE NDIV1 NDIV2 NDIV3 RATIO1, // RATIO2 RATIO3 PROGRESSION CBIAS1 CBIAS2 CBIAS3 //Assigns mesh subdivision data to a set of geometry volumes. The data can be in the form of a //specified element size, or the number of divisions along the edges of the geometry volume. //The subdivision data is actually assigned to the geometry lines which comprise the edges of //the geometry volumes. k = 0; i = 0; int ok = 1; while ((ok !=0) & (k < H)) { k++; j = 0; while ((ok !=0) & (j < L)) { j++; i; = 0 while ((ok !=0) & (i < B)) { i+; + if (Egroup[k][j][i].get_type() == AIR_VOID) ok = 0; } } } outFile << "SUBDIVIDE VOLUME NAME="<< (k-1)*(B*L) + (j-1)*B + i <<" MODE=DIVISIONS NDIV1=" << mesh_x <<" NDIV2=" << mesh_y <<" NDIV3=" << mesh_z <<" ," << endl; outFile << " RATIO1=1.00000000000000 RATIO2=1.00000000000000," << endl; outFile << " RATIO3=1.00000000000000 PROGRESS=GEOMETRIC EXTEND=NONE CBIAS1=NO," << endl; outFile << " CBIAS2=NO CBIAS3=NO" << endl; outFile << "@CLEAR" << endl; for (k = 1; k<= H; k++) { for (j = 1; j <= L; j++) { for (i = 1; i <= B; i++) { if (Egroup[k][j][i].get_type() == AIR_VOID) { outFile << (k-1)*(B*L) + (j-1)*B + i << endl; } } } } outFile << "@" << endl; // Writing Material outFile << "MATERIAL CONSTF NAME=1 XMU=0.000170000000000000 CP=0.00000000000000," << endl;

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138 outFile << " XKCON=0.00000000000000 BETA=0.00000000000000 QB=0.00000000000000," << endl; outFile << " RHO=0.00100000000000000 TREF=0.00000000000000," << endl; outFile << " GRAV-X=0.00000000000000 GRAV-Y=0.00000000000000," << endl; outFile << " GRAV-Z=0.00000000000000 SIGMA=0.00000000000000," << endl; outFile << " KAPPA=1.00000000000000E+20 CV=0.00000000000000" << endl; outFile << "*" << endl; // Boundary condition, FSI // Slip condition is used. This enable a coarse mesh int n; n = Egroup[H][L][B].get_Sfront(); // The number of surface int count = 0; for (i=1; i<= n; i++) { if (Sgroup[i].get_type() == AirS) // FSI interface { count ++; outFile << "BOUNDARY-CON FLUID-STRUCTURE NAME=" << count << " GTYPE=SURFACES," << endl; outFile << " SLIPC=1.00000000000000 FSBOUNDA=" << count << " VTYPE=CONVENTIONAL," << endl; outFile << " VT=0.00000000000000 NCURVT=0 DX=0.00000000000000," << endl; outFile << " DY=0.00000000000000 DZ=0.00000000000000 X0=1.00000000000000," << endl; outFile << " Y0=0.00000000000000 Z0=0.00000000000000 ALL-EXT=NO" << endl; outFile << "@CLEAR" << endl; outFile << i << " 0" << endl; outFile << "@" << endl; outFile << "*" << endl; } } count ++; // Boundary condition, Wall // Apply for all the fluid face on the side //Defines a "wall" fluid boundary-condition. This specifies a geometry boundary across which //(i.e., normal to) no flow takes place. k = 0; i = 0; ok = 1; while ((ok !=0) & (k < H)) { k++; j = 0; i = 0; while ((ok !=0) & (j < L)) { j++; if ((Egroup[k][j][1].get_type() == AIR_VOID) || (Egroup[k][j][B].get_type() == AIR_VOID)) ok = 0;

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139 } while ((ok !=0) & (i < B)) { i++; if ((Egroup[k][1][i].get_type() == AIR_VOID) || (Egroup[k][L][i].get_type() == AIR_VOID)) ok = 0; } } if (ok == 0) // Need wall boundary { outFile << "BOUNDARY-CON WALL NAME="<< count <<" GTYPE=SURFACES SLIPC=1.00000000000000," << endl; outFile << " MOVING=NO VTYPE=CONVENTIONAL VT=0.00000000000000 NCURVT=0," << endl; outFile << " DX=1.00000000000000 DY=0.00000000000000 DZ=0.00000000000000," << endl; outFile << " X0=0.00000000000000 Y0=0.00000000000000 Z0=0.00000000000000," << endl; outFile << " ALL-EXT=NO" << endl; outFile "@CLEAR" endl; << << for (k=1; k<=H; k++) { for ( j=1; j<= L; j++) { if (Egroup[k][j][1].get_type() == AIR_VOID) { outFile << Egroup[k][j][1].get_Sleft() << " 0" << endl; } if (Egroup[k][j][B].get_type() == AIR_VOID) { outFile << Egroup[k][j][B].get_Sright() << " 0" << endl; } } for ( i=1; i<= B; i++) { if (Egroup[k][1][i].get_type() == AIR_VOID) { outFile << Egroup[k][1][i].get_Sfront() << " 0" << endl; } if (Egroup[k][L][i].get_type() == AIR_VOID) { outFile << Egroup[k][L][i].get_Sback() << " 0" << endl; } } } outFile << "@" << endl; } /* // Boundary condition at top count = 1; for (j = 1; j <= L; j++) {

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140 for (i = 1; i <= B; i++) { if (Egroup[H][j][i].get_type() == AIR_VOID) { int point_1 = SFP*H + j*RP + i; outFile << "CONSTRAINT NAME="<< count <<" SLAVETYP=SURFACE SLAVENAM="<< Egroup[H][j][i].get_Stop() << " SLAVEDOF=Z-VELOCITY," << endl; outFile << " MASTERTY=POINT SBODY=0 OPTION=0" << endl; outFile << "@CLEAR" << endl; outFile << point_1 <<" 'Z-VELOCITY' 1.00000000000000 0" << endl; outFile << "@" << endl; count++; } } } */ // Apply normal traction for all the fluid surface at the bottom // Defines a normal-traction load. Note that the command only defines a normal-traction load, // to apply it to the model you must use APPLY-LOAD. outFile << "LOAD NORMAL-TRACTION NAME=1 MAGNITUD=.001000000000000" << endl; outFile << "*" << endl; outFile << "APPLY-LOAD BODY=0" << endl; outFile << "@CLEAR" << endl; count = ; 0 for (i=1; i<= B; i++) { for (j=1; j<=L; j++) { if (Egroup[1][j][i].get_type() == AIR_VOID) { count++; outFile << count << " 'NORMAL-TRACTION' 1 'SURFACE' " << Egroup[1][j][i].get_Sbottom() << " 0 1 0.00000000000000 0," << endl; outFile << "0.00000000000000 0.00000000000000 0" << endl; } } } outFile << "@" << endl; outFile << "*" << endl; // Defines an element group consisting of three-dimensional fluid flow elements. // AUI command for Adina F-page 8-5 outFile << "EGROUP THREEDFLUID NAME=1 MATERIAL=1 RSINT=3 TINT=3 RESULTS=STRESSES," << endl; outFile << " DISSP=NO SOLID=NO UPWINDIN=DEFAULT" << endl; outFile << "*" << endl; // Generates elements on a set of geometry volumes. // Elements can be created within element groups of type THREEDFLUID. //See more at page 8-36 AUI command for Adina F

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141 outFile << "GVOLUME NODES=4 PATTERN=0 NCOINCID=BOUNDARIES NCFACE=123456 NCEDGE=," << endl; outFile << "'123456789ABC' NCVERTEX=12345678 NCTOLERA=1.00000000000000E-05," << endl; outFile << " SUBSTRUC=0 GROUP=1 MESHING=MAPPED PREFSHAP=AUTOMATIC," << endl; outFile << " DEGENERA=YES COLLAPSE=NO MIDNODES=CURVED METHOD=DELAUNAY" << endl; outFile << < #include

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142 #include #include #include #include const NMAX = 50;//maximum number of iterations int ncol; // number of columns int nrow; // number of rows int dcol; // position of the dam double ke[50][50]; // coefficient K in the est face double kw[50][50]; // coefficient K in the west face double kn[50][50]; // coefficient K in the north face double ks[50][50]; // coefficient K in the south face double kp[50][50]; // coefficient K in the center double phi[50][50]; // Flux array double Sc[50][50]; // Constant part of source double Sp[50][50]; // Constant part of source double conr = 1.0E-7; double conl = 1.0E-6; // Procedure Initialize // Zeros out the arrays ke, kw .... int Initialize() { int i, j; for (i; nrow; i++) =1i<= for (j=1; j<= ncol; j++) { ke[][j]= 0; i kw[i][j] = 0; kn[i][j] = 0; ks[][j]= 0; i kp[i][j] = 0; phi[i][j] = 0; Sc[][j]= 0; i Sp[i][j] = 0; } return 0; } int Coefficients() { // Procedure Coefficients // Calculates the coefficient for each nodes // phi=6 Dam phi=5 // irow = n ***********+++++*********** // + * + // + conl=1E-6 * conr=1E-7 + // + * +

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143 // + * + // + * + // + * + // + * + // + * + // irow = 1 +++++++++++++++++++++++++++ // jcol = 1 jcol = m // The coefficents of the element in the left is 1E-6 // The coefficents of the element in the right is 1E-6 // The coefficents of the element under the dam is calculate by the following formulas: // kw = conl // ke = conr // kn = (conl + conr)/2 // ks = (conl + conr)/2 int i,j; // Boundry condition for (i=1; i<=nrow; i++) { for (j=1; j<=ncol; j++) { // kw Calculate if (j>l)[i][] =r; dco kwj con else if (j==1) kw[i][j] = 0; else kw[i][j] = conl; // ke Calculate if (j< dcol) ke[i][j] = conl; else if (j==ncol) ke[i][j] = 0; else ke[i][j] = conr; // Calculate ks if (j==1) ks[i][j] = 0; else if (j==dcol) ks[i][j] = conl/2.0 + conr/2.0; else if (j>dcol) ks[i][j] = conr; else ks[i][j] = conl; // Calculate kn if (i==nrow) kn[i][j] = 0; else if (j==dcol) kn[i][j] = conl/2.0 + conr/2.0; else if (j>dcol) kn[i][j] = conr; else kn[i][j] = conl; // Calculate kp-point coefficient kp[i][j] = kw[i][j] + ke[i][j] + kn[i][j] + ks[i][j]; } } return 0; } int Boundary() // Calculates the constant part of source Sc and Coefficient part for source

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144 { int i,j; // Coefficients in the top for (j=1; j
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145 bool loop; maxit = 400; minit = 20; relax = 1.2; tol = 1E-5; iter = 0; cout << "\n Solving problem" <cormax) cormax = fabs(cor); phi[i][j] += relax*cor; } iter++; cout << "\n" << iter <<" "<< cormax<< " "<< tol < maxit) { cout << "Max iteration in Solver exceeded"< minit //co ait if ((cormax minit)) loop = 0; } return 0; } int PrintMatrix2D (double a[NMAX][NMAX], int n, int m, int width) { int i, j;

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146 for(i = 1; i<=n; i++) { cout << endl; for (j=1; j<=m; j++) cout << setw(width)<
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APPENDIX E AIR VOID DISTRIBUTION Fine Mix Air Void Distribution through the thickness of (GA-F1-6)0204060801004%6%8%10%12%14%16%18%AV, %Thickness, mm Figure D-5. Air void distribution for F1 147

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148 Air Void Distribution through the thickness of (GA-F2-16)0204060801004%6%8%10%12%14%16%18%AV, %Thickness, mm Figure D-6. Air void distribution for F2 Air Void Distribution through the thickness of (GA-F3-5)0204060801004%5%6%7%8%9%10%11%AV, %Thickness, mm Figure D-7. Air void distribution for F3

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149 Coarse Mix Air Void Distribution through the thickness of (GA-C1-6)0204060801004%6%8%10%12%14%16%AV, %Thickness, mm Figure D-8. Air void distribution for C1 Air Void Distribution through the thickness of (GA-C2-5)0204060801004%5%6%7%8%9%10%11%AV, %Thickness, mm Figure D-9. Air void distribution for C2

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150 Air Void Distribution through the thickness of (GA-C3-17)0204060801003%5%7%9%11%13%15%AV, %Thickness, mm Figure D-10. Air void distribution for C3

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LIST OF REFERENCES ADINA R&D, Inc. “ADINA User Interface Command Reference Manual, Volume I: ADINA Model Definition,” Report ARD 01-2, June 2001a ADINA R&D, Inc. “ADINA User Interface Command Reference Manual, Volume III: ADINA-F Model Definition,” Report ARD 01-2, June 2001b Al-Omari, A., Tashman. L., Masad, E., Cooley, A., and Harman, T. “Proposed Methodology for Predicting HMA Permeability,” Journal of the Association of the Asphalt Paving Technologists, Volume 71, 2002, pp 30-58 Ariza, P., and Birgisson, B. “Evaluation of Water Flow Through Pavement Systems,” Research Report, Minnesota Department of Transportation, St. Paul, MN, In press Birgisson, B., Roque, R., Page, G., “Evaluation of Water Damage Using Hot Mix Asphalt Fracture Mechanics,” Journal of the Association of Asphalt Paving Technologists, Vol. 73, 2003 pp 56-79 Black, D. K. and Lee, K. L., “Saturday Laboratory Samples by Backpressure,” Proceeding Paper 9484, Journal of the Soil Mechanics and Foundation Division, Proceedings of the American Society of Civil Engineers, Vol. 99, N0. SM 1, Jan. 1973, pp. 75-93 Chaney, R. C., Steven, E., and Sheth, N., “Suggested Test Method for Determination of Degree of Saturation of Soil Samples by B Value Measurement,” Geotechnical Testing Journal, GTJODJ, Vol. 2, No. 3, Sept. 1979, pp. 158-1652 Curray, J. R. ‘‘Analysis of Two Dimensional Orientation Data,’’ J. Geol., 64, 1956, pp 117. Denison, C., Carlson, W. D., and Ketcham, R. A. ‘‘Three Dimensional Quantitative Textural Analysis of Metamorphic Rocks Using High-Resolution Computed X-Ray Tomography: Part I. Methods and Techniques,’’ J. Metamorph. Geol., 15, D.C. 1997, pp 29. Findley, W.N., Lai, J., and Onaran, K. Creep and Relaxation of Nonlinear Viscoelastic Materials, Dover Publications Inc., Toronto (1989). “Imagetool: Image Analysis Program,” Dept. of Dental Diagnostic Science, Univ. of Texas Health Science Center, San Antonio, 1997 151

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152 Jailiardo, A. “Development of Specification Criteria to Mitigate Top-Down Cracking,” Master’s Thesis, University of Florida, Gainesville, FL, 2003. Linh P. “Dynamic Torsional Shear Test for Hot Mix Asphalt,” Master’s Thesis, University of Florida, Gainesville, FL. 2003 Masad, E., Muhunthan, B., Shashidhar, N., and Harman, T. “Internal Structure Characterization of Asphalt Concrete Using Image Analysis,” Journal Of Computing In Civil Engineering, Volume 13, Number 2, April 1999, Pages 88-95 Masad, E., Tashman, L., Niranjanan, S.,and Little, D. "Micromechanics Based Analysis of Stiffness Anisotropy in Asphalt Mixes," Journal of Materials in Civil Engineering, ASCE, Vol. 14, No. 5, 2002a, pp 65-87 Masad, E., V. K. Jandhyala, N. Dasgupta, N. Somedavan, N. Shashidhar. “Characterization of Air Void Distribution in Asphalt Mixes Using X-Ray CT,” Journal of Materials in Civil Engineering, Vol. 14, No. 2, April 1, 2002b, pp 122-129 Masad, E., Birgisson, B., Al-Omari, A., and Cooley A. “Analytical Derivation and Numerical Simulation of Permeability and Fluid Flow Patterns in Hot Mix Asphalt,” Journal of Materials in Civil Engineering, ASCE, in press McVay, M., Ahmad, Z., Bhanushali, G., Basterrachea, B., and Hashimi, S. “Three Dimensional Finite Element Program To Predict The Behavior of Soils and Substructure Components,” Final Report 99700-3583-119. FDOT. 2000 Monismith, C. L. ‘‘Analytically Based Asphalt Pavement Design and Rehabilitation,’’ Transportation Research Record 1354, Transportation Research Board, Washington, D.C., 1992, pp 5-26 Oda, M., and H. Nakayama. “Yield Function for Soil with Anisotropic Fabric,” Journal of Engineering Mechanics, ASCE, Vol. 15(1), 1989, pp 89-104. Pinto, Paulo. “Coupled Finite Element Formulations for Dynamic Soil-Structure Interaction,” Ph.D. Dissertation, University of Florida, Gainesville, 1998 Walsh J. B. and Brace, W. F. “The Effect of Pressure on Porosity and the Transport Properties of Rocks,” J. Geophys. Res., Vol. (89) 2001, pp. 9425-9431 Stroup-Gradiner, M. and Brown, E. R., Segregation in Hot mix asphalt pavements. Interim Report, Study No. 9-11, National Cooperative Highway Research Program. Transportation Research Board, Washington, D.C. 1998 Swan, D.J. “Evaluation of The Testing Procedure and Data Analysis for The Uniaxial Complex Modulus Test on Hot Mix Asphalt,” Masters Thesis, University of Florida, Gainesville, FL. 2002

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153 Sousa, J.M.B. and Monismith, C.L.. “Dynamic Response of Paving Materials,” Transportation Research Record, Vol. 1136, 1987, pp 57-68 Tashman, L., Masad, E., Peterson, B.,and Saleh, H. "Internal Structure Analysis of Asphalt Mixes to Improve the Simulation of Superpave Gyratory Compaction to Field Conditions," Journal of the Association of Asphalt Paving Technologists, Vol. 70. 2001, pp 88-95 Zhang, Z, R. Roque, and B. Birgisson. “Evaluation of Laboratory-Measured Crack Growth Rate for Asphalt Misxtures,” Transportation Research Record, Vol. 1767, 2001, pp 67-75 Wang, L.B., and J.S. Lai. “Quantify Specific Surface Area of Aggregates Using An Imaging Technique,” Transportation Research Board, Washington, D.C., Vol. 1782, 1998, pp 98 Wissa, A. E. Z., and Blouin, S. E. “Strength Behavior of Selected Asphalt-Aggregate System in Triaxial Compression,” 47th Annual meeting of the Highway Research Board, Washington, D.C. 1968, pp 156-194 Witczak M. W., Kaloush K. El-Basyouny. Simple Performance Test for Superpave Mix Design, NCHRP Report 465, National Academy Press, Washington D.C. 2002 Yue, Z. Q., Bekking, W., and Morin, I. ‘‘Application of Digital Image Processing to Quantitative Study of Asphalt Concrete Microstructure,’’ Transportation Research Board, National Research Council, Washington, D.C., 1995, pp 53.

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BIOGRAPHICAL SKETCH Minh H. Le was born on September 12, 1977, in the district of Trieu Son, Thanh Hoa, Vietnam. After completing high school at Trieu Son I high school, he enrolled at Hanoi University of Civil Engineering. He received a Bachelor of Civil Engineering from the Hanoi University of Civil Engineering in June 1999. After his undergraduate studies, he worked for the Center of Technology and Foundation Engineering, Hanoi University of Civil Engineering. He began attending the University of Florida to pursue a Master of Engineering degree in August 2001. He plans to work in the field of civil engineering after graduation. 154