MATERIAL CHARACTERIZATION IN SUPPORT OF IMPLEMENTATION … · material characterization in support...

MATERIAL CHARACTERIZATION IN SUPPORT OF IMPLEMENTATION OF THE

MECHANISTIC-EMPIRICAL PAVEMENT DESIGN GUIDE

A THESIS SUBMITTED TO THE GRADUATE DIVISION OF THE

UNIVERSITY OF HAWAIʻI AT MĀNOA IN PARTIAL FULFILLMENT

OF THE REQUIREMENTS FOR THE DEGREE OF

MASTER OF SCIENCE

IN

CIVIL ENGINEERING

AUGUST 2012

By

Jayanth Kumar Rayapeddi Kumar

Thesis Committee:

Adrian Ricardo Archilla, Chairperson

Phillip Ooi

Lin Shen

ii

ABSTRACT

Use of the Mechanistic-Empirical Pavement Design Guide (MEPDG) and its associated

software requires a large number of inputs about traffic loading, environmental conditions, and

material characteristics. Except for very important projects, for which many of the material

characteristics may be determined directly from laboratory tests, practical implementation of the

MEPDG for routine pavement design projects requires the development of a database containing

properties for the most commonly used materials within the state.

In the analysis of flexible pavements in the MEPDG, the dynamic modulus (|E*|) and

resilient modulus (Mr) are the primary input parameters used to characterize the elastic response

of Hot Mix Asphalt (HMA) mixtures and base course (unbound granular) materials, respectively.

In addition to the elastic properties of the materials used in the mechanistic analysis of the

pavement structures, the MEPDG relies on deterioration model parameters to relate empirically

the mechanistic pavement responses (strains) on different points of the pavement structure to

distresses such as rutting (permanent deformation), cracking, and roughness.

This study focuses on measuring in the laboratory the resilient moduli of two types of

base course materials and the elastic and permanent deformation characteristics of three types of

HMA materials.

The continuous demand of aggregates for maintenance and rehabilitation (M&R) of

existing pavements and to a lesser degree for construction of new ones as well as the increasing

need to reduce the disposal of construction waste is putting pressure on agencies to find ways to

increase the recycling of materials such as Recycled Asphalt Pavement (RAP) into the pavement

structure. Experiences around the world indicate that Foamed Asphalt (FA) base course

mixtures, which are a typically produced by stabilizing Reclaimed Asphalt Pavement (RAP) with

iii

foamed (expanded) asphalt, have shown improved performance relative to unbound base

materials. Hence in this study, one of the base materials considered is a Foamed Asphalt (FA)

base mixture. The other base material studied is a virgin aggregate base course material. The

resilient moduli of both materials were studied at different density levels. The results of the study

showed that the Mr of FA mixtures is in general between 2.5 and 5 times (corresponding to

lowest and highest levels of bulk stress respectively) higher than the Mr of virgin aggregates

(Type B) at 98% and 100% of maximum dry density, whereas at 102% of maximum dry

density, the Mr of FA mixtures is in general between 2.8 and 1.8 times of maximum dry density

(corresponding to lowest and highest levels of bulk stress respectively) higher than the Mr of

virgin aggregates. Further, it was observed that the Mr of FA mixtures increased with increases

in bulk stress, and the Mr decreased with increases in octahedral shear stress. On the other hand,

the Mr of the virgin base course material increase mostly with the octahedral shear stress and to a

much lesser degree also increased with the bulk stress.

For HMA, this study focuses on comparing the test results of dynamic modulus and

permanent deformation tests performed in the laboratory on unmodified, polymer modified

asphalt (PMA) mixes (modified with Elvaloy RET©) , and mixes reinforced with FORTA fibers.

The laboratory experiments included testing two replicates of HMA specimens of each type at

three target air voids. The results of the tests show that the mixes prepared using the PMA binder

show relatively better resistance to rutting at high temperatures and low frequencies. For the

mixes prepared using fibers, it was observed that the rate of failure in a permanent deformation

test remains relatively constant irrespective of the of air voids of the specimen. The effect of the

fibers is to hold the coated particles together under these unfavorable conditions, thus providing

a level of safety for mixes compacted with high air voids.

iv

ACKNOWLEDGMENTS

I would like to express my deepest gratitude to Dr. Adrian Ricardo Archilla, my research

advisor, for giving me the opportunity to pursue a graduate program at the University of Hawaii

at Manoa (UH). Further, thanks to Dr. Archilla for providing invaluable technical and moral

support during the course of my graduate study at UH.

Sincere thanks to Dr. Phillip Ooi and Dr. Lin Shen for agreeing to participate in my

graduate thesis committee and providing helpful comments.

Heartfelt thanks to Dr. Jonathan E.D Richmond for helping me to get into the University

of Hawaii at Manoa for graduate studies.

Thanks to Hawaii Department of Transportation for providing all the assistance for my

graduate studies at UH.

Special thanks to Jaw W. Glover Ltd, Grace Pacific Corporation, FORTA Corporation,

Alakona Corporation, and Hawaiian Cement – Halawa Quarry for providing the materials used

in this study.

Special thanks to Richard S. Gribbin of Jas W. Glover Ltd for helping me in more than

one ways for timely completion of my thesis.

Sincere thanks to Mitchell Pinkerton of the University of Hawaii at Manoa for all his help

during the course of my laboratory studies.

Thanks to Dr. Arudi Rajagopal, Dr. Luis G. Dias Vasquez, Letizia de Lannoy, Chao

Huang, Diego Munar, Angel Panezo, Steve Havel, and Amir Mohammadipour for helping me

during the course of my graduate stay at UH.

Thanks to my parents, brother, wife, and a number of friends for being there at all times.

v

TABLE OF CONTENTS

ABSTRACT ................................................................................................................................... ii

ACKNOWLEDGMENTS ........................................................................................................... iv

TABLE OF CONTENTS ............................................................................................................. v

LIST OF FIGURES ................................................................................................................... viii

LIST OF TABLES ..................................................................................................................... xiv

CHAPTER 1 INTRODUCTION AND OBJECTIVES ............................................................ 1

1.1 Introduction ........................................................................................................................... 1

1.2 Problem Statement ................................................................................................................ 4

1.3 Research Objectives .............................................................................................................. 6

CHAPTER 2 Literature Review ................................................................................................. 8

2.1 Introduction ........................................................................................................................... 8

2.2 Foamed Asphalt Mixture ...................................................................................................... 8

2.2.1 Asphalt Foaming Technology ........................................................................................ 9

2.2.2 Factors Affecting Foamed Asphalt Mixtures ............................................................... 10

2.2.2.1 Asphalt Properties ................................................................................................. 11

2.2.2.2 Aggregate Properties ............................................................................................. 13

2.2.2.3 Mixing Moisture Content ...................................................................................... 15

2.2.2.4 Curing Conditions ................................................................................................. 17

2.2.2.5 Mixing Temperature ............................................................................................. 18

2.3 Polymer Modification ......................................................................................................... 18

2.4 Polymer Modifier Used in this Study ................................................................................. 19

2.5 Fiber Reinforced Asphalt Concrete Mixtures ..................................................................... 19

2.6 Fibers Used in this Study .................................................................................................... 20

2.7 MEPDG Material Input Parameters .................................................................................... 21

2.8 Dynamic Modulus |E*| ........................................................................................................ 23

2.9 Resilient Modulus ............................................................................................................... 29

2.9.1 Factors Affecting Mr of New Unbound Granular Materials ....................................... 30

2.9.1.1 Aggregate Physical State ...................................................................................... 31

2.9.1.2 State of Stress ........................................................................................................ 33

vi

2.9.1.3 Structure/Type of Material .................................................................................... 35

2.9.2 Resilient Modulus Models for New Unbound Granular Material ............................... 36

2.9.3 Recent Studies on Mr of Foamed Asphalt Mixes ........................................................ 42

2.9.3.1 Discussion ............................................................................................................. 46

2.10 Repeated Load Axial Test (RALT) .................................................................................. 47

CHAPTER 3 Laboratory Experiments ................................................................................... 52

3.1 Background ......................................................................................................................... 52

3.2 Material Sources ................................................................................................................. 52

3.2.1 Base Course Materials ................................................................................................. 52

3.2.2 Hot Mix Asphalt .......................................................................................................... 53

3.3 Base Course Material Information ...................................................................................... 54

3.3.1 Gradation Analysis of Aggregates ............................................................................... 54

3.3.2 Maximum Dry Density and Optimum Moisture Content ............................................ 57

3.4 Test Specimen Preparation for Resilient Modulus Testing ................................................ 58

3.5 Resilient Modulus Testing .................................................................................................. 60

3.6 Hot Mix Asphalt Mixtures Information .............................................................................. 72

3.6.1 Gradation Analysis of Aggregates ............................................................................... 73

3.6.2 Asphalt Binder ............................................................................................................. 74

3.6.3 Preparation of modified binder .................................................................................... 74

3.6.4 Mixing and Compaction Temperatures of Unmodified and Modified Binder ............ 76

3.6.5 Fibers Used in the Study .............................................................................................. 78

3.7 Test Specimen Preparation for Dynamic Modulus and Permanent Deformation Testing . 80

3.8 Dynamic Modulus Testing .................................................................................................. 90

3.9 Repeated Load Axial Test (RALT) .................................................................................. 107

CHAPTER 4 Summary and Conclusions ............................................................................... 115

4.1 Resilient Modulus of Base Course Materials ................................................................... 115

4.2 Dynamic Modulus and Permanent Deformation of HMA Mixtures ................................ 116

4.2.1 Dynamic Modulus of HMA Mixtures ........................................................................ 116

4.2.2 Flow Number Test on HMA Mixtures ....................................................................... 117

4.3 Contributions of the Study ................................................................................................ 118

References .................................................................................................................................. 119

vii

Appendix A: Base Course Material ChartS ........................................................................... 130

Appendix B: Dynamic Modulus Charts .................................................................................. 138

Appendix C: Permanent Deformation Charts ....................................................................... 164

viii

LIST OF FIGURES

Figure 1-1 Current Pavement Design Practices in the United States (FHWA, 2007) .................... 2

Figure 1-2 Schematic Representation of MEPDG Process (Coree et al., 2005) ............................. 3

Figure 2-1 Asphalt Foaming Technology (Construction Equipment, 2005) .................................. 9

Figure 2-2 Relationship Between Foaming Properties ................................................................. 12

Figure 2-3 Desired Aggregate Grading Zones for Foamed Asphalt ............................................. 15

(Redrawn after Akeroyd & Hicks, 1988) ...................................................................................... 15

Figure 2-4 Elvaloy RET Pellets (Photo courtesy: Archilla (2008)) ............................................ 19

Figure 2-5 FORTA fibers (HMA blend) ....................................................................................... 20

Figure 2-6 Asphalt Material Properties – Asphalt Mix Input Values for Level 1 Analysis ......... 22

Figure 2-7 Asphalt Material Properties – Asphalt Mix Input Values for Level 1 Analysis ......... 23

Figure 2-8 Typical Stress-Strain curve obtained during dynamic modulus testing of viscoelastic

materials ................................................................................................................................. 24

Figure 2-9 Dynamic modulus test data (Archilla, 2008) .............................................................. 26

Figure 2-10 Master Curve constructed at a reference temperature of 69.8 °F (Archilla, 2008) ... 27

Figure 2-11 Typical stress-strain behavior of unbound granular materials subjected to traffic-type

loading ................................................................................................................................... 29

Figure 2-12 Stresses Applied in a Triaxial Test............................................................................ 34

Figure 2-13 Range of resilient moduli values (Long and Ventura 2004). .................................... 43

Figure 2-14 HMA permanent deformation behavior .................................................................... 48

Figure 3-1 Gradation analysis of RAP compared with HDOT requirements for ¾” maximum

nominal untreated base .......................................................................................................... 55

Figure 3-2 Gradation analysis of virgin aggregates from Hawaiian Cement – Halawa Quarry

compared with HDOT requirements for 1-1/2” maximum nominal untreated base ............. 56

Figure 3-3 RAP Gradation and desired aggregate grading for FA ............................................... 57

Figure 3-4 Moisture-density relationship of base course materials .............................................. 58

Figure 3-5 Compacted specimen connected to vacuum supply line ............................................. 59

Figure 3-6 Specimen ready for testing .......................................................................................... 60

Figure 3-7 Test specimen inside the testing chamber along with sample LVDTs ....................... 61

Figure 3-8 Example of dynamic modulus data collection ............................................................ 62

ix

Figure 3-9 Effect of bulk stress on resilient modulus for virgin aggregates compacted at three

different densities ................................................................................................................... 63

Figure 3-10 Effect of bulk stress on resilient modulus of FA mixtures compacted at three

different densities ................................................................................................................... 63

Figure 3-11 Mr vs. deviator stress for specimens compacted at different densities using virgin

aggregates .............................................................................................................................. 65


aggregates at low (3 psi), intermediate (5 psi), and high (20 psi) confining stress level ...... 66

Figure 3-13 Mr vs. deviator stress for specimens compacted at different densities using FA

mixtures ................................................................................................................................. 67

Figure 3-14 Mr vs. Bulk Stress for Coral sample ......................................................................... 71

Figure 3-15 Mr vs. deviator stress at different confinement stresses for Coral material .............. 72

Figure 3-16 Gradation information for laboratory produced HMA mixtures ............................... 73

Figure 3-17 Gradation information for plant produced HMA mixtures ....................................... 74

Figure 3-18 Evaloy®RET Pebbles (left) and mixing Elvaloy to Unmodified PG64-16 binder

(right) ..................................................................................................................................... 75

Figure 3-19 Fibers in its manufactured condition ......................................................................... 79

Figure 3-20 The setup used to fluff the fibers............................................................................... 79

Figure 3-21 Fibers after fluffing ................................................................................................... 79

Figure 3-22 Steps involved in preparation of test specimens ....................................................... 80

Figure 3-23 Mechanical mixer used for mixing HMA samples ................................................... 82

Figure 3-24 HMA mixture produced using virgin asphalt in the plant ......................................... 83

Figure 3-25 HMA mixture prepared in the laboratory using virgin asphalt ................................. 83

Figure 3-26 HMA mixture prepared in the laboratory using polymer modified asphalt .............. 83

Figure 3-27 HMA mixture prepared in the laboratory using virgin asphalt and FORTA-FI fibers

............................................................................................................................................... 84

Figure 3-28 A specimen extruded after compaction in a Rainhart SGC ...................................... 85

Figure 3-29 Specimen being cored (left) and sawed (right) to required size ................................ 86

Figure 3-30 Cored and sawed specimen ....................................................................................... 86

Figure 3-31 Gauge point fixing jig ............................................................................................... 87

Figure 3-32 Test specimen ready for dynamic modulus testing ................................................... 88

x

Figure 3-33 IPC Global Simple Performance Tester .................................................................... 90

Figure 3-34 Specimen assembly inside the testing chamber ........................................................ 91

Figure 3-35 An example of repeated attempts to glue the gauge point(s) for a specimen ........... 92

Figure 3-36 Example of dynamic modulus data collection .......................................................... 93

Figure 3-37 Master curves for VPPM at three different air voids ................................................ 95

Figure 3-38 Master curves for VLPM at three different air voids ................................................ 97

Figure 3-39 Master curves for PMALPM at three different air voids .......................................... 98

Figure 3-40 Master curves of all specimens for VPPM at three different air voids ..................... 99

Figure 3-41 Master curves for FRACLPM at three different air voids ...................................... 100

Figure 3-42 Comparison of master curves for mixes prepared using polymer modified binder and

compacted at different air voids .......................................................................................... 101

Figure 3-43 Master curve comparison among the three types of laboratory prepared mixtures

compacted at target Va=3% ................................................................................................. 102


compacted at target Va=5% ................................................................................................. 103


compacted at target target Va=7% ....................................................................................... 104

Figure 3-46 Comparison of dynamic modulus values for three different types of HMA mixtures

at 40 °F at 10 Hz .................................................................................................................. 105

Figure 3-47 Unconfined Dynamic Modulus Master Curves for FORTA Evergreen Control, 1

lb/Ton and 2 lb/Ton Mixtures (Kaloush et al, 2008) ........................................................... 106

Figure 3-48 Specimen assembly inside the testing chamber ...................................................... 107

Figure 3-49 Deformed specimen at the end of flow number test (Specimen ID shown in this

figure is VPPM5) ................................................................................................................. 108

Figure 3-50 Screenshot of the Permanent Deformation test output ............................................ 109

Figure 3-51 Example of the accumulation of permanent strain and fitting of three parameter

model proposed by Archilla et al (2007) for Specimen ID VLPM6 ................................... 110

Figure 3-52 Example of fitting the power model for Specimen ID VLPM6 .............................. 111

Figure 3-53 Comparison of flow number vs. air voids for different types of laboratory produced

HMA mixtures ..................................................................................................................... 113

xi

Figure A-1 Mr vs. deviator stress at different confinement stresses for specimens compacted

using virgin aggregates at 98% of dmax (Specimen ID: HCH1) .......................................... 131


using virgin aggregates at 98% of dmax (Specimen ID: HCH2) .......................................... 131


using virgin aggregates at 100% of dmax (Specimen ID: HCH1) ........................................ 132








using FA mixtures at 98% of dmax (Specimen ID: FA1) ..................................................... 134


using FA mixtures at 98% of dmax (Specimen ID: FA2) ..................................................... 134


using FA mixtures at 100% of dmax (Specimen ID: FA1) ................................................... 135







Figure A-13 Mr vs. deviator stress at different confining stresses for specimens compacted using

virgin aggregates at different density levels ........................................................................ 137

Figure B-1 Master Curve for Specimen ID: VPPM1.................................................................. 139




xii



Figure B-7 Master Curve for Specimen ID: VLPM1 ................................................................. 145



Figure B-10 Master Curve for Specimen ID: VLPM3B ............................................................. 148

Figure B-11 Master Curve for Specimen ID: VLPM4 ............................................................... 149



Figure B-14 Master Curve for Specimen ID: FRACLPM1 ........................................................ 152






Figure B-20 Master Curve for Specimen ID: PMALPM1.......................................................... 158






Figure C-1 Fitting the power model for Specimen ID VPPM1 .................................................. 165






Figure C-7 Fitting the power model for Specimen ID VLPM1 .................................................. 168

Figure C-8 Fitting the power model for Specimen ID VLPM2 .................................................. 168

Figure C-9 Fitting the power model for Specimen ID VLPM3B ............................................... 169

Figure C-10 Fitting the power model for Specimen ID VLPM4 ................................................ 169

xiii



Figure C-13 Fitting the power model for Specimen ID PMALPM1 .......................................... 171






Figure C-19 Fitting the power model for Specimen ID FRACLPM1 ........................................ 174






xiv

LIST OF TABLES

Table 3-1 Maximum Dry Density and Optimum Moisture Content values ................................. 58

Table 3-2 Mr coefficients calculated using the NCHRP 1-37A model ........................................ 69

Table 3-3 Mr coefficients calculated using the NCHRP 1-37A model ........................................ 72

Table 3-4 Mixing and compaction temperature range for asphalt binders ................................... 78

Table 3-5 Results of theoretical specific gravity .......................................................................... 81

Table 3-6 Characteristics of HMA specimens .............................................................................. 89

Table 3-7 Conditioning time for different testing temperature ..................................................... 91

Table 3-8 Data quality statistics requirements in dynamic modulus test...................................... 92

Table 3-9 Dynamic modulus master curve parameters and shift factors ...................................... 96

Table 3-10 Permanent deformation parameters and Flow Number ............................................ 112

1

CHAPTER 1

INTRODUCTION AND OBJECTIVES

1.1 Introduction

Pavement design is an effort to determine the number and thickness of layers, and

material composition within a pavement structure in order to cater to a given amount of traffic in

a cost-effective way. Several different design procedures are followed by different highway

agencies in the United States. These methods range from the simple empirical methods to the

complex mechanistic-empirical methods. Some of the examples of empirical methods include the

design method followed by the California Department of Transportation (Caltrans) and the 1993

AASHTO pavement design procedure. The Hawaii Department of Transportation (HDOT) uses

the Caltrans procedure to design pavements. The result of a survey conducted by Federal

Highway Administration (FHWA) (FHWA, 2007) is illustrated in Figure 1-1. As can be seen

from the figure, the 1993 AASHTO Guide for Design of Pavement Structures has been the

primary pavement design tool for most highway agencies, which is based on the empirical

equations derived from the AASHO road test performed in the late 1950s near Ottawa, Illinois.

The AASHO road test was limited to: a) one specific geographic location, b) moderate traffic

levels, and c) limited structural conditions and materials typically found in the region. According

to Lekarp, Isacsson, & Dawson (2000a), the empirical design procedures have limitations with

regard to adapting to the growing needs of the transportation system. This has led research

efforts to develop mechanistic design procedures, which analyze the response of materials under

different traffic and environmental conditions. Similar limitations could be attributed to other

empirical procedures such as the HDOT procedure of designing pavements.

2

Figure 1-1 Current Pavement Design Practices in the United States (FHWA, 2007)

The Guide for Mechanistic-Empirical Design of New and Rehabilitated Pavement

Structures and its associated software1 developed through a comprehensive research effort by the

National Cooperative Highway Research Program initiative NCHRP Project 1-37A is a state-of-

the-art pavement design tool that has attempted to overcome the limitations of the empirical

pavement design procedures.

A schematic representation of the Mechanistic-Empirical Pavement Design Guide

(MEPDG) process for flexible pavements is illustrated in Figure 1-2.

1 Hereon referred to as Mechanistic-Empirical Pavement Design Guide (MEPDG)

12%

63%

13%

8% 4%

AASHTO 1972

AASHTO 1993

State Design Procedure

AASHTO/State Design Procedure

Other

3

Figure 1-2 Schematic Representation of MEPDG Process (Coree et al., 2005)

As can be seen in Figure 1-2, there are three major components in the MEPDG: (a) Input

Data, (b) Analysis, and (c) Output. The analysis part of the MEPDG represents the major change

in the way pavement design is performed compared to the HDOT and other empirical

procedures. The mechanistic part of the MEPDG refers to the application of principles of

engineering mechanics to determine pavement responses (stress, strain, and deflection) to wheel

loads and/or climatic effects and the empirical part uses transfer functions to convert the

pavement responses to predict pavement distresses.

An important feature of the MEPDG software is the hierarchical approach with regard to

traffic, material characteristics, and environmental inputs. Three levels of design – Level 1 to

Level 3 – are available for determining the input values.

Level 1 provides site and/or material specific inputs for the segment or project through

direct testing or measurements. This level of input provides more precise and accurate

information compared to the other two levels of design. Level 1 is used when there is a need for

designing pavements that require higher level of reliability. Level 2 input values are typically

determined using correlations with other relatively simpler testing procedures. Level 3 provides

4

the lowest level of accuracy. The input values for level 3 are usually default values from the

MEPDG.

The characterization of pavement construction materials is one of the most important

inputs in designing pavements using the MEPDG. As pointed by Yoder and Witczak (1975), for

any pavement design procedure to be completely rational, three elements must be fully

considered: (1) the theory used to predict the assumed failure or distress parameter, (2) the

evaluation of the materials properties applicable to the selected theory, and (3) the determination

of the relationship between the magnitude of the parameter in question to the performance level

desired. The MEPDG considers the aforementioned elements.

The pavement inputs for the MEPDG is extremely extensive compared to other pavement

design procedures. For an effective and efficient implementation of the MEPDG, it is necessary

to develop a database either through testing of materials or compile information of design inputs

of locally used materials. This research attempts to contribute to the development of database by

testing Hot Mix Asphalt materials and base course materials.

1.2 Problem Statement

First: Construction of new pavements or maintenance and rehabilitation (M&R) of in-service

pavements is an on-going process because pavements deteriorate with passage of time. This fact

leads to two concerns: a) growing demand for construction aggregates and b) increase in amount

of construction waste2. For instance, construction and maintaining a freeway pavement of one

lane-mile can use 7,000 to 12,000 tons of raw materials (The Bridge, 2009). With the production

of construction aggregates estimated to increase from 2.0 billion tons to 2.5 billion tons by 2020

(FHWA, 2004), there is concern about the availability of new aggregates. One alternative to

2 The definition of construction waste is deferred until Section 2.3.

5

address the aforesaid challenges is to recycle pavements and use the waste as a substitute

material in road construction. The process of pavement recycling has proved to be economically

beneficial and environmentally sustainable to building long-lasting roads (Kennedy, Tam, &

Solaimanian, 1998, Saeed, 2008). The reusable material that results from removing and/or

reprocessing asphalt pavements is known as Reclaimed Asphalt Pavement (RAP). Some of these

include its use a substitute for new aggregate in Hot Mix Asphalt (HMA), granular base

(stabilized and otherwise), and subbase. RAP contains asphalt and aggregates, which when

properly crushed and screened can be used in a number of paving applications. Although the

benefits of using RAP have resulted in virtually all states recycling the material (Wilburn &

Goonan, 1998), the percent of RAP in recycled mixtures is kept to relatively low values because

of the inability to accurately characterize binder properties (Al-Qadi, Elseifi, & Carpenter, 2007).

A number of studies have shown performance, economic, and environmental benefits of using

RAP in paving applications, and there is a general agreement that pavements constructed using

RAP have proven to perform well to be used in various applications in building asphalt

pavements (Al-Qadi et al., 2007). One type of material produced by stabilizing RAP is Foamed

Asphalt (FA) base course mixtures.

One of the primary input parameters for base course materials in the MEPDG is the

material’s resilient modulus. Several past research efforts have found that the resilient modulus

of FA mixtures is higher compared to virgin material from those studies (Long and Ventura,

2004, Huan et al., 2010). However, no studies have been performed on FA mixtures to evaluate

its stiffness at different compaction levels. Also, the resilient modulus of base course materials

being one of the input parameters in the pavement design will affect the performance of

pavements. Hence, determining the Mr of a particular type of material at different densities

6

would allow highway agencies to select the minimum level of field compaction required for that

type of material in a pavement design. As a result, a rationale for agreeable levels of pay factors

and penalties could be decided by knowing the achievable, target, and actual densities in the

field. The limited supply of FA mixture that was available was used to evaluate the material’s

resilient modulus property at three different densities. This study also included resilient modulus

testing of virgin aggregates compacted at three densities. This research aims to perform the

comparative analysis and estimate the model parameters which can further be used as inputs in

the MEPDG to compute pavement distress information.

Second: This study is also concerned with the characterization of three types of HMA materials.

The availability of different alternatives to enhance the performance of HMA mixtures has been

available for several decades. The use of modified binder (polymer modified, crumb rubber

modified, and so on) has proven to improve the rutting and fatigue cracking performance of the

HMA mixtures compared to unmodified mixture (Archilla, 2008, ARTS, 2010, Shih et al. Xiao

et al.). Similarly, the addition of fibers such as FORTA fibers to HMA mixture has shown

improved results vis-à-vis resistance to rutting and fatigue cracking (Kaloush et al., 2008). This

study aims to estimate the dynamic modulus parameters, and flow number and permanent

deformation parameters of HMA mixtures. The parameters can be used as input parameters in

the MEPDG to compute and compare pavement distresses.

1.3 Research Objectives

The main objectives of this study are to:

1. Estimate the dynamic modulus and permanent deformation parameters of three types of

laboratory produced and one type of plant produced HMA mixtures. The laboratory

7

produced mixtures include (a) mixes prepared using unmodified binder, (b) mixes

prepared using polymer modified binder, and (c) mixes prepared using unmodified binder

which are blended with fibers.

2. Estimate the resilient modulus parameters of two types of base course materials. The two

types of materials include: (a) virgin aggregates and (b) foamed asphalt (FA) mixtures.

8

CHAPTER 2

LITERATURE REVIEW

2.1 Introduction

This chapter begins with a review of different types of materials characterized in this

study. Section 2.2 discusses the history and technology of FA mixtures and foaming technology.

Next, a brief introduction to polymer modified asphalts and the types of modifier used in this

study are introduced in Sections 2.3 and 2.4. Further, the types of fibers and past research

experience about blending HMA mixtures with fibers is presented in Sections 2.5. Section 2.6

gives a brief introduction to the type of fibers used in this study. Later in Section 2.7 through

Section 2.9, material input parameters and testing protocols for HMA and base course materials

at Level 1 accuracy are briefly described. Finally, the characterization of HMA mixtures using

the permanent deformation test is introduced.

2.2 Foamed Asphalt Mixture

Foamed Asphalt mixture refers to a mixture of pavement construction aggregates and

foamed asphalt. A wide variety of aggregates can be used to produce FA mixtures. However,

Reclaimed Asphalt Pavement (RAP) is typically stabilized using foamed asphalt to produce FA

mixturs. The history and technology of asphalt foaming is explained in the following section.

Foamed asphalt mixtures used in base course layers of pavements have shown a lot of

promise for restoring existing pavements and producing a surface with less cost compared to

using new material (Kendall, Baker, Evans, & Ramanujam, 1999). The use of RAP may reduce

the cost of production of foamed asphalt mixtures, because, firstly, the need to quarry and

9

transport new aggregates is avoided, and secondly, RAP contains binder, thereby reducing the

amount of asphalt required to produce the mix (Muthen, 1998, Raffaelli, 2004).

Saeed, Hall, & Barker (2008) mention that poor performance of granular base materials

contribute to the reduced life and costly maintenance of pavements. Therefore, to achieve an

economical pavement design, the properties of granular materials need to be evaluated

thoroughly.

2.2.1 Asphalt Foaming Technology

Asphalt foaming technology is a process where cold water in a proportion of between 1

and 5% by the mass of asphalt binder is injected together with compressed air into hot asphalt

(140º – 170 ºC) in a specially designed expansion chamber to produce foamed asphalt, as shown

in Figure 2-1.

Figure 2-1 Asphalt Foaming Technology (Construction Equipment, 2005)

Air Water

Foamed

Bitumen

Hot

Bitumen

10

When the injected water comes in contact with hot asphalt, the water vaporizes resulting

in spontaneous foaming, which is trapped in thousands of tiny asphalt bubbles producing foamed

asphalt. The foamed asphalt binder is typically added to aggregates in a proportion of less than

3% by the mass of dry aggregates to form FA mixtures. The tiny asphalt bubbles that are formed

during the mixing process disperse throughout the aggregate by adhering to the finer particles to

form a mastic. Typically, a small quantity of filler (cement or hydrated lime) is added to assist in

dispersing the asphalt and improving the retained strength after exposure to moisture. The

quantity of filler material is usually restricted to 1.0% in order for the mixture to be classified

as asphalt stabilized (TG2, 2009). Chiu & Lewis (2002) suggested that the use of cement content

in excess of 2.0% by mass would result in a negative effect on the fatigue properties of the

stabilized layer.

The possibility of using foamed asphalt as a stabilizing agent was originally conceived by

Prof. Ladis Csanyi in 1957 of the Iowa State University. The process consisted of injecting steam

into hot asphalt. This process was, however, impractical for in situ foaming operations, because

of the need for steam producing equipment such as steam boilers. In 1968, Mobil Australia

acquired the patent rights for Prof. Csanyi’s idea, modified the original process by adding cold

water into hot asphalt in an expansion chamber to produce foam. This process was more practical

and economical to use (TG2 2009).

2.2.2 Factors Affecting Foamed Asphalt Mixtures

The performance of foamed asphalt mixtures are determined based on asphalt and

aggregate properties, mixing moisture conditions, mixing temperature, and curing conditions.

11

2.2.2.1 Asphalt Properties

The foamed asphalt binder is a result of a temporary change in the viscosity of binder by

addition of a small percentage of water along with compressed air to hot asphalt. The viscosity is

greatly reduced allowing an increase in the surface area per unit mass, which allows for a

uniform dispersion of the foamed binder onto the aggregates. The two primary properties that

influence asphalt foaming are: a) Expansion Ratio and b) Half-Life (Muthen, 1998, TG2, 2009,

Wirtgen, 2004).

Expansion Ratio (ER) is a measure of the viscosity of the foam, which determines its

dispersion potential in the mix. Mathematically, it is the ratio of maximum volume of the foam to

the final volume of the binder once the foam is dissipated. Half-Life 21 is a measure of the

stability of the foam, which provides an indication of the rate of its collapse (Muthen, 1998,

TG2, 2009, Wirtgen, 2004). It is the time (in seconds) for the foam to collapse to half of its

maximum volume. Figure 2-2 illustrates a typical relationship between the percentage of

foamant water added and expansion ratio and half-life. The following paragraphs explain the

factors that influence the asphalt foaming properties.

12

Figure 2-2 Relationship Between Foaming Properties

(Redrawn using data from Alakona, 2008)

Foamant Water: It can be seen from Figure 2-2 that increasing the percentage of water injected

into the foaming chamber increasing the expansion ratio. The increase in the ER is because of

the increase in the size of asphalt bubbles when water and air comes in contact with hot asphalt.

The increase in the size of bubbles reduces the film thickness, making it less stable, which results

in reduction in half-life. Adequate foam dispersion for effective stabilization is possible when the

amount of foamant water is selected considering an acceptable trade-off between maximum

expansion ratio and half-life (Muthen, 1998, TG2, 2009, Wirtgen, 2004).

Asphalt Content: Unlike in HMA mixtures, the process of determining optimum asphalt content

for FA mixtures is not straightforward. This is because the FA mixtures are prepared using a

known quantity of asphalt and water. According to Muthen ((1998), “in foamed-asphalt mixes

the optimum bitumen content often cannot be clearly determined as it can in the case of hot-mix

5

5.5

6

6.5

7

7.5

7

8

9

10

11

12

13

14

15

16

17

1 1.5 2 2.5 3 3.5

Hal

f-lif

e (

seco

nd

s)

Exp

ansi

on

Rat

io

% Water (Foamant Water)

Expansion Ratio

Half-life

13

asphalt. The range of binder contents (BC) that can be used is limited by the loss in stability of

the mix at the upper end of the range and by water susceptibility at the lower end. It appears that

one significant parameter is the ratio of binder content to fines content, i.e. the viscosity of the

binder-fines mortar plays a significant role in mix stability”.

Asphalt Grade: Lee (1981) mentions that there was no substantial difference between measured

properties of FA produced using different grades of asphalt. Sakr & Manke (1985) conclude that

viscosity or binder cohesion has relatively lesser effect compared to aggregate interlock in the

stability of foamed asphalt mixes.

Asphalt Temperature: The inverse relationship between temperature and viscosity logically leads

to reduced viscosity and therefore increase in the size of asphalt bubbles when water comes in

contact with hot asphalt. The temperature of asphalt should be above 160° C and less than 195°

C to achieve satisfactory foaming (Wirtgen, 2004, TG2, 2009).

2.2.2.2 Aggregate Properties

Typically, RAP is used as aggregates. However, a wide variety of new aggregates can

also be used to produce foamed asphalt mixtures (Muthen, 1998). Bowering & Martin (1976)

indicate that certain aggregates may require treatment with lime and gradation adjustments for

satisfactory performance of the mix. The type and size of aggregates play an important role in

the performance of FA. The importance of RAP gradation on the performance of FA has been

well documented by several researchers over the last few decades. Csanyi (1957), Bowering et

al. (1984), and Lee (1981), suggested a minimum of 3 percent passing No. 200 sieve (referred to

14

as fines in this research) as a basic requirement for good performance of foamed asphalt mixes.

The Wirgten Cold Recycling manual (2004), Ruckel, Acott, & Bowering (1982), and Kendall et

al. (1999) suggested a minimum of 5 percent passing No. 200 sieve in order for foamed asphalt

to mix with and coat the RAP fines to achieve a good end product. Lee (1981), Kendall et al.

(1999), and Ramanujam & Jones (2000) suggested an upper limit of 35-40, 15, and 20 percent

respectively. The Technical Guideline on Bituminous Stabilised Materials published by the

Asphalt Academy (TG, 2009) mentions the Optimum Mixing Moisture Content (OMMC) varies

with the gradation and, in particular, the size of fraction smaller than 0.075 mm. Therefore, the

guide suggests an ideal range of 6 to 10% of mass of material passing No. 200 sieve to achieve

desirable density. Akeroyd & Hicks (1988) suggested three aggregate grading zones (as shown in

Figure 2-3) to select the size of aggregates to enable them to perform satisfactorily in the mix.

Zone A points to the desired grading zone, while Zone B and Zone C refers to the gradation

being either too fine or too coarse respectively, and therefore need to be stabilized by either

adding coarse or fine material correspondingly.

15

Figure 2-3 Desired Aggregate Grading Zones for Foamed Asphalt

(Redrawn after Akeroyd & Hicks, 1988)

2.2.2.3 Mixing Moisture Content

The mixing and compacting moisture content is an important consideration in the design

criteria of foamed asphalt mixes. During the mixing stage, moisture helps to break up

agglomeration of aggregates so that they are uniformly distributed throughout the mix. Unlike

new aggregates, where the Optimum Moisture Content (OMC) is determined using a standard

test procedure, the functional nature of moisture in FA during mixing and compaction stages has

resulted in a different rationale about the procedure to determine the optimum moisture content.

Brennen, Tia, Altschaeffl, & Wood (1983) after studying the consequences of varying

moisture before mixing with the foamed binder concluded that too little moisture reduces the

dispersion of the foam, and therefore workability and compaction of the mix, while too much

moisture increases the curing time and reduces the strength and density of the mix. Chiu (2002)

0.0

75

0.1

50

0.3

00

0.6

00

1.1

8

2.3

6

4.7

5

6.7

9.5

13.2

19.5

26.5

32.5 53

0

10

20

30

40

50

60

70

80

90

100

Sieve Size (mm)

Perc

en

t P

assin

g

Zone A

Zone C

Zone B

16

used the AASHTO T180 procedure to determine the optimum moisture content. However, 90%

of OMC was used during the mixing process. Ruckel et al. (1982) and Wirtgen (2004) also

recommend that OMC be derived from the moisture-density relationship using AASHTO T180

procedure. Lee (1981) and Bissada (1987) found that the optimum mixing moisture content

occurred between 65% and 85% of the modified AASHTO T180 procedure.

Because of the functional influence of moisture on foamed asphalt mixes, some

researchers have proposed to specifically address the issue of determining optimum moisture

content during mixing and compaction separately.

Castedo-Franco, Beaudoin, Wood, & Altschaeffl (1982) considered the idea of optimum

fluid content, which is the sum of asphalt content and moisture content, approximately equal to

the aggregate’s OMC as determined by ASTM D 698 to provide the best compaction.

A relationship considering percentage of fines and OMC was used by Sakr & Manke

(1985), as shown in the following equation.

BCPFOMCMMC 39.04.048.192.8 (3.20)

Where:

MMC = Compaction Moisture Content

OMC = Optimum Moisture Content as determined by AASHTO T180 specification

PC = Percentage of fines of the aggregate passing the #200 sieve

BC = Bitumen (Asphalt) Content, percentage by dry weight of aggregates

It was found that there was no significant difference in mix properties using the OMC

(which is 10% to 20% higher than MMC) and compacting moisture content (Sakr & Manke,

17

1985). Therefore, to prevent the waiting time for the mix to reach compaction moisture content,

it was suggested MMC be used for both mixing and compaction.

2.2.2.4 Curing Conditions

The effect of curing or removing moisture from FA has been extensively reported over

the years by several researchers. The Wirtgen (2004) manual suggests two separate curing

durations based on the size of specimen. For 100 mm diameter specimens, it is suggested to cure

samples by placing them on a smooth flat tray in a forced-draft oven for 72 hours at 40° C. In

case of 150 mm diameter specimens, the manual recommends each specimen be cured separately

in a sealed plastic bag at 40° C for 48 hours. Bowering (1970) reported the moisture content in

FA samples to reach between 0 and 4 percent by curing the samples in an oven at 60° C for 3

days. It 1976 Bowering & Martin concluded that there was little or no effect on the performance

of FA at temperatures ranging from 23° C to 60° C. However, Muthen (1998) reports the

concerns of binder softening and aging at 60° C, which might change the dispersion

characteristics during curing. Lee (1981), using laboratory results, also concluded that curing had

no impact on the strength gained by foamed asphalt mixes. Contradicting this argument, Ruckel

et al. (1982) reported there was effect of curing on FA’s strength. Three different curing times: a)

1 day in mold b) 1 day in mould + 1 day at 40° C, and c) 1 day in mould + 3 days at 40° C to

simulate short, intermediate, and long term field curing effects respectively were also suggested.

From the past research it can be observed that there is no consensus about both the procedure of

curing FA samples in the laboratory. Jenkins (2000) supports this view stating “it is difficult to

ascertain the type and level of laboratory curing required to simulate field curing for a given

material in a specific environment”.

18

2.2.2.5 Mixing Temperature

The temperature of aggregates influences the determination of foamant water from the

Expansion Ratio/Half-Life chart (TG2, 2009). Bowering & Martin (1976) found the optimum

mixing temperature of aggregates for FA lies between 13° C to 23° C, depending on the

aggregate type, and temperatures below this resulted in poor quality of mixes.

2.3 Polymer Modification

The modification of unmodified binder to enhance its properties has been in practice for

over 5 decades (Asphalt Institute, 2007). In a survey result summarized in the Asphalt Institute

(2007), it has been noted that the reason for using Polymer Modified Asphalt (PMA) was to

increase the mixture’s resistance to rutting. The use of polymer modified asphalt in producing

HMA mixtures has been reported to reduce pavement cracking caused by thermal stresses and

decrease the rate of accumulation of permanent deformation (Dwyer and Betts, 2011, Bouldin

and Collins, 1992; Lu and Isacsson, 1999). A comprehensive study by Archilla (2008)

comparing the dynamic modulus and permanent deformation of HMA mixtures prepared using

unmodified and polymer modified binder has shown that the mixtures prepared using polymer

modified binder performed better compared to the unmodified mixes. The results from Archilla

(2008) show that the potential benefits of using polymer in modifying unmodified asphalt are

that it stiffens the binder at high temperatures without affecting the stiffness of asphalt at low

temperatures. This property enhancement is particularly beneficial because the resulting

modified binder is resistant to permanent deformation at high temperatures.

19

2.4 Polymer Modifier Used in this Study

The polymer modifier used in this study is Elvaloy® RET, which is obtained in the form

of pellets as illustrated in Figure 2-4. Elvaloy® RET is produced by DuPont (DuPont 2008) and

is a reactive elastomeric terpolymer (hence the RET in the name). It is claimed to be effective

when used with a wide range of asphalts, at proportion levels as low as 1−2% by weight of

asphalt. In this study, the unmodified asphalt binder is modified using 1% by weight of asphalt.

Figure 2-4 Elvaloy RET Pellets (Photo courtesy: Archilla (2008))

2.5 Fiber Reinforced Asphalt Concrete Mixtures

Several studies have shown that blending fibers with HMA mixtures have improved the

performance of control mixtures against rutting and fatigue cracking (Bueno et al, 2003, Lee et

al, 2005, Kaloush, 2008). The study performed by Kaloush et al. (2008) is of interest because the

same fibers are used in this study. Kaloush et al. (2008) studied the effect of FORTA fibers

(1lb/ton and 2lb/ton by weight of mix) on the performance of HMA mixtures and compared the

test results with HMA mixtures prepared using unmodified binder. Results from their study have

shown a significant increase in the flow number compared to control mixes, and a higher fatigue

20

life compared to control mixes. It was found that FORTA fibers at 1lb/ton showed the best

performance with regard to accumulation of permanent strain in flow number test and higher

moduli values at high temperatures in dynamic modulus test. Specifically, the FN for 1lb/ton mix

was 115 times higher compared to the control mix.

2.6 Fibers Used in this Study

FORTA fibers have been used in HMA mixtures to improve the performance of the blend

against rutting and fatigue cracking. The fibers comprise of polypropylene and aramid fibers in

different proportions depending on the type of blend. The HMA blend of FORTA fibers are used

in this study. Figure 2-5 shows the fibers in its manufactured state.

Figure 2-5 FORTA fibers (HMA blend)

21

2.7 MEPDG Material Input Parameters

The material input parameters for HMA material include the time-temperature dependent

dynamic modulus (|E*|) and Poisson’s ratio (). The general input parameters include layer

thickness which is used to predict pavement responses. The screenshot of the MEPDG software

for HMA material at Level 1 accuracy is shown in Figure 2-6. Further explanation about

dynamic modulus is presented in Section 2.8.

In case of base course materials, the material input parameters required to compute

pavement response are resilient modulus (Mr) and Poisson’s ratio (. Both these parameters are

used for quantifying stress dependent stiffness of base course materials under moving loads. The

screenshot of the MEPDG software for HMA material at Level 1 is shown in Figure 2-7. Further

explanation about resilient modulus is presented in Section 2.8.

22

Figure 2-6 Asphalt Material Properties – Asphalt Mix Input Values for Level 1 Analysis

23

Figure 2-7 Asphalt Material Properties – Asphalt Mix Input Values for Level 1 Analysis

2.8 Dynamic Modulus |E*|

Dynamic modulus is a property necessary to accurately predict the in-situ pavement

responses to varying speeds and temperatures throughout the pavement’s cross-section. The

primary stiffness property of HMA materials used in the Guide for Mechanistic-Empirical

Design of New and Rehabilitated Pavement Structures is the dynamic modulus.

The effects of temperature and frequency under continuous sinusoidal loading for linear

viscoelastic materials such as HMA mixtures is defined by its dynamic modulus (|E*|).

24

According to NCHRP Report 547, dynamic modulus is defined as “the ratio of the amplitude of

the sinusoidal stress (at any given time, t, and angular load frequency, ω), σ = σ0 sin(ωt), and the

amplitude of the sinusoidal strain ε = ε0 sin(ωt −φ), at the same time and frequency, that results

in a steady-state response”. A graphical illustration of the stress and strain versus time in a

dynamic modulus test is presented in Figure 2-8.

(2.1)

Where σ = stress, = strain, Φ = phase angle, degrees, σo = peak (maximum) stress, = peak

(maximum) strain, t = time, seconds

Figure 2-8 Typical Stress-Strain curve obtained during dynamic modulus testing of viscoelastic

materials

Mathematically, the dynamic modulus is defined as the norm value of complex modulus.

It can be expressed as:

(2.2)

σo sin(ωt)

εo sin(ωt −φ)

φ/ω

εo σo

25

The phase angle (ϕ) is used to describe the viscous properties of asphalt materials. In

Equation 2.1, the value of ϕ = 0 for purely elastic material and ϕ = 90° for purely viscous

material. HMA material exhibits more of elastic behavior at low temperatures and high

frequencies, and more of viscous behavior at high temperatures and low frequencies. In general,

the dynamic modulus of HMA is a function of temperature, rate of loading, age, and mixture

characteristics such as asphalt binder stiffness, aggregate gradation, asphalt binder content, and

air voids.

The dynamic modulus values at different temperatures and frequencies are required as

input parameters in the MEPDG design process. To determine the |E*| values at different

temperatures and frequencies, the test is performed using either the AASHTO TP62 or AASHTO

TP79 procedure. The difference between the two test procedures is that the AASHTO TP62

procedure was to test HMA specimens for dynamic modulus. On the other hand, the AASHTO

TP79 procedure describes test methods for measuring the dynamic modulus and flow number of

HMA mixes. The test consists of subjecting a cylindrical HMA specimen to a uniaxially applied

sinusoidal stress pattern while measuring the deformation. The test can be performed with or

without the effect of confining pressure. Although the test using AASHTO TP62 procedure

provides the dynamic modulus values at different temperatures and frequencies, the |E*| values

required for a pavement design at temperatures and frequencies other than the tested values need

to be determined. Therefore, a system to interpolate these values is required for predicting

dynamic modulus at any combination of temperature and loading. The interpolation is achieved

using the time-temperature superposition principle, which allows horizontal shifting of test

points at a given temperature and frequency onto a “Master Curve” constructed at a reference

26

temperature. In the MEPDG, the reference temperature used is 70 °F. Figure 2-9 and Figure 2-10

illustrate the use of time-temperature superposition principle to construct a Master Curve.

Figure 2-9 Dynamic modulus test data (Archilla, 2008)

10,000

100,000

1,000,000

10,000,000

0.00001 0.0001 0.001 0.01 0.1 1 10 100 1000 10000 100000

Time of loading (s)

|E*|

(p

si)

129.2F

113.0F

100.4F

69.8F

39.9F

27

Figure 2-10 Master Curve constructed at a reference temperature of 69.8 °F (Archilla, 2008)

Figure 2-9 illustrates the results from a dynamic modulus test on an HMA specimen for

temperatures ranging from 40 ºF (4.4ºC) to 104ºF (40ºC) and time of loading ranging from 0.04

seconds to 10 seconds. The data presented in the figure indicate the influence of temperature and

frequency on the stiffness of the mix, which was explained earlier. The Master Curve developed

using the time-temperature superposition principle is illustrated in Figure 2-10. The master curve

is useful because the dynamic modulus values at any combination of temperature and frequency

can be predicted with it. The amount of shifting the original test data onto the Master Curve and

its sign are temperature dependent. The shift factor is formally defined as:

(2.3)

Where

10,000

100,000

1,000,000

10,000,000

0.00001 0.0001 0.001 0.01 0.1 1 10 100 1000 10000 100000

Time of loading (s)

|E*|

(p

si)

129.2F

113.0F

100.4F

69.8F

39.9F

Master Curve

28

t = time of loading at a given temperature of interest,

tr = time of loading at the reference temperature (i.e., after shifting),

f = frequency of loading at a given temperature of interest (1/t), and

fr = frequency of loading at the reference temperature (1/tr).

By taking the logarithm of equation (2.3), the following equation is obtained:

(2.4)

Once all the data points at different frequencies are shifted to a reference temperature, the

following equation used in the MEPDG is used to construct the Master Curve.

(2.5)

Where , , , and are the model parameters

According to the MEPDG CHRP 1-37A, 2004), the parameters and depend on the

aggregate gradation, asphalt binder content, and air voids. The parameters and , which control

the shape of the master curve, depend on the characteristics of asphalt binder and the magnitude

of and

One of the equations that have been used to model the shift factor as a function of

temperature is:

(2.6)

Where A, B, C are model parameters and Ti is the temperature.

29

While Equation (2.5) describes the time dependency of the modulus at the reference

temperature, the shift factors describe the temperature dependency of the modulus.

2.9 Resilient Modulus

The deformation behavior of base course materials under traffic-type loading is

characterized by recoverable (resilient) strain and permanent (plastic) strain , which is

illustrated in Figure 2-11. According to Huang (1993), if a small load compared to the strength of

the material is applied a number of times, the recoverable deformation is nearly completely

recoverable and the material can be considered elastic, and the modulus based on the recoverable

strain under repeated loads is called the resilient modulus.

Figure 2-11 Typical stress-strain behavior of unbound granular materials subjected to traffic-type

loading

Resilient modulus is a measure of the stiffness of a material. In other words, it is the

elastic modulus (E) of a material for rapidly applied loads like those experienced by pavements.

Axial Strain (in./in.)

Dev

iato

r S

tres

s (σ

d =

σ1 –

σ3)

Total Strain (εt)

Resilient Strain (εr)

Plastic

Strain

(εp)

εt = εr + εp

30

Typically, the Mr of a material is used to characterize base, subbase, and subgrade materials for

the purpose of pavement design and evaluation. The resilient modulus of a material provides a

basic relationship between stress and deformation of pavement materials for the structural

analysis of layered pavements. Mathematically, it is calculated using the Equation 2.7.

r

drM

(2.7)

Where:

Mr = Resilient Modulus of the material

d = 31 = Deviator Stress

r = Resilient (recoverable) Strain

1 = Axial Stress

3 = Confining Stress

2.9.1 Factors Affecting Mr of New Unbound Granular Materials

Several research efforts to characterize resilient modulus of granular materials show a

nonlinear and time-dependent elastoplastic response under repeated loads, simulating the actual

traffic. According to Li and Selig (1994), the resilient modulus behavior is affected by three

factors. These factors are: soil3 physical state, state of stress, and structure/type of material. In

case of visco-elastic materials such as foamed asphalt mixes, in addition to the state of stress, Mr

is influenced by loading rate and temperature (Muthen, 1998).

3 To be consistent in the terminology used in this research, ‘soil’ is hereafter referred to as ‘aggregate’.

31

The models developed to predict resilient modulus should include all the significant

factors for higher reliability. The following paragraphs give a background to the factors affecting

resilient modulus of unbound granular material used in pavement construction. Because of its

relevance to this research, particular emphasis is given to the physical state and state of stress of

UGMs.

2.9.1.1 Aggregate Physical State

The physical state of aggregates is related to four factors: moisture content )(w , dry

density )( dry , degree of saturation S , and temperature.

Moisture Content and Degree of Saturation: Moisture content has two separate effects on the

material (NCHRP 1-37A, 2004): a) decrease in effective stress and therefore stiffness because of

pore-water pressure and b) destruction of cementation between particles. It has been reported by

(Lekarp, Isacsson, & Dawson, 2000b) that higher moisture content lowers the stiffness of

unbound granular material. Several field and laboratory studies performed to address the issue of

moisture changes on resilient modulus have led to conclusion that moisture content or degree of

saturation (a parameter defined by moisture content) affects the resilient modulus of unbound

granular materials (Hicks & Monosmith, 1971, Heydinger, Xie, Randolph, & Gupta, 1996).

The relationship between the first three physical state parameters is shown in Equation

2.8 and Equation 2.9.

1dry

wsG

wS

(2.8)

32

e

wGS s

(2.9)

Where:

S = degree of saturation (%)

Gs = Specific gravity of the aggregate

w = moisture content (%)

w = unit weight of water

dry = dry unit weight

e = void ratio

Density: Density is a result of volume change. Therefore, void ratio may be used as an

alternative for dry density (NCHRP 1-37A, 2004). This argument was further supported by

Archilla et al (2007), who reported better correlation between Mr and void ratio as opposed to

density. It is known that increasing density results in improving the stiffness of unbound granular

material under static loading. However, the influence of density on stiffness has been less

thoroughly researched and hence remains rather ambiguous (Lekarp et al, 2000b).

Temperature: The effect of temperature becomes important in predicting rM of frozen materials.

For thawed materials, it has no significant influence (NCHRP 1-37A, 2004). Unlike new

aggregates, foamed asphalt mixes being visco-elastic are influenced by temperature. The

performance properties of FA were superior compared to hot-mix asphalt mixes at temperatures

higher than 30º C (Muthen, 1998). Nataatmadja (2002) concluded a 30-44% decrease in stiffness

when the temperature increased from 10º C to 40º C. The temperature sensitivity of resilient

33

modulus between foamed asphalt and hot-mix asphalt mixes was studied by Saleh (2006). It was

found from the study, which was conducted at 10º C, 15º C, and 25º C, there was higher decrease

in Mr of HMA at 25C, while foamed asphalt mixes maintained high resilient modulus value at

that temperature. However, the indirect tensile test procedure was used to determine the Mr

values. In a laboratory concluded study, Fu & Harvey (2007) investigated effect of temperature

on foamed asphalt mixes. It was reported that the bulk stress dominated the effects of deviator

stress (or octahedral stress), and is largely independent of temperature. The study also observed

interaction between deviator stress and temperature. It was concluded that resilient modulus of

FA depends on temperature. Kim, Lee, & Heitzman (2008) concluded from the dynamic

modulus test results performed on RAP mixed with foamed asphalt between 1 and 3% at 4.4º C

that coarser RAP materials with small amount of residual asphalt exhibited smaller dynamic

values. However, it was found that finer RAP materials with higher amounts of harder binder

amount at 37.8º C exhibited higher modulus values.

2.9.1.2 State of Stress

The importance of state of stress has been reported since the 1960s. It has been agreed

without doubt that stress level has the most significant impact on the resilient modulus of

unbound granular materials (Lekarp et al., 2000b). The degree of influence that Bulk Stress

and Octahedral Stress oct have on the resilient modulus has been historically reported by

several researchers (Monismith, Seed, Mitry, & Chan, 1967, Uzan, 1985, Lekarp et al., 2000b).

Figure 2-12 illustrates the stresses applied on a specimen in a triaxial test. As shown in the

Figure, 1 is the major principal stress, 2 and 3 are intermediate and minor principal stresses

34

respectively, and is the Shear Stress. The Bulk Stress (Equation 2.10) and Octahedral Stress

(Equation 2.11) are calculated using major and minor principal stresses.

Bulk Stress = 321 (2.10)

Octahedral Stress oct = 2

32

2

31

2

21 )()()(3

1 (2.11)

Figure 2-12 Stresses Applied in a Triaxial Test

(Redrawn after NCHRP, 1997)

The increase in confining pressure and sum of principal stresses results in increase in the

resilient modulus of the material. Particularly, the effect of confining stress has been found to

have more influence compared to deviator or shear stress on the material stiffness (Lekarp et al.,

2000b).

3321 3 d

Total Axial Stress, 1

(Major Principal Stress)

31 d

(Deviator Stress)

3

32

3 = Confining Pressure

(Minor Principal Stress)

Shear Stress = = 0

35

2.9.1.3 Structure/Type of Material

The structure/type of material is related to four factors that have a bearing on the stiffness

of unbound granular material. The four factors are: compaction method, gradation, particle

shape, and nature of bonds between particles and their sensitivity to moisture.

Compaction Method: The resilient modulus is directly related to the compaction effort, which

means increase in compaction increases stiffness. The increase in stiffness varies with different

materials and the moisture content at which the samples are compacted (Nazarian, Pezo, &

Picornell, 1996, Pezo, Claros, Hudson, & Stokoe II, 1992).

Gradation: The stiffness of material, to some extent, is reported to be influenced by the

gradation of aggregates. Hicks & Monismith (1971) observed some reduction in resilient

modulus with increase in fines. However, Muthen (1998) states increase in resilient modulus

with increase in fines in foamed asphalt mixtures. Saleh (2006), using results from a laboratory

study, concluded that coarse gradations resulted in higher modulus compared to finer gradations.

Particle Shape: Several researchers have reported that crushed material having angular to

subangular shaped particles result in higher resilient modulus compared to uncrushed aggregates

(Hicks & Monismith, 1971, Barksdale & Itani, 1989, Heydinger et al., 1996).

As the properties of materials continuously keep changing due to the effects of chemical

forces, physical forces, climatic variations, and onset of fracture or deformation (NCHRP 1-37A,

2004), a good understanding of the deformational behavior of pavement construction materials

36

under varying traffic and climatic conditions is a prerequisite in mechanistic approach to design

pavements.

2.9.2 Resilient Modulus Models for New Unbound Granular Material

As explained in the previous section, there are several factors that affect the resilient

modulus of unbound granular materials. Of all the factors, the effect of stress is recognized as the

most important factor. As a result, constitutive models including the effects of state of stress

have been proposed by many researchers over the years. The Mr models computed based on state

of stress can be basically divided into three categories.

The first category is expressing the resilient modulus as a function of minor principal

stress or sum of principal stresses. Dunlap (1963) proposed a model in which confining stress

)( 3 was used as the independent variable. Seed, Mitry, Monismith, & Chan, (1967) formulated

a model (commonly known as the K-θ model) considering bulk stress (θ) as the stress attribute.

Equations 2.12 and 2.13 present the Dunlap (1963) and Seed et al. (1967) models respectively.

2

31

k

a

arp

pkM

(2.12)

2

1

k

a

arp

pkM

(2.13)

Where 21,kk = regression parameters, ap = atmospheric pressure, 3 = minor principal or

confining stress, = bulk stress

37

The second category of models uses only shear stress (expressed in terms of deviator

stress) to predict resilient modulus. Moosazadeh & Witczak (1981) and Pezo, Kim, Stokoe, &

Hudson, (1992) used deviator stress in a power model (Equation 2.14).

2

1

k

dr kM (2.14)

Where:

21,kk = regression parameters

d = deviator stress

The simplicity of K model has made it extremely useful in computing the stiffness of

granular materials. However, May and Witczak (1981) noted the field resilient modulus is not

only influenced by bulk stress as suggested in K model, but also by shear or deviator stress.

Since then, several researchers have proposed the third category of models known as the three-

parameter models, which includes the effects of both confining stress (expressed in terms of

bulk, minor principal, and octahedral stress ]3[ oct ) and shear stress (expressed in terms of

deviator stress or octahedral shear stress ][ oct ).

The general form of a three-parameter model is as shown in Equation 2.15 (Ooi, Archilla,

& Sandefur, 2004).

32 )]([)]([1

KK

ar sgcfpKM (2.15)

Where:

)(cf = function of confinement

38

)(sg = function of shear

321 ,, KKK = regression constants

The deficiency of not considering shear stress effect in the K model was addressed

by Uzan (1985), who modified it by including bulk stress and deviator stress. The effect of shear

stress is captured using deviator stress, which is directly related to maximum shear stress )( max

applied to the specimen (i.e., 2max d ).

Pezo (1993) found it was necessary to include deviator stress in the analysis. However,

the parameters of the K model were considered statistically not significant since deviator

stress is hidden in the prediction variable, bulk stress. This problem was overcome by replacing

bulk stress with confining stress in the Uzan (1985) model.

The Uzan (1985) and Pezo (1993) equations are shown in Equation 2.16 and 2.17

respectively.

32

1

K

a

d

K

a

arpp

pKM

(2.16)

32

31

K

a

d

K

a

arpp

pKM

(2.17)

Where:

ap = atmospheric pressure

d = 31 = deviator stress

3 = confining or minor principal stress

39

Witczak and Uzan (1988) modified Equation 2.17 by replacing the deviator stress with

octahedral shear stress )( oct (calculated using Equation 2.11) because it considers stresses in all

three orthogonal directions. The modified model is shown in Equation 2.18.

32

1

K

a

oct

K

a

arpp

pKM

(2.18)

There are two limitations in Uzan (1985), Witczak and Uzan (1988), and Pezo (1993)

models according to Ni, Hopkins, Sun, & Beckham (2002). Firstly, these three models predict

0rM when 03 K and rM when 03 K . Secondly, when there is no confinement

(i.e., 0321 ), rM is predicted to be zero. These two limitations were overcome by Ni

et al. (2002) using the following equation.

32

11 31

K

a

d

K

a

arpp

pKM

(2.19)

Ooi et al. (2004) found the following two models fit the data better compared to the

previous models.

32

111

K

a

d

K

a

arpp

pKM

(2.20)

32

111

K

a

oct

K

a

arpp

pKM

(2.21)

40

The Mechanistic-Empirical Pavement Design Guide (NCHRP 1-37A, 2004) recommends

the use of a new model (Equation 2.22) to predict the variations of rM with changes in degree of

saturation.

ropt

SSKEXP

aba

r MM opts )).((110

(2.22)

41

Where:

rM = Resilient Modulus at degree of saturation S (in decimal)

roptM = Resilient Modulus at maximum dry density and optimum moisture content

optS = Degree of saturation at maxd and OMC (in decimal)

sK = Material constant which can be obtained by regression

a = minimum of )(log roptr MM

b = maximum of )(log roptr MM

= location parameter – obtained as a function of a and b by imposing the condition of a zero

intercept; )ln( ab meaning the ratio of )(log roptr MM = 1 at optimum

optSS = Variation in degree of saturation (in decimal)

According to the MEPDG, roptM is calculated using the following equation.

32

11

K

a

oct

K

a

aroptpp

pkM

(2.23)

Where:

321 ,, KKk = regression constants

Assuming constants K2 and K3 are independent of water content or degree of saturation,

substituting roptM from Equation 2.23 in Equation 2.22 gives the following two formulations.

32

110 1

)).((1

K

a

oct

K

a

a

SSKEXP

aba

rpp

pkM opts

(2.24)

42

Or

32

11

K

a

oct

K

a

arpp

pKM

(2.25)

Where:

1

)).((1

1 10 kK opts SSKEXP

aba

Hence, K1 is a function of degree of saturation

2.9.3 Recent Studies on Mr of Foamed Asphalt Mixes

Numerous laboratory studies have been conducted to determine the resilient modulus of

FA. Some of the recent ones are presented below. When available, the Mr values from different

studies are presented. The importance of presenting the Mr values is described in section 2.9.7.1.

Resilient behavior of foamed asphalt mixtures was investigated using the triaxial set up

by Jenkins (2000). Foamed asphalt stabilized material was compacted by adding “sufficient

material” in the gyratory compactor to produce 100 mm high specimens after a certain number of

gyrations. Three such samples were place on top of one another without tack coat or any

adhesives to achieve a height of 300 mm required for triaxial testing. Compacted specimens were

cured using different procedures simulating an initial cure equivalent to early trafficking

conditions and medium-term cure for a moderate climate. Testing was performed at 25º C. It was

observed that the behavior of FA without cement resembled that of granular material, i.e. stress

dependent. The stress dependent behavior was found to be less evident or insignificant with a)

the addition of cement in the mix, b) foamed asphalt contents reaching 4% or higher, and c)

specimens tested without conditioning cycles.

43

Long and Ventura (2004) studied the stiffness behavior of FA produced using different

foamed asphalt contents on laboratory compacted specimens. Specimens (150 mm height and

300 mm diameter) were compacted in usually 3 lifts on the vibratory compaction table to

selected levels of density. Because it was difficult to achieve high densities, specimens were

sometimes compacted with 4 lifts with improved tamping on each lift. The compacted samples

were cured at ambient temperature for 28 days in the laboratory. Plastic strain triaxial tests (not

resilient modulus dynamic triaxial tests) were performed on specimens to determine the Mr. The

plastic strain dynamic triaxial test performed to determine the permanent deformation behavior

was used to calculate the Mr of the mixes. The range of resilient modulus values is presented in

Figure 2-13. It was observed from the figure that addition of foamed asphalt to the parent

material resulted in slight reduction in the Mr of the mixture compared to that of the parent

material. The addition of cement to the foamed asphalt stabilized mixture shows increase in Mr.

Figure 2-13 Range of resilient moduli values (Long and Ventura 2004).

Nataatmadja (2001) tested indirect tensile modulus of foamed asphalt specimens prepared

using varying asphalt contents and compacted with 50 and 75 blows per face using Marshall

Res

ilie

nt

Mod

ulu

s

44

compaction and gyratory compaction with different curing types and time. Each specimen was

tested under three different curing conditions: a) immediately after compaction, b) after oven

curing, and c) after soaking. The magnitude of modulus values for specimens cured at 60ºC for 3

days, 40ºC for 3 days, and at the end of 28 days at ambient (25ºC) temperature are in the order of

around 15,000 Mpa, 6,000 Mpa, and 8,000 Mpa respectively. The Mr value of the air-cured

specimen at the end of three days was around 4,000 Mpa, which is because the specimens are

more susceptible to moisture resulting in relatively low modulus as compared with the other two

methods. Test results for samples tested immediately after compaction have shown highest

resilient modulus corresponding to about 2.2% of asphalt content. The gyratory specimens,

however, seemed less sensitive to asphalt content variation. It was also seen that the modulus

values for specimens compacted with 75 blows were lower compared to the ones compacted

using 50 blows.

Chiu and Huang (2010) performed Mr testing of foamed asphalt stabilized mixes using

Indirect Tensile Stiffness Modulus (ITSM) test. The specimens were cured for 72 hours at 40 ºC.

Resilient modulus test results on the four mix types (in the order presented in the table) was

found to be 7027, 10489, 5943, and 8028 Mpa respectively.

45

Saleh (2004b) investigated the effect of asphalt source and grade and the type of fines on

the Mr of FA. Two groups of aggregates were used to produce the foamed asphalt mixtures. Fly

ash and cement was used to adjust the fine fraction of the aggregates in order for the gradation to

comply with the midpoint of the “ideal” zone, which is illustrated in Figure 3. The first group

was produced using aggregates passing 20mm, fly ash, and 2% cement, while the second group

was identical to the first, except that no cement was used. Both mixes were produced using OMC

and 3.5% asphalt content. All specimens were cured for 7 days at room temperature (19°C),

except that the second group of specimens was further oven-dried. Resilient modulus testing was

performed using the repeated load ITSM test at room temperature. It was found from the test

results that the modulus values were comparable with or in excess of that of asphalt concrete.

The investigation also revealed that addition of 2% cement had a significant effect on the value

of Mr.

Fu & Harvey (2007) investigated the potential interaction between temperature sensitivity

and stress states on foam asphalt mix stiffness using a cyclic triaxial test. No active filler was

used to produce the mixes, so the effects of foamed asphalt as the only stabilizer could be

captured. Different combinations of confining pressure and deviator stress at relatively small

temperature variation (between 10º C and 22º C) for different specimens were tested in a

chamber with no temperature control. It was found that Mr of FA was influenced by both stress

state and temperature. The study proposed a modified model (Equation 2.26), based on Witczak

and Uzan (1988), to predict resilient modulus of unbound granular material.

(2.26)

Tk

oct

oct

Tk

oct TMrTMr

54

00

0,,

46

Where:

),,( octr TM = Resilient modulus of foamed asphalt at temperature T stress state ),( oct

In a triaxial test, 3/)23(0 octp and 23 octd

)(0 TMr = ),,( 00 octr TM

00 , oct = Bulk stress and octahedral shear stress, respectively, for a reference stress state where

0p = 103.4 and 02pd

)(),( 54 TkTk = Material and temperature dependent constants

Huan et al. (2010) determined the resilient modulus on foamed asphalt mixtures using the

repeated load triaxial. The aggregate mixture consisted of 75% Crushed Rock Base and 25%

Crushed Limestone, treated with 1% hydrated lime. The specimens were compacted at 0%, 3%,

and 5% foamed asphalt content. The results of the test show the mixture with 0% asphalt content

had the highest Mr value, between 235 and 570 Mpa, compared to Mr of mixes stabilized with

3% and 5% foamed asphalt.

2.9.3.1 Discussion

A number of studies have evaluated the resilient modulus of foamed asphalt mixtures

using different variables. However, none of the studies have evaluated the influence of density

on the Mr of the FA material.

It can be seen that, depending on the variation in the factors affecting the Mr of FA, the

range of resilient modulus values are between 235 Mpa and about 15000 Mpa. The range of

values seems to be unrealistically large. The higher end of the stiffness values are closer to the

47

stiffness values that is generally exhibited by HMA mixtures. Further investigation to have more

confidence in the range of stiffness values for FA mixtures seems warranted.

Of all the past research efforts presented in this review, three studies (Saleh 2004,

Nataatmadja 2001, Chiu and Huang 2010) use ITSM test to measure resilient modulus. It is

known that, among several factors that influence the resilient modulus, the stress level has been

found to show the most significant impact on the resilient properties of granular materials

(Lekarp et al. 2000). Furthermore, the effect of bulk stress on weakly bonded materials such as

FA has been found to be fairly sensitive (Fu and Harvey 2007). Since ITSM test protocol neither

applies confinement to the specimen nor can control stress state of the specimen, the measured

stiffness and the actual stiffness of the material in all three studies may not be the identical.

2.10 Repeated Load Axial Test (RALT)

The result of repeated loading on the pavement, which accumulates over time, causes

permanent deformation or rutting. As defined by Mallick and El-Korchi (2009):

“the one-dimensional densification-consolidation rutting, resulting from a decrease

in air voids, occurs with volume change and is vertical deformation only (primary rutting),

whereas the two-dimensional rutting is caused by shear failure and is accompanied by both

vertical and lateral movement of material (secondary and tertiary rutting)”.

The test is performed by applying a repeated haversine pulse load of 0.1 seconds with a

rest period of 0.9 seconds. The typical permanent deformation behavior of HMA, when subjected

to repeated axial load in the laboratory and under specific environmental conditions, is

represented in Figure 2-14.

48

Figure 2-14 HMA permanent deformation behavior

There are typically three stages of permanent deformation. The first stage or the primary

stage is related to volumetric change, characterized by a high and decreasing rate of change. The

secondary stage is characterized by decrease in incremental permanent strain. The tertiary stage

is characterized by no volumetric change and an increasing rate of shear deformation until failure

occurs (Mallick and El-Korchi, 2009).

The beginning of the tertiary stage (or the point between the secondary and tertiary stage)

is designated as the flow number (FN). The FN is defined as the number of cycles at which the

tertiary permanent strain begins.

The permanent deformation damage model adopted by the MEPDG considers test data

only for the primary and secondary stages of permanent deformation with the first stage being

considered only an extrapolation of the secondary stage. The model is a modified version of the

widely used power law model and it is expressed in the form:

(2.27)

Primary Secondary Tertiary

Flow Point

Load Repetitions

Pe

rman

en

t Str

ain

49

where

p is the accumulated plastic strain at N repetitions of load,

r is the resilient strain of the

asphalt concrete (

r is a function of |E*| and the stress level), T is the pavement temperature, k1,

k2, and k3 are non linear regression coefficients, and

r1,r2, and r3, are field calibration factors.

A log-log chart relationship between the number of load repetitions and permanent strain

is typically expressed using the classical power model as shown in Equation 2.10.

(2.28)

Where, a and b are regression constants, which depends on the material and test conditions, and

N is the number of load repetitions.

Without the calibration factors, Equation 2.9 can be rewritten as:

(2.29)

For a given temperature, Equation 2.29 is simply equivalent to Equation 2.28.

Concerns regarding the limitation of Equation 2.29 were expressed by several researchers

including Mohammed et al. (2006) and Archilla (2008). The concern is that the mixture

properties such as binder viscosity, volume of effective binder content, and maximum air voids

are only taken into account by their effects on the elastic response of the material.

The approach used to estimate the FN by the IPC Global Universal Testing Software is

based on the moving average periods as proposed in Appendix D of NCHRP Report No. 513

(Bonaquist et al, 2003). This procedure is based on data smoothing techniques and provides an

acceptable FN. However, the estimated FN can affected by noise in the data and thus could be

different for the same specimen if different moving average periods are used for smoothing.

Since the estimated FN is used to determine the data to fit the power model (Equation 2.11), the

50

importance of estimating relatively accurate FN cannot be overemphasized. As mentioned

earlier, the FN values reported by the IPC Global Universal Testing Software may not be

accurate in some cases. Therefore, to provide a unifying criterion to calculate the FN of a mix,

Archilla et al. (2007) proposed the following model (Equation 2.30) in order to determine

mathematically the location of the inflection point (the Flow Number).

(2.30)

where εp is the permanent strain after N load repetitions, and and are model parameters

estimated by non-linear regression.

Once the model parameters and are estimated for a given specimen, the FN for that

specimen and permanent strain at FN can be estimated using the following expressions (Equation

2.31 and Equation 2.32).

(2.31)

(2.32)

As mentioned previously, the widely used power model (Equation 2.28) uses the

secondary and primary stage to estimate the model parameters. Further, the parameter estimates

can be affected by the number of initial observations that are included in the estimation.

Therefore, the dataset was trimmed between the initial observation (estimated using a technique

explained in the next paragraph) and FN. The FN is estimated using Equation 2.31. For

51

determining the number of observations to be included (or excluded) from the primary stage in

the estimation process, the test data for each specimen was trimmed down by eliminating the first

10% of the data in the series. A rationale and justification for this procedure is provided in (Diaz

et al. 2008). Once the data range is determined, fitting of Equation 2.28 and Equation 2.29 to

estimate k1 and k3, respectively, becomes simple. Figure 2-15 illustrates the data of the

permanent deformation test for one of the specimens after trimming together with power model.

Figure 2-15 Example of fitting of power model to trimmed data (Specimen ID: VLPM6)

100

1000

10000

100000

1000000

1 10 100 1000

Pe

rman

en

t St

rain

(

p)

Number of Load Repetitions

Test Points

Power (Model)

52

CHAPTER 3

LABORATORY EXPERIMENTS

3.1 Background

This chapter focuses on all the laboratory tests and testing details performed on base

course materials and Hot Mix Asphalt (HMA) for surface courses used in this study. The

laboratory tests performed on base course materials include: (a) Gradation analysis, (b) Modified

Proctor test, and (c) Resilient Modulus test. For the HMA, the laboratory tests performed are (a)

the Dynamic Modulus test and (b) the repeated load axial permanent deformation test. The

availability of materials and equipment limited to some extent the experimental plan for how and

what should be investigated, particularly for the foamed asphalt material. The following sections

provide information about the materials being characterized and the testing procedures used in

this study.

3.2 Material Sources

3.2.1 Base Course Materials

The experimental plan for base course materials included 2 different types of aggregates

namely, (a) virgin and (b) recycled. Virgin aggregates (Type B) were collected from the

Hawaiian Cement – Halawa Quarry in Aiea, Honolulu, Hawaii. A limited amount of recycled

material (foamed asphalt mixture) (~300 lbs) was delivered to the University of Hawaii at Manoa

pavement engineering laboratory by Alakona Corporation, Honolulu, Hawaii. The FA mixture

used in this study was produced using 100% RAP, stabilized using 2% of foamed (expanded)

asphalt, and 1% of Portland cement as filler.

53

3.2.2 Hot Mix Asphalt

In order to evaluate the potential effects of the use of polymer modified asphalt or fiber

reinforcement, testing was performed on sets of six specimens of an unmodified control mix, a

polymer modified mix, and a fiber reinforced mix. For each mix, two specimens were compacted

at three different target air voids. The mix design adopted was used recently by Grace Pacific

Corporation (GPC) in a paving project. GPC provided the samples of the same aggregates and

the same asphalt binder used in that project, which were used in the preparation of specimens in

the laboratory. In addition, testing was performed on six specimens (2 replicates at three target

air voids) of another unmodified mix produced at a local asphalt plant. The four types of

mixtures tested in this study along with their designation are:

1. Plant produced mixtures prepared using virgin asphalt binder: VPPM

2. Laboratory produced mixtures prepared using virgin asphalt binder: VLPM

3. Laboratory produced mixtures prepared using polymer modified asphalt binder:

PMALPM

4. Laboratory produced mixtures prepared using unmodified binder and fibers: FRACLPM

The aggregates used in the preparation of HMA samples in the laboratory were from Ameron

Kapaa quarry from the island of Oahu, Hawaii. In case of plant produced mixes, while the coarse

aggregates were from Ameron Kapaa quarry from the island of Oahu, Hawaii, the fine

aggregates were from Ameron Puunene quarry from the island of Maui, Hawaii. The unmodified

asphalt binder used in this study is from Asphalt Hawaii.

The required amount of mix to compact the VPPM specimens was collected from Jas W.

Glover Ltd (JWG), Honolulu, Hawaii. As indicated before, the remaining three types of

54

mixtures were laboratory mixed and laboratory compacted using material provided by Grace

Pacific Corporation (GPC), Honolulu, Hawaii.

The details of the base course and the HMA component materials and various tests

performed are provided in the following sections.

3.3 Base Course Material Information

In this section, the details of two tests performed on base course materials are provided.

First, the gradation analysis of aggregates is presented. Next, the Modified Proctor test

performed to determine the optimum moisture content and maximum dry density is explained.

3.3.1 Gradation Analysis of Aggregates

The gradation analysis of RAP was performed using the AASHTO T27 procedure.

According to AASHTO T27, the aggregate sample used for sieve analysis is dried at 110 °C.

However, the RAP sample used for gradation analysis in this study was oven dried at only 60 °C

for 48 hours prior to sieving. The reason for using a lower temperature to dry the RAP material is

because it contains asphalt binder, which could soften and help create lumps. The presence of

lumps could result in misrepresentation of actual gradation if the lumps are not broken during

sieving. For virgin aggregates, the gradation analysis provided by Hawaiian Cement Halawa –

Quarry was used. The gradation analysis results for RAP along with the minimum and maximum

requirements for 3/4” maximum nominal aggregate size allowed by the HDOT for untreated base

course materials is presented in Figure 3-1. Correspondingly, the gradation data collected from

Hawaiian Cement – Halawa (HCH) quarry along with the minimum and maximum requirements

for 1-1/2” maximum nominal aggregate size allowed by the HDOT for untreated base course

55

materials is presented in Figure 3-2. Figure 3-2 also includes the gradation analysis test data

performed using the AASHTO T11 procedure (typically known as wet sieve analysis) to

determine the actual percentage of virgin material passing the #200 sieve.

Figure 3-1 Gradation analysis of RAP compared with HDOT requirements for ¾” maximum

nominal untreated base

2"

1-1

/2"

1"

3/4

"

1/2

"

#4

#8

#16

#20

#40

#50

#100

#200

0

10

20

30

40

50

60

70

80

90

100

Perc

en

t P

assin

g

Sieve Designation

Reclaimed Asphalt Pavement

HDOT Minimum Specif ication

HDOT Maximum Specif ication

56

Figure 3-2 Gradation analysis of virgin aggregates from Hawaiian Cement – Halawa Quarry

compared with HDOT requirements for 1-1/2” maximum nominal untreated base

Based on the dry sieve analysis results, both virgin material and RAP gradation fall

within the HDOT requirements for untreated base course material. However, for the virgin

material, the wet sieve analysis results indicate that the material did not meet the HDOT

specifications.

The RAP material used in this study is also compared with the gradation requirements

recommended by Akeroyd and Hicks (1988), which is widely considered by several researchers

to provide the limits of desired gradation of RAP for producing foamed asphalt mixtures. Figure

3-3 illustrates the gradation analysis of RAP superimposed on the grading requirements

recommended by Akeroyd and Hicks. As can be seen from the figure, the material falls within

Zone A, which indicates the material is in the “ideal” grading limits for foamed asphalt

stabilization.

2"

1-1

/2"

1"

3/4

"

1/2

"

3/8

"48

16

30

50

100

200

0

10

20

30

40

50

60

70

80

90

100P

erc

en

t P

assin

g

Sieve Designation

Hawaiian Cement - Halawa Quarry

Hawaiian Cement - Halawa Quarry (wet sieve analysis)

HDOT Minimum Specif ication

HDOT Maximum Specif ication

57

Figure 3-3 RAP Gradation and desired aggregate grading for FA

(Redrawn after Akeroyd and Hicks, 1988)

3.3.2 Maximum Dry Density and Optimum Moisture Content

The maximum dry density (γdmax) and optimum moisture content (OMC) of both

materials were determined using the standard AASHTO T180 – Method D procedure. The OMC

and maximum dry density values are presented in Figure 3-4. Table 3-1 summarizes the test

results.

2"

1"

3/4

"

1/2

"

3/8

"

1/4

"

No.4

No.8

No.1

6

No.2

0

No.3

0

No.4

0

No.5

0

No.1

00

No.2

00

50.0

25

.0

19.0

12.5

9.5

6.3

4.7

50

2.3

60

1.1

80

0.8

50

0.6

00

0.4

25

0.3

00

0.1

50

0.0

75

0

10

20

30

40

50

60

70

80

90

100 P

erc

en

t P

assin

g

Sieve Size (mm)

RAP

Zone C

Zone A

Zone B

Zone A: Ideal Materials Zone B: Suitable Materials Zone C: Unsuitable Materials

58

Figure 3-4 Moisture-density relationship of base course materials

Table 3-1 Maximum Dry Density and Optimum Moisture Content values

Material Maximum Dry Density

(kg/m3)

Maximum Dry

Density (lb/f3)

Optimum Moisture

Content (%)

Hawaiian Cement – Halawa 2098 131.0 11.2


(RAP) 2032 126.9 8.1

3.4 Test Specimen Preparation for Resilient Modulus Testing

The resilient modulus of base course materials included compaction and testing the

materials at three different densities; 98%, 100%, and 102% of the maximum dry density. The

specimens were tested using the repeated load triaxial resilient modulus in accordance with

AASHTO T307; except that the number of load repetitions applied during each testing sequence

was reduced. The nominal maximum size of the virgin aggregates and RAP, which is used to

1,900

1,925

1,950

1,975

2,000

2,025

2,050

2,075

2,100

2,125

4.00 5.00 6.00 7.00 8.00 9.00 10.00 11.00 12.00 13.00 14.00 15.00 16.00 17.00 18.00

Dry

Den

sit

y (

kg

/m3)

Moisture Content (%)


Hawaiian Cement - Halawa Quarry

59

produce foamed asphalt mixtures, was found to be 50 mm and 19.0 mm respectively. Based on

AASHTO T307, the dimensions of the cylindrical test specimen for testing the virgin material

and FA was required to be compacted using a vibratory hammer in a split mold with a target

diameter of a 150 mm and a height between 305 mm and 318 mm.

Further, since there was no prior experience with in characterization of foamed asphalt

mixtures, and because of limited availability of FA, it was decided to reduce the size of the test

specimens so as to compact two replicates at three target densities. Accordingly, each specimen

using FA was compacted using a vibratory hammer in a split mold with a target diameter of 100

mm and a height of 203.2 mm. All the specimens compacted using FA mixtures were cured at 40

°C for 2 days.

All specimens were compacted in accordance with the AASHTO T307 procedure. Figure

3-5 shows a compacted specimen ready to be placed inside the cell prior to testing. The

compacted specimen inside the testing chamber placed in the loading frame is shown in Figure

3-6.

Figure 3-5 Compacted specimen connected to vacuum supply line

60

Figure 3-6 Specimen ready for testing

3.5 Resilient Modulus Testing

The resilient modulus testing was performed using the IPC Global Universal Testing

System (UTS) consisting of a hydraulic axial stress and a pneumatic confining stress loading

system, and a computer-controlled data acquisition system (CDAS) connected to a personal

computer. The machine is capable of applying repeated cycles of a haversine-shaped load pulse

of 0.1 seconds with a 0.9 seconds rest period. The deformation produced in the sample during

testing is captured by two external sample Linear Variable Differential Transducers (LVDTs)

and a system LVDT that is attached to the actuator that provides the system deformation. The

test specimen placed inside the testing chamber along with sample LVDTs is shown in Figure 3-

7.

61

Figure 3-7 Test specimen inside the testing chamber along with sample LVDTs

The resilient modulus test was performed in accordance with the AASHTO T307

procedure. A total of 15 combinations (from Table 2 of AASHTO T307) of deviator and

confining stresses were applied to the compacted sample. The two stages of the resilient

modulus test are: (a) Conditioning and (b) Measuring stress and strains to calculate Mr.

Conditioning: AASHTO T307 requires between 500 and 1000 repetitions of the conditioning

deviator stress. The reason for applying conditioning sequence is to eliminate the effects of the

initial loading versus reloading. Further, the conditioning also helps in reducing the effects of

any imperfect contact between the top platen, base plate, and the test specimen. However, in

order to prevent damage of the compacted specimens, all tests were performed by applying 50

cycles of deviator stress.

Measuring stress and strains to calculate Mr: Following the conditioning cycles, the resilient

modulus testing was performed by applying 50 cycles at each combination of confining stress

and deviator stress. Repeated cycles of haversine-shaped load pulse of 0.1s with a rest period of

Sample LVDT

62

0.9s were applied for both conditioning and testing. Mr was calculated as the average of the

ratios of the deviator stress to resilient strain for the last five cycles (46-50). Figure 3-8 shows a

screen shot during a typical testing procedure.

Figure 3-8 Example of dynamic modulus data collection

The repeated load triaxial resilient modulus tests were performed to evaluate the behavior

of virgin aggregates and FA mixtures when compacted at three different density levels. The

effect of bulk stress at each combination of the loading sequence on the resilient modulus of

virgin aggregates and FA specimens compacted at three different densities was observed. For

brevity, the results of one specimen from each of the three densities are presented in Figure 3-9

and Figure 3-10. The figures show resilient modulus of three specimens plotted against the bulk

63

stress (θ = 3σ3 + σd), where σ3 = the confining pressure and σd = the deviator stress on a log-log

graph. As can be seen from the figure, Mr increases with increase in density.

Figure 3-9 Effect of bulk stress on resilient modulus for virgin aggregates compacted at three

different densities

Figure 3-10 Effect of bulk stress on resilient modulus of FA mixtures compacted at three

different densities

1000

10000

100000

10 100 1000

Resi

lient

Mod

ulus

(ps

i)

Bulk Stress (psi)

Hawaiian Cement - Halawa Quarry @ 98% of Max. Dry Density

Hawaiian Cement - Halawa -Quarry @ 100% of Max. Dry Density

Hawaiian Cement - Halawa Quarry @ 102% of Max. Dry Density

10000

100000

10 100 1000

Resi

lient

Mod

ulus

(ps

i)

Bulk Stress (psi)

FA @ 98% of Max. Dry Density



64

When granular materials are subjected to triaxial state of stress, deviator stress is found to

have an important effect on the material’s resilient modulus. Witczak and Uzan (1988) found

that for granular materials tested in a triaxial stress state, the deviator stress has two contrary

effects on the stiffness of the material; first, increase in deviator stress will result in an increase

in bulk stress (θ=3σ3+σd), which leads to increase in the stiffness of the material and second, an

increase in deviator stress also increases the octahedral shear stress, which tends to decrease the

modulus. Further, Hicks and Monismith (1971) reported a “slight softening of the granular

material at low deviator stress levels and a slight stiffening behavior at higher levels of deviator

stress”.

Figures 3-11 shows the effect that deviator stress on the resilient modulus of the

specimens compacted at 98%, 100%, and 102% of the maximum dry density using virgin

aggregates. The figure is constructed using the average values of Mr and deviator stress from two

replicate specimens. For these specimens, regardless of the compaction level, it is clear that a

higher compaction level translates into a higher resilient modulus for the same stress level. The

effect of deviator stress on Mr for each specimen of virgin aggregates is presented individually in

Appendix A, where the same trends observed in Figure 3-11 arte observed.

65


aggregates

Figure 3-12 shows the same information as Figure 3-11 except that data for two of the

confining stresses are not included. This figure is presented to illustrate the effect that confining

stress has on the modulus of virgin aggregates, which is not obvious from Figure 3-11. As can be

observed in the figure, except at the low level of confining stress (3 psi) for specimens

compacted at 102% of maximum dry density, where the modulus shows a “slight” softening

behavior and subsequently increases marginally with increase in deviator stress, the Mr values

increase with confining stress for specimens compacted at all densities. A figure illustrating the

effect of all 5 different levels of confining stress on the modulus is presented in Appendix A.

5000

10000

15000

20000

25000

30000

35000

40000

45000

50000

0 5 10 15 20 25 30 35 40 45 50

Resil

ien

t M

od

ulu

s (

psi)

Deviator Stress (psi)

HCH @ 98%

HCH @ 100%

HCH @ 102%

66


aggregates at low (3 psi), intermediate (5 psi), and high (20 psi) confining stress level

Figure 3-13 shows the variation of resilient modulus with deviator stress at each

confining stress level for foamed asphalt mixture specimens compacted at percent of maximum

densities of 98, 100, and 102% respectively. This figure is again constructed using the average

values of Mr and deviator stress from two replicate specimens. For these specimens, an increase

in the modulus is observed with increase in deviator stress at all confining stress levels for

specimens compacted at 98% of maximum dry density. For the specimens compacted at 100% of

maximum dry density, a slight increase in modulus with deviator stress is observed. Furthermore,

for the specimens compacted at 102% of maximum dry density, it is observed that the resilient

modulus decreases with increase in deviator stress at all confining levels.

5000

10000

15000

20000

25000

30000

35000

40000

45000

50000

0 5 10 15 20 25 30 35 40 45 50

Resil

ien

t M

od

ulu

s (

psi)


HCH @ 98%; Confining stress = 3 psi









67

For the specimens compacted at 102% of maximum dry density, at low and intermediate

level of confining stress (σ3 = 3, 5, and 10 psi), the modulus values show a “slight” softening

behavior and subsequently increase marginally with increase in deviator stress. It is also

observed from the figure that at the higher confining stresses (10, 15 and 20 psi) the trend lines

with deviator stress tend to cross for the 100% and 102% compaction levels. The relative

position of the crossing point also appears to depend on the confining stress.

The relationship between deviator stress and Mr for all the specimens is individually

presented in Appendix A.

Figure 3-13 Mr vs. deviator stress for specimens compacted at different densities using FA

mixtures

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000

110000

120000

0 5 10 15 20 25 30 35 40 45 50

Resil

ien

t M

od

ulu

s (

psi)


FA @ 98%; Conf ining stress = 3 psi















68

To evaluate the effects of deviator stress and octahedral shear stress on Mr of virgin

aggregates and FA mixtures, the coefficients of the three-parameter model was determined using

the following equation.

32

11

K

a

oct

K

a

arPP

pKM

Where:

Pa = normalizing stress (atmospheric pressure = 14.68 psi)

σ1, σ2, and σ3 = principal stresses, and σ2 = σ3

σd = deviator stress = σ1 - σ3

θ = bulk stress = (σ1 + σ2 + σ3) = (3σ3 + σd)

τoct = octahedral shear stress =

K1, K2, and K3 are material specific regression constants.

Using the above equation, the coefficients of bulk stress and octahedral shear stress, and

its statistical significance in the model are determined. Table 3-2 presents the results.

69

Table 3-2 Mr coefficients calculated using the NCHRP 1-37A model

Specimen ID K1

p-value

(K1)

K2

p-value

(K2)

K3

p-value

(K3)

R2

FA1 @ 98 2887.61 2.03E-27 0.39 2.04E-09 -0.09 3.42E-01 0.97

FA2 @ 98 3022.21 1.25E-26 0.39 1.31E-08 -0.18 1.14E-01 0.96

Average FA @ 98 2954.91 0.39 -0.14

FA1 @100 3312.90 3.22E-26 0.47 3.67E-09 -0.29 2.79E-02 0.97

FA2 @ 100 3362.65 8.75E-27 0.39 1.01E-08 -0.26 3.14E-02 0.96

Average FA @ 100 3337.77 0.43 -0.27

FA1 @ 102 3662.43 1.14E-24 0.44 2.20E-07 -0.57 2.94E-03 0.91

FA2 @ 102 3645.89 5.15E-26 0.43 1.96E-08 -0.43 4.08E-03 0.95

Average FA @ 102 3654.16 0.44 -0.50

HCH1 @ 98 575.57 8.46E-22 0.09 1.34E-01 1.75 9.81E-07 0.95

HCH2 @ 98 595.97 2.54E-25 0.08 2.57E-02 1.54 2.91E-09 0.98

Average HCH @ 98 585.77 0.09 1.65

HCH1 @ 100 667.78 4.90E-23 0.16 5.03E-03 1.42 1.10E-06 0.96

HCH2 @ 100 694.08 6.36E-23 0.09 1.05E-01 1.62 3.46E-07 0.96

Average HCH @ 100 680.93 0.13 1.52

HCH1 @ 102 1051.43 1.70E-24 0.07 9.67E-02 1.34 2.53E-07 0.96

HCH2 @ 102 1091.80 6.28E-25 0.06 1.34E-01 1.33 1.18E-07 0.96

Average HCH @ 102 1071.6 0.07 1.34

From the summary of regression coefficients presented in Table 3-2, the following

observations are made:

70

1. The resilient modulus of virgin aggregates and FA mixtures show an increasing trend

with increase in bulk stress at increasing levels of compaction.

2. For virgin aggregates, a higher compaction level translates into a higher resilient modulus

for the same deviator stress. However, for FA mixture specimens, an increase in the

modulus is observed with increase in deviator stress at all confining stress levels for

specimens compacted at 98% of maximum dry density. For the specimens compacted at

100% of maximum dry density, a slight increase in modulus with deviator stress is

observed. Furthermore, for the specimens compacted at 102% of maximum dry density, it

is observed that the resilient modulus decreases with increase in deviator stress at all

confining levels.

3. The coefficient K2 in NCHRP 1-37A equation, which is the exponent for the bulk stress

term, is positive. This indicates increase in bulk stress increases the stiffness of virgin

aggregates and FA mixture.

4. The coefficient K3 in NCHRP 1-37A equation, which is the exponent for the shear stress

term, is negative for FA mixture, suggesting the stiffness of FA mixture decreases with

increase in octahedral shear stress. This behavior is analogous to the observations made

by Witczak and Uzan (1988) as explained earlier. Further, it can be seen from the p-

values of coefficient K3 that the octahedral shear stress is not statistically significant for

specimens compacted at 98% of maximum dry density.

5. The sign of the coefficient K3 in NCHRP 1-37A equation is positive for specimens

compacted using virgin aggregates, which means an increase in octahedral shear stress

increases the resilient modulus of the material. This observation is contrary to the widely

held belief that, for unbound materials, the coefficient K3 should be negative (NCHRP 1-

71

37A 2004, FHWA, 2002, George, 2004, Hossain, 2008). The sign of coefficient K3 has

been reported to be positive by several researchers including Heydinger et al. (1996) and

Bennert and Maher (2005). Studies performed by Song (2009) in the same laboratory at

the University of Hawaii at Manoa has also reported positive coefficient values for the

octahedral shear stress term in the NCHRP 1-37A model on Mr tests performed on

granular materials using the AASHTO T307 procedure. Results of a Mr test performed

by Dr.Adrian Ricardo Archilla of the University of Hawaii on a coral sample using the

AASHTO T307 procedure is presented below (Figure 3-14, Figure 3-15, Table 3-3). As

can be seen from the table, the coefficient of octahedral shear stress, K3, is positive.

Figure 3-14 Mr vs. Bulk Stress for Coral sample

y = 9356.6x0.4258

R² = 0.8454

10000

100000

10 100 1000

Re

silie

nt

Mo

du

lus

(psi

)

Bulk Stress (psi)

72

Figure 3-15 Mr vs. deviator stress at different confinement stresses for Coral material

Table 3-3 Mr coefficients calculated using the NCHRP 1-37A model

Specimen ID K1

p-value

(K1)

K2

p-value

(K2)

K3

p-value

(K3)

R2

Coral 1755.79 1.40E-24 0.17 1.28E-03 0.96 8.47E-06 0.96

3.6 Hot Mix Asphalt Mixtures Information

This section provides a detailed description of the materials used to compact specimens

for dynamic modulus and permanent deformation tests. First, the aggregate gradation used to

produce HMA mixtures is presented. Next, the asphalt binder used in the preparation of HMA

mixtures is discussed. Later, the modification process for producing polymer modified binder is

reviewed. The particulars of mixing and compaction temperature for unmodified and modified

10000

20000

30000

40000

50000

60000

70000

80000

90000

0 10 20 30 40 50

Re

silie

nt

Mo

du

lus

(psi

)


Confining stress = 3 psi





73

binder are presented. Lastly, the type of FORTA-FI fibers and the procedure followed to blend

the fibers with HMA mixture is discussed.

3.6.1 Gradation Analysis of Aggregates

This study included HMA mixtures prepared using two gradations for surface course in

Hawaii. As mentioned in section 3.2.2, the mix design and materials used in this study was

provided by paving contractors in Hawaii. Neither of the gradations is as a result of a mix design

procedure performed as a part of this study. Figure 3-16 and Figure 3-17 presents the two

gradation blend information collected from the local contractors on a 0.45 power chart. Figure 3-

16 is the gradation used for preparing mixes in the laboratory. The gradation conforms to the

requirements of the HDOT specification for mix type IV for surface courses and also falls within

the control points of the 12.5 mm Superpave mix. Figure 3-17 shows the gradation used in

producing plant produced mixes. The gradation curve falls within the requirements of the 19.0

mm Superpave mix.

Figure 3-16 Gradation information for laboratory produced HMA mixtures

1"

3/4

"

1/2

"

3/8

"

#4

#8

#16

#30

#50

#100

#200

0

10

20

30

40

50

60

70

80

90

100

Perc

en

t P

assin

g

Sieve Designation

Gradation for Laboratory Produced Mix

HDOT Mix Type IV - Minimum Specif ication

HDOT Mix Type IV - Maximum Specif ication

12.5 mm Superpave Control Points - Lower

12.5 mm Superpave Control Points - Upper

74

Figure 3-17 Gradation information for plant produced HMA mixtures

3.6.2 Asphalt Binder

Unmodified PG64-16 binder distributed to JWG by Asphalt Hawaii was used to produce

VPPM. For the two types of HMA mixtures prepared in the laboratory, one is an unmodified

PG64-16 binder distributed to GPC by Asphalt Hawaii, which is used to prepare VLPM, and the

other is the polymer modified asphalt binder which was used to prepare PMALPM. The polymer

modified binder was prepared by modifying the PG64-16 binder distributed to GPC by Asphalt

Hawaii with 1.0% of DuPont’s Elvaloy®RET and mixed with 0.3% (by weight of binder)

polyphosphoric acid. The latter is added to act as a catalyst of the reaction between Elvaloy RET

and the binder.

3.6.3 Preparation of modified binder

The Evaloy®RET manufacturers recommend two procedures for modification using

Elvaloy: (a) with a catalyst and (b) without a catalyst. The procedure used in this study is

1"

3/4

"

1/2

"

3/8

"

#4

#8

#16

#30

#50

#100

#200

0

10

20

30

40

50

60

70

80

90

100

Perc

en

t P

assin

g

Sieve Designation

Gradation for Plant Produced Mix

19.0 mm SuperPave Control Points - Lower

19.0 mm SuperPave Control Points - Upper

75

modification of the unmodified binder using the catalyst. First, the unmodified binder to be

modified is heated in a heating pot at a temperature of 185 ºC. Once the sample becomes less

viscous, a lab mixer is set inside the softened binder to rotate at a speed high enough to create a

small vortex. Care was taken to ensure air bubbles were not formed. Subsequently, a calculated

amount of Elvaloy pellets (1% of the weight of the unmodified binder) was added at an

approximate rate of 10 g/min. Mixing is continued at the same speed for two hours after adding

all the pellets. Subsequently, polyphosphoric acid in a concentration of 105% is added to the

mixture as a catalyst while the mixing is in progress for an additional 15 to 30 minutes. Next, the

modified binder is transferred to new containers and the lids are tightly covered. The cans are

placed inside an oven set at 185ºC for 3 hours. Finally, the asphalt cans are removed from the

oven, allowed to air-cool for 10 minutes and the lid is opened. The modified binder is now ready

to be used. Figure 3-18 shows the Elvaloy pellets and the hot pot where the modification process

was performed.

Figure 3-18 Evaloy®RET Pebbles (left) and mixing Elvaloy to Unmodified PG64-16 binder

(right)

76

3.6.4 Mixing and Compaction Temperatures of Unmodified and Modified Binder

The mixing and compaction temperature ranges for unmodified binder used to prepare

HMA mixtures were obtained from the temperature-viscosity charts provided by JWG and GPC.

For the modified binder, the mixing and compaction temperature was taken from Archilla

(2008). The same grade of binder (PG64-16) was modified by Archilla (2008) in a study that

evaluated the performance of polymer modified and unmodified HMA mixtures. Given that the

grade of the binder is the same, their mixing and compaction temperatures were similar, and that

the same proportion of polymer was used, it is expected that the mixing and compaction ranges

would be similar to those found by Archilla (2008). The fiber reinforced asphalt concrete

mixture was prepared using unmodified binder. The effect of modifying virgin binder with fibers

was studied by Kaloush et al. (2008). The modification process was done by using only

Polypropylene fibers. It was found that the (a) at lower temperatures the viscosity-temperature

susceptibility relationship did not show any changes compared to original binder and (b) at high

temperatures, higher binder viscosities were observed indicating that the modified binder is less

susceptible to viscosity change with increased temperatures. Although improved properties were

observed at high temperatures, for this study, the variation of the viscosity of the binder with

fibers was not measured, because according to The Asphalt Handbook (MS-2) (Asphalt Institute,

2007), one of the assumptions in performance graded asphalt binder specifications is that the

asphalt binders should exhibit isotropic behavior. With respect to testing asphalt binders

incorporated with fibers, the Asphalt Handbook states:

“Asphalt binders should exhibit isotropic behavior. Isotropic behavior occurs when

specimen loading or particle orientation has no effect on the response. Asphalt binders

77

that incorporate fibers could exhibit anisotropic behavior – meaning the fiber orientation

affects the test response”.

Furthermore, as indicated in section 3.7, all specimens were aged in accordance with

AASHTO R30 in an oven at 135 °C irrespective of the viscosity of the binder. The rationale

behind not using the compaction temperature from the viscosity-temperature charts is because

the temperature ranges obtained from these charts are important to be used during mix design to

achieve equiviscous mixing and compaction in the laboratory. However, in the field, it is

important that the temperatures are high enough (above what is called cessation temperature) to

achieve the required density. The cessation temperature for compaction of HMA in the field is

reported to be 79 °C. It is also reported that the cessation temperature of 79 °C is reported to be a

general rule of thumb and will change from mix to mix depending on the properties of the binder

(West et al, 2010). Although the actual cessation temperatures for the two types of binder used in

this study is not known, the compaction temperature of 135 °C is much higher compared to the

cessation temperature reported by West et al.

Further, it can be seen from the results in the following sections that there were no

problems in achieving the target densities.

Table 3-4 presents the mixing and compaction temperature ranges for the two types of

binders used in this study.

78

Table 3-4 Mixing and compaction temperature range for asphalt binders

Asphalt Binder

Temperature (°C)

Mixing Compaction

Unmodified binder used to produce VPPM 150 - 155 143 – 147

Unmodified binder (PG64-16) used to prepare VLPM 150 - 155 143 – 147

Modified binder (PG64-16 + 1% Elvaloy) 160 - 165 150 – 155

3.6.5 Fibers Used in the Study

FORTA-FI HMA blend fibers are used in this study. In its manufactured condition, the

fibers are clasped together. The fibers were fluffed using a makeshift procedure prior to mixing

them with hot aggregates. This is done to enhance the effect of fibers and improve the

distribution of fibers in the HMA mixture. The procedure involved placing packaged fibers

inside a hollow cylinder, the top of which was then covered using a perforated disc. Next,

compressed air was blown from the top to achieve the desired result. Figure 3-19 through Figure

3-21 shows the fibers in its manufactured condition, the fluffing setup and method, and fluffed

fibers. The fluffed fibers were then weighed as required and mixed with hot aggregates before

asphalt was introduced into the mixing bowl.

79

Figure 3-19 Fibers in its manufactured condition

Figure 3-20 The setup used to fluff the fibers

Figure 3-21 Fibers after fluffing

80

3.7 Test Specimen Preparation for Dynamic Modulus and Permanent Deformation Testing

The dynamic modulus and permanent deformation tests were performed on compacted

HMA samples prepared at three different target air voids (Va); Va=3%, 5%, and 7%. Both tests

require a 100 mm diameter by 150 mm height cored and sawed from 150 mm diameter by 170

mm specimens compacted in the Superpave gyratory compactor. Asphalt mixtures used to

compact cylindrical specimens were prepared in accordance with AASHTO T312. The mixtures

were conditioned according to AASHTO R30 at 135 °C for 4 hours prior to compaction. The

following steps (as shown in Figure 3-22) are followed in preparation of the test specimens.

Figure 3-22 Steps involved in preparation of test specimens

Material quantity calculation: The first step is to determine the amount of material required to

compact a specimen to achieve certain amount of air voids in the test specimen. The amount of

Material Quantity Calculation

Batching

Mixing

Conditioning

Compaction

Coring and Sawing

81

material is determined using the target air voids value and the theoretical specific gravity (Gmm)

of the mixture, which is determined in accordance with AASHTO T209. Subsequently, a

batching sheet is developed to give the following details that will assist in preparing the

compacted specimen.

a) target air voids

b) mass of different types and sizes of aggregates

c) asphalt type and content

d) temperature at which the mixture has to be prepared, and

e) mixture conditioning details

The theoretical specific gravity test was performed using AASHTO T209 procedure. The

results of the tests are presented in Table 3-5. The Gmm test on mixes with fibers was not

performed because it was assumed that the addition of a small percentage of fibers (1 lb per ton

of HMA mixture, which is equivalent to 0.05% by weight of mix) would have a negligible effect.

Therefore, the Gmm of mixes prepared using unmodified binder was used to calculate the

amount of HMA material required to achieve a target density. The amount of fibers to be added

was then determined based on the total mass of the HMA mixture.

Table 3-5 Results of theoretical specific gravity

Material Type Theoretical Specific Gravity

VPPM 2.560

VLPM 2.460

PMALPM 2.452

FRACLPM 2.460 (same as for VLPM)

82

Batching: Based on the mass calculations in the batching sheet, aggregates of different types and

sizes are combined together to achieve the desired gradation and provide enough room for

asphalt to produce a mixture with target air voids, height, and diameter. The batched aggregates

were place inside an industrial oven at 175 °C (350 °F) for a minimum of 5 hours prior to

mixing.

Mixing: Except for VPPM, which is plant produced, all HMA samples were mixed in a

mechanical mixer (as shown in Figure 3-23). The mixing temperature ranges used for different

types of asphalt binder are shown in Table 3-4.

Regardless of the type of binder used, the HMA mixtures prepared in the laboratory had

very similar appearance except for the mixture with fibers. The fibers appear to hold the material

together. Figure 3-24 through Figure 3-27 illustrate the three different types of mixes.

Figure 3-23 Mechanical mixer used for mixing HMA samples

83

Figure 3-24 HMA mixture produced using virgin asphalt in the plant

Figure 3-25 HMA mixture prepared in the laboratory using virgin asphalt

Figure 3-26 HMA mixture prepared in the laboratory using polymer modified asphalt

84

Figure 3-27 HMA mixture prepared in the laboratory using virgin asphalt and FORTA-FI fibers

Conditioning: According to AASHTO R30, all HMA mixed samples were placed in an oven at

135 °C for 4 hours prior to compaction.

Compaction: The conditioned samples were compacted in a 150 mm diameter mold to a height

of 170 mm using a Rainhart SuperPave gyratory compactor. Since the HMA samples were

immediately compacted after conditioning, the samples were not subjected to the compaction

temperature as prescribed in Table 3-4 prior to compaction. The compacted specimens were

then extruded from the mold. Figure 3-28 shows the gyratory compactor used for compaction

and a specimen extruded after compaction.

85

Figure 3-28 A specimen extruded after compaction in a Rainhart SGC

The extruded specimens were clearly labeled and allowed to cool to room temperature.

Next, the bulk specific gravities of the compacted specimens were determined in accordance

with AASHTO T166.

Coring and Sawing: All air-dried samples were cored and sawed to obtain a 150 mm tall by 100

mm diameter test sample. Figure 3-29 shows the coring and sawing machine used to core and

saw the specimens to achieve the required diameter and height. A cored and sawed specimen is

shown in Figure 3-30.

86

Figure 3-29 Specimen being cored (left) and sawed (right) to required size

Figure 3-30 Cored and sawed specimen

Subsequently, the cored and sawed samples were washed under water to remove all loose

debris and allowed to dry in air. Finally, the samples were tested for bulk specific gravity in

accordance with AASHTO T 166. The specimens were now ready for the preparation for the

dynamic modulus test.

87

All specimens were glued with six gauge points using epoxy to hold three LVDTs.

Figure 3-31 shows the gauge point fixing jig used to glue the gauge points. The glued gauge

points were allowed to dry and set for at least 5 hours before removing the specimen from the

gauge point fixing jig. An example of a test specimen ready for testing is shown in Figure 3-32.

Figure 3-31 Gauge point fixing jig

88

Figure 3-32 Test specimen ready for dynamic modulus testing

The steps explained in Section 3.6 were followed to prepare specimens for VLPMs,

PMALPMs, FRACLPMs. In total, 19 specimens were prepared in these three categories. Six

additional specimens were prepared using plant produced HMA mixtures, which belong to

VPPMs. The specimens prepared using plant produced mixtures were heated to 135 °C for 4

hours prior to compaction. A summary of the volumetric characteristics of all the HMA

specimens is presented in Table 3-6. As can be seen from the table, the actual Va and target Va

don’t match all the time. This is primarily because of the variability involved in determining the

theoretical (rice) specific gravity of the loose HMA mixture, which determines the mass of HMA

material required to compact a specimen of known dimension and target air voids. Furthermore,

cored specimens usually have lower air voids compared to the original compacted specimen.

89

Table 3-6 Characteristics of HMA specimens

Specimen ID Mix Type Pb (%) Target

Va (%) Gmm Gmb

Actual

Va (%) VMA VFA

VPPM1 Virgin 5.5% 3.0% 2.560 2.539 0.8% 9.8 91.8

VPPM2 Virgin 5.5% 3.0% 2.560 2.543 0.7% 9.6 93.1

VPPM3 Virgin 5.5% 5.0% 2.560 2.498 2.4% 11.2 78.4

VPPM4 Virgin 5.5% 5.0% 2.560 2.496 2.5% 11.3 77.8

VPPM5 Virgin 5.5% 7.0% 2.560 2.419 5.5% 14.0 60.7

VPPM6 Virgin 5.5% 7.0% 2.560 2.420 5.5% 14.0 60.9

VLPM1 Virgin 6.7% 3.0% 2.460 2.408 2.1% 13.5 84.2

VLPM2 Virgin 6.7% 3.0% 2.460 2.418 1.7% 13.1 86.9

VLPM3 Virgin 6.7% 5.0% 2.460 2.349 4.5% 15.6 71.1

VLPM3B Virgin 6.7% 5.0% 2.460 2.337 5.0% 16.0 68.7

VLPM4 Virgin 6.7% 5.0% 2.460 2.341 4.8% 15.8 69.6

VLPM5 Virgin 6.7% 7.0% 2.460 2.282 7.2% 18.0 59.7

VLPM6 Virgin 6.7% 7.0% 2.460 2.264 8.0% 18.6 57.2

PMALPM1 Polymer Modified 6.7% 3.0% 2.452 2.413 1.6% 13.3 88.0






FRACLPM1 Fiber Reinforced 6.7% 3.0% 2.460 2.404 2.3% 13.6 83.2






90

3.8 Dynamic Modulus Testing

The dynamic modulus testing was performed using the IPC Global Simple Performance

Tester (SPT), which is shown in Figure 3-33. The SPT is a relatively small, computer-controlled

hydraulic loading and testing machine that can perform tests on compacted HMA specimens

over temperatures ranging from 4 °C to 60 °C. The specimen is seated inside a testing chamber,

which facilitates axial testing of specimens with or without confinement.

Figure 3-33 IPC Global Simple Performance Tester

The compacted HMA specimens were tested for dynamic modulus in accordance with the

AASHTO TP 62: “Standard Method of Test for Determining Dynamic Modulus of Hot Mix

Asphalt (HMA)” procedure. Figure 3-34 shows the sample connected with LVDTs mounted

inside the testing chamber.

91

Figure 3-34 Specimen assembly inside the testing chamber

Each sample was tested at three different temperatures (4.4 °C, 21 °C, and 40 °C) and

seven different frequencies (25, 10, 5, 1, 0.5, 0.1, 0.01 Hz). The conditioning time for each

temperature is presented in Table 3-7.

Table 3-7 Conditioning time for different testing temperature

Testing Temperature 4.4 °C 21 °C 40 °C

Conditioning Time 6 Hours 3 Hours 2 Hours

The test is run starting at the lowest temperature to the highest, and the frequency starts

from the highest to the lowest. In cases where the specimens were prepared using virgin binder,

the gauge points attached to the sample would repeatedly fall off at higher temperatures and

lowest frequency, forcing to stop the test. In such instances, all six gauge points were re-glued on

a different location of the sample and the test was attempted again. Figure 3-35 shows an

92

extreme example in which repeated attempts were necessary because the gauge points kept

coming off from the sample and had to be re-glued to finish the test. The figure also makes it

clear that the glued gauge points came off because of the softening of the binder and not because

of the epoxy.

Figure 3-35 An example of repeated attempts to glue the gauge point(s) for a specimen

During the test, several parameters are checked to see if they meet the data quality

statistics requirement. The parameters and corresponding allowable limits are listed in Table 3-8.

Table 3-8 Data quality statistics requirements in dynamic modulus test

Data Quality Parameter Allowable Limit

Deformation Drift 400%

Load Standard Error 10%

Deformation Standard Error 10%

Deformation Uniformity 30%

Phase Uniformity 3 Degrees

Load Drift 3%

93

Figure 3-36 shows a typical screen shot during a test. As can be seen from the figure, the

temperature at which the sample is being tested, dynamic modulus and other parameters listed in

Table 3-8 at different frequencies is recorded. It was ensured that, for each specimen, test data

within the aforementioned allowable limits was used to derive the master curve using the shift

factor. Once the dynamic modulus test was completed at all temperatures and frequencies, the

specimen was removed from the testing chamber, the LVDTs, LVDT holders, and gauge points

were removed from the specimen, and the specimen was prepared for the flow number or

repeated axial load test.

Figure 3-36 Example of dynamic modulus data collection

94

The results from the dynamic modulus test consist of a set of dynamic modulus values

obtained at different temperatures and frequencies. As explained in section 2.8, the master curve

can be used to compute the dynamic modulus values for any desired combination of temperature

and frequency. The dynamic modulus test data from all specimens was used to derive the

“Master Curve” for each specimen using the quadratic equation for the shift factor (Equation

2.6). The dynamic modulus parameters and shift factors are calculated for each specimen. The

results are tabulated in Table 3-9 and the Master Curves for individual specimens are presented

in Appendix B. Master curves developed using these parameters are presented in Figures 3-37

through Figure 3-41. The figures show the master curves for different types of HMA mixtures

used in this study. For brevity, Master Curves for one specimen at three different air voids are

presented.

95

Figure 3-37 Master curves for VPPM at three different air voids

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1.00E-06 1.00E-05 1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01 1.00E+02 1.00E+03 1.00E+04 1.00E+05 1.00E+06

Dy

na

mic

Mo

du

lus

E*

(ps

i)

Frequency (Hz)

VPPM1: Pb=5.5%, Va=0.8%

VPPM4: Pb=5.5%, Va=2.5%

VPPM5: Pb=5.5%, Va=5.5%

96

Table 3-9 Dynamic modulus master curve parameters and shift factors

Specimen Information Dynamic Modulus Parameters and Shift Factors

Sample ID Mix Type Pb

(%)

Target

Va (%)

Actual Va

(%) a b c

VPPM1 Virgin 5.5% 3.0% 0.8% 2.4499 -0.7961 0.6139 4.1120 2.20E-04 -0.1039 6.1977

VPPM2 Virgin 5.5% 3.0% 0.7% 3.2024 -1.2148 0.5192 3.4064 1.86E-04 -0.1006 6.1324

VPPM3 Virgin 5.5% 5.0% 2.4% 4.0469 -1.4948 0.4117 2.5969 -2.26E-05 -0.0808 5.7657

VPPM4 Virgin 5.5% 5.0% 2.5% 3.5585 -1.2857 0.4735 3.0174 2.62E-04 -0.1137 6.6724

VPPM5 Virgin 5.5% 7.0% 5.5% 6.4968 -1.9279 0.3820 0.1224 2.52E-04 -0.1069 6.2468

VPPM6 Virgin 5.5% 7.0% 5.5% 8.3188 -2.1990 0.3777 -1.7090 2.27E-04 -0.1065 6.3398

VLPM1 Virgin 6.7% 3.0% 2.1% 5.2913 -1.7662 0.3813 1.3471 2.76E-04 -0.1121 6.4881

VLPM2 Virgin 6.7% 3.0% 1.7% 4.5099 -1.5705 0.4269 2.1074 3.01E-04 -0.1145 6.5384

VLPM3 Virgin 6.7% 5.0% 4.5% 7.3521 -2.0255 0.3493 -0.6909 4.98E-04 -0.1447 7.6910

VLPM3B Virgin 6.7% 5.0% 5.0% 4.9543 -1.7057 0.4049 1.5869 3.47E-04 -0.1185 6.5942

VLPM4 Virgin 6.7% 5.0% 4.8% 7.9998 -2.1602 0.3573 -1.3853 2.44E-04 -0.1068 6.2824

VLPM5 Virgin 6.7% 7.0% 7.2% 8.4071 -2.1188 0.3799 -1.9033 5.51E-04 -0.1416 7.2103

VLPM6 Virgin 6.7% 7.0% 8.0% 5.0538 -1.5131 0.4263 1.4048 4.43E-03 -0.5667 17.9429

PMALPM1 PMA 6.7% 3.0% 1.6% 2.5919 -1.1184 0.4718 3.9754 3.12E-04 -0.1190 6.7992

PMALPM2 PMA 6.7% 3.0% 1.7% 2.7471 -1.1822 0.4273 3.8449 2.82E-04 -0.1173 6.8271

PMALPM3 PMA 6.7% 5.0% 4.6% 3.4742 -1.3601 0.4365 3.0593 2.92E-04 -0.1171 6.7657

PMALPM4 PMA 6.7% 5.0% 4.4% 2.9967 -1.1645 0.4678 3.5098 2.64E-04 -0.1140 6.6793

PMALPM5 PMA 6.7% 7.0% 7.1% 4.8144 -1.5924 0.3927 1.6264 2.54E-04 -0.1114 6.5480

PMALPM6 PMA 6.7% 7.0% 6.7% 3.8065 -1.3463 0.4286 2.6299 2.57E-04 -0.1115 6.5434

FRACLPM1 Fiber Reinforced 6.7% 3.0% 2.3% 3.3866 -1.3658 0.4641 3.1645 2.64E-04 -0.1101 6.4134



FRACLPM4 Fiber Reinforced 6.7% 5.0% 4.4% 6.6733 -1.8883 0.3755 -0.0342 2.81E-04 -0.1142 6.6140



97

Figure 3-38 Master curves for VLPM at three different air voids

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1.00E-06 1.00E-05 1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01 1.00E+02 1.00E+03 1.00E+04 1.00E+05 1.00E+06

Dy

na

mic

Mo

du

lus

E*

(ps

i)

Frequency (Hz)

VLPM1: Pb=6.7%, Va=2.1%

VLPM3B: Pb=6.7%, Va=5.0%

VLPM6: Pb=6.7%, Va=8.0%

98

Figure 3-39 Master curves for PMALPM at three different air voids

As can be seen from Figure 3-37, Figure 3-38, Figure 3-39, and Figure 3-41, air voids

show considerable influence on the stiffness of each of the mixtures. Furthermore, the effect of

air voids appear to be similar for all laboratory produced mixes. For the plant produced mixes,

which has a coarser gradation with 19.0 mm nominal maximum aggregate size, air voids appears

to have an effect only for the high temperatures and low frequencies (as shown in Figure 3-40).

10

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100000

1000000

10000000

1.00E-06 1.00E-05 1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01 1.00E+02 1.00E+03 1.00E+04 1.00E+05 1.00E+06

Dy

na

mic

Mo

du

lus

E*

(ps

i)

Frequency (Hz)

PMALPM1: Pb=6.7%, Va=1.6%



99

Figure 3-40 Master curves of all specimens for VPPM at three different air voids

10

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10000000

1.00E-06 1.00E-05 1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01 1.00E+02 1.00E+03 1.00E+04 1.00E+05 1.00E+06

Dy

na

mic

Mo

du

lus

E*

(ps

i)

Frequency (Hz)

VPPM1: Pb=5.5%, Va=0.8%

VPPM2: Pb=5.5%, Va=0.7%

VPPM3: Pb=5.5%, Va=2.4%

VPPM4: Pb=5.5%, Va=2.5%

VPPM5: Pb=5.5%, Va=5.5%

VPPM6: Pb=5.5%, Va=5.5%

100

Figure 3-41 Master curves for FRACLPM at three different air voids

The trend seen in the dynamic modulus Master Curves (Figures 3-38, 3-39, and 3-41) for

the laboratory prepared mixes is consistent with the results obtained by Archilla (2010). That is,

an increase in air voids results in a decrease in dynamic modulus. Figure 3-42 (from Archilla,

2010) shows the comparison of Master Curves for mixes prepared using polymer modified

asphalt with a binder content of 5.8% and compacted at four different air voids (3%, 5%, 7%,

and 9%).

10

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100000

1000000

10000000

1.00E-06 1.00E-05 1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01 1.00E+02 1.00E+03 1.00E+04 1.00E+05 1.00E+06

Dy

na

mic

Mo

du

lus

E*

(ps

i)

Frequency (Hz)

FRACLPM1: Pb=6.7%, Va=2.3%



101

Figure 3-42 Comparison of master curves for mixes prepared using polymer modified binder and

compacted at different air voids

A comparison among the three different mix types is presented in Figures 3-43 through 3-

45 for target air voids at 3%, 5%, and 7% respectively.

1,000

10,000

100,000

1,000,000

10,000,000

1.00E-05 1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01 1.00E+02 1.00E+03 1.00E+04

|E*|

(p

si)

Reduced Frequency (Hz)

Va = 3%, VFA = 78.1, Pb = 5.8%

Va = 5%, VFA = 67.7, Pb = 5.8%

Va = 7%, VFA = 59.4, Pb = 5.8%

Va = 9%, VFA = 52.7, Pb = 5.8%

102


compacted at target Va=3%

10

100

1000

10000

100000

1000000

10000000

1.00E-06 1.00E-05 1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01 1.00E+02 1.00E+03 1.00E+04 1.00E+05 1.00E+06

Dy

na

mic

Mo

du

lus

E*

(ps

i)

Frequency (Hz)

VLPM1: Pb=6.7%, Va=2.1%



103


compacted at target Va=5%

10

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100000

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10000000

1.00E-06 1.00E-05 1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01 1.00E+02 1.00E+03 1.00E+04 1.00E+05 1.00E+06

Dy

na

mic

Mo

du

lus

E*

(ps

i)

Frequency (Hz)

VLPM3B: Pb=6.7%, Va=5.0%



104


compacted at target target Va=7%

From Figure 3-43 through Figure 3-45, it is clear that, regardless of air voids, PMA

mixtures are stiffer at high temperatures and low frequencies compared to fiber reinforced

asphalt concrete mixtures and mixtures prepared using virgin binder. It must however be noted

that the PMA mixes had lower air voids. Thus the actual differences at exactly the same air voids

are expected to be slightly smaller. Furthermore, the dynamic modulus master curves at lowest

test temperature (40 °F) at high frequencies cluster over the top of one another. For clearer

understanding of the difference in the behavior of different types of HMA mixtures used in this

study, a separate comparison of dynamic modulus values at different frequencies needs to be

10

100

1000

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100000

1000000

10000000

1.00E-06 1.00E-05 1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01 1.00E+02 1.00E+03 1.00E+04 1.00E+05 1.00E+06

Dy

na

mic

Mo

du

lus

E*

(ps

i)

Frequency (Hz)

VLPM6: Pb=6.7%, Va=8.0%



105

performed. For brevity, the actual test data comparing the dynamic modulus values at 10 Hz is

provided in Figure 3-46. The chart at 10 Hz is shown because 10 Hz typically represent the

speeds of vehicles on actual arterial streets.

Figure 3-46 Comparison of dynamic modulus values for three different types of HMA mixtures

at 40 °F at 10 Hz

At low temperature, in order for the mixtures to have better resistance to cracking, it is

desirable to have mixes with less stiffness. Figure 3-46 shows that neither polymer modified

asphalt nor fibers have any effect on the stiffness of the mixture at low temperature (40 °F) and

10 Hz.

The dynamic modulus test results at high temperature on mixes prepared using FORTA

fibers and compacted at intermediate air voids (~5%) show lower stiffness values compared to

the |E*| values observed with the mixes prepared using unmodified binder. For mixes that are

compacted at high air voids (~7%) and tested at high temperature and low frequency, there is no

25

85

49

5

23

05

79

0

16

75

54

8

25

33

51

3

22

51

56

0

16

99

03

8

26

53

79

0

22

44

89

0

16

59

01

8

1000000

1400000

1800000

2200000

2600000

3000000

Va=

3%

Va=

5%

Va=

7%

Dyn

amic

Mo

du

lus

(psi

)

Target Air Voids

Virgin Mix Fiber Reinforced Asphalt Concrete Mix Polymer Modified Asphalt Concrete Mix

106

conclusive difference between the stiffness values for mixes prepared using unmodified binder

and mixes prepared using fibers. The comparison of stiffness values using dynamic modulus

tests on control mix and mixes blended with FORTA fibers (one sample at 1lb/ton and the

second one at 2lb/ton) were performed by Kaloush et al. (2008). In that study, the dynamic

modulus tests were performed on HMA samples compacted at target air voids of 7%. The master

curves constructed using the results of the study are presented in Figure 3-47. As can be seen

from the figure, the dynamic modulus values at low temperature is higher than the |E*| values of

mixes prepared using unmodified binder, and the |E*| values of mixes prepared using 1lb/ton and

2lb/ton fibers at high temperature and low frequencies are lower compared to control mixes.

Figure 3-47 Unconfined Dynamic Modulus Master Curves for FORTA Evergreen Control, 1

lb/Ton and 2 lb/Ton Mixtures (Kaloush et al, 2008)

107

3.9 Repeated Load Axial Test (RALT)

The RALT was performed using the IPC Global Simple Performance Tester (SPT),

which is shown in Figure 3-33. The preparation of the test specimen for the RALT is relatively

simple. The specimen is placed inside a rubber latex membrane and the top and bottom loading

platens are tightly sealed using O-rings. Next, the entire assembly is placed inside the testing

chamber (as shown in Figure 3-48) and the hydraulic system is connected to the bottom loading

platen. In RALT, the steel ball is not placed on top of the top loading platen. The testing chamber

is closed and the temperature control unit is used to set the desired temperature.

Figure 3-48 Specimen assembly inside the testing chamber

The RALT is performed by repeatedly applying a compressive load on the test

specimens. The compressive load applied is in the haversine form with a loading pulse of 0.1

seconds followed by a rest period of 0.9 seconds. The test specimens were conditioned inside the

testing chamber at 54 °C for a period of 3 hours if the test specimen was followed from a

dynamic modulus test or 4 hours if the sample was at the room temperature. A confining stress of

108

138 kPa (20 psi), contact stress of 41.4 kPa (6 psi), and a deviator stress of 828 kPa (120 psi) was

applied to the specimen for the entire duration of the test. The values for different stresses were

selected based on the recommendations from previous research efforts by Witczak (2002) in

NCHRP report No. 465. As documented in Archilla (2008), the test temperature of 54 °C was

selected based on the following factors: (a) according to the Long Term Pavement Performance

(LTPP) bind software, considering 35 weather stations in Hawaii, it was observed that the testing

temperatures between 54 °C and 64 °C would cover most of the situations to which pavements in

Hawaii would be subjected to and (b) the capability of SPT to achieve and maintain 54 °C inside

the testing chamber was considered reasonable. The test was terminated when a maximum of

20,000 cycles was reached or when the sample accumulated a deformation of 100,000 micro

strains. Since this is a destructive test, the specimen is damaged at the end of the test. An

example of how the specimen looks like at the end of a test is shown in Figure 3-49.

Figure 3-49 Deformed specimen at the end of flow number test (Specimen ID shown in this

figure is VPPM5)

109

A sample output from the IPC Global Flow Test software is presented in Figure 3-50.

The figure shows a monotonically increasing total axial strain and axial strain rate on the two y-

axes, and the number of (cycles) repetitions on the x-axis. The vertical line is the flow number

calculated by the IPC Global software. It can be seen that the total axial strain (permanent strain)

displays the typical three stages of a permanent deformation tests. The vertical line provides an

estimate of the boundary between the secondary and tertiary stages, which defines the inflection

point of the permanent deformation curve and which as indicated before is known as the Flow

Number (FN). This number is used as the upper limit of the data used in calculating the

parameters k1 and k3 for Equation 2.31.

Figure 3-50 Screenshot of the Permanent Deformation test output

110

An example showing the accumulation of permanent strain (Test Points) for a specimen

is presented in Figure 3-51. The FN for this specimen reported by the SPT software was 107.

The FN estimated using the three parameter model proposed by Archilla et al (2007) was found

to be 122. It should be noted that the difference in FN values in this example is not “large”.

However, the difference in some cases can be substantial, as can be seen from the FN values in

Table 3-9.

Figure 3-51 Example of the accumulation of permanent strain and fitting of three parameter

model proposed by Archilla et al (2007) for Specimen ID VLPM6

The most widely used power model includes the first two deformation stages and

excludes the tertiary stage. The model parameters can be greatly affected by the consideration

given to the number of initial observations (Test Points) included in the estimation. Since the

data from tertiary stage is excluded from the analysis, it becomes straightforward to accept the

FN as the end point of the secondary stage. The number of initial observations is considered

1000

10000

100000

1000000

1 10 100 1000

Perm

an

en

t S

train

(ε

p)


Test Points

FN estimated by SPT Machine

FN estimated using Archilla et al. (2007)

Power (Model)

FN estimated using Archilla et al. (2007) procedure

FN estimated by SPT Machine

Trimmed Data range used to Estimate the Power Model

111

based on the justification provided by Diaz et al (2008). Accordingly, 10% of the initial

observations were excluded and the parameters were estimated. An example showing the actual

data (Test Points), trimmed data, and estimated power model is shown in Figure 3-52. This

procedure was repeated to all specimens and the values are tabulated in Table 3-10. The power

model for trimmed data for all the samples is included in Appendix C.

Figure 3-52 Example of fitting the power model for Specimen ID VLPM6

100

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100000

1000000

1 10 100 1000

Pe

rman

en

t St

rain

(

p)


Test Points

Power (Model)

112

Table 3-10 Permanent deformation parameters and Flow Number

Specimen Information FN From

SPT

Machine

Equation 2.30 parameters

FN p @ FN

Equation 2.28 parameters Average

k3 r Mix ID Mix Type

Pb

(%)

Target

Va (%)

Actual

Va (%) k1 k3

VPPM1 Virgin 5.5% 3.0% 0.8% 316 3.194 1.01E-04 695.8 346 8820.1 -3.9513 0.321 0.415

2630.6

VPPM2 Virgin 5.5% 3.0% 0.7% 249 2.093 1.01E-04 652.6 265 7279.7 -5.0816 0.509 11208.2

VPPM3 Virgin 5.5% 5.0% 2.4% 432 2.186 5.68E-05 1072.4 449 13304.3 -4.2733 0.480 0.386

2909.5

VPPM4 Virgin 5.5% 5.0% 2.5% 221 3.739 7.96E-05 456.8 237 11555.2 -3.8063 0.292 3270.9

VPPM5 Virgin 5.5% 7.0% 5.5% 196 2.283 3.97E-05 469.8 202 19568.4 -3.8605 0.417 0.476

3394.8

VPPM6 Virgin 5.5% 7.0% 5.5% 138 2.084 2.97E-05 364.6 148 24592.7 -3.9320 0.535 3161.6

VLPM1 Virgin 6.7% 3.0% 2.1% 338 2.782 9.22E-05 776.6 367 9244.5 -4.0782 0.363 0.356

2833.5

VLPM2 Virgin 6.7% 3.0% 1.7% 244 2.988 7.13E-05 533.0 259 12239.3 -3.8824 0.348 2939.7

VLPM3 Virgin 6.7% 5.0% 4.5% Sample damaged while fixing the SPT machine.

VPLM3B Virgin 6.7% 5.0% 5.0% 76 1.811 4.70E-05 509.9 184 13645.5 -4.0703 0.441 0.444

3516.5

VLPM4 Virgin 6.7% 5.0% 4.8% 201 2.124 5.26E-05 470.3 193 14104.7 -4.0514 0.448 3279.0

VLPM5 Virgin 6.7% 7.0% 7.2% 103 3.097 6.87E-05 232.3 114 12843.2 -3.9444 0.364 0.340

4398.0

VLPM6 Virgin 6.7% 7.0% 8.0% 107 3.304 4.30E-05 242.4 122 20842.5 -3.8678 0.316 7356.2

PMALPM1 PMA 6.7% 3.0% 1.6% 1234 5.685 9.70E-05 3112.6 1747 9969.4 -3.7838 0.194 0.203

3118.8

PMALPM2 PMA 6.7% 3.0% 1.7% 3813 5.199 1.62E-04 7023.5 3892 5931.7 -4.0647 0.212 2594.9

PMALPM3 PMA 6.7% 5.0% 4.6% 544 2.582 3.85E-05 1238.2 567 21485.8 -3.9874 0.424 0.406

3097.1

PMALPM4 PMA 6.7% 5.0% 4.4% 516 2.698 5.03E-05 1307.8 611 16748.9 -4.0270 0.388 3237.7

PMALPM5 PMA 6.7% 7.0% 7.1% 150 2.237 2.32E-05 386.5 164 33149.1 -3.9149 0.501 0.422

4624.8

PMALPM6 PMA 6.7% 7.0% 6.7% 194 2.994 3.81E-05 428.1 208 22921.7 -3.7963 0.342 5041.3

FRACLPM1 Fiber Reinforced 6.7% 3.0% 2.3% 289 2.898 8.06E-05 595.1 286 10725.9 -3.9223 0.333 0.340

2971.2

FRACLPM2 Fiber Reinforced 6.7% 3.0% 2.3% 291 3.016 7.84E-05 565.5 276 11155 -3.9199 0.348 2870.3


3829.1



4991.7


113

As explained in section 2.10, the flow number is the point at which the specimen begins

to fail. Also, as seen from Table 3-10, the FN can be different when calculated using different

models. Flow Number is a good indicator to characterize permanent deformation behavior of

HMA mixes, but it should probably not be used as the sole indicator to characterize the mixes.

Figure 3-53 presents a visual plot of actual air voids of each specimen plotted against the

corresponding FN value. Because the FN values had a large range, the y-axis (FN) is plotted on a

log scale.

Figure 3-53 Comparison of flow number vs. air voids for different types of laboratory produced

HMA mixtures

As can be seen from Figure 3-52, the FN values for mixes prepared using unmodified

binder decrease with increase in the air voids. This trend is also true for specimens prepared

using polymer modified mixes. Note that the FN values for mixes prepared using FORTA fibers

10

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10000

0.0% 1.0% 2.0% 3.0% 4.0% 5.0% 6.0% 7.0% 8.0% 9.0%

Flo

w N

um

be

r

Air Voids (Va)

VPPM VLPM PMALPM FRACLPM

114

are almost constant irrespective of the air voids. In a study by Kaloush et al. (2008) it has been

reported that the FN for mixes with 1lb/ton of fibers was 115 times higher than the FN for mixes

prepared using unmodified binder. It must be noted that the repeated load axial test was

performed using a deviator stress of 15 psi (105 kPa).

Another important indicator of the performance of HMA mixtures is the rate at which the

specimen accumulates the permanent strain. The parameter k3 in the power model (Equation

2.28) indicates the rate at which the sample is accumulating permanent strain.

Logically, the rate at which the specimens accumulate permanent deformation should

increase with increase in air voids. In other words, the denser the material, the smaller is the rate

at which the permanent deformation accumulates. A cursory look at the k3 values in Table 3-10

indicates a noisy trend in many cases.

The average slope (k3) value for polymer modified asphalt concrete mixtures is the

lowest compared to virgin and fiber reinforced concrete mixtures at low air voids (~3%). At

intermediate and higher air voids, the fiber reinforced asphalt concrete mixtures had the lowest

K3 value. Kaloush et al. (2008) reported that for the samples prepared using FORTA fibers (at a

target Va = 7%), the slope of the permanent strain curve for mixes prepared using unmodified

binder was higher compared to the slope of the permanent strain curve for mixes prepared using

fibers.

The plant produced mixtures produced using virgin binder does not show any particular

trend vis-à-vis the rate at which the sample fails.

115

CHAPTER 4

SUMMARY AND CONCLUSIONS

4.1 Resilient Modulus of Base Course Materials

1. The resilient modulus of virgin aggregates and FA mixtures show an increasing trend

with increase in bulk stress at increasing levels of compaction.

2. For virgin aggregates, a higher compaction level translates into a higher resilient modulus

for the same deviator stress. However, for FA mixture specimens, an increase in the

modulus is observed with increase in deviator stress at all confining stress levels for

specimens compacted at 98% of maximum dry density. For the specimens compacted at

100% of maximum dry density, a slight increase in modulus with deviator stress is

observed. Furthermore, for the specimens compacted at 102% of maximum dry density, it

is observed that the resilient modulus decreases with increase in deviator stress at all

confining levels.

3. The coefficient K2 in the NCHRP 1-37A equation, which is the exponent for the bulk

stress term, is positive. This indicates that increases in bulk stress increase the stiffness of

virgin aggregates and FA mixtures.

4. The coefficient K3 in NCHRP 1-37A equation, which is the exponent for the shear stress

term, is negative for FA mixtures, suggesting the stiffness of FA mixtures decrease with

increases in octahedral shear stress.

5. The sign of the coefficient K3 in the NCHRP 1-37A equation is positive for specimens

compacted using virgin aggregates, which means an increase in octahedral shear stress

increases the resilient modulus of the material.

116

6. The results of the study showed that the Mr of FA mixtures is in general between 2.5 and

5 times (corresponding to lowest and highest levels of bulk stress respectively) higher

than the Mr of virgin aggregates at 98% and 100% of maximum dry density, whereas at

102% of maximum dry density, the Mr of FA mixtures is in general between 2.8 and 1.8

times (corresponding to lowest and highest levels of bulk stress respectively) higher than

the Mr of virgin aggregates.

4.2 Dynamic Modulus and Permanent Deformation of HMA Mixtures

The Dynamic modulus tests using AASHTO TP62 were performed on HMA specimens

produced using virgin and polymer modified binder, and HMA mixtures blended with FORTA

fibers. With the caveat that (a) there are some differences in the actual air voids of the compacted

specimens with the same target air voids and (b) a small sample size is used to make the

conclusions, the testing results lead to the following conclusions:

4.2.1 Dynamic Modulus of HMA Mixtures

1. The stiffness of compacted HMA specimens prepared using polymer modified mixes

show an increase in the dynamic modulus values at high temperature (104 °F) and lowest

frequency (0.01 Hz) compared to the mixes prepared with virgin binder or fiber

reinforced asphalt concrete mixes.

2. For the plant produced mixes, which has a coarser gradation with 19.0 mm nominal

maximum aggregate size, air voids appears to have an effect only for the high

temperatures and low frequencies.

117

3. There was no effect of either polymer modification or addition of fibers to the dynamic

modulus values at low temperature and high frequency at all target air voids.

4.2.2 Flow Number Test on HMA Mixtures

1. The FN values of mixes prepared using polymer modified mixes at low and medium air

voids are higher compared to the FN values for other types of laboratory prepared mixes

at same approximate air voids. For higher air voids (~7%), the FN for PMA mixes are

higher than the FN for the mixes prepared using unmodified binder.

2. The FN values for all specimens prepared using fibers are relatively constant at all air

voids.

3. The average slope (k3) value for polymer modified asphalt concrete mixtures is the

lowest compared to virgin and fiber reinforced concrete mixtures at low air voids (~3%).

At intermediate and higher air voids, the fiber reinforced asphalt concrete mixtures had

the lowest K3 value.

4. Between the virgin and fiber reinforced mixtures, the average k3 values for fiber

reinforced asphalt concrete mixes show a relatively lower strain rate compared to

mixtures prepared using virgin binder at corresponding target air voids.

5. The plant produced and laboratory produced mixes using unmodified binder does not

show a particular trend with respect to the rate of accumulation of permanent strain.

6. The FN values estimated by the SPT software is always lower compared to the FN values

estimated using the Archilla et al (2007) procedure. This is because the FN estimated

using SPT software relies on the moving average points for data smoothing, which can be

118

affected by noise in the data, whereas the FN estimated using Archilla et al (2007) fits the

data using non-linear regression and is relatively insensitive to such noise.

4.3 Contributions of the Study

In addition to the above conclusions, the following are additional contributions of this

study.

1. This study has contributed dynamic modulus test results of 25 samples involving

different air voids, two different aggregate gradations, and two different asphalt binder

contents to the existing database of 84 samples that were prepared and tested at two

different aggregate gradations, three different target air voids, and three different asphalt

binder contents by Archilla (2008).

2. Test results of six fiber reinforced HMA specimens at three different target air voids are

added to the existing database of 84 specimens.

3. The dynamic modulus and permanent deformation test results from these 25 samples can

be added to the existing database of 84 samples and used to re-compute the model

estimated by Archilla (2008).

119

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130

APPENDIX A: BASE COURSE MATERIAL CHARTS

131


using virgin aggregates at 98% of dmax (Specimen ID: HCH1)



5000

10000

15000

20000

25000

30000

35000

40000

45000

50000

0 5 10 15 20 25 30 35 40 45 50

Re

silie

nt

Mo

du

lus

(p

si)


Confining Stress = 3 psi





5000

10000

15000

20000

25000

30000

35000

40000

45000

50000

0 5 10 15 20 25 30 35 40 45 50

Re

silie

nt

Mo

du

lus

(p

si)







132





5000

10000

15000

20000

25000

30000

35000

40000

45000

50000

0 5 10 15 20 25 30 35 40 45 50

Resilie

nt

Mo

dulu

s (p

si)


Conf ining Stress = 3 psi





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10000

15000

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30000

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45000

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0 5 10 15 20 25 30 35 40 45 50

Re

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nt

Mo

du

lus

(p

si)







133





5000

10000

15000

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45000

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0 5 10 15 20 25 30 35 40 45 50

Re

silie

nt

Mo

du

lus

(p

si)







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40000

45000

50000

0 5 10 15 20 25 30 35 40 45 50

Re

silie

nt

Mo

du

lus

(p

si)







134


using FA mixtures at 98% of dmax (Specimen ID: FA1)



10000

20000

30000

40000

50000

60000

70000

80000

90000

100000

110000

120000

0 5 10 15 20 25 30 35 40 45 50

Resilie

nt

Mo

dulu

s (p

si)







10000

20000

30000

40000

50000

60000

70000

80000

90000

100000

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120000

0 5 10 15 20 25 30 35 40 45 50

Re

silie

nt M

od

ulu

s (p

si)







135





10000

20000

30000

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50000

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0 5 10 15 20 25 30 35 40 45 50

Re

silie

nt

Mo

du

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(p

si)







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0 5 10 15 20 25 30 35 40 45 50

Re

silie

nt

Mo

du

lus

(p

si)







136





10000

20000

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0 5 10 15 20 25 30 35 40 45 50

Re

silie

nt

Mo

du

lus

(p

si)







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20000

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0 5 10 15 20 25 30 35 40 45 50

Re

silie

nt

Mo

du

lus

(p

si)







137

Figure A-13 Mr vs. deviator stress at different confining stresses for specimens compacted using

virgin aggregates at different density levels

5000

10000

15000

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30000

35000

40000

45000

50000

0 5 10 15 20 25 30 35 40 45 50

Resil

ien

t M

od

ulu

s (

psi)

















138

APPENDIX B: DYNAMIC MODULUS CHARTS

139

Figure B-1 Master Curve for Specimen ID: VPPM1

140


141


142


143


144


145

Figure B-7 Master Curve for Specimen ID: VLPM1

146


147


148

Figure B-10 Master Curve for Specimen ID: VLPM3B

149


150


151


152

Figure B-14 Master Curve for Specimen ID: FRACLPM1

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154


155


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157


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Figure B-20 Master Curve for Specimen ID: PMALPM1

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160


161


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163


164

APPENDIX C: PERMANENT DEFORMATION CHARTS

165

Figure C-1 Fitting the power model for Specimen ID VPPM1


y = 1307.5x0.3213

R² = 0.993

100

1000

10000

100000

1000000

1 10 100 1000 10000

Pe

rman

en

t St

rain

(

p)


Test Points

Power (Model)

y = 413.59x0.5089

R² = 0.9978

100

1000

10000

100000

1000000

1 10 100 1000 10000

Pe

rman

en

t St

rain

(

p)


Test Points

Power (Model)

166



y = 687.85x0.4798

R² = 0.9953

100

1000

10000

100000

1000000

1 10 100 1000 10000

Pe

rman

en

t St

rain

(

p)


Test Points

Power (Model)

y = 2287.9x0.292

R² = 0.9959

100

1000

10000

100000

1000000

1 10 100 1000 10000

Pe

rman

en

t St

rain

(

p)


Test Points

Power (Model)

167



y = 2063.3x0.4151

R² = 0.9902

100

1000

10000

100000

1000000

1 10 100 1000 10000

Pe

rman

en

t St

rain

(

p)


Test Points

Power (Model)

y = 1663.3x0.5354

R² = 0.9993

100

1000

10000

100000

1000000

1 10 100 1000

Pe

rman

en

t St

rain

(

p)


Test Points

Power (Model)

168

Figure C-7 Fitting the power model for Specimen ID VLPM1


y = 1045.5x0.3629

R² = 0.9915

100

1000

10000

100000

1000000

1 10 100 1000 10000

Pe

rman

en

t St

rain

(

p)


Test Points

Power (Model)

y = 1718x0.3476

R² = 0.9934

100

1000

10000

100000

1000000

1 10 100 1000 10000

Pe

rman

en

t St

rain

(

p)


Test Points

Power (Model)

169

Figure C-9 Fitting the power model for Specimen ID VLPM3B


y = 1291.7x0.4386

R² = 0.9848

100

1000

10000

100000

1000000

1 10 100 1000

Pe

rman

en

t St

rain

(

p)


Test Points

Power (Model)

y = 1283.9x0.4463

R² = 0.9911

100

1000

10000

100000

1000000

1 10 100 1000 10000

Pe

rman

en

t St

rain

(

p)


Test Points

Power (Model)

170



y = 2249.7x0.3644

R² = 0.9993

100

1000

10000

100000

1000000

1 10 100 1000

Pe

rman

en

t St

rain

(

p)


Test Points

Power (Model)

y = 4478.3x0.3154

R² = 0.9973

100

1000

10000

100000

1000000

1 10 100 1000

Pe

rman

en

t St

rain

(

p)


Test Points

Power (Model)

171

Figure C-13 Fitting the power model for Specimen ID PMALPM1


y = 2309x0.1936

R² = 0.9929

100

1000

10000

100000

1000000

1 10 100 1000 10000 100000

Pe

rman

en

t St

rain

(

p)


Test Points

Power (Model)

y = 1005.8x0.2124

R² = 0.9941

100

1000

10000

100000

1 10 100 1000 10000 100000

Pe

rman

en

t St

rain

(

p)


Test Points

Power (Model)

172



y = 1426x0.4241

R² = 0.9981

100

1000

10000

100000

1000000

1 10 100 1000 10000

Pe

rman

en

t St

rain

(

p)


Test Points

Power (Model)

y = 1354.3x0.387

R² = 0.9921

100

1000

10000

100000

1000000

1 10 100 1000 10000

Pe

rman

en

t St

rain

(

p)


Test Points

Power (Model)

173



y = 2532.4x0.5005

R² = 0.9994

100

1000

10000

100000

1000000

1 10 100 1000

Pe

rman

en

t St

rain

(

p)


Test Points

Power (Model)

y = 3571.1x0.3422

R² = 0.993

100

1000

10000

100000

1000000

1 10 100 1000 10000

Pe

rman

en

t St

rain

(

p)


Test Points

Power (Model)

174

Figure C-19 Fitting the power model for Specimen ID FRACLPM1


y = 1563.3x0.3333

R² = 0.9856

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1000

10000

100000

1000000

1 10 100 1000 10000

Pe

rman

en

t St

rain

(

p)


Test Points

Power (Model)

y = 1536.6x0.3476

R² = 0.9947

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1000

10000

100000

1000000

1 10 100 1000 10000

Pe

rman

en

t St

rain

(

p)


Test Points

Power (Model)

175



y = 1089.4x0.4808

R² = 0.9823

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1000

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100000

1000000

1 10 100 1000 10000

Pe

rman

en

t St

rain

(

p)


Test Points

Power (Model)

y = 1508.3x0.33

R² = 0.976

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1000

10000

100000

1000000

1 10 100 1000 10000

Pe

rman

en

t St

rain

(

p)


Test Points

Power (Model)

176



y = 3500.8x0.2892

R² = 0.9979

100

1000

10000

100000

1000000

1 10 100 1000 10000

Pe

rman

en

t St

rain

(

p)


Test Points

Power (Model)

y = 3602x0.3167

R² = 0.9991

100

1000

10000

100000

1000000

1 10 100 1000 10000

Pe

rman

en

t St

rain

(

p)


Test Points

Power (Model)

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