AN INVESTIGATION INTO DYNAMIC MODULUS OF HOT-MIX ASPHALT AND
ITS CONTRIBUTING FACTORS
Except where reference is made to the work of others, the work described in this thesis
is my own or was done in collaboration with my advisory committee. This thesis does
not include proprietary or classified information.
_________________________
Mary Marjorie Robbins
Certificate of Approval:
_________________________________ ________________________________
Rod E. Turochy David H. Timm, Chair
Associate Professor Associate Professor
Civil Engineering Civil Engineering
_________________________________ ________________________________
Randy C. West George T. Flowers
Director Dean
National Center for Asphalt Technology Graduate School
AN INVESTIGATION INTO DYNAMIC MODULUS OF HOT-MIX ASPHALT AND
ITS CONTRIBUTING FACTORS
Mary Marjorie Robbins
A Thesis
Submitted to
the Graduate Faculty of
Auburn University
in Partial Fulfillment of the
Requirements for the
Degree of
Masters of Science
Auburn, Alabama
May 9, 2009
iii
AN INVESTIGATION INTO DYNAMIC MODULUS OF HOT-MIX ASPHALT AND
ITS CONTRIBUTING FACTORS
Mary Marjorie Robbins
Permission is granted to Auburn University to make copies of this thesis at its discretion,
upon requests of individuals or institutions and at their expense. The author reserves all
publication rights.
_________________________
Mary Marjorie Robbins
_________________________
Date of Graduation
iv
VITA
Mary Marjorie Robbins, daughter of Gail and Nancy (McClure) Robbins, was
born January 31, 1983 in Kettering, Ohio. She graduated from Centerville High School
in June, 2001. She attended the University of Toledo from where she graduated magna
cum laude in December, 2005 with a Bachelor?s of Science in Civil Engineering. As an
undergraduate student she participated in the Co-operative Education Program, working
for Lewandowski Engineers, and Wright Patterson Air Force Base. She also participated
in the Undergraduate Summer Internship in Transportation held at the University of
Texas during the summer of 2004. After graduation she worked for the Ohio
Department of Transportation as a Transportation Engineer for one year and eight
months prior to starting her graduate studies at Auburn University in August, 2007.
v
THESIS ABSTRACT
AN INVESTIGATION INTO DYNAMIC MODULUS OF HOT-MIX ASPHALT AND
IT?S CONTRIBUTING FACTORS
Mary Marjorie Robbins
Master of Science, May 9, 2009
(B.S.C.E., University of Toledo, 2005)
174 Typed Pages
Directed by David H. Timm
One of the key elements of mechanistic-empirical (M-E) flexible pavement
design is the characterization of material properties. One material property in particular,
the dynamic modulus of HMA, E*, influences tensile strain levels, therefore it is
necessary to investigate this property to successfully predict fatigue cracking.
E* can be determined directly by laboratory testing or it can be estimated using
predictive equations as a function of mixture properties. The more recently developed
M-E design program, the Mechanistic-Empirical Pavement Design Guide (MEPDG),
offers both methods to characterize E*.
An investigation into the Witczak 1-37A and the Witczak 1-40D E* predictive
equations, both utilized by the MEPDG and another recently developed predictive
vi
equation, the Hirsch model, was completed. Comparisons were drawn with E*
laboratory results for mixtures constructed as part of the National Center for Asphalt
Technology?s (NCAT) 2006 Test Track structural study. The investigation revealed that
the Hirsch E* model most accurately predicted measured E* values, while the Witczak
1-40D overpredicted values and the Witczak 1-37A varied inconsistently.
To validate and optimize M-E designs it is necessary to link pavement
performance to material properties. The field parameters that influence E*, load duration
and temperature, and the field parameter that is most affected by E*, tensile strain, were
measured under varying speeds and temperatures at the NCAT Test Track. These
measurements enabled comparisons with the MEPDG analysis procedure. In comparing
load durations, it was found that those determined by the MEPDG were nearly 70%
greater than those measured in the field. These load durations enabled the computation
of E* of each HMA layer, and the prediction of strain in a layered elastic program.
Strains estimated from both load duration methods (MEPDG and measured) closely
replicated each other; however they poorly replicated those strains found in the field,
indicating the inaccuracy of the time-frequency relationship currently used in the
MEPDG.
It is suggested that State DOT?s wishing to supplement laboratory E* testing
while utilizing the MEPDG for design, substitute laboratory results required for a level
one design with predictions from the Hirsch model. It is not recommended that the
MEPDG be used as a primary design method until further refinement of the time-
frequency relationship, and further investigation into the accuracy of the pavement
distresses can be completed.
vii
ACKNOWLEDGEMENTS
I would like to thank my family and friends who have always supported me in
my endeavors with patience and love, and for being a voice of reason throughout this
journey. I would also like to express my deep appreciation to my advisor, Dr. David
Timm for granting me this opportunity and for his guidance, wisdom and patience. I am
also grateful for the guidance and support offered by my advisory committee, Dr. Randy
West and Dr. Rod Turochy. I would like to thank the National Center for Asphalt
Technology for the use of their facilities and support for this research. I would like to
acknowledge the Alabama Department of Transportation, the Federal Highway
Administration, and the Oklahoma Department of Transportation for their financial
support and their commitment to development through research.
viii
Style used: Publication Manual of the American Psychological Association, Fifth
Edition
Computer software used: Microsoft Word, Microsoft Excel, WESLEA, Mechanistic-
Empirical Pavement Design Guide Version 1.0
ix
TABLE OF CONTENTS
LIST OF TABLES ............................................................................................................ xv
LIST OF FIGURES ........................................................................................................ xviii
CHAPTER ONE ................................................................................................................. 1
INTRODUCTION ............................................................................................................... 1
1.1 BACKGROUND ...................................................................................................... 1
1.2 OBJECTIVES ............................................................................................................ 4
1.3 SCOPE ....................................................................................................................... 4
1.4 ORGANIZATION OF THESIS ................................................................................ 5
CHAPTER TWO................................................................................................................. 7
LITERATURE REVIEW .................................................................................................... 7
2.1 INTRODUCTION ..................................................................................................... 7
2.2.1 E* Defined in the Laboratory .......................................................................... 9
2.2.2 Factors Affecting E* ...................................................................................... 11
2.2.2.1 Effect of Aggregate Properties ................................................................... 13
x
2.2.2.2 Effect of Binder Properties ......................................................................... 15
2.3 PREDICTING E* FROM OTHER PARAMETERS .............................................. 17
2.3.1 Andrei, Witczak and Mirza?s Revised Model (Witczak 1-37A Model) ........ 21
2.3.1.1 Accuracy of the Witczak 1-37A Model ....................................................... 24
2.3.2 Hirsch Model for Estimating HMA Modulus ................................................ 27
2.3.2.1 Accuracy of Hirsch Model .......................................................................... 30
2.3.3 Newly Revised Witczak Model ..................................................................... 31
2.3.3.1 Accuracy of the Witczak 1-40D Model ....................................................... 33
2.4 E* IN THE MECHANISTIC-EMPIRICAL PAVEMENT DESIGN GUIDE ........ 34
2.5 FACTORS AFFECTING LOAD DURATION AND STRAIN ............................. 37
2.5.1 Load Duration ................................................................................................ 38
2.5.2 Strain .............................................................................................................. 41
2.6 SUMMARY ............................................................................................................ 42
CHAPTER THREE ........................................................................................................... 45
TEST FACILITY .............................................................................................................. 45
3.1 INTRODUCTION ................................................................................................... 45
3.2 2006 STRUCTURAL STUDY ................................................................................ 46
xi
3.3 PAVEMENT CROSS-SECTIONS ......................................................................... 46
3.4 INSTRUMENTATION ........................................................................................... 49
3.5 TRAFFIC ................................................................................................................. 54
3.6 DATA ACQUISITION ........................................................................................... 55
3.7 SUMMARY ............................................................................................................ 56
CHAPTER FOUR ............................................................................................................. 57
LAB INVESTIGATION ................................................................................................... 57
4.1 INTRODUCTION ................................................................................................... 57
4.2 MODELS TO DETERMINE E* ............................................................................. 58
4.2.1 Witczak 1-37A E* Predictive Equation ......................................................... 60
4.2.2 Witczak 1-40D E* Predictive Equation ......................................................... 62
4.2.3 Hirsch E* Predictive Model ........................................................................... 63
4.3 TESTING PROTOCOL .......................................................................................... 65
4.4 MIXTURES TESTED ............................................................................................. 66
4.5 RESULTS AND DISCUSSION .............................................................................. 70
4.6 SUMMARY ............................................................................................................ 80
CHAPTER FIVE ............................................................................................................... 82
xii
FIELD DATA ................................................................................................................... 82
5.1 INTRODUCTION ................................................................................................... 82
5.2 TESTING ................................................................................................................ 82
5.3 STRAIN RESPONSES ........................................................................................... 83
5.3.1 Definition of Strain ........................................................................................ 84
5.3.2 Effect of Speed on Tensile Strain .................................................................. 86
5.3.3 Effect of Temperature on Tensile Strain ....................................................... 89
5.3.4 Combined Effects of Speed and Temperature on Tensile Strain ................... 93
5.4 LOAD DURATION ................................................................................................ 95
5.4.1 Definition of Load Duration .......................................................................... 96
5.4.2 Effect of Depth on Strain Pulse Duration ...................................................... 99
5.4.3 Effect of Speed on Strain Pulse Duration .................................................... 100
5.4.4 Effect of Temperature on Strain Pulse Duration ......................................... 102
5.4.5 Modeling Strain Pulse Duration for Field Conditions ................................. 103
5.5 SUMMARY .......................................................................................................... 106
CHAPTER SIX ............................................................................................................... 108
MEPDG EVALUATION ................................................................................................ 108
xiii
6.1 INTRODUCTION ................................................................................................. 108
6.2 EVALUATION OF MEPDG LOAD DURATION PROCEDURE ..................... 108
6.2.1 MEPDG Load Duration Procedure .............................................................. 109
6.2.2 N9 E* Regression Analysis ......................................................................... 111
6.2.3 Load Duration Computation ........................................................................ 113
6.2.4 Load Duration Comparisons ........................................................................ 117
6.3 Effect of MEPDG Load Duration Calculations ..................................................... 118
6.3.1 Strain Predictions Based on MEPDG Load Durations ................................ 119
6.3.2 Strain Predictions Based on Field-Modeled Load Duration ........................ 129
6.3.3 Strain Predictions Based on Field Modeled Tensile Strain ......................... 133
6.3.4 Comparison among Strain Predictions ........................................................ 134
6.4 SUMMARY .......................................................................................................... 139
CHAPTER SEVEN ......................................................................................................... 142
CONCLUSIONS AND RECOMMENDATIONS ......................................................... 142
7.1 SUMMARY .......................................................................................................... 142
7.2 CONCLUSIONS .................................................................................................. 143
7.2.1 Evaluation of E* Predictive Equations ........................................................ 143
xiv
7.2.2 Evaluation of Field Measured Strain and Strain Pulse Durations ............... 144
7.2.3 Evaluation of the MEPDG?s Method for Determining Load Duration ....... 145
7.3 RECOMMENDATIONS ...................................................................................... 146
REFERENCES ................................................................................................................ 148
xv
LIST OF TABLES
TABLE 2.1 List of E* Predictive Models (Bari and Witczak, 2006) .............................. 17
TABLE 2.2 Minimum and Maximum Values for the Ratio of Predicted to Measured E*
(Flintsch et al., 2007)......................................................................................................... 26
TABLE 2.3 Asphalt Dynamic Modulus (E*) Estimation at Different Hierarchical Input
Levels for New and Reconstruction Design (ARA Inc., 2004) ........................................ 35
TABLE 2.4 Recommended Frequencies and Temperatures for E* and G*, at Level One
Design (ARA Inc., 2004) .................................................................................................. 35
TABLE 2.5 Conventional Binder Tests to Achieve Viscosity (ARA Inc., 2004) ............ 36
TABLE 3.1 Location of Thermistors ............................................................................... 54
TABLE 3.2 Location of Additional Probes in Section N9 .............................................. 54
TABLE 3.3 Spacing Between Axles (Taylor, 2008) ....................................................... 55
TABLE 3.4 Axle Weight by Truck (Taylor, 2008) .......................................................... 55
TABLE 4.1 Material Property Requirements by Model .................................................. 60
TABLE 4.2 HMA Mixes by Section and Layer............................................................... 68
TABLE 4.3 Gradation Information by Mix # .................................................................. 68
xvi
TABLE 4.4 Binder Information (Section N1) ................................................................. 69
TABLE 4.5 Binder Information (Section N2) ................................................................. 69
TABLE 4.6 Binder Information (Sections N8 & N9) ...................................................... 69
TABLE 4.7 Binder Information (Section N8 & N9) ....................................................... 69
TABLE 4.8 Binder Information (Sections N8 & N9) ...................................................... 69
TABLE 4.9 Binder Information (Section N10) ............................................................... 70
TABLE 4.10 Binder Information (Section N10) ............................................................. 70
TABLE 4.11 Binder Information (Section S11) .............................................................. 70
TABLE 4.12 Binder Information (Section S11) .............................................................. 70
TABLE 4.13 Linear Regression Coefficients for Each Model ........................................ 73
TABLE 4.14 Percent of Total E* Values Underpredicted by Hirsch Model ................... 75
TABLE 4.15 Ratio of Predicted to Measured E* for Witczak 1-40D E* Model ............ 76
TABLE 5.1 Average Mid-Depth Temperatures by Date ................................................. 87
TABLE 5.2 Regression Coefficients by Axle Type and Direction of Strain ................... 94
TABLE 6.1 E* Regression Coefficients by Lift ............................................................ 113
TABLE 6.2 Location of Temperature Probes ................................................................ 114
TABLE 6.3 Conditions for Strain Predictions ............................................................... 121
xvii
TABLE 6.4 Computed E* Values for N9 HMA Layers ................................................ 121
TABLE 6.5 HMA Moduli for Transformed N9 Structure ............................................. 123
TABLE 6.6 Regression Coefficients for MR (Taylor, 2008) ........................................ 123
TABLE 6.7 Unit Weight by HMA Layer (Timm, 2008) ............................................... 126
TABLE 6.8 Properties Defined for WESLEA ............................................................... 128
TABLE 6.9 Final Resilient Moduli Values .................................................................... 128
TABLE 6.10 Tensile Strain Based on MEPDG Load Durations ................................... 129
TABLE 6.11 Moduli of Layers in Transformed Structure from Field Modeled Load
Durations ......................................................................................................................... 132
TABLE 6.12 Tensile Strain Based on Field Modeled Load Durations .......................... 133
TABLE 6.13 Tensile Strain Based on Field Modeled Tensile Strain ............................. 134
TABLE 6.14 Resulting Strain Predictions ..................................................................... 138
xviii
LIST OF FIGURES
FIGURE 1.1 M-E Pavement Design Framework............................................................... 1
FIGURE 2.1 Phase Lag between Sinusoidal Stress and Induced Strain (Huang, 1993).... 9
FIGURE 2.2 E* Master Curves by JMF (Tashman and Elangovan, 2007) ..................... 12
FIGURE 2.3 E* and E*/sin? for LA Asphalt Mixtures (Mohammad et al., 2007) ......... 14
FIGURE 2.4 Dynamic Modulus Results for Gravel at 10?C (Huang et al., 2007) .......... 16
FIGURE 2.5 Nomograph for Predicting Stiffness Modulus of Bituminous Mixes
(Bonnaure et al., 1977) ...................................................................................................... 18
FIGURE 3.1 2006 Test Track Structural Study Test Sections (Timm, 2008) ................. 48
FIGURE 3.2 Location of Gages, Sections N1-N6, N8, N10, S11 ................................... 50
FIGURE 3.3 Location of Gages, Section N7. .................................................................. 52
FIGURE 3.4 Location of Gages, Section N9. .................................................................. 53
FIGURE 4.1 The AMPT Machine and Close-up of Specimen. ....................................... 65
FIGURE 4.2 Comparison of Predicted E* to Measured E* by Predictive Model ........... 71
FIGURE 4.3 Comparison of Predicted E* to Measured E* for the Hirsch E* Model ... 74
xix
FIGURE 4.4 Comparison of Predicted E* to Measured E* for the 1-40D Model .......... 74
FIGURE 4.5 Comparison of Measured E* to Predicted E* for SMA Mixes .................. 77
FIGURE 4.6 Comparison of Measured E* to Predicted E* for Superpave Mixes .......... 77
FIGURE 4.7 Comparison of Measured E* to Predicted E* for Mixes with PG 64-22
Binder ................................................................................................................................ 78
FIGURE 4.8 Comparison of Measured E* to Predicted E* for Mixes with PG 76-28
Binder ................................................................................................................................ 79
FIGURE 5.1 Cross-section of N9. ................................................................................... 84
FIGURE 5.2 Longitudinal Strain Pulse. .......................................................................... 85
FIGURE 5.3 Transverse Strain Pulse. .............................................................................. 86
FIGURE 5.4 Effect of Speed on Tensile Strain by Date. ................................................. 88
FIGURE 5.5 Rate of Strain Change by Mid-Depth Temperature. ................................... 88
FIGURE 5.6 Effect of Temperature on Longitudinal Strain ............................................ 91
FIGURE 5.7 Effect of Temperature on Transverse Strain ............................................... 92
FIGURE 5.8 Calculated vs. Measured Strain .................................................................. 95
FIGURE 5.9 Strain Pulse Near Neutral Axis ................................................................... 99
FIGURE 5.10 Strain Pulse Duration by Gage Depth ..................................................... 100
FIGURE 5.11 Effect of Speed on Strain Pulse Duration ............................................... 102
xx
FIGURE 5.12 Effect of Temperature on Strain Pulse Duration .................................... 103
FIGURE 5.13 Goodness of Fit of Predicted Strain Pulse Durations ............................. 105
FIGURE 6.1 MEPDG Load Duration Procedure (Eres, 2003). ..................................... 110
FIGURE 6.2 Example of E* Convergence .................................................................... 117
FIGURE 6.3 Measured Load Duration Versus Theoretical. .......................................... 118
FIGURE 6.4 Evaluation of MEPDG by Pavement Response ........................................ 119
FIGURE 6.5 Transformation of Structure for Use in WESLEA ................................... 122
FIGURE 6.6 Field Modeled Strain Pulse Duration at 45 mph and 60 ?F ...................... 132
FIGURE 6.7 Predicted Strains by Temperature and Speed. .......................................... 135
FIGURE 6.8 Simulated Strains Compared with Modeled Strains ................................. 137
1
CHAPTER ONE
INTRODUCTION
1.1 BACKGROUND
In a mechanistic-empirical (M-E) framework for pavement design, four major
inputs are utilized to predict pavement responses and ultimately pavement performance
enabling the selection of a cross-section meeting the specified requirements. M-E design
enables the mechanical properties of the selected materials to be used in conjunction
with empirical performance information and site conditions (traffic and climate), as
shown in Figure 1.1. Inputs include an initial pavement structure, climatic data, traffic
volume and weight distributions, and material properties of the hot mix asphalt (HMA),
base and subgrade materials. These inputs are used to predict the pavement?s responses,
stress (?) and strain (?), at critical locations through mechanical analysis. Such
predictions may be made with the aid of layered elastic analysis (LEA) or finite element
models. Historical performance data help create accurate transfer functions used to
estimate the number of loads to failure given the predicted pavement responses for
comparison to failure criteria. Recently, one specific M-E design program, the
Mechanistic-Empirical Pavement Design Guide (MEPDG) has come to the forefront of
design, sparking interest among state Departments of Transportation (DOTs) for
implementation as their primary design method. Such a program should be validated
under field conditions to determine its benefits and suitability to state DOTs.
1
FIGURE 1.1 M-E Pavement Design Framework.
In M-E pavement design, accurate representation of material characteristics is
imperative to a successful and reliable design. One in particular is the HMA dynamic
modulus, E*. E* helps to define the viscoelastic nature of HMA by quantifying the
effects of temperature and frequency on stiffness under dynamic loading. This is
necessary to accurately predict the in-situ pavement responses to varying speeds, and
Traffic
Climate Material
Properties
Pavement Structure
Mechanical
Analysis
?, ?
Transfer
Functions
Performance Criteria
? Fatigue Cracking
? Rutting
2
temperatures throughout the pavement?s cross-section. E* can be determined in the
laboratory through the AASHTO TP-62 procedure or it can be predicted by one of many
E* predictive models, the three most recent including: Hirsch, Witczak 1-37A, and
Witczak 1-40D (Bari and Witczak, 2006) (Christensen et al., 2003). To predict E* from
one of these three models, no laboratory testing is required beyond viscosity testing,
determination of gradation information and rudimentary volumetric testing. At the
highest degree of complexity for design, the MEPDG utilizes E* laboratory test results,
and for lower levels of design, it utilizes one of the Witczak equations (Eres, 1999).
Equipment to run E* testing is costly ($75,000-$90,000) (FHWA, 2009) and many state
DOTs do not currently have such equipment. For example, the Alabama DOT (ALDOT)
currently operates without such equipment since it is not needed for their current design
framework. However, a pooled fund study, ?Implementation of the Asphalt Mixture
Performance Tester (AMPT) for Superpave Validation,? (Study No. TPF-5(178))
launched by the FHWA in 2008 makes this technology more economical for state
transportation agencies (FHWA, 2009). As states contemplate implementing the
MEPDG, it is necessary to assess the accuracy of the revised Witczak model, as well as
the original Witczak and Hirsch models in estimating E* in comparison to laboratory E*
test results for a range of mix types.
Although E* can be measured directly in the laboratory, it is very difficult to
accurately measure it in the field. However, knowledge of E* is imperative in
developing relationships between pavement response and material properties. Given the
difficulty of direct measurements, focus should be placed on the factors that influence
changes in E*. Due to the viscoelastic nature of HMA, the dynamic modulus is heavily
3
influenced by three factors: rate of loading, temperature, and depth within the pavement
structure (Eres, 2003). Temperature and pavement depth are relatively easy parameters
to measure in the field. Rate of loading on the other hand is much more difficult to
quantify in the field. In the laboratory, rate of loading can be correlated to the applied
testing frequency. During lab testing, controlling and measuring rate of loading is a
simple task, but in the field it is much more arduous due to the shape of the loading
waveforms transmitted throughout the pavement. Because of the complexity in
measuring frequency, some design procedures simply use a fixed value such as the
Asphalt Institute which assumes a value of 10Hz regardless of the conditions (Asphalt
Institute, 1999). The MEPDG however, uses an iterative process to compute the time of
loading that relies on E* of each HMA layer, temperature, depth in pavement and
modulus of subgrade (Eres, 2003). From this computation, frequency is then computed
(Eres, 2003). It should be noted that as a result of this iterative process, E* is ultimately
computed for each HMA layer. Although frequency is not a measurable parameter, load
duration is. It is therefore necessary that the MEPDG?s load duration procedure be
validated with field data to assess its accuracy.
Material properties significantly influence pavement responses. In particular, one
such pavement response, tensile strain, is significantly dependent on E* (Eres, 2003).
Tensile strain at the bottom of the HMA layers is of importance in designing a pavement
that is resistant to fatigue (bottom-up) cracking. Thus, for a reliable pavement design it
would be ideal to develop relationships between field measured E* and field measured
tensile strain. Although E* cannot be accurately measured in the field, the factors
influencing it can be directly measured. Thus, relationships can be drawn between these
4
factors and the field-measured tensile strain. Unfortunately, the design procedure
investigated in this analysis (MEPDG) fails to output strain levels. However, tensile
strain can be computed through external mechanical analysis using layered elastic
analysis for a given pavement structure and known traffic loads. To assess the viability
of the MEPDG as a pavement design method, it is necessary that the MEPDG be
evaluated with respect to the effect of load duration and E* values on tensile strain.
1.2 OBJECTIVES
Given the onset of the MEPDG as a powerful pavement design tool that may be
implemented as a primary design method for roadways among state DOTs, the
following objectives were established to assess its benefits:
1. Evaluate the Witczak 1-37A, Witczak 1-40D, and Hirsch E* predictive models
for general use HMA mixtures in the southeastern United States.
2. Evaluate the MEPDG?s procedure for determination of time of loading for use in
estimating E* values and strain levels.
3. Make recommendations for use by state DOTs pertinent to characterizing E* in
design procedures.
1.3 SCOPE
To meet the above objectives, a laboratory investigation was completed on test
sections from the 2006 structural study as part of the National Center for Asphalt
Technology?s (NCAT) Test Track. E* testing was completed on HMA mixtures
included in that study, following the AASHTO TP-62 procedure for HMA dynamic
modulus testing. Three models, the Witczak 1-37A, Witczak 1-40D and Hirsch models
5
were used to compute E* from gradation, binder and volumetric data of the same
mixtures tested in the laboratory. Comparisons were drawn to assess the quality of the
MEPDG?s analysis and for recommendations to state DOTs.
One of the test sections in the 2006 structural study, section N9, was selected for
further field investigation. For this section, regression analyses were completed on
laboratory E* test results to determine the in-place dynamic modulus of the HMA layers
under live traffic loading. The deep cross-section of N9 allowed for instrumentation at
various depths within the HMA, thus enabling the collection of extensive data pertaining
to temperature and strain with depth. Field testing was completed on this section over a
one month period in the spring of 2007, in which live traffic was applied at a range of
speeds. At various depths within N9?s pavement structure, longitudinal tensile strains
and in-situ pavement temperatures were captured. From the captured longitudinal strain
traces at multiple depths, strain values and loading durations were measured. From
these measurements, regression analyses were conducted to quantify tensile strain and
load duration. Using the load durations computed by both the MEPDG and the model
developed in this analysis, E* was computed using the regression equation based on
laboratory test results. The effect of the E* estimates on tensile strain were then assessed
and conclusions were drawn regarding pavement response as a function of material
properties and the use of the MEPDG.
1.4 ORGANIZATION OF THESIS
A literature review in Chapter Two details aspects of HMA dynamic modulus,
including the definition, procedure for laboratory testing, means to estimate, and its use
in the MEPDG. Additionally, the literature review is extended to a discussion of factors
6
affecting load duration and strain. Both field and laboratory testing were completed for
this investigation. Chapter Three discusses the details of the test facility, the NCAT Test
Track, utilized to complete the field testing. Chapter Four includes the details of the
laboratory testing to determine E* for the mixes constructed in 2006 and the comparison
of the three E* models with laboratory results. Chapter Five describes the conditions of
the field testing on section N9. Results of the field testing are discussed, as well as the
analysis of the effect of vehicle speed, pavement temperature, and depth on load
durations and strain levels. Chapter Six evaluates the MEPDG?s use of E* in its design
procedure. Contained in this chapter are comparisons with field measurements for load
durations computed using the MEPDG procedure and strain levels resulting from the
MEPDG?s load duration computation. Chapter Seven concludes the aspects of this
investigation, and provides recommendations to state DOTs for characterizing E* in an
M-E design framework.
7
CHAPTER TWO
LITERATURE REVIEW
2.1 INTRODUCTION
In an M-E framework, accurate material characterization is vital in successfully
predicting pavement responses and ultimately pavement performance. The difficulty in
accurately characterizing HMA material properties lies in the viscoelastic nature of
HMA. One such material property, dynamic modulus of HMA (E*), reflects the time
and temperature dependency of HMA. This material property is the ratio of stress to
strain of the mixture, and thus influences the response under loading. Therefore, a
complete understanding of this material property and its contributing factors is necessary
to accurately characterize it for use in structural design procedures. The factors affecting
and the methods to determine dynamic modulus are further investigated through
previous literature discussed in the following subsections. Additionally, given that
dynamic modulus cannot be measured directly in the field, literature on the factors
affecting dynamic modulus that are measurable are also investigated.
2.2 E* DEFINED
The viscoelastic nature of HMA can be characterized in part by its dynamic
modulus. The dynamic modulus is a measure of the HMA?s resistance to deformation
under sinusoidal loading. It is the absolute value of the complex modulus. The complex
modulus consists of two parts, the real part, which represents elastic stiffness, and the
8
imaginary part, representing the internal damping of the materials (Huang, 1993). The
dynamic modulus is determined from the maximum applied stress and peak recoverable
axial strain, described by Equation 2-1 (Huang, 1993). It should be noted that although
dynamic modulus is the absolute value of complex modulus, it is denoted from this point
forward in this thesis, simply by E*.
0
0
2
0
0
2
0
0 sincos*
?
??
?
??
?
? =
???
?
???
?+
???
?
???
?=E (2-1)
where:
E* = dynamic Modulus (psi)
?0 = stress amplitude (psi )
?0 = strain amplitude (??)
? = phase angle (radians)
The phase angle describes the lag in the induced axial strain relative to the applied
compressive stress, illustrated in Figure 2.1 (Huang, 1993), where the sinusoidal stress
pulse is defined by angular velocity, ?, and time, t. This phase lag illustrates the time-
dependency of HMA. Due to time-frequency relationships, it can further be stated that
HMA is dependent on the loading frequency. This is illustrated by the equations
defining the sinusoidal loading (stress) and the sinusoidal response (strain) in Figure 2.1.
The stress pulse and resulting strain pulse are both defined by the angular frequency,
which is in turn a function of loading frequency, illustrated by Equation 2-2.
fpi? 2= (2-2)
where:
? = angular frequency (rad/sec)
9
f = loading frequency (Hz)
FIGURE 2.1 Phase Lag between Sinusoidal Stress and Induced Strain (Huang,
1993).
HMA is not only frequency-dependent, it is also temperature dependent. Laboratory
testing of E* revealed that varying the HMA temperature results in different magnitudes
of recoverable strain and thus, varied dynamic moduli (Bonnaure et al., 1977).
2.2.1 E* Defined in the Laboratory
Previous laboratory testing of E* consisted of a 2-point bending test, in which
trapezoidal specimens were loaded under sinusoidal compressive stress (Bonnaure et al.,
1977). From the 2-point bending test developed for Shell Laboratories, the stiffness
modulus (E*) could be determined in two ways. First, E* could be determined from a
simple calculation using the measured applied force and the measured displacement at
the free end of the specimen. The second method utilized measured strain and the
applied stress to calculate E*. By testing multiple mixes at three frequencies (4, 40, and
50Hz) and three temperatures (-15, 9, and 30?C) Bonnaure et al. found that loading time
10
and temperature were ?significant parameters for the bending strains of asphalt mixes
since, under standard service conditions the stiffness may vary from 1,400 to 6,000,000
psi (1977).? It was reported that increasing the temperature or loading time resulted in a
decrease in stiffness, defined by E* (1977). Furthermore, Bonnaure et al. discovered that
an equivalency among these two factors existed, such that E* curves from different
temperatures and frequencies could be superimposed (now referred to as time-
temperature superposition), enabling a master curve to be created for a reference
temperature (1977). Master curves have since become a useful tool to translate
laboratory results to one reference temperature, as is done in the MEPDG.
Laboratory testing has since evolved with the ASTM specification, ?D3497-79
(2003) Standard Test Method for Dynamic Modulus of Asphalt Mixtures? (2003). This
method requires the application of a haversine compressive stress pulse to a cylindrical
specimen at three temperatures, 41, 77, and 104?F, as well as three frequencies, 1, 4, and
16 Hz. The sinusoidal load is applied to the specimen for a minimum of 30 seconds, but
not to exceed 45 seconds. Strain gages bonded to the mid-height of the specimen
measure axial strain from which the dynamic modulus is computed as the ratio of axial
stress to recoverable axial strain.
The most recent and widely used laboratory test for E* is the AASHTO TP62-07
standard method (2007). Again a cylindrical specimen is used, to which haversine axial
compressive stress is applied at a given temperature and frequency. Five temperatures,
14, 40, 70, 100, and 130?F and six frequencies, 0.1, 0.5, 1.0, 5, 10, and 25 Hz are
specified for testing. Linear variable differential transformers (LVDT) are mounted as a
minimum in two locations to measure axial deformation, from which recoverable strain
11
is calculated. Dynamic modulus is defined in this procedure as the ratio of the stress
magnitude to average strain magnitude. Furthermore, phase angle computations are
outlined in this procedure.
2.2.2 Factors Affecting E*
Dynamic modulus has been sufficiently proven to be dependent on two
parameters: temperature and frequency. The decrease in dynamic modulus with an
increase in temperature and decrease in loading frequency has been consistently reported
by researchers for many years (e.g., Bonnaure et al., 1977; Flintsch et al., 2007;
Tashman and Elangovan, 2007; Mohammad et al., 2007). Looking at the test specimen
itself, it is evident that there are many parameters that may present variability in the
dynamic modulus. HMA has two main components: aggregate and binder. Each
component has numerous properties which influence the overall response of the mixture.
Thus, it is only logical that the properties of each component may further influence
dynamic modulus.
This sentiment was echoed in research findings at the Virginia Tech
Transportation Institute (VTTI) (Flintsch et al., 2007). Dynamic modulus tests produced
different master curves for the various mixtures tested, causing Flintsch and colleagues
to conclude that ?the dynamic modulus test is sensitive to variation in the mix
properties? (Flintsch et al., 2007). In recent research conducted for the Washington State
Department of Transportation (WSDOT) different mixes were found to possess
statistically significantly different dynamic moduli (Tashman and Elangovan, 2007).
The objective of this study was to determine typical dynamic moduli values for their
Superpave mixes as well as the sensitivity to mix properties. Seven job mix formulas
12
(JMF) were investigated with aggregates of different type and source. Dynamic modulus
tests were completed using the Asphalt Performance Mixture Tester (AMPT), formerly
the Simple Performance Tester (SPT) from which master curves were created, illustrated
in Figure 2.2. Although variations in dynamic moduli were evident in Figure 2.2,
statistical measures (Type I p-value) confirmed that overall the seven different
Superpave mixtures were significantly different (Tashman and Elangovan, 2007).
Comparing the mixes side-by-side, using a Tukey pair-wise comparison, the results
shown indicated that only some mixes were significantly different than others (presented
in bold font) (Tashman and Elangovan, 2007). Because these mixtures were tested using
the same procedure, AASHTO TP-62-03 (e.g. same temperatures and frequencies), the
differences in the aggregate properties, as well as the differences in asphalt properties
may account for the variations in dynamic moduli.
FIGURE 2.2 E* Master Curves by JMF (Tashman and Elangovan, 2007).
13
2.2.2.1 Effect of Aggregate Properties
Previous investigations into dynamic moduli revealed that some aggregate
properties are more influential than others. At the very simplest level, the amount of
aggregate significantly influences the mix design and its performance. Likewise,
Bonnaure and colleagues found that the percent of aggregate by volume also influences
the stiffness (dynamic modulus) of the mix (Bonnaure et al., 1977). The percent by
volume of air voids was also observed to influence the stiffness of the mix (Bonnaure et
al., 1977). Research for WSDOT into aggregate gradation found that small variations
(?2% from the JMF) in the percent passing the #200 sieve did not consistently show
significant differences in the dynamic modulus of the mix (Tashman and Elangovan,
2007). A look into asphalt mixtures in Louisiana revealed that nominal maximum
aggregate size (NMAS) contributed to variations in dynamic moduli (Mohammad et al.,
2007). Shown in Figure 2.3, is the trend of increasing dynamic moduli among mixes
with higher NMAS. Mixes with a 25mm NMAS were found to be associated with higher
dynamic moduli than those mixes with a 19mm or 12.5mm NMAS within each mixture
category. Mohammad and colleagues attributed this trend to the stronger stone-to-stone
contact among larger aggregates (Mohammad et al., 2007).
14
FIGURE 2.3 E* and E*/sin? for Louisiana Asphalt Mixtures (Mohammad et al.,
2007).
The effect of confining pressure was investigated as part of a larger investigation
into dynamic moduli of HMA mixtures in Tennessee (Huang et al., 2007). At higher
temperatures the effect of aggregate properties was more significant, causing the
dynamic moduli to increase with confining pressure. For more rounded aggregate such
as gravel, confining pressure was more influential in the improvement of dynamic
moduli. From this, Huang and colleagues concluded that the effect of confining pressure
on dynamic moduli was ?dependent on the role of aggregate structures in asphalt
mixtures? (Huang et al., 2007).
Aggregate interactions were found to also influence the phase angle associated to
the dynamic moduli. In research conducted at VTTI, phase angles were found to
increase up to a certain frequency, and beyond that frequency, phase angles began to
decrease for a temperature of 100?F (Flintsch et al., 2007). Whereas at 130?F, phase
angles consistently increased with increased frequencies. ?The predominant effect of
aggregate interlock? was credited for the observed behavior (Flintsch et al., 2007).
15
In addition to aggregate gradation, shape, and interaction, the type of aggregate
was also found to contribute to variations in dynamic modulus values of asphalt
mixtures. Research at the Florida Department of Transportation (FDOT) was conducted
on several mixes in which the binder type remained constant, while aggregate properties
varied (Ping and Xiao, 2007). Because the binder type was consistent among all mixes,
the differences in HMA stiffness were attributed to the different aggregate types (Ping
and Xiao, 2007). Asphalt mixtures containing either granite or RAP were found to be
stiffer (higher E*) than the limestone mixtures (Ping and Xiao, 2007).
2.2.2.2 Effect of Binder Properties
Some properties associated with the asphalt binder used in HMA mixtures have
been found to influence the dynamic modulus values. The PG grade of an asphalt binder
is related to its performance under certain temperature ranges. Higher graded binders are
generally stiffer to prevent deformation under hot weather conditions. The stiffer binder
would likely contribute to the overall stiffness of the mix. Findings from Huang and his
associates were consistent with this, as an increase in dynamic moduli was observed as
the PG grade progressed from PG 64-22 to PG 70-22 to PG 72-22 for a given
temperature (Huang et al., 2007). However for a different type of aggregate (gravel
rather than limestone), they found the trend was reversed, such that the dynamic moduli
decreased with an increase in binder grade, shown in Figure 2.4.
16
FIGURE 2.4 Dynamic Modulus Results for Gravel at 10?C (Huang et al., 2007).
Further investigation on the Tennessee plant produced mixes revealed that the
asphalt content was influencing the stiffness of the mix as well (Huang et al., 2007). The
mixes containing gravel had different asphalt contents for each binder grade used, and
overall higher binder contents than the limestone mixes. It was found that the lower
dynamic moduli values were associated with higher asphalt contents, leading them to
conclude that small variations in binder content influenced the dynamic modulus values
(Huang et al., 2007). The sensitivity of the dynamic modulus to asphalt content found in
Tennessee mixes was consistent with findings at VTTI (Flintsch et al., 2007). By
comparing mixes of the same type, Flintsch et al. also found that the mix with the
highest asphalt content exhibited the lowest dynamic modulus (2007). The findings by
both these researchers reiterate those from early research by Bonnaure et al., in which
sensitivity to the percent of bitumen, the hardness of the bitumen and the temperature
susceptibility of the bitumen in the mix were reported (1977).
Reclaimed asphalt pavement (RAP) is often used in mixes across the country to
reduce costs. Using RAP in a mixture reduces the amount of new binder required in the
17
mix because of the contributing asphalt content of the RAP. The aged binder (and
therefore higher binder stiffness) from the RAP has been credited with contributing to
higher dynamic modulus for Louisiana HMA mixtures (Mohammad et al., 2007).
2.3 PREDICTING E* FROM OTHER PARAMETERS
Although E* can be determined in the laboratory, it is time-consuming and
requires expensive specialized equipment and operator training. As a result, the
development of equations to predict E* strictly from mix properties have been attempted
for many decades. The predictive models, according to Bari and Witczak (2006),
developed in the last 60 years are as listed in Table 2.1.
TABLE 2.1 List of E* Predictive Models (Bari and Witczak, 2006)
Model No. E* Predictive Model Year (Published)
1 Van der Poel Model 1954
2 Bonnaure Model 1977
3 Shook and Kallas? Models 1969
4 Witczak?s Early Model, 1972 1972
5 Witczak and Shook?s Model 1978
6 Witczak?s 1981 Model 1981
7 Witczak, Miller and Uzan?s Model 1983
8 Witczak and Akhter?s Models 1984
9 Witczak, Leahy, Caves and Uzan?s Models 1989
10 Witczak and Fonseca?s Model 1996
11 Andrei, Witczak and Mirza?s Revised Model 1999
12 Hirsch Model of Christensen, Pellinen and Bonaquist 2003
Although not the first attempt to model E*, in 1977 Bonnaure et al. developed a
nomograph to model E* as a function of the volume of the binder, the volume of the
mineral aggregate and stiffness modulus of the binder in Figure 2.5 (1977). This
nomograph is commonly referred to as the Shell nomograph, as it was developed for
Shell International Petroleum. Additionally, from the same findings, Bonnaure et al.,
developed a computer program, Module, to predict the stiffness modulus (dynamic
modulus) of the mix using the following equations (1977):
18
FIGURE 2.5 Nomograph for Predicting Stiffness Modulus of Bituminous Mixes
(Bonnaure et al., 1977).
19
bg
g
VV
V
+
??= )100(342.182.10
1? (2-3)
2
2 0002135.000568.00.8 gg VV ++=? (2-4)
???
?
???
?
?
?=
133.1
137.1log6.0 2
3
b
b
V
V? (2-5)
)(7582.0 214 ??? ?= (2-6)
For 5 x 106 N/m2 < Sb < 109 N/m2,
2
3434 8log
2)8(log2log ?
???? +??+?+=
bbm SSS (2-7)
For 109 N/m2 < Sb < 3 x 109 N/m2,
)9)(log(0959.2log 42142 ???++= bm SS ????? (2-8)
where:
Sm = stiffness modulus of the mix (dynamic modulus) (N/m2)
Vg = percent volume of aggregate (%)
Vb = percent volume of binder (%)
Sb = stiffness modulus of the bitumen (N/m2)
The Asphalt Institute (A.I.) developed a method for design in which the dynamic
modulus is determined from the following equations, as presented in Huang?s Pavement
Analysis and Design textbook (1993):
110000,100* ??=E (2-9)
1.1
2231 00189.0000005.0
??+= f???? (2-10)
55.0
42
??? T= (2-11)
20
02774.01703.0
2003 931757.0070377.003476.0)(028829.0553833.0
?? ++?+= fVfP
a ??
(2-12)
bV483.04 =? (2-13)
flog49825.03.15 +=? (2-14)
1939.2
77 )(2.508,29
?=
FP o? (2-15)
where:
E* = dynamic modulus (psi)
f = loading frequency (Hz)
T = temperature (?F)
Va = volume of air voids (%)
? = asphalt viscosity at 70?F, or use equation 2-15 (106 poise)
P200 = percentage by weight of aggregate passing the No. 200 sieve (%)
Vb = volume of bitumen (%)
P77?F = penetration at 77?F
While the equations developed for Module and the nomograph (Bonnaure et al., 1977)
incorporate the volume of all of the aggregate, the A.I. equations utilize only the volume
of the fines (percent passing the No. 200 sieve). This indicates possible dependency on
the percent of fines, which is contrary to laboratory results in the WSDOT study that
found small variations in P200 did not significantly affect the dynamic moduli (Tashman
and Elangovan, 2007). Although both consider the percent of bitumen in the mix, the
A.I. equations also incorporate the viscosity of the bitumen as well as the temperature of
the bitumen. Furthermore, the A.I. equations utilize loading frequency as a factor in the
21
determination of the dynamic modulus of the mix. Although loading frequency is used
to compute E*, it is assumed to be 10 Hz for the A.I. design charts (Huang, 1993).
Since, the development of the A.I. method and associated E* predictive model,
there have been many more models developed to supplement laboratory testing. Over
the last sixty years, these models have progressed by the factors used to determine E*
and the overall accuracy of the models. The three most recent models include the
Andrei, Witczak and Mirza?s Revised Model (1999), the Hirsch Model of Christensen,
Pellinen and Bonaquist (2003), and the new revised version of the Witczak E*
predictive model (2006). Each of the three is discussed in more detail below.
2.3.1 Andrei, Witczak and Mirza?s Revised Model (Witczak 1-37A Model)
The Andrei, Witczak and Mirza?s revised model was developed in 1999 (called
the Witczak 1-37A model from this point forward), as an update to the previous E*
predictive equation, by Witczak and Fonseca in 1996 (Andrei et al., 1999). The previous
model considered the binder properties by means of the asphalt viscosity, and effective
asphalt content. The model also includes the loading frequency as a variable. Other
parameters included air voids, and aggregate gradation information. Laboratory E* test
results were used to re-calibrate the previous model by the addition of various mix
properties. This was done by establishing a new database consisting of 56 additional
mixes, 34 of which were composed of modified asphalt binders, for a total of 1,320 new
data points. While the new database had E* test results for only 5 different aggregate
gradations, it had a much wider range of viscosity values, as 5 temperatures were tested
for the 20 binders. By combining the new database with the database used to develop the
previous model, a re-calibration of the previous model was completed, with the revised
22
model listed below in Equation 2-16 (Bari and Witczak, 2006). As shown in Equation 2-
16, the same factors as used for the previous model were utilized for the revised
predictive equation. It should be noted that the equation listed in Equation 2-16 was
reported by Bari and Witczak in the most recent document regarding the revised
Witczak E* predictive equations and it appears that the sixth coefficient is contrary to
other sources. The coefficient, listed below as ?-0.0822?, is contrary to the ?-0.08022?
reported by Andrei et al. (1999) as well as in other comparative studies (Dongre et al.,
2005; Ping and Xiao, 2007). Given that this was the most recent resource by one of the
developers of the model and that the difference is negligible, the -0.0822 coefficient was
taken as the correct value.
))log(393532.0)log(313351.0603313.0(
34
2
38384
4
2
200200
1
0055.0)(000017.0004.00021.0872.3
0822.0058.00028.0)(0018.0029.025.1*log
?
????
???
???+
+?+?+
+????+?=
f
abeff
beff
a
e
VV
VVE
(2-16)
where:
E* = dynamic modulus of mix, 105 psi
? = viscosity of binder, 106 poise
f = loading frequency, Hz
?200 = % passing #200 sieve
?4 = cumulative % retained on #4 sieve
?38 = cumulative % retained on 3/8 in. sieve
?34 = cumulative % retained on 3/4 in. sieve
23
Va = air voids, % by volume
Vbeff = effective binder content, % by volume
For use in this model (Andrei et al., 1999), the viscosity of the binder is determined by a
linear relationship between log-log viscosity and log temperature, illustrated by
Equations 2-17 (Bari and Witczak, 2006). In plotting the log-log of the viscosity versus
the log of temperature, the slope of the line is the parameter VTS, and the intercept is A.
If viscosity information is not obtainable, viscosity can be determined by the
relationship with the binder shear complex modulus and binder phase angle, shown in
Equation 2-18 (Bari and Witczak, 2006).
RTVTSA logloglog +=? (2-17)
where:
? = viscosity of binder, centipoise (cP)
A, VTS = regression parameters
TR = temperature, ?Rankine
8628.4
sin
1
10
*
???
?
???
?=
b
bG
?? (2-18)
Where:
Gb* = dynamic shear modulus of binder, psi
?b = phase angle of Gb*, degrees
In comparing this model with previous predictive equations, it is evident that it is much
more detailed in terms of both aggregate and binder composition of the mix. Similar to
the A.I. equations (Huang, 1993), the Witczak 1-37A model requires the percent of
fines, air voids, and loading frequency. Like the equations behind the Shell nomograph
24
(Bonnaure et al., 1977), this model also utilizes the stiffness of the binder, in terms of
the shear complex modulus used to determine the viscosity. Rather than considering the
percent binder as does the previous equations, this model makes use of the effective
binder content, incorporating the ability of the aggregate to absorb the binder.
Additionally, the Witczak 1-37A model requires more detailed gradation information
beyond the percent of fines needed by previous equations.
2.3.1.1 Accuracy of the Witczak 1-37A Model
This model was developed through regression analyses based on the measured
dynamic moduli of mixtures ranging in gradation, ?from sand-asphalt mixtures to dense-
graded mixes,? asphalt cements, both conventional and modified, and their degree of
aging (Andrei et al., 1999). A coefficient of determination of 0.886 in arithmetic space
and 0.941 in logarithmic space was reported for the model (Andrei et al., 1999).
Although the model proved to accurately predict the E* values from the database, it is
necessary to determine its ability to predict E* for other gradation and binder variations
not included in the database, before suggesting its use globally. Several comparison
studies have been completed to assess the quality of this model, with various results.
Comparisons were drawn from AMPT laboratory E* testing conducted by the
FHWA mobile laboratory with calculated E* values for the properties of the specimens
tested (Dongre et al., 2005). For each measured value, three E* values were calculated
given the same conditions (temperature and frequency) as the measured values; varying
only the binder information for the three different aging scenarios. The three different
aged conditions were the original, rolling thin film oven (RTFO), and pressure aging
vessel (PAV). Five different mixes, composed of four different binders (PG 64-22, PG
25
58-28, PG 64-28, and PG 70-22) were tested in this investigation. From this study, it
was reported that the Witczak 1-37A model using RTFO aged binder most closely
estimated the measured E* values among the three aged conditions (Dongre et al.,
2005). Furthermore, the Witczak 1-37A model was found to overestimate E* for the
specimens tested at moduli values below 125,000 psi (Dongre et al., 2005). Causes for
overpredictions of E* were assumed to be associated with the A and VTS parameters
(Dongre et al., 2005). Originally those parameters were developed prior to Superpave
specifications, however, Dongre utilized G* results and the associated phase angles to
determine viscosity, through Equation 2-18, and thus citing this difference as a potential
cause for overprediction (2005). The A and VTS parameters were also credited for the
decreased precision (R2 = 0.88) of this model when applied to an expanded database
which added 5,820 data points to the database used to create the Witczak 1-37A model
(Bari and Witczak, 2006). Furthermore, Bari and Witczak stated ?The inherent problem
with the ASTM Ai-VTSi relationship is that it does not consider the effect of loading
frequency (or time) on the stiffness of the binder itself (2006).?
The overestimation of E* at lower moduli values reported by Dongre and his
associates (Dongre et al., 2005), was echoed in later investigations. In a comparison
study on Louisiana asphalt mixtures, the Witczak 1-37A model generally
underestimated the measured values, except at high temperatures and/or low frequencies
(Mohammad et al., 2007). At these lower measured E* values, the model was found to
overpredict dynamic moduli values for the thirteen Superpave mixtures tested
(Mohammad et al., 2007). Although Dongre et al. reported overprediction for the mixes
tested at moduli values of 125,000 psi and less, Azari and colleagues observed
26
overprediction across the board, with the overprediction more significant at 500,000 psi
and lower (Azari et al., 2007). In a comparison study at the VTTI, the Witczak 1-37A
was found to overestimate measured values in some instances, with a predicted value
reported nearly twice the measured value (Flintsch et al., 2007). Wide ranges were
reported for the ratio of predicted to measured E* for each of the eleven mixes
investigated; the minimum and maximum ratios are listed in Table 2.2 for each mix
(Flintsch et al., 2007). Overestimating low dynamic moduli values could present
potential design failures as higher strains result from low moduli, thereby causing
premature distresses. Thus, the repeated observed overprediction of dynamic moduli at
low frequency and high temperatures is a point of concern.
TABLE 2.2 Minimum and Maximum Values for the Ratio of Predicted to
Measured E* (Flintsch et al., 2007)
Ratio SM1 SM2 SM3 IM1 IM2 IM3 IM4 BM1 BM2 BM3 BM4
Min 0.54 0.58 0.75 0.60 0.60 0.48 0.64 0.54 0.52 0.45 0.68
Max 0.90 1.07 1.56 0.90 1.01 0.75 1.24 0.80 1.90 0.84 1.05
A study on Louisiana asphalt mixtures was completed, in which measured E*
values of various mixtures were compared with predicted values from the Witczak 1-
37A model (Mohammad et al., 2007). The thirteen mixtures tested included Superpave
mixes designed for high, medium and low volume roads, SMA mixes, and Marshall
mixes. Three types of binder were used: PG 76-22M, PG 70-22M and PG 64-22, of
which the first two were modified. Aggregate structures varied with NMAS ranging
from 12.5 mm to 25.0 mm, and various amounts of RAP were used in the mixtures.
Mohammad et al. reported generally good agreement between measured and predicted
values, with coefficients of determination greater than 0.90 in logarithmic space (2007).
27
However, it should be noted that logarithmic space can be deceiving and the goodness of
fit for arithmetic space was not reported.
As mentioned previously, Mohammad and colleagues reported sensitivity to
NMAS in laboratory tests. The Witczak 1-37A model also exhibited sensitivity to
NMAS as it produced more accurate predictions for larger NMAS. For the 12.5, 19.0,
and 25 mm NMAS mixtures, the predicted modulus was found to be 0.75, 0.93 and 1.01
of the measured values, respectively (Mohammad et al., 2007).
In addition to aggregate gradation, aggregate type was also found to influence
the accuracy of the prediction using Witczak?s 1-37A model. In a study conducted on
Florida DOT mixes, twenty Superpave mixes containing three different aggregate types
were investigated using the same binder in all of the mixes (Ping and Xiao, 2007). For
mixes containing granite or RAP material, the predictive equation was found to be
conservative, as the measured values were slightly underestimated (Ping and Xiao,
2007). Predicted values for mixes containing limestone materials fell above the line of
equality when compared with measured values, indicating a slight overprediction for
this aggregate type (Ping and Xiao, 2007).
2.3.2 Hirsch Model for Estimating HMA Modulus
The Hirsch model for estimating HMA modulus is based on a law of mixtures
for composite materials (Christensen et al., 2003). The law of mixtures, called the
Hirsch model, was developed by T.J. Hirsch in the 1960s and combines phases of a
material by the arrangement of its elements (Christensen et al., 2003). The elements of a
material may be in parallel or series arrangement. The Hirsch model allows for the
prediction of a material property (commonly the modulus) of a composite material from
28
the sum of the same material property of two separate phases of the material, shown in
Equation 2-19 in parallel, and Equation 2-20 in series.
2211 EEEc ?? += (2-19)
2211 ///1 EEEc ?? += (2-20)
where:
Ec = modulus of the composite material
?1, ?2 = the volume fraction of a given phase
E1, E2 = moduli of each phase
In applying the Hirsch model to HMA, Christensen et al. developed a model to predict
the modulus of HMA, E*, from the shear modulus of the binder, G*, and volumetric
properties of the mix (2003).
This model was developed in part to meet the objectives of the NCHRP Projects
9-25 and 9-31 for Superpave requirements, and to analyze the effects of air voids, voids
in mineral aggregate (VMA) and other volumetric properties on E* (Christensen et al.,
2003). According to Christensen, the Hirsch model was selected for application to HMA
because ?asphalt concrete tends to behave like a series composite at high temperature,
but more like a parallel composite at low temperatures (2003).? The resulting model for
estimating HMA modulus is for ?a simple three-phase system of aggregate, asphalt
binder, and air voids (Christensen et al., 2003).? The aggregate phase in the parallel
portion of the model represents that portion of the aggregate particles in intimate contact
with each other, termed aggregate contact volume, Pc (Christensen et al., 2003).
Temperature dependency of HMA is partially represented by Pc, such that high values
of Pc are related to mixtures with high stiffness and strength, typical at low
29
temperatures, whereas low values of Pc represent mixtures with low strength and
stiffness, typical at high temperatures (Christensen et al., 2003). A database consisting
of 18 different mixtures, with 8 different binders and 5 different gradations was utilized
in the development of the model, as presented in Equation 2-21 (Christensen et al.,
2003). In addition to a predictive equation for E*, an equation to predict the phase angle
was also developed, although it is not presented here.
( ) ( )
1
*3000,200,4
100/11
000,10*31001000,200,4*
?
?
?
?
?
?
?
?
? +??
+?
?
?
??
? ?
?
??
?
? ?+?
?
??
?
? ?=
b
bmix
GVFA
VMAVMAPc
VMAVFAGVMAPcE
(2-21)
where:
58.0
58.0
*3650
*320
???
?
???
? ?+
???
?
???
? ?+
=
VMA
GVFA
VMA
GVFA
Pc
b
b
where:
?E*?mix = dynamic modulus, psi
VMA = voids in mineral aggregate, %
VFA = voids in aggregate filled with mastic, %
VFA = 100*(VMA-Va)/VMA
Va = air voids, %
?G*?b = dynamic shear modulus of binder, psi
30
In comparison with the Witczak 1-37A predictive equation, and other previous
models, this model is much simpler, requiring only three parameters (G*, VMA and
VFA). Rather than incorporating frequency and temperature directly into the Hirsch
predictive equation, they are inherent to the shear modulus of the binder. Also, the need
to translate viscosity data to shear modulus is eliminated, which not only simplifies the
equation but is also intuitive given the Superpave Performance Grading system for
which Gb* testing is conducted. This could possibly reduce errors highlighted by Dongre
and colleagues in their evaluation of the Witczak 1-37A model (2005).
2.3.2.1 Accuracy of Hirsch Model
The database used to develop the Hirsch predictive model captured a wide range
of measured E* values (183 to 20,900 MPa) from test temperatures of -9, 4, 21, 38, and
54?C, but only two frequencies, 0.1 and 5 Hz (Christensen et al., 2003). Although the
database reflected various conditions, it lacked in the robustness of the test mixes. The
range of air voids leaned towards the high end of the spectrum, with only 5.6% air voids
(Christensen et al, 2003) tested at the low end. The coefficient of determination of the
model was reported as 98.2% (in log space) for the measured E* values in the database
(Christensen et al., 2003).
Christensen also applied the Hirsch predictive model to mixes used in a
sensitivity study by Witczak, as well as comparing results with measured values and
predictions made by Witczak?s 1-37A predictive equation (2003). These comparisons
revealed that the Hirsch model resulted in a standard error of 41%, a slight improvement
over the standard error for the Witczak 1-37A model of 45% (Christensen et al., 2003).
31
In a comparison study conducted by Dongre and his associates, findings similar
to Christensen?s were reported, in which predictions by the Hirsch model for E* were
closer to the laboratory measured values than those predicted by the Witczak 1-37A
model (Dongre et al., 2005). Dongre observed that overall the Hirsch model showed a
slight improvement over the Witczak 1-37A model with R2 values of 0.96 and 0.92
respectively, and Se/Sy (where Se is standard error and Sy is standard deviation) values of
0.192 and 0.284 respectively in logarithmic scale (2005). Witczak and colleagues
applied the Hirsch model first to their smaller original database of 206 data points and
second to the expanded database of 7400 data points (2006). An excellent goodness of
fit, R2 = 0.98 in logarithmic scales, was reported when applied to the first database
(Witczak et al., 2006). However, when applied to the second, the Hirsch model did not
accurately predict the E* values, returning a coefficient of determination of 0.61 in
logarithmic scale and 0.23 in arithmetic scale (Witczak et al., 2006).
2.3.3 Newly Revised Witczak Model
Upon the expansion of the database used to enhance the original Witczak
predictive model, resulting in the Witczak 1-37A model, Witczak discovered a decrease
in accuracy of the 1-37A model (2006). As a result of this decrease, R2 = 0.88 compared
to R2 = 0.94 for the development of the 1-37A model, a new model was developed from
the expanded database, called the Witczak 1-40D predictive equation from this point
forward. The 1-40D model is presented in Equation 2-22.
32
( )
)log8834.0*log5785.07814.0(
34
2
3838
2
3838
2
4
4
2
200200
0052.0
1
01.0)(0001.0012.071.003.056.2
06.108.0
)(00014.0006.0)(0001.0
011.0)(0027.0032.065.6
*754.0349.0*log
bbG
beffa
beff
a
beffa
beff
a
b
e
VV
VV
VV
VV
GE
?
???
???
???
+??
?
+
??+??
?
?
???
?
++++
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
???
?
???
?
+??
?+?
++?
?+?=
(2-22)
where:
E* = dynamic modulus of mix, psi
?Gb*?= dynamic shear modulus of binder, psi
?200 = % passing #200 sieve
?4 = cumulative % retained on #4 sieve
?38 = cumulative % retained on 3/8 in. sieve
?34 = cumulative % retained on 3/4 in. sieve
Va = air voids, % by volume
Vbeff = effective binder content
The combined database used to develop the 1-40D model expanded the mix
properties and incorporated various aging conditions including short-term oven aging,
laboratory aging, plant aging, and field aging (Witczak et al., 2006). This was an
improvement from the previous database that included only un-aged laboratory blended
mixes. Discrepancies in the accuracy of the 1-37A model for the combined database
33
were believed to be due to the representation of stiffness of the binder and extrapolation
of the model beyond the initial range of variables (Witczak et al., 2006).
The 1-37A model requires viscosity by means of the A-VTS relationship shown
in Equation 2-17, however, this relationship, as Witczak states, ?does not consider the
effect of loading frequency (or time) on the stiffness of the binder itself (2006).? This
was accounted for in the 1-40D model by replacing the viscosity by means of the A-
VTS relationship with a direct input of the complex shear modulus of the binder, Gb*,
which ?can more effectively take care of the binder rheology with changing temperature
and loading rate (Witczak et al., 2006).? Furthermore, the associated binder phase angle,
?b, was also incorporated into the new model. Similar to the 1-37A model, the 1-40D
model also makes use of aggregate gradation, air voids, effective binder volume, voids
in mineral aggregate, and voids filled with asphalt to predict E*.
2.3.3.1 Accuracy of the Witczak 1-40D Model
The database which enabled the development of the Witczak 1-40D predictive
equation used 7400 data points from 346 mixes, from which a coefficient of
determination of 0.90 was reported in logarithmic scale, and 0.80 in arithmetic scale
(Witczak et al., 2006). This was an improvement over the 1-37A model for the same
database, as was the ratio of standard error to standard deviation (Se/Sy) which was
reported for the 1-40D model as 0.32 in logarithmic scale and 0.45 in arithmetic scale
(Witczak et al., 2006). In looking at the coefficients of determination, it is evident that
the 1-40D model (R2 = 0.90) offers a slight improvement over the 1-37A model (R2 =
0.88) for the wide range of mix properties, including varying binder types and aging
conditions tested.
34
Both the 1-37A and 1-40D Witczak equations were evaluated for pavements at
the FHWA?s Accelerated Loading Facility (ALF) (Azari et al., 2007). Both equations
were found to be good predictors of the measured E* values contained in the study. The
1-40D model, however, returned a slightly higher coefficient of determination, 0.936 (in
logarithmic scale) than the 1-37A model, which produced an R2 of 0.917 (also in
logarithmic scale) (Azari et al., 2007). Although this reiterates the improvement reported
by Witczak (2006), the overestimation at low modulus values reported in numerous
evaluations of the 1-37A model (Dongre et al., 2005; Mohammad et al., 2007; Azari et
al, 2007) was not improved by the 1-40D model in the study completed by Azari (2007).
2.4 E* IN THE MECHANISTIC-EMPIRICAL PAVEMENT DESIGN GUIDE
The MEPDG offers three levels of design which are dependent on the user?s
available data and desired accuracy of the design. One significant difference in the three
levels of design is the determination of the dynamic modulus. Upon the determination of
E*, a master curve is created at a reference temperature of 70?F. The degree of
complexity required for material property inputs is dictated by the level of design
chosen. A brief description of the methods to estimate E* at each level is listed in
Chapter Two of Part Two of the Guide for the MEPDG, presented in Table 2.3 (ARA
Inc., 2004). At the highest level of complexity, level one requires laboratory E* and G*
results. At levels two and three, laboratory test results for E* are replaced by the
estimation of E* from either the 1-37A or 1-40D Witczak predictive equation. At the
current stage of development of the MEPDG, the user can select which E* predictive
model is run. However, this is likely to change in the future, given the improvement of
the 1-40D model over the 1-37A model.
35
TABLE 2.3 Asphalt Dynamic Modulus (E*) Estimation at Different Hierarchical
Input Levels for New and Reconstruction Design (ARA Inc., 2004)
Input level Description
1 ? Conduct E* (dynamic modulus) laboratory test (NCHRP 1-28A) at loading
frequencies and temperatures of interest for the given mixture
? Conduct binder complex shear modulus (G*) and phase angle (?) testing on
the proposed asphalt binder (AASHTO T315) at ? = 1.59 Hz (10 rad/s) over a
range of temperatures.
? From binder test data estimate Ai-VTSi for mix-compaction temperature.
? Develop master curve for the asphalt mixture that accurately defines the time-
temperature dependency including aging.
2 ? No E* laboratory test required.
? Use E* predictive equation.
? Conduct G*-? on the proposed asphalt binder (AASHTO T315) at ? = 1.59 Hz
(10 rad/s) over a range of temperatures. The binder viscosity of stiffness can
also be estimated using conventional asphalt test data such as Ring and Ball
Softening Point, absolute and kinematic viscosities, or using the Brookfield
viscometer.
? Develop Ai-VTSi for mix-compaction temperature.
? Develop master curve for asphalt mixture that accurately defines the time-
temperature dependency including aging.
3 ? No E* laboratory testing required.
? Use E* predictive equation.
? Use typical Ai-VTS ? values provided in the Design Guide software based on
PG viscosity, or penetration grade of the binder.
? Develop master curve for asphalt mixture that accurately defines the time-
temperature dependency including aging.
For a level one design, E* laboratory testing must be completed for a range of
frequencies and temperatures. G* testing on RTFO-aged binder must also be completed,
however, at a fixed loading frequency of 1.59 Hz for a range of temperatures. The
recommended temperatures and frequencies for these tests are listed in Table 2.4.
TABLE 2.4 Recommended Frequencies and Temperatures for E* and G*, at Level
One Design (ARA Inc., 2004)
Temperature (?F)
Mixture E* and ? Binder G* and
?, 1.59 Hz 0.1 Hz 1 Hz 10 Hz 25 Hz
10 X X X X
40 X X X X X
55 X
70 X X X X X
85 X
100 X X X X X
115 X
130 X X X X X
36
In Table 2.3, the A-VTS relationship is mentioned as a requirement for a level one
design, as well as levels two and three. The A-VTS relationship is described by
Equation 2-17 and characterizes the effect of temperature on viscosity for a particular
binder. It is used mainly in a level one design to complete the master curve. To obtain
viscosity, conventional binder testing can be completed, as listed in Table 2.5, or
Equation 2-18 can be used to convert Gb* test results (at f = 1.59 Hz) to viscosity. Once
viscosity is obtained the A-VTS relationship is obtained through a linear regression on
the viscosity-temperature data, allowing the determination of viscosity at any
temperature.
TABLE 2.5 Conventional Binder Tests to Achieve Viscosity (ARA Inc., 2004)
Test Temp, ?C Conversion to Viscosity, Poise
Penetration 15 See Equation 2-23
Penetration 25 See Equation 2-23
Brookfield Viscosity 60 None
Brookfield Viscosity 80 None
Brookfield Viscosity 100 None
Brookfield Viscosity 121.1 None
Brookfield Viscosity 135 None
Brookfield Viscosity 176 None
Softening Point Measured 13,000Poise
Absolute Viscosity 60 None
Kinematic Viscosity 135 Value x 0.948
2)log(00389.0)log(2601.25012.10log PenPen +?=? (2-23)
where:
? = viscosity, Poise
Pen = penetration for 100 g, 5 sec loading, mm/10
A level two design uses one of the two models previously discussed to estimate
E*, requiring volumetric properties, gradation information and depending on which
model is selected, either G* testing or viscosity testing. For the Witczak 1-37A model,
viscosity is required and can be obtained in the same manner as described above for a
37
level one design. Although G* testing (at f = 1.59 Hz) can be used for the Witczak 1-
37A model, it is not required. For a level two design using the Witczak 1-40D model,
G* testing is necessary. Rather than testing at a fixed loading frequency, G* testing must
be completed for a range of frequencies and temperatures.
A level three design also utilizes volumetric properties, and gradation
information, however no laboratory testing is required. If the user selects the Witczak 1-
37A model to estimate E*, viscosity values are estimated from typical temperature-
viscosity relationships, programmed into the MEPDG, for the selected binder grade.
Similarly, the Witczak 1-40D E* model selects typical G* values from the temperature-
viscosity relationship for the binder grade.
2.5 FACTORS AFFECTING LOAD DURATION AND STRAIN
It is known from laboratory testing that HMA modulus is frequency and
temperature dependent. In the field the dynamic modulus of HMA characterizes how a
particular mixture is likely to respond to a moving load under varying pavement
temperatures. Neither E* nor frequency can be measured directly in the field; however
time of loading is measurable. Due to time-frequency relationships, time significantly
influences the HMA stiffness, and therefore should be investigated. Pavement responses
under moving loads are heavily dependent on the HMA modulus. From the defining
equation (2-1) for E*, it is evident that strain is inversely influenced by E*. Therefore, it
is important that the factors affecting strain be detailed in order to better understand the
factors affecting E*.
38
2.5.1 Load Duration
Historically, time of loading has been defined by either a stress pulse or a strain
pulse and found to be dependent on speed and depth. Through the use of finite element
and elastic layer theory, Barksdale estimated the shape and length of compressive stress
pulses under a rolling wheel load (Barksdale, 1971). He concluded that compressive
stress pulse durations are a function of pavement depth and vehicle speed and could be
characterized by either a sinusoidal or triangular pulse for vehicle speeds up to 45 mph
depending on the depth within the pavement. Further investigation by Brown extended
Barksdale?s research to stress pulses in three directions, using again elastic layered
theory and sinusoidal curves to estimate the length of such pulses (Brown, 1973). From
this research Brown developed Equation 2-24, such that the loading time represents the
average pulse times of the three orthogonal stresses (vertical, radial, and tangential)
which resulted in a loading time equal to 0.48 times that of Barksdale?s.
log (t) = 0.5d ? 0.2 ? 0.94log(v) (2-24)
where:
d = depth (m)
v = vehicle speed (km/hr)
Measuring load durations in the field has presented challenges in defining the
boundaries of the load pulse. More recent research by Loulizi et al. at the Virginia Smart
Road facility characterized the effects of speed, depth and temperature on measured
vertical compressive stress pulse times (2002). Pulse durations were measured for truck
speeds ranging from 8 km/h (5 mph) to 72 km/h (45 mph) at various pavement depths.
Similar testing conducted at a later date was used for temperature comparisons, resulting
39
in maximum in-situ temperature differences between test dates of 13.2?C (55.8?F) and
6.8 ?C (44.2 ?F) for the two pavement types investigated. Due to the lack of symmetry
in the stress pulses, the loading time was taken to be twice the time of the rising
normalized vertical compressive stress pulse beginning at a normalized stress of 0.01
(Loulizi et al., 2002). Loulizi et al. concluded that normalized compressive stress pulse
durations generally increased with depth and were related to vehicle speed by a power
function (2002). For the conditions tested, no significant relationship with temperature
was determined (Loulizi et al., 2002).
In 2008, Garcia and Thompson utilized strain pulses to measure the loading
times, reporting that load durations for strain pulses were also influenced primarily by
load speed and pavement thickness (2008). A traffic load simulator, the Advanced
Transportation Loading Assembly (ATLAS), was employed to apply loads with no
lateral displacement under a single tire inflated to 110 psi (Garcia and Thompson, 2008).
For the strain measurements recorded during ATLAS testing, the longitudinal and
transverse strain pulses were of different shapes, requiring two different definitions for
strain pulse duration. In the longitudinal direction, it was taken to be the time that the
pavement experienced only tensile strain, whereas in the transverse direction, it was
taken to be twice the rising portion (in the tensile region) of the pulse using the unloaded
condition as a reference point.
ATLAS testing was conducted at very low speeds, 2 mph, 6 mph, and 10 mph
for loads ranging from 5-11 kips. Load duration measurements were taken at various
depths in the pavement; however in-situ pavement temperatures were not considered.
Generally speaking, pulse durations were found to increase with depth and decrease with
40
speed, consistent with prior research on stress pulses (Garcia and Thompson, 2008).
Specifically, in the longitudinal direction, loading durations were compared with
Ullidtz?s method for calculating loading times from vertical stress pulses (Garcia and
Thompson, 2008). As presented by Garcia and Thompson, the method outlined by
Ullidtz is described in Equations 2-25 and 2-26 (2008). From this comparison it was
found that for the conditions tested, the Ullidtz method very accurately estimated the
measured strain pulse times, over estimating measured longitudinal strain pulse
durations by only 2.21% (Garcia and Thompson, 2008).
zLeff 2200 += (2-25)
where:
Leff = effective length (mm)
z = actual depth (mm)
v
Lt eff= (2-26)
where:
t = time of loading
Leff = effective length (mm)
v = vehicle speed
The newly-developed Mechanistic-Empirical Pavement Design Guide (MEPDG)
considers depth, vehicle speed and temperature in the determination of loading time
(ARA Inc., 2003). The MEPDG assumes the time of loading to be the duration of a
haversine stress pulse (ARA Inc., 2003). The method outlined by the MEPDG is similar
to the method of Ullidtz as described by Garcia and Thompson (2008), in that an
41
effective length, Leff, of the load pulse is calculated as a function of the depth, and that
time is then a function of the effective length and vehicle speed. However, the MEPDG
uses effective depth, Zeff, to compute Leff by considering the modulus of each layer as
well as the thickness of each layer above the point of interest. Additionally, the MEPDG
takes into account the actual contact radius of the applied load. Given that the HMA
modulus is frequency and temperature dependent, and that the MEPDG calculates time
of loading ultimately as a function of the HMA modulus, the process is an iterative one.
The MEPDG procedure for calculating load duration is described in greater detail in
Chapter 6.
2.5.2 Strain
Pavement responses, specifically tensile strain, can be difficult to characterize
due to the viscoelastic nature of HMA. Because of its viscous properties, HMA
responses are time-dependent, such that as a load is applied, a response is not
immediately induced throughout the pavement. Additionally, it is dependent on
temperature, causing increased flexibility under warmer temperatures and increased
stiffness under colder temperatures. The prediction model becomes increasingly
complex when the pavement is under dynamic loading, such as the loading that occurs
with live traffic.
Researchers and engineers have characterized these time-temperature
relationships both theoretically and through physical measurement. Although developing
a temperature-strain relationship was not the primary area of investigation in Mateos and
Snyder?s validation of a response model from the Minnesota Road Research
(Mn/ROAD) test facility, a trend of increasing strain with increasing pavement
42
temperatures was illustrated in their findings (2002). Observations from the National
Center for Asphalt Technology (NCAT) Test Track have reported that an increase in
temperature has resulted in an increase in horizontal tensile strain. This relationship was
found to be well-modeled by a power function of the mid-depth pavement temperature
(Priest and Timm, 2006).
Investigations at the PACCAR Technical Center into the effects of vehicle speed
on strain have revealed a reduction in tensile strain with increasing speed (Chatti et al.,
1996). For tensile strain in the longitudinal direction at the bottom of the HMA layer, a
maximum reduction of 30-40% was reported as vehicle speeds were increased from
creeping motion to 64 km/h (Chatti et al., 1996). Similarly, transverse strain at the
bottom of the HMA layer was also reported to decrease with speed, although not as
significantly (Chatti et al., 1996). Mateos and Snyder (2002) also recorded a decrease in
tensile strains in both the transverse and longitudinal direction with changes in vehicle
speed.
2.6 SUMMARY
HMA is a viscoelastic material that responds differently to varying conditions.
When a load is applied to HMA, the response, strain, is not immediately induced, but
rather a time lag exists between the applied stress and induced strain. The dynamic
modulus, E*, characterizes this viscoelasticity through its dependency on frequency and
temperature. E* is defined as the ratio of peak recoverable stress to peak recoverable
strain when HMA is under sinusoidal loading. There have been numerous laboratory
tests developed over the years to determine the dynamic modulus of HMA, the most
recent and commonly used is the AASHTO TP 62-07 (2007).
43
Although it has been established that the dynamic modulus is frequency and
temperature dependent, laboratory testing has shown that E* is also influenced by mix
properties. Aggregate properties such as the type of aggregate, NMAS, air voids and
aggregate interactions were found to influence E*. Furthermore, the binder grade,
asphalt content, and RAP content were reported as contributing parameters as well.
There have been numerous attempts over the last sixty years with varying
degrees of success to develop a means to predict E* without conducting an E*
laboratory test. Nomographs and predictive equations have been developed using
gradation information, volumetric and binder properties to estimate E*. The three most
recently developed equations include the Witczak 1-37A E* predictive model, the
Hirsch E* predictive model, and the Witczak 1-40D E* predictive model. The accuracy
of the 1-37A model has been reported to vary among NMAS, and aggregate type. The
Hirsch E* model was found to be an improvement over the 1-37A model for some
databases, but was found to be poor for the database used to create the 1-40D model.
Both the 1-37A and 1-40D were reported to overpredict E* at low moduli values.
E* is an important parameter that is essential to accurate pavement designs. The
method to determine E* varies among the levels of design in the MEPDG. The
hierarchical levels of design (1-3) dictate the extent of required material properties.
Levels two and three are particularly useful to those State DOTs which do not have E*
laboratory equipment because E* laboratory results are supplemented with E*
predictions. At the most complex level, level one, laboratory test results for E* and G*
are required. At levels two and three the user may select which model, the Witczak 1-
37A or the Witczak 1-40D, is employed to estimate E* from mix properties. At level
44
two, design gradation information and volumetric properties are required regardless of
which model is selected. If the 1-37A model is selected, G* testing at a frequency of
1.59 Hz or viscosity testing is required. For the 1-40D model G* testing at a range of
frequencies and temperatures is necessary. At a level three design only gradation and
volumetric information is required as the necessary binder information is selected based
on typical temperature-viscosity relationships for the selected binder grade.
It is important to be able to link field performance with material properties to
further refine the accuracy of M-E pavement design. However, E* cannot be measured
in the field. However, two important parameters can be measured: time of loading and
strain. Understanding these parameters under varying conditions may lend insight into
how E* is characterized under field conditions. Tensile strain has been found to increase
under high temperatures and decrease with an increase in vehicle speed. Load durations
are influenced by vehicle speed, as well as depth in the pavement. Load durations have
been measured by stress and strain pulses, although the MEPDG considers it to be
characterized by a haversine stress pulse.
45
CHAPTER THREE
TEST FACILITY
3.1 INTRODUCTION
The National Center for Asphalt Technology at Auburn University has a full-
scale test facility for the evaluation of flexible pavements under live traffic. The test
facility is located in Opelika, Alabama, and consists of a 1.7 mile oval test track, with
applied traffic similar to open access highways using real trucks and human drivers.
The Test Track has enabled its sponsors, state Departments of Transportation (DOT)
from the Southeast region and beyond, the Federal Highway Administration (FHWA)
and other contributors from the industry to collaborate on advancing HMA technology
through the construction and evaluation of flexible pavements in an accelerated
pavement testing framework. The Test Track is comprised of 46 200-ft pavement
sections with varying cross-sections. Some sections have embedded instrumentation for
the evaluation of pavement response and Mechanistic-Empirical analysis. Three
complete testing cycles have been completed in the years 2002, 2005, and 2008
respectively. For this investigation, only data from the third cycle, constructed in 2006
and completed in 2008, were utilized, focusing only on those test sections that were
newly constructed in the 2006 Test Track structural study.
46
3.2 2006 STRUCTURAL STUDY
Assessments of the first two test cycles highlighted the sponsors? need for further
investigation into structural pavement response (Timm, 2008). To address this need, the
third test cycle (2006-2008) included 11 test sections as part of the structural study. The
11 test sections were equipped with embedded instrumentation to capture pavement
response under live loading. Of the 11 sections, five (N3, N4, N5, N6, and N7) were left
in place from the 2003-2006 test cycle to continue evaluation under additional traffic,
and six sections (N1, N2, N8, N9, N10, and S11) were newly constructed with
embedded instrumentation in 2006 (Timm, 2008). Additionally, N5 was milled and
inlaid with 2 inches of HMA to correct previous top-down cracking in the section.
Under normal testing operations, pavement responses were captured on a weekly basis
throughout the testing cycle for analysis. Also, the surface performance of each test
section was monitored on a weekly basis.
3.3 PAVEMENT CROSS-SECTIONS
Each of the 11 test sections was designed based on the individual sponsor?s need
and common practices. As a result, the cross-sections varied by the HMA mixtures and
unbound materials utilized in the structures. The cross-sections of each are shown in
Figure 3.1, labeled by its associated sponsor and whether it was left in place from the
2003-2006 test cycle or newly constructed in 2006.
One commonality among the test sections was the local unbound material used
to construct the sections. All 11 pavement sections utilized the local soil at the Test
Track, referred to as ?Track soil,? which is classified as an AASHTO A-4(0) soil
47
containing large cobbles and stones (Timm, 2008). Excluding section N8 and N9, all of
the test sections utilized this material as a compacted subgrade. Sections N8 and N9
instead used a compacted soft subgrade material, on top of the uncompacted Track soil
(not shown in Figure 3.1) and the compacted Track soil as a base material. The soft
subgrade material was imported from Seale, Alabama and had a high clay content which
closely replicates subgrade materials typically encountered in Oklahoma. A Limerock
base quarried in Florida and typically used by the Florida DOT was placed in sections
N1 and N2. The Granite base used in sections N3-N7, and S11 was quarried in
Columbus, Georgia, and is typically utilized by ALDOT for road construction in the
Southeastern part of Alabama. Section N10 used a Missouri Type 5 base material.
Laboratory testing and backcalculation was conducted on each of the unbound materials
to determine the resilient modulus, MR, as a function of the state of stress (Taylor,
2008). Discussion of these results appears in Chapter Six of this thesis.
48
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
18.0
20.0
22.0
24.0
N1 N2 N3 N4 N5 N6 N7 N8 N9 N10 S11
As
B
uil
t T
hic
kn
es
s,
in.
PG 67-22 PG 76-22 PG 76-22 (SMA) PG 76-28 (SMA)
PG 76-28 PG 64-22 PG 64-22 (2% Air Voids) PG 70-22
Limerock Base Granite Base Type 5 Base Track Soil Soft Subgrade
Florida
(new)
Alabama & FHWA
(left in-place)
Oklahoma
(new)
FHWA
Missouri
(new)
Alabama
(new)
FIGURE 3.1 2006 Test Track Structural Study Test Sections (Timm, 2008).
In terms of HMA mixtures, five different binder types were used to create unique
mixes by varying aggregate gradations, air voids, and binder contents. HMA layers in
seven sections, N1, N2, N3, N5, N6, N7, and S11 employed a PG 67-22 unmodified
binder. The PG 76-22 binder used in the HMA layers in sections N2, N4, N5, and S11
was modified with styrene-butadiene-styrene (SBS) (Timm, 2008). The surface course
of N7 also used a PG 76-22; however it was a stone-matrix asphalt (SMA) mix. PG 76-
28 binder was used in sections N8 and N9 in the surface course SMA and in the second
HMA layers. These sections used PG 64-22 binder in the bottom two HMA layers.
Although the binder type was common to both layers, the bottom layer was designed for
only 2% air voids, referred to as a ?rich bottom? layer. Lastly, the PG 70-22 binder was
used for one HMA layer in section N10. As-built properties of each layer were
49
recorded, as well as the designed properties. For the sections constructed in 2006,
including the top layer of section N5, binder testing was completed to determine the
dynamic shear modulus, G*, and viscosity values. Additionally, laboratory tests were
completed to determine the dynamic modulus, E*, of the HMA layers. As mentioned
previously, only the datasets from the newly constructed 2006 sections and the top lift in
N5 were utilized for this investigation. Detailed information about these laboratory test
results is discussed in Chapter Four of this thesis.
3.4 INSTRUMENTATION
In order to characterize pavement response, instrumentation was embedded
within each section at the time of construction, providing extensive information on
temperature, stress and strain within the structures. Embedded within each of the 11
sections was at a minimum, one pair of earth pressure cells, twelve strain gages, and
four temperature probes. Based on the research objectives of the corresponding
sponsors, some sections included more extensive instrumentation. Figures 3.2, 3.3, and
3.4 illustrate the arrangement of the pressure cells and strain gages for the various
sections, though this investigation focused primarily on Section N9 (Figure 3.4).
50
-12
-10
-8
-6
-4
-2
0
2
4
6
8
10
12
-12 0 12
Transverse Offset from Center of Outside Wheelpath, ft
Lo
ng
itu
din
al
Of
fse
t f
ro
m
Ce
nte
r o
f A
rra
y,
ft
.
Earth Pressure Cell
Asphalt Strain Gauge
Direction of
Travel
1 2 3
4 5 6
7 8 9
10 11 12
13
14
C/L Edge StripeInside Wheel Path Outside Wheel Path
FIGURE 3.2 Location of Gages, Sections N1-N6, N8, N10, S11 (Timm, 2008).
Strain gages were installed to capture the induced tensile strain in both the
longitudinal and transverse directions. Regardless of the year of construction, 2003 or
2006, the same type of gage was consistent. The gages were purchased from
Construction Technologies Laboratories, Inc. (CTL). They were designed for most
pavement cross-sections with a maximum range of 1,500 ??, well within typical strain
magnitudes experienced in most pavement cross-sections (Timm, 2008). A strain gage
array, gages 1-12, was installed in each of the sections at the bottom of the HMA layer.
The gages were installed in groups of three by direction, oriented either longitudinally or
transversely. Within a group, one gage was aligned with the centerline of the outside
wheel path, and the remaining two were offset to the right and left of the outside wheel
path. Doing so helped to account for wheel wander, allowing the best hit to be captured.
51
Two groups each of strain gages were installed in both the longitudinal and transverse
directions to create redundancy in the system.
Figure 3.2 illustrates the configuration of gages for sections N1-N6, N8, N10
and S11. Additional strain gages, gages 18-21 were installed in section N7 at a depth of
5 inches, located along the centerline of the outside wheel path atop the gages installed
at the bottom of the HMA layers, as shown in Figure 3.3. Carrying this idea further,
Section N9 included twelve strain gages in addition to the gage array at the bottom of
the HMA layers. The additional twelve were installed in groups of four along the
centerline of the outside wheel paths at various depths, downstream from the three by
four gage array, illustrated in Figure 3.4. Within each array, two each longitudinal and
transverse gages were installed inline with the outside wheel path. Gages 16-19 were
installed at the bottom of the fourth HMA layer (11.04 inches), gages 20-23 were placed
at the bottom of the third HMA lift, 8.76 inches deep and lastly, gages 24-27 were
placed at the bottom of the second HMA lift, 6.00 inches deep. These depths were
determined using surveying equipment.
52
-12
-10
-8
-6
-4
-2
0
2
4
6
8
10
12
-12 0 12
Transverse Offset from Center of Outside Wheelpath, ft
Lo
ng
itu
din
al
Of
fse
t fr
om
C
en
ter
of
A
rra
y,
ft
.
Earth Pressure Cell
Asphalt Strain Gauge
Direction of
Travel
1 2 3
4 5 6
7 8 9
10 11 12
13
14
C/L Edge StripeInside Wheel Path Outside Wheel Path
16
17
18
19
20
21
FIGURE 3.3 Location of Gages, Section N7 (Timm, 2008).
53
-12
-10
-8
-6
-4
-2
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
-12 0 12
Transverse Offset from Center of Outside Wheelpath, ft
Lo
ng
itu
din
al
Of
fse
t f
ro
m
Ce
nt
er
of
Ar
ra
y,
ft
.
Earth Pressure Cell
Asphalt Strain Gauge
Direction of
Travel
1 2 3
4 5 6
7 8 9
10 11 12
13
14
C/L Edge Stripe
Inside
Wheel Path
Outside
Wheel Path
Gages 16-19,
Top of Lift 5
Gages 20-23,
Top of Lift 4
Gages 24-27,
Top of Lift 3
FIGURE 3.4 Location of Gages, Section N9 (Timm, 2008).
Temperature probes were installed at various depths within the structure,
creating a complete temperature profile for each. For consistency, Campbell-Scientific
model 108 temperature thermistors were installed in the sections constructed in both
2003 and 2006. Four thermistors were placed as a minimum in each section, as listed in
Table 3.1. Sections N3-N7 (those left in place from the 2003-2006 cycle) were installed
at consistent depths, regardless of the cross-section. However, for the sections
constructed in 2006, one thermistor each was installed at the surface, mid-depth and
bottom of the HMA layer and three inches into the base layer (Timm, 2008). Section N9
employed additional thermistors, installed at the depths listed in Table 3.2, which
provided a much more detailed view of the temperature gradients experienced.
54
TABLE 3.1 Location of Thermistors
Depth of Probe, inches
Section T1 T2 T3 T4
N1 0.0 3.7 7.4 10.4
N2 0.0 3.5 7.0 10.0
N3 0.0 2.0 4.0 10.0
N4 0.0 2.0 4.0 10.0
N5 0.0 2.0 4.0 10.0
N6 0.0 2.0 4.0 10.0
N7 0.0 2.0 4.0 10.0
N8 0.0 5.0 10.0 13.0
N9 0.0 7.2 14.4 17.4
N10 0.0 3.9 7.7 10.7
S11 0.0 3.8 7.6 10.6
TABLE 3.2 Location of Additional Probes in Section N9
Probe Depth, in.
T5 0.0
T6 1.0
T7 2.0
T8 3.7
T9 5.4
T10 6.9
T11 8.4
T12 9.6
T13 10.8
T14 12.4
T15 14.1
T16 17.1
3.5 TRAFFIC
Live traffic was applied at the Test Track on a daily basis. Heavy trucks were
operated by truck drivers for 16-hours a day, 5 days a week, totaling nearly 10 million
Equivalent Single Axle Loads (ESALs) in the 3-year testing cycle. The trucks had
approximately a 12-kip steer axle, 40-kip tandem axle, and 5 trailing 20-kip single axles.
The Test Track operates five different trucks with the following axle spacing and axle
weights listed in Tables 3.3 and 3.4.
55
TABLE 3.3 Spacing Between Axles (Taylor, 2008)
Distance Between Axles (ft)
Truck # Steer
Front
Tandem
Rear
Tandem Single 4 Single 5 Single 6 Single 7 Single 8
1 0.0 13.6 4.3 18.7 11.2 20.0 11.2 20.0
2 0.0 13.6 4.3 17.1 17.0 17.0 17.0 17.0
3 0.0 13.6 4.3 17.1 17.0 17.0 17.0 17.0
4 0.0 13.6 4.3 17.1 17.0 17.0 17.0 17.0
5 0.0 13.6 4.3 14.8 12.4 17.2 11.0 17.2
TABLE 3.4 Axle Weight by Truck (Taylor, 2008)
Axle Weights (lb)
Truck # Steer
Front
Tandem
Rear
Tandem Single 4 Single 5 Single 6 Single 7 Single 8
1 9,400 20,850 20,200 20,500 20,850 20,950 21,000 20,200
2 11,200 20,100 19,700 20,650 20,800 20,650 20,750 21,250
3 11,300 20,500 19,900 20,500 20,500 21,000 20,650 21,100
4 11,550 21,200 19,300 21,000 21,050 21,000 20,750 20,800
5 11,450 20,900 19,400 20,100 20,450 21,000 20,050 20,650
3.6 DATA ACQUISITION
Wireless data transmission was utilized in the 2006 Test Track structural study to
transmit pavement response measurements. However, data were collected through hard-
connection at roadside data acquisition enclosures during the 2003-2006 testing cycle.
For consistency the same data acquisition devices were utilized in both the sections from
the 2003-2006 testing cycle and those constructed in 2006. To do so meant upgrading
the left-in-place sections with new devices to meet the needs of the 2006 wireless
system. This enabled safe data acquisition wirelessly from an enclosed building away
from the track and live traffic, which was a significant improvement given the frequency
of data collection. For normal operations, data were collected on each of the structural
sections on a weekly basis. Weekly data collection consisted of recording the in-situ
pavement temperatures and strain responses under three passes of live traffic. As
mentioned previously, an additional field study was conducted utilizing section N9. To
56
do so, data was collected on four different test dates over a one month testing period.
For this testing strain responses were measured under a variety of speeds, rather than at
the normal 45 mph. The details of the N9 field investigation are discussed in more detail
in Chapter Five of this thesis.
3.7 SUMMARY
This chapter served in describing the test facility. The test facility encompasses
the application of live traffic over 46 different pavement cross-sections on a 1.7 mile test
track. Approximately 10 million ESALs were applied via the five 132-kip trucks
operated at the Test Track. Eleven of the 46 test sections were included in the 2006 Test
Track structural study which utilized embedded instrumentation to record pavement
responses at various critical locations within a structure. On a weekly basis strain and
stress data were collected from these sections through the use of data acquisition devices
and wireless transmittal. Laboratory testing was conducted on the sections constructed
in 2006 as well as the top lift of N5 which was milled and inlaid in 2006. Testing
included G*, E*, and viscosity testing. Also, detailed as-built information regarding the
volumetric properties of each section was recorded. Using those datasets for these six
sections (plus N5 top lift), further analysis was completed on the accuracy of E* models.
Additional analysis was completed on the relationship between E* and pavement
response, as discussed in Chapters Five and Six.
57
CHAPTER FOUR
LAB INVESTIGATION
4.1 INTRODUCTION
There are three levels of design that one can choose from when using the
MEPDG for flexible pavement design (ARA Inc., 2004). One significant difference in
the three levels of design is how the dynamic modulus of HMA is computed and
therefore the degree of complexity required for material property inputs. Level one is the
most complex degree of design, requiring laboratory test results for both mixture
dynamic modulus (E*) and binder shear modulus (Gb*). However, dynamic modulus
laboratory testing is time consuming and expensive. Therefore, it is likely that many
state DOTs will opt to use levels two or three design which do not require E* test
results, but rather estimate E* from predictive equations. The required material property
inputs for these levels are minimal and are parameters that are typically measured as part
of a specification. Level two, the second most complex design, utilizes either the 1-37A
or the 1-40D Witczak Predictive E* equation (at the discretion of the user) as a function
of binder information, gradation information, and other volumetric information. Level
three, the least complex of the three designs also utilizes either the 1-40D or the1-37A
Witczak Predictive E* equation, however laboratory binder test results are not required.
Interestingly, when using the MEPDG, the designer is simply presented with the option
of running either equation, but no guidance to aid in this decision.
58
Although the MEPDG utilizes the Witczak equations in its determination of E*,
there are many other equations that have been developed over the years to predict E*
from similar properties. One such model, the Hirsch E* predictive model was developed
in 2003 as a response to the objectives of the NCHRP 9-25 and 9-31 projects
(Christensen et al., 2003). It is among the most recently developed models used to
predict E* from mix properties. Although the Hirsch E* predictive model is not
currently used in the MEPDG, it should be evaluated to offer comparisons with the
MEPDG methods and to determine the most effective predictive model for pavement
designers.
Due to the lack of finances and means to run difficult laboratory tests, there is a
need to validate the MEPDG?s procedure in calculating E* at the two lowest levels of
design. To evaluate the accuracy of these two designs, three E* predictive equations
were analyzed and compared with E* laboratory test results. E* testing on the mixtures
in the newly-constructed 2006 Test Track structural study formed the basis of this
investigation.
4.2 MODELS TO DETERMINE E*
Three E* predictive equations were utilized to assess the accuracy of the
MEPDG, both Witczak equations contained within the program and a third equation, the
Hirsch model for estimating E*. As part of the NCHRP 1-37A project, a predictive
model for E* was developed utilizing rudimentary mix information including basic
binder test results to be included in the MEPDG (Bari and Witczak, 2006). An initial
model was developed in 1996 by Witczak and Fonseca, however it was quickly updated,
expanding the dataset and re-calibrating the model. This model, updated by Witczak and
59
Andrei, was implemented for use in both levels two and three of the MEPDG in 1999
(Bari and Witczak, 2006). To alleviate confusion, this model will be referred to as the
Witczak 1-37A E* predictive equation, given that it was developed under the NCHRP 1-
37A project. In 2005, a third Witczak equation was developed under the NCHRP 1-40D
initiative which again updated Witczak?s E* predictive equation (Bari and Witczak,
2006). This third equation, termed here as the Witczak 1-40D E* predictive equation,
was implemented in the MEPDG version 1.0 allowing the user to select between the 1-
37A and 1-40D equation for use in level two and three design. However, the user is
heeded that the 1-40D equation has not yet been nationally calibrated.
Aside from the 1-37A and 1-40D equations, there have been many other E*
predictive equations developed over the years. One of the more recent models is the
Hirsch E* predictive model developed in 2003 (Christensen et al., 2003). In meeting the
objectives of this thesis, the two Witczak models embedded within the MEPDG, the
Witczak 1-37A and the Witczak 1-40D E* predictive equations were analyzed as well as
the Hirsch E* predictive model.
The information required for each model is listed in Table 4.1. As mentioned
previously, the level of complexity of the material property inputs varies among the
three models. Two of the three require Gb* testing, while only one requires the phase
angle associated with Gb*. It is worthy of noting that while both the Witczak models
incorporate the gradation of the mix, the Hirsch model does not. In fact, the Hirsch
model relies only on four properties of the mix.
60
TABLE 4.1 Material Property Requirements by Model
4.2.1 Witczak 1-37A E* Predictive Equation
The original Witczak model was developed in 1996 by Dr. Witczak and his
colleagues using 149 unaged HMA mixtures (Bari and Witczak, 2006). The binder types
utilized in the mixtures were conventional binders only (i.e., unmodified), which
severely limits the use of this model. This equation was revised in 1999, by expanding
the dataset and deriving an equation that more accurately fit a wider range of gradations,
binder stiffness and air voids (Andrei et al., 1999). The revised equation, the Witczak 1-
37A E* predictive equation (Bari and Witczak, 2006), listed in Equation 4-1, is a
function of gradation of the aggregate, air voids, effective binder content, viscosity of
the binder, and loading frequency:
))log(393532.0)log(313351.0603313.0(
34
2
38384
4
2
200200
1
0055.0)(000017.0004.00021.0872.3
0822.0058.00028.0)(0018.0029.025.1*log
?
????
???
???+
+?+?+
+????+?=
f
abeff
beff
a
e
VV
VVE
(4-1)
Information Witczak (1-37A) Witczak (1-40D) Hirsch
Gradation:
?200 pass. X X
?4 ret. X X
?38 ret. X X
?34 ret. X X
VMA X
Va X X X
VFA X
Vbeff X X
f X
? X
Gb* X X
?b X
61
where:
E* = dynamic modulus of mix, 105 psi
? = viscosity of binder, 106 poise
f = loading frequency, Hz
?200 = % passing #200 sieve
?4 = cumulative % retained on #4 sieve
?38 = cumulative % retained on 3/8 in. sieve
?34 = cumulative % retained on 3/4 in. sieve
Va = air voids, % by volume
Vbeff = effective binder content
Equation 4-1 is currently used for a level two design in the MEPDG (ARA Inc., 2004).
It is also employed for the level three design with the use of typical viscosity values of
the binder based on the binder grading (ARA Inc., 2004). The viscosity can be
determined by conventional binder tests or from a dynamic shear modulus (Gb*) test.
When using the Gb* to determine viscosity, Gb* and its associated phase angle must be
measured at a variety of temperatures for a loading frequency of 1.59 Hz or 10 rad/sec,
from which Equation 2-18 is employed to calculate viscosity (ARA Inc., 2004). The
loading frequency for Gb* testing should not be confused with the loading frequencies
required for the 1-37A model, as the loading frequencies selected for the model are
typical of an E* laboratory test (0.1, 1, 10, 25 Hz, etc.). Viscosity can also be determined
from conventional binder tests: Penetration, Softening Point, Absolute Viscosity,
62
Kinematic Viscosity or Brookfield Viscosity. However some require a conversion to
achieve a viscosity in Poise.
4.2.2 Witczak 1-40D E* Predictive Equation
The Witczak 1-37A E* predictive model was revised in 2006, again expanding
the dataset beyond the original model, using a total of 346 HMA mixes to calibrate the
model (Bari and Witczak, 2006). One important difference to note between the 1-37A
E* predictive model and the 1-40D E* predictive model is the replacement of the
viscosity and loading frequency parameters with the dynamic shear modulus of the
binder, Gb*, and its associated phase angle, ?b, as shown in Equation 4-2 (Bari and
Witczak, 2006):
( )
)log8834.0*log5785.07814.0(
34
2
3838
2
3838
2
4
4
2
200200
0052.0
1
01.0)(0001.0012.071.003.056.2
06.108.0
)(00014.0006.0)(0001.0
011.0)(0027.0032.065.6
*754.0349.0*log
bbG
beffa
beff
a
beffa
beff
a
b
e
VV
VV
VV
VV
GE
?
???
???
???
+??
?
+
??+??
?
?
???
?
++++
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
???
?
???
?
+??
?+?
++?
?+?=
(4-2)
where:
E* = dynamic modulus of mix, psi
?Gb*?= dynamic shear modulus of binder, psi
?200 = % passing #200 sieve
?4 = cumulative % retained on #4 sieve
?38 = cumulative % retained on 3/8 in. sieve
63
?34 = cumulative % retained on 3/4 in. sieve
Va = air voids, % by volume
Vbeff = effective binder content
?b = phase angle of binder associated with ?Gb*?, degrees
This newly established Witczak equation (Bari and Witczak, 2006), the Witczak 1-40D
E* Predictive equation was implemented in the MEPDG for use in level two and three
design. As mentioned previously, the user has the option of selecting the 1-37A or the 1-
40D model for design. At a level three design, typical Gb* and ?b values are estimated
within the program depending on the selected grade of the binder. Although the loading
frequency parameter has been omitted in the new model, the time and temperature
dependency of dynamic modulus is characterized by Gb* and ?b. Witczak and colleagues
attempt to define the time-frequency relationship used to characterize Gb* and ?b,
however, the relationships are unclear and inconsistent throughout the document (Bari
and Witczak, 2006). Therefore, it is assumed that the loading frequency used in Gb*
testing is equivalent to loading frequency for the mixture modulus test, E*.
4.2.3 Hirsch E* Predictive Model
The Hirsch E* predictive equation is similar to the Witczak equations in that it
also utilizes volumetric information and Gb* laboratory test results. However, this model
requires only two volumetric properties: VMA and VFA, as a function of Va. The Hirsch
E* model was developed based on the law of mixtures, also referred to as the Hirsch
model, for composite materials (Christensen et al., 2003). The Hirsch E* predictive
equation for asphalt mixtures, as developed by Christensen and his colleagues is:
64
( ) ( )
1
*3000,200,4
100/11
000,10*31001000,200,4*
?
???
?
???
? +??
+?
?
?
??
? ?
?
??
?
? ?+?
?
??
?
? ?=
b
bmix
GVFA
VMAVMAPC
VMAVFAGVMAPcE
where:
58.0
58.0
*3650
*320
???
?
???
? ?+
???
?
???
? ?+
=
VMA
GVFA
VMA
GVFA
Pc
b
b
(4-3)
where:
?E*?mix = dynamic modulus, psi
VMA = voids in mineral aggregate, %
VFA = voids in aggregate filled with mastic, %
VFA = 100*(VMA-Va)/VMA
Va = air voids, %
?G*?b = dynamic shear modulus of binder, psi
Just as in the 1-40D model, the time and temperature dependency of E* is characterized
in the Hirsch E* predictive model by Gb*. According to Christensen, the Gb* ?should be
at the same temperature and loading time selected for the mixture modulus, and in
consistent units (Christensen et al., 2003).? For this evaluation, it was assumed that the
frequency-time relationship is consistent for both Gb* and E* tests such that a selected
frequency applies the load for the same time in either test. Therefore, the loading
frequencies and temperatures selected associated with Gb* were the same as those from
65
the measured E* values, which enabled a direct comparison of predicted to measured E*
values.
4.3 TESTING PROTOCOL
To complete the dynamic modulus testing for each unique mix listed, the testing
protocol outlined by AASHTO TP 62-07 was followed (AASHTO, 2007). An Asphalt
Mixture Performance Tester (AMPT), formerly called the Simple Performance Testing
machine (SPT), shown in Figure 4.1, was utilized to apply haversine compressive
loading for a range of frequencies and temperatures. For this investigation E* results at
three temperatures, 40, 70, and 100?F and seven frequencies, 0.5, 1, 2, 5, 10, 20, and 25
Hz were obtained.
FIGURE 4.1 The AMPT Machine and Close-up of Specimen.
Viscosity was obtained for the various binders using the Brookfield Viscometer.
The test procedure was in compliance with the ASTM D2983-04a (ASTM, 2004). The
66
binders were aged in a Rolling Thin-Film Oven (RTFO) and Brookfield viscosities were
obtained at two temperatures, 135 and 165?C.
Dynamic shear modulus, Gb*, testing, in accordance with AASHTO T 315-06
(AASHTO, 2006), was also conducted on RTFO aged binders using a Dynamic Shear
Rheometer (DSR). Although testing was conducted at four temperatures, 4, 21, 37.8,
and 54.4?C (40, 70, 100, and 130?F), results at 4?C (40?F) were inconsistent and
unreliable due to the inability to maintain a constant temperature and thus excluded from
the analysis. A frequency sweep, in which thirteen frequencies (0.1, 0.2, 0.3, 0.4, 0.6,
1.0, 1.6, 2.5, 4.0, 6.3, 10.0, 15.9, and 25 Hz) were applied, was completed at each of the
four temperatures.
4.4 MIXTURES TESTED
E* laboratory testing was completed for the mixes in each section constructed in
2006 as part of the structural study. The mixes investigated are described in Table 4.2,
listed by the section and layer in which it was placed. Four different mix types were
incorporated in the investigation including Superpave mixes (super), stone matrix
asphalt mixes (SMA), and a rich bottom layer (RBL). Each mixture is described by a
unique mix number and unique binder number. The gradation information acquired from
as-built records (quality control laboratory tests at time of construction), as well as the
nominal maximum aggregate size (NMAS) for each mix number is listed in Table 4.3.
The air voids associated to the specimens produced for E* testing were used to predict
E* following each of the models, enabling a direct comparison to measured E*. Using
the maximum specific gravity of the mix (Gmm) recorded in quality control as-builts,
the bulk specific gravity of the mix (Gmb) was back calculated for each specimen tested
67
using the associated air voids. The remaining volumetric properties, voids filled with
asphalt (VFA), voids in mineral aggregate (VMA), and effective binder content (Vbeff)
were calculated using the Gmb of each specimen, and the known bulk specific gravity of
the aggregate (Gsb), and percent aggregate (Ps) from quality control as-builts. The
VMA of the specimens tested ranged from 13.14% to 21.77%, the VFA ranged from
48.67% to 65.15%, and the air voids were between 6% and 8.6%. Due to the large
number of data points, these individual, specimen-specific data (Va, VMA, VFA) are not
listed. As shown in Table 4.2, a total of ten unique mixes were evaluated, however,
some unique mixes were used in multiple pavement layers. Associated with a unique
binder number is the performance grade (PG), viscosity and G* test results (including
phase angle values, ?b); these values are listed for each binder in Tables 4.4 through
4.12. A total of nine binders were used in the HMA layers investigated, and similar to
the unique mix number, some unique binders were used in multiple pavement layers.
For this evaluation a Brookfield viscometer was used to determine the viscosity
of various binders at 135 and 165?C. After the test temperatures were converted to
?Rankine, Equation 2-17 was utilized to extrapolate viscosity for the temperatures (40,
70, and 100?F) at which E* testing was completed. Viscosity values were not obtained
for unique binder #4, which was contained only in unique mix #7. From these data the
dynamic moduli of the mixes, aside from mix #7, were predicted for the 1-37A E*
predictive model at three temperatures and seven loading frequencies. Gb* and ?b values
were obtained at multiple temperatures and frequencies. However, to compare
laboratory E* values with E* predictions from either the Hirsch or 1-40D E* predictive
models, the loading frequencies and test temperatures for Gb* must equal those used in
68
the E* laboratory test. As a result, the 1-40D and Hirsch E* predictive models were
evaluated at two temperatures, 70 and 100?F, and three frequencies, 1, 10, and 25 Hz.
TABLE 4.2 HMA Mixes by Section and Layer
Section Layer Sponsor Mix Type Binder
Unique
Binder #
Unique
Mix #
N1 1 FL Super 67-22 1 1
N1 2 FL Super 67-22 1 1
N1 3 FL Super 67-22 14 2
N2 1 FL Super 76-22 2A 3
N2 2 FL Super 76-22 2A 3
N2 3 FL Super 67-22 14 2
N8 1 OK SMA 76-28 3 4
N8 2 OK Super 76-28 3 5
N8 3 OK Super 64-22 4A 6
N8 4 OK RBL 64-22 4 7
N9 1 OK SMA 76-28 3 4
N9 2 OK Super 76-28 3 5
N9 3 OK Super 64-22 4A 6
N9 4 OK Super 64-22 4A 6
N9 5 OK RBL 64-22 4 7
N10 1 MO Super 70-22 5 8A
N10 3 MO Super 64-22 6 9
S11 1 AL Super 76-22 13 28A
S11 3 AL Super 67-22 14 2
S11 4 AL Super 67-22 14 2
TABLE 4.3 Gradation Information by Mix #
Unique
Mix #
Unique
Binder #
?200 %
passing
?4 %
retained
?38 %
retained
?34 %
retained
NMAS
(mm)
1 1 8.79 39.61 16.44 0.00 12.5
2 14 5.48 45.82 25.19 4.47 19
3 2A 8.10 38.61 16.62 0.00 12.5
4 3 10.71 68.55 28.62 0.00 12.5
5 3 6.90 34.80 19.53 4.71 19
6 4A 6.90 36.31 21.13 5.48 19
7 4 10.51 39.93 13.68 0.00 12.5
9 6 6.28 51.79 25.60 1.81 19
8A 5 5.40 47.71 16.83 0.79 12.5
28A 13 8.59 13.98 0.10 0.00 9.5
69
TABLE 4.4 Binder Information (Section N1)
Unique Binder # Temp, F Frequency, Hz G*, psi Delta, ? Viscosity, cP
1 40 - - - 44,720,000,000
1 70 1 246.64 55.49 623,700,000
1 70 10 520.55 56.86 623,700,000
1 70 25 473.71 58.09 623,700,000
1 100 1 24.61 62.77 21,870,000
1 100 10 91.80 61.25 21,870,000
1 100 25 138.46 60.05 21,870,000
TABLE 4.5 Binder Information (Section N2)
Unique Binder # Temp, ?F Frequency, Hz G*, psi Delta, ? Viscosity, cP
2A 40 - - - 1.553E+11
2A 70 1 261.73 55.64 2,068,000,000
2A 70 10 565.94 57.48 2,068,000,000
2A 70 25 590.01 58.21 2,068,000,000
2A 100 1 29.71 59.78 68,120,000
2A 100 10 103.04 59.91 68,120,000
2A 100 25 156.75 58.73 68,120,000
TABLE 4.6 Binder Information (Sections N8 & N9)
Unique Binder # Temp (F) Frequency, Hz G*, psi Delta, ? Viscosity, cP
3 40 - - - 3.527E+11
3 70 1 325.09 53.89 4,147,000,000
3 70 10 667.87 55.76 4,147,000,000
3 70 25 692.95 54.5 4,147,000,000
3 100 1 38.69 57.81 123,500,000
3 100 10 129.85 56.28 123,500,000
3 100 25 207.21 49.12 123,500,000
TABLE 4.7 Binder Information (Section N8 & N9)
Unique Binder # Temp (F) Frequency, Hz G*, psi Delta, ? Viscosity, cP
4 40 - - - -
4 70 25 1232.21 45.94 -
4 100 25 177.77 58.69 -
TABLE 4.8 Binder Information (Sections N8 & N9)
Unique Binder # Temp (F) Frequency, Hz G*, psi Delta, ? Viscosity, cP
4A 40 - - - 595,100,000
4A 70 1 251.43 56.12 28,820,000
4A 70 10 560.86 57.4 28,820,000
4A 70 25 581.59 58.07 28,820,000
4A 100 1 24.87 63.06 2,506,000
4A 100 10 94.93 61.08 2,506,000
4A 100 25 148.19 59.04 2,506,000
70
TABLE 4.9 Binder Information (Section N10)
Unique Binder # Temp (F) Frequency, Hz G*,psi Delta, ? Viscosity, cP
5 40 - - - 11,950,000,000
5 70 1 284.925 60.01 257,400,000
5 70 10 641.48 61.22 257,400,000
5 70 25 619.15 62.04 257,400,000
5 100 1 23.78 65.96 12,290,000
5 100 10 100.166 65.18 12,290,000
5 100 25 158.775 63.4 12,290,000
TABLE 4.10 Binder Information (Section N10)
Unique Binder # Temp (F) Frequency, Hz G*,psi Delta, ? Viscosity, cP
6 40 - - - 26,150,000,000
6 70 1 245.48 56.16 431,700,000
6 70 10 555.64 57.42 431,700,000
6 70 25 577.68 58.17 431,700,000
6 100 1 23.81 62.74 17,060,000
6 100 10 92.51 61.12 17,060,000
6 100 25 144.80 59.35 17,060,000
TABLE 4.11 Binder Information (Section S11)
Unique Binder # Temp (F) Frequency, Hz G*,psi Delta, ? Viscosity, cP
13 40 - - - 306,100,000
13 70 25 573.19 60.07 26,720,000
13 100 25 133.34 59.37 3,530,000
TABLE 4.12 Binder Information (Section S11)
Unique Binder # Temp (F) Frequency, Hz G*,psi Delta, ? Viscosity, cP
14 40 - - - 76,590,000,000
14 70 1 258.24 55.68 936,600,000
14 70 10 571.01 57.03 936,600,000
14 70 25 585.80 57.89 936,600,0009
14 100 1 26.29 62.13 29,800,000
14 100 10 98.96 60.59 29,800,000
14 100 25 152.54 59.11 29,800,000
4.5 RESULTS AND DISCUSSION
In following Equation 4-1 to evaluate the Witczak 1-37A E* model, 644 data
points were produced from mixture properties of each individual specimen. The values
were plotted against the laboratory measured log E* values in Figure 4.2. For the
Witczak 1-40D and Hirsch E* models, 177 data points were evaluated for each, again
71
using individual mix properties of the specimen, and were plotted against measured log
E* values in Figure 4.2. Ideally, all points would fall along the line of equality, but this
clearly is not the case. Upon visual inspection, it can be concluded that overall the 1-
40D E* model consistently overpredicts the measured values, with 99% of the data
points lying above the line of equality. While there is a large amount of scatter in the
data, the 1-37A E* model generally follows the line of equality, with data points both
above and below this line. Similarly, the Hirsch E* model also generally follows this
line, although there is much less scatter in these data. Some of the scatter evident in this
plot may be related to inherent errors in measured values, as E* laboratory testing is not
a flawless test and has limitations, particularly at high frequencies.
Evaluation of E* Models on Structural Test Track Sections
4.5
5
5.5
6
6.5
7
4.5 5 5.5 6 6.5 7
Measured Log E* (psi)
Pr
ed
ict
ed
L
og
E
* (
ps
i)
1-37A
1-40D
Hirsch
Witczak 1-37A:
n = 644
y = 0.93x+0.36
R2 =0.75
Witczak 1-40D:
n = 177
y = 0.65x+2.34
R2 =0.74
Hirsch:
n = 177
y = 0.79x+1.16
R2 = 0.88
FIGURE 4.2 Comparison of Predicted E* to Measured E* by Predictive Models.
72
Attaching a linear regression equation indicates how precisely the modeled
values are linearly related to the measured values, in log space. Some researchers (Bari
and Witczak, 2006; Dongre et al., 2005, Andrei et al., 1999, Christensen et al, 2003;
Azari et al., 2007; Mohammad et al., 2007) have used the coefficient of determination
from this relationship as an indication of the quality of the model. Inset in Figure 4.2 are
the sample sizes, linear regression equations and associated coefficients of determination
in log scale for each model evaluated. All three models produced predictions that
correlated well to the measured values by a linear relationship. The Hirsch E* model
produced the highest R2 value, 0.88 in log scale, while the Witczak 1-40D produced the
lowest, 0.74 in log scale. This is contrary to previous findings in which the 1-40D model
was found to be an improvement over both the Hirsch and 1-37A model (Bari and
Witczak, 2006; Azari et al., 2007). All three models, 1-37A, 1-40D, and Hirsch,
returned significantly lower R2 values than reported in their development, 0.941, 0.90,
and 0.982 in log scale, respectively (Andrei and Witczak, 1999; Bari and Witczak, 2006,
Christensen et al., 2003). Although these models were found to linearly correlate very
well with the measured values used to create them, they may not be applicable to
mixtures not included in their original database. This is of concern since the purpose of
these equations is to provide a reasonable estimation of E* without having to run the E*
test.
The coefficient of determination is a measure of how precisely the linear
regression equation matches the data. For the model to be accurate, the linear regression
equation should be as close to y = x as possible, therefore the slope and intercepts of the
73
regression equations should also be investigated. Table 4.13 lists the linear regression
coefficients and goodness of fit in arithmetic scale for each of the models.
TABLE 4.13 Linear Regression Coefficients for Each Model
Model Slope Intercept (psi) R2
Witczak 1-37A 0.90 48,623 0.66
Hirsch 0.64 125,416 0.80
Witczak 1-40D 1.25 447,561 0.60
According to these lines of best fit, the Witczak 1-37A has the smallest difference in
slopes from the line of equality, deviating above the line by only 12.22%. Additionally,
the y-intercept is the smallest of the three models. However, indicated by the R2 and
Figure 4.2, the 1-37A E* model does not consistently predict the measured values
accurately. The Hirsch model is more consistent than the Witczak 1-40D model,
however, the slope for the Hirsch model deviates from one the most. In looking at
Figure 4.2, the data for both the Hirsch and 1-40D models appear to level out,
approaching a slope close to zero at intermediate measured moduli values (725,000-
1,400,000 psi) and at lower moduli values (100,000-250,000 psi). When the data are
plotted in arithmetic scale, this trend at intermediate and low moduli values is more
predominant in the Hirsch model (shown in Figure 4.3) than the 1-40D model (Figure
4.4), which may explain the large deviation in slope from the line of equality.
74
Evaluation of E* Models on Structural Test Track Sections
0
250,000
500,000
750,000
1,000,000
1,250,000
1,500,000
0 250,000 500,000 750,000 1,000,000 1,250,000 1,500,000
Measured E* (psi)
Pr
ed
ict
ed
E
* (
ps
i)
Hirsch
FIGURE 4.3 Comparison of Predicted E* to Measured E* for the Hirsch E*
Model.
Evaluation of E* Models on Structural Test Track Sections
0
500,000
1,000,000
1,500,000
2,000,000
2,500,000
0 500,000 1,000,000 1,500,000 2,000,000 2,500,000
Measured E* (psi)
Pr
ed
ict
ed
E
* (
ps
i)
1-40D
FIGURE 4.4 Comparison of Predicted E* to Measured E* for the 1-40D E*
Model.
75
Given that both of these models follow this trend and utilize Gb*, such inconsistencies
could be related to the use of Gb* values. This could indicate errors in Gb* test results at
high frequencies and the low end of the temperature range, 70?F. Similar to E* testing,
Gb* testing also has limitations, particularly at high frequencies. Although, testing errors
may exist, no obvious errors were noted during testing, thus, this trend may also be due
in part to the use of Gb* in the development of these two models. Table 4.14 lists the
percentage of E* values that are underpredicted by the Hirsch model for each of the
frequencies and temperatures used for the comparisons. As the frequency increases for
either temperature, the percent of predicted E* values that are less than its measured
counterpart increases. This trend is contrary to the time-dependency of HMA, such that
increases in frequency should result in higher E* values. Additionally, at the higher
temperature, 100?F, the percent of values underpredicted at 10 and 25 Hz are less than at
the lower temperature. The number of E* values that are under predicted by the Hirsch
model are greatest at a temperature of 70?F and 25 Hz. In general, it appears that the
Hirsch E* model predicts the measured values most accurately and precisely for lower
dynamic moduli (250,000-725,000 psi).
TABLE 4.14 Percent of Total E* Values Underpredicted by Hirsch Model
Frequency 70?F 100?F
1 Hz 5% 6%
10 Hz 12% 8%
25 Hz 18% 10%
Consistent with previous research (Azari et al., 2007), the 1-40D E* model
grossly overpredicts dynamic moduli at low values which are characterized by high
temperatures and/or low frequencies. To further investigate this trend, the ratio of
76
predicted to measured E* values was calculated by frequency and temperature. Table
4.15 lists the minimum, maximum and average ratios.
TABLE 4.15 Ratio of Predicted to Measured E* for Witczak 1-40D E* Model
70?F 100?F
Frequency Min Max Avg Min Max Avg
1 Hz 1.5 4.5 2.7 1.9 5.6 3.2
10 Hz 1.3 3.2 2.0 1.6 4.3 2.6
25 Hz 0.9 3.3 1.7 1.4 4.3 2.5
Of the 177 data points, only one underpredicts the measured value, by just 2%,
corresponding to a ratio of 0.9. At the highest temperature (100?F) and lowest
frequency (1 Hz) which corresponded to low measured moduli; the 1-40D model
produces dynamic moduli 3.2 times greater, on average. Table 4.15 reveals that at a low
frequency (1 Hz) and a high temperature (100?F) the model overpredicts the greatest
among test frequencies and temperatures, reiterating previous findings. At the minimum,
the 1-40D model overpredicts by 1.9 times at low frequencies (1 Hz) and high
temperatures (100?F). Similarly, among the three frequencies tested at an intermediate
temperature, 70F, the model results in predicted values drastically greater than the
corresponding measured values.
The models were further analyzed by mixture parameters: mixture type, binder
type, gradation, and NMAS. Initially three mixture types were included in the
evaluation: SMA, Superpave, and RBL. The RBL mixture was excluded from further
analysis, due to the lack of viscosity values for the associated binder and the small
sample size (only six data points) for the Hirsch and 1-40D predictive models. Despite
the small sample sizes for SMA mixtures, the trends discussed earlier were not found to
be independent of mixture type, illustrated by Figures 4.5 and 4.6.
77
E* Models Evaluated for SMA Mixes
0
500,000
1,000,000
1,500,000
2,000,000
2,500,000
3,000,000
3,500,000
0 500,000 1,000,000 1,500,000 2,000,000 2,500,000 3,000,000 3,500,000
Measured E* (psi)
Pr
ed
ict
ed
E
* (
ps
i)
1-37A
1-40D
Hirsch
FIGURE 4.5 Comparison of Measured E* to Predicted E* for SMA Mixes.
E* Models Evaluated for Superpave Mixes
0
1,000,000
2,000,000
3,000,000
4,000,000
0 1,000,000 2,000,000 3,000,000 4,000,000
Measured E* (psi)
Pr
ed
ict
ed
E
* (
ps
i)
1-37A
1-40D
Hirsch
FIGURE 4.6 Comparison of Measured E* to Predicted E* for Superpave Mixes.
78
As was found earlier, the 1-37A model is largely scattered about the line of equality,
neither consistently over nor underpredicting E*. The 1-40D model was found to return
E* values much larger than those measured in the laboratory. The Hirsch model
generally follows the unity line for both mixtures. Figure 4.6 again illustrates the
leveling out of the data for both the 1-40D and Hirsch models.
Similar to the evaluation of mixture types, measured moduli were plotted against
predicted values for each of the five binder types included in the study. Comparisons
were plotted for two binder types, PG 64-22 and PG 76-28 in Figures 4.7 and 4.8,
respectively.
E* Models Evaluated for PG 64-22
0
500,000
1,000,000
1,500,000
2,000,000
2,500,000
3,000,000
0 500,000 1,000,000 1,500,000 2,000,000 2,500,000 3,000,000
Measured E* (psi)
Pr
ed
ict
ed
E
* (
ps
i)
1-37A
1-40D
Hirsch
FIGURE 4.7 Comparison of Measured E* to Predicted E* for Mixes with PG 64-
22 Binder.
79
E* Models Evaluated for PG 76-28
0
1,000,000
2,000,000
3,000,000
4,000,000
0 1,000,000 2,000,000 3,000,000 4,000,000
Measured E* (psi)
Pr
ed
ict
ed
E
* (
ps
i)
1-37A
1-40D
Hirsch
FIGURE 4.8 Comparison of Measured E* to Predicted E* for Mixes with PG 76-
28 Binder.
The same general trends discussed previously were again evident: large scatter in the 1-
37A predictions, overestimation by the 1-40D model, and fairly accurate predictions by
the Hirsch model. Although not shown, the Witczak 1-37A model improved for binder
types PG 67-22 and PG 70-22, predicting E* most accurately, while the other two
models preformed in accordance with previously noted trends. However, for these two
binder types only one mixture each was represented. Therefore, it was concluded that
binder types have no discernible affect on E* predictions for the three models evaluated.
Plotting measured moduli against predicted moduli for coarse and fine mixes
showed that the same trends existed regardless of the gradation of the mixture. Likewise
for NMAS, the same trends spotted in Figure 4.2 were exhibited no matter the NMAS.
Although mixture properties such as binder shear modulus, and gradation (percent
80
retained or passing specific sieves) inherently influence model predictions, no
relationship between model accuracy and binder type or coarseness of the aggregate was
found to exist.
4.6 SUMMARY
Three E* predictive models were evaluated for asphalt mixtures from the
southeastern region. The dynamic moduli of ten different HMA mixtures from the 2006
Test Track were measured in the laboratory and compared with moduli predicted by the
1-37A, 1-40-D, and Hirsch E* predictive models. Following the Witczak 1-37A E*
model, E* was estimated for three temperatures (40, 70, and 100?F) and seven
frequencies (0.1, 1, 2, 5, 10, 20, and 25 Hz). E* was also estimated using the Witczak 1-
40D and Hirsch E* predictive models for two temperatures (70, and 100?F) and three
frequencies (1, 10, 25 Hz). The findings from these comparisons are summarized below:
? The Witczak 1-37A E* model was found to be unreliable with a large amount of
scatter.
? The Hirsch E* model was found to be the most precise model, with the highest
coefficient of determination, 0.707 in log scale and 0.766 in arithmetic scale.
? The Witczak 1-40D E* model consistently overpredicts E* particularly for low
dynamic moduli.
? The Hirsch E* model is most accurate at low dynamic moduli values (250,000-
700,000 psi).
81
? At an intermediate test temperature (70?F), both the Witczak 1-40D E* and
Hirsch E* models flatten out, thus misrepresenting the time-dependency of E*.
? Mixture parameters, such as mixture type, binder type, gradation (coarse/fine) or
NMAS of the mix were not found to significantly influence the accuracy of E*
predictions by any of the three models.
At the current state of the MEPDG, Witczak E* predictive equations, 1-40D and 1-37A,
are employed to determine dynamic modulus given volumetric, gradation and binder
properties of a mixtures. In applying these models to ten mixtures included in the 2006
Test Track Structural study, neither model consistently estimated laboratory dynamic
moduli values to a high degree of accuracy. Because both the 1-37A and 1-40D models
were found to be unreliable and the 1-40D model largely overpredicts dynamic modulus,
it is recommended that the Hirsch E* model be used. It should be used with caution
however, as discrepancies at lower temperatures and/or higher frequencies were
observed.
82
CHAPTER FIVE
FIELD DATA
5.1 INTRODUCTION
Further investigation into E* was conducted through a field experiment. Section
N9 was utilized to explore various factors on strain and loading duration. As mentioned
previously, load duration ultimately affects E*; E* in turn influences tensile strain
levels. Since E* cannot be measured in the field, factors affecting it such as temperature,
and load duration at various depths were measured under live traffic at the Test Track.
Strain levels were also recorded to evaluate the effects of temperature and velocity.
5.2 TESTING
In order to understand E* in the field, a better understanding of pavement
responses was necessary. Section N9 was selected for further investigation given its
deep HMA cross-section and multiple strain gages at various depths. Field testing was
conducted in the spring of 2007, on four separate test dates over the course of a one
month testing period. A minimum of four speeds were tested on any given test day,
ranging from 15 mph to 55 mph. On the first two dates, April 6 and 10, 2007, testing
was completed for five speeds: 15, 25, 35, 45, and 55 mph. Testing at the highest speed,
55 mph, was abandoned for the last two dates, April 25 and May 2, 2007, for safety
reasons, as the Test Track was designed for only 45 mph. Live traffic was applied to the
section in three passes of each truck, following the findings of previous research at the
83
Test Track, enabling the best hit to be detected by the instrumentation (Timm, 2006). As
mentioned previously, live traffic was applied with the heavy trucks employed by the
Test Track, composed of a steer axle, tandem axle and five trailing single axles. A
minimum of four trucks traveled over the section at each speed tested. The in-situ
pavement temperatures were recorded, enabling a complete evaluation of strain
measurements and load durations for a variety of speeds and temperatures.
5.3 STRAIN RESPONSES
Strain measurements were evaluated to determine the effects of temperature and
speed on tensile strain to give a broader understanding of E*. Tensile strain
measurements were analyzed for the strain induced at the bottom of the HMA layers,
13.9 inches deep, as this is the most critical location for tensile strain and the prevention
of fatigue cracking. Measurements were recorded in both the longitudinal and transverse
directions by gages 1-12, as discussed in Chapter Three. The layout of these twelve
gages is displayed in the inset of Figure 5.1. Temperatures were recorded at the surface
(T1), mid-depth (T2) and bottom (T3) of the HMA layer, also illustrated in Figure 5.1.
Temperature probes were also embedded within each HMA layer, as described in
Chapter Three, Table 3.2. From these measurements relationships were analyzed for
tensile strain with temperature and speed.
84
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
De
pth
, in
.
SMA
(2.16")
ThermistorAsphalt Strain Gauge
Plan View
OWP
CL
PG 76-28
(3.84")
PG 64-22
(2.76")
T1
T2
T3
Direction of
Travel
PG 64-22
Rich Bottom
(2.88")
PG 64-22
(2.28")
13.92"
Deep
11.04"
Deep
8.76"
Deep
6.00"
Deep
FIGURE 5.1 Cross-section of N9.
5.3.1 Definition of Strain
To analyze the effect of temperature and speed on tensile strain, the recorded
strain pulses were first evaluated. Figure 5.2 illustrates the longitudinal strain induced
under a single axle of a moving load. It was found that as the load approached the strain
gage, compressive strain was experienced first, and as the HMA layers began to bend
under loading, the strain pulse transitioned into the tensile realm. At the peak of the
strain pulse, the HMA layers experienced maximum tensile strain, ?t, max, at which time
the load was directly over or nearly directly over the strain gage. Figure 5.2 reveals that
the tensile strain lessened as the load moved further away from the gage, eventually
85
transitioning into compressive strain, ?c, again before it returned to the baseline strain
level.
Longitudinal Strain Pulse
-40
-20
0
20
40
60
80
100
120
140
0 0.05 0.1 0.15 0.2 0.25
Time (sec)
St
ra
in
( ?
???????)
Strain Pulse Load
Duration
FIGURE 5.2 Longitudinal Strain Pulse.
Strain induced in the transverse direction was slightly different than in the
longitudinal direction, displayed in Figure 5.3 for an entire truck pass. The HMA layers
experienced only tensile strain in the transverse direction. As the truck approached the
gage, the strain went directly into tension. As the load was directly or nearly directly
atop the gage, maximum tensile strain was induced in the transverse direction just as it
was in the longitudinal. However, once the load moved past the gage, the strain
remained in tension until it returned and remained at the baseline strain level. Since the
maximum tensile strain values are most critical, they were utilized to evaluate the effects
of temperature and speed on tensile strain under a moving load. It was found that the
maximum tensile strain levels in the transverse direction were notably less than that in
?t, max
?c
Baseline
86
the longitudinal direction, consistent with previous research at the Test Track (Timm
and Priest, 2008). To account for wheel wander, the ?best hit? among the truck passes
was used for each condition tested. The ?best hit? was considered the maximum tensile
strain value recorded among all of the strain gages in a given direction, for a given date,
speed and axle type. Using the best hit approach, the effect of temperature and speed on
tensile strain in both directions were first analyzed separately. After individual
relationships were developed, the combined effects of temperature and speed on tensile
strain were quantified.
Transverse Strain
-10
0
10
20
30
40
50
60
70
80
90
0 0.5 1 1.5 2 2.5 3
Time (sec)
????????
FIGURE 5.3 Transverse Strain Pulse.
5.3.2 Effect of Speed on Tensile Strain
The tensile strains determined from the best hit approach were investigated to
determine the effects of speed on tensile strain at the bottom of the HMA layers. To
Baseline
87
determine the relationship between speed and tensile strain, strain values in each
direction were plotted by speed for each axle type. Figure 5.4 plots the tensile strain
values in the longitudinal direction for a single axle. For the first two dates, April 6, and
April 10, 2007 the induced longitudinal strain decreases with an increase in speed. The
same trend exists for the last two dates; however, the strain decreased at a greater rate
than on the first two dates for each increase in speed. This trend was investigated further
in Figure 5.5 which plots the rate of change (the slope of each regression line) of the
tensile strain with the mid-depth pavement temperature from Figure 5.4. The average
mid-depth pavement temperature for each date is listed in Table 5.1. This plot reveals
that at high mid-depth temperatures vehicle speed reduced the longitudinal strain at a
greater rate. Therefore, at warmer temperatures, vehicle speed has a greater effect on the
tensile strain at the bottom of the HMA than at colder temperatures. This was to be
expected since warmer temperatures induce a greater viscoelastic behavior from the
HMA which would therefore increase the impact of vehicle speed.
TABLE 5.1 Average Mid-Depth Temperatures by Date
Date Avg. Temperature
4/6/2007 63.9 ?F
4/10/2007 70.8 ?F
4/25/2007 89.0 ?F
5/2/2007 99.0 ?F
88
Longitudinal Strain at Single Axle by Vehicle Speed
y = -21.07Ln(x) + 173.4
R2 = 0.90
y = -34.34Ln(x) + 221.7
R2 = 0.96
y = -56.12Ln(x) + 375.4
R2 = 0.97
y = -71.77Ln(x) + 500.4
R2 = 0.97
0
50
100
150
200
250
300
350
0 10 20 30 40 50 60
Vehicle Speed (mph)
Lo
ng
itu
di
na
l S
tra
in
4/6/2007
4/10/2007
4/25/2007
5/2/2007
FIGURE 5.4 Effect of Speed on Tensile Strain by Date.
-80
-70
-60
-50
-40
-30
-20
-10
0
40 60 80 100 120
Mid-Depth Pavement Temperature (oF)
Ra
te
of
S
tra
in
C
ha
ng
e d
ue
to
S
pe
ed
FIGURE 5.5 Rate of Strain Change by Mid-Depth Temperature.
89
Plots were developed for all three axle types in each direction, from which it was
found that regardless of direction or axle type the same general trend existed: increasing
the vehicle speed resulted in a decrease in tensile strain levels at the bottom of the HMA.
By completing a regression analysis on the data, it became evident that the longitudinal
strain was proportional to the natural logarithm of the speed of the applied load,
modeled by Equation 5-1. The coefficient of determination, corresponding to the trend
line for each axle type on each test date revealed that Equation 5-1 models the
relationship for longitudinal strain very well, returning R2 values ranging from 0.80 to
0.99 with ten of the twelve R2 values greater than 0.90. The same trends existed for
strains under each axle type in the transverse direction, again returning relatively high
R2 values.
bvat += ln? (5-1)
where:
?t = tensile strain (??)
v = vehicle speed of applied load (mph)
a, b = regression coefficients
5.3.3 Effect of Temperature on Tensile Strain
A broad range of in-situ pavement temperatures were recorded during the one
month testing period, with surface temperatures ranging from 78?F to 120?F. This
enabled a robust analysis of the relationship between tensile strain and pavement
temperature. During testing, pavement temperatures from each of the sixteen
temperature probes were recorded at the onset of testing each new speed. As to be
90
expected, the temperatures throughout the structure rose as the experiment progressed
from the start in April to the termination in May. Also, temperature gradients were
observed in which the surface temperatures of the asphalt concrete were significantly
higher than temperatures at the bottom of the structure.
In determining the effect of temperature on strain, it was necessary to select one
of the sixteen thermistors embedded within the structure for analysis. A regression
analysis was completed for thermistors T1-T3 which offered a complete temperature
profile of the HMA layers. Recorded temperatures from each of the probes were plotted
against the resulting strain values in each direction under the steer axle for all speeds
tested. Attaching a trend line to each allowed for a comparison of accuracy among the
three probes via R2 values. From this it was found that the temperatures recorded at the
mid-depth by thermistor T2 resulted in consistently high R2 values. This follows the
findings of a previous investigation at the Test Track which reported mid-depth
temperatures as the best predictor of strain (Priest and Timm, 2006). From this, the mid-
depth pavement temperatures were selected for the analysis of the effect of temperature
on tensile strain at the bottom of the HMA. The average mid-depth temperatures are
listed in Table 5.1.
Plots were developed for tensile strain and mid-depth pavement temperature in
each direction, longitudinal and transverse, and for each axle type at the various speeds
tested. Figure 5.6 displays the temperature-strain relationship in the longitudinal
direction under a single axle.
91
Longitudinal Strain due to Mid-Depth Temperature
y = 19.423e0.0275x
R2 = 0.9807
0
50
100
150
200
250
300
350
55 65 75 85 95 105
Temperature (oF)
Mi
cr
os
tra
in 15 mph
25 mph
35 mph
45 mph
FIGURE 5.6 Effect of Temperature on Longitudinal Strain.
From this plot it is evident that an increase in mid-depth pavement temperature causes a
significant increase in tensile strain, a relationship that can be described by an
exponential function. In Figure 5.6 the equation for the trend line generated by Excel is
displayed for a vehicle speed of 15 mph which illustrates a very high R2 value indicating
that an equation of the form listed in Equation 5-2 is a very good fit for these data.
Although only the regression equation and R2 value for 15mph is displayed, the R2
values for the relationships at the other three speeds were also very high, ranging from
0.961-0.985. Likewise, plots for temperature-strain relationships under the steer axle and
tandem axle also illustrated very close fits with an exponential function described by
Equation 5-2. Similarly, in the transverse direction, shown by Figure 5.7 (for a single
axle), the temperature-strain relationship was closely fitted by the same exponential
92
function regardless of axle type. Given the consistently high R2 values, it was concluded
that Equation 5-2 most accurately describes the temperature-strain relationship in both
directions for all axle types.
dT
t ce=? (5-2)
where:
?t = Tensile strain (micro strain)
T = Mid-depth Temperature (?F)
e = the base of natural logarithm
c, d = regression coefficients
Transverse Strain under Single Axle by Mid-depth
Temperatures
y = 14.525e0.0266x
R2 = 0.9914
0
25
50
75
100
125
150
175
200
225
45 55 65 75 85 95 105
Temperature (oF)
St
ra
in
(m
icr
o
str
ain
)
15 mph
25 mph
35 mph
45 mph
FIGURE 5.7 Effect of Temperature on Transverse Strain.
93
5.3.4 Combined Effects of Speed and Temperature on Tensile Strain
Although the effects of speed and temperature were first investigated separately,
their effects are not independent of each other due to the fact that HMA is a material for
which properties are temperature and time-dependent. The investigations into the effects
of speed and temperature revealed that tensile strain is directly proportional to the
natural logarithm of the vehicle speed and directly proportional to the exponential
function of temperature. Furthermore, it was found that the highest strain levels, critical
for design, were experienced under slow vehicle speeds and high mid-depth pavement
temperatures. To quantify this combined effect, DataFit, a regression analysis software
program, was utilized to generate regression equations from the recorded data. DataFit
allows the user to enter forms of regression equations not built into Excel. The program
then iterates through possible coefficients and checks the validity of the user defined
equation by calculating the correlation to the provided data. From this program,
Equation 5-3 was selected to represent the effect of speed and temperature on
longitudinal strain at the bottom of the HMA layers (13.9 inches deep). The equation of
the form listed in Equation 5-3 was selected because it linearly combined the individual
effects of speed and temperature (Equations 5-1 and 5-2) with regression coefficients
that were statistically significant, and it resulted in high coefficients of determination. It
was found that axle type (assuming all axles within each category were of approximately
the same weight) influenced strain values; therefore regression equations of the form
listed in Equation 5-3 were developed for each axle type as well as each direction,
longitudinal and transverse. The regression coefficients for each axle type are listed in
Table 5.2. As Table 5.2 illustrates, these equations very closely fit the measured data.
94
Figure 5.8 also exhibits the accuracy of these regression equations as the measured data
points for a single axle in the longitudinal direction lay in close proximity to the line of
equality.
hevf gTt ++= ln? (5-3)
where:
?t = tensile strain at the bottom of the HMA (13.9 in.) (??)
v = vehicle speed (mph)
T = mid-depth pavement temperature (?F)
e = base of natural logarithm
f, g, h = regression coefficients
TABLE 5.2 Regression Coefficients by Axle Type and Direction of Strain
Regression Coefficients
Gauge Orientation Axle Type f h i R2
Longitudinal Steer -24.25 0.047 108.81 0.955
Longitudinal Tandem -34.67 0.051 172.93 0.970
Longitudinal Single -40.57 0.053 206.67 0.983
Transverse Steer -19.70 0.050 101.40 0.986
Transverse Tandem -15.05 0.500 112.57 0.971
Transverse Single -16.23 0.051 102.18 0.986
95
Longitudinal Strain under Single Axle
R2 = 0.98
0
50
100
150
200
250
300
350
0 50 100 150 200 250 300 350
Measured Strain (microstrain)
Ca
lcu
lat
ed
S
tra
in
(m
icr
os
tra
in
)
FIGURE 5.8 Calculated vs. Measured Strain.
The above equations were derived for the N9 test section and allow for the
prediction of tensile strain under a variety of conditions. This is useful in comparing to
critical strain levels essential to perpetual pavement design. Also, quantifying the effects
of temperature and speed on tensile strain allow for further investigation into the
material property that ultimately affects such responses, E*.
5.4 LOAD DURATION
It is necessary to characterize E* under field conditions to validate mechanistic-
empirical design procedures such as the MEPDG. It is has been established through
laboratory testing that the HMA stiffness is dependent on temperature and frequency.
However, frequency cannot be measured or controlled directly in the field. Given that
96
frequency is inversely proportional to the time of loading, focus has been placed on
modeling load duration in the field. It has been established by previous researchers that
time of loading varies with pavement depth and vehicle speed (Barksdale, 1971).
Additionally, given the viscoelastic nature of HMA it is expected that load duration also
varies with temperature. Thus, further investigation has been conducted in modeling
load durations in the field under various temperatures, depths and speeds.
5.4.1 Definition of Load Duration
Previous researchers such as Barksdale, Brown and Loulizi et al., have utilized
stress pulses to model time of loading with speed and depth (Barksdale, 1971; Brown,
1973; Loulizi et al., 2002). Stress pulses are often of the haversine waveform, with
distinguishable termination points. Although stress pulses enable a fairly easy
measurement of load duration at the bottom of the HMA, such time corresponds to a
response that is not critical. The critical response at the bottom of the HMA layer that is
absolutely imperative to one of the most severe distresses, fatigue cracking, is tensile
strain. Therefore, to evaluate the effect of vehicle speed, pavement thickness and
temperature on load duration, the time of loading was defined by the strain pulses
recorded by the embedded strain gages.
Strain pulses in each direction were described in Figures 5.2 and 5.3 in which
strain levels were plotted in time. As previously noted, strain levels were most critical in
the longitudinal direction, therefore only load durations from longitudinal strain pulses
were examined. The strain pulses experienced in this experiment were very similar to
those described by Garcia and Thompson (2008). It is evident from their research
(Garcia and Thompson, 2008) as well as Figures 5.2 and 5.3 that strain pulses are not of
97
a defined waveform, making the task of measuring and modeling load duration more
complicated. Given that the strain values asymptotically approach the baseline strain,
and the cyclical noise inherent in the signal, it is difficult to define a distinct begin and
end of the loading phase of the strain pulse. Although the pavement is loaded from the
point it deviates from the baseline strain to the point in which it returns to the baseline
strain, it is difficult to determine exactly where the points of deviation and return are
located. This is especially true when the strain pulse experienced excessive noise or was
located at shallow depths where gages were more sensitive to vibrations and/or were
nearing the neutral axis of the pavement that experiences no tensile strain. Due to these
difficulties, the definition of load pulse duration described by Garcia and Thompson
(2008) was adopted. Figure 5.2 illustrates this definition, as the strain pulse duration was
taken as the time that the HMA was experiencing only tensile strain. Using this
definition of strain pulse duration, the durations were measured for each of the eight
axles (1 steer axle, 2 axles in the tandem axle group and each of the 5 trailing single
axles) using the baseline as a reference point to dictate the point at which the strain pulse
crossed into the tensile realm. It should be noted that the axles in the tandem axle group
were considered separate axles when the trace crossed the baseline strain level in
between the two axles. Therefore a total of eight strain pulse durations were measured
for each truck.
As discussed in Chapter Three, and shown in Figure 5.1, longitudinal strain
gages were embedded at four depths within the pavement: 6.0, 8.8, 11.0, and 13.9
inches. At shallow depths the gages were more sensitive to vibrations, creating noisy
traces that in some cases made termination points of the traces completely
98
undistinguishable. Additionally, strain pulses recorded at 6.0 inches deep illustrated that
the strain was mostly compressive, indicating that it was above the neutral axis. At
depths above the neutral axis, the strain levels are predominately compressive, whereas,
deeper in the structure, the strain is predominately tensile. Strain levels diminish to zero
at the neutral axis, making it difficult to measure strain levels when in close proximity to
the neutral axis. Thus, strain pulses recorded near the neutral axis were small
(approximately 20?? compressive), but exhibited primarily compressive strain, as
shown in Figure 5.9. In the figure there is a line drawn to help distinguish where the
baseline is approximately located, and the small amount of strain that is in the tensile
realm (above the baseline). As it might be expected, measuring tensile load duration
from a trace similar to that in Figure 5.9 is nearly impossible, therefore strain pulse
durations were only measured from gages located at 8.8, 11.0 and 13.9 inches deep
where the signal was more discernible.
The effects of speed, depth and temperature on strain pulse duration were
characterized first individually. From the individual relationships, the combined effect
of these three factors on load duration was then characterized to provide a means to
predict the load duration for any set of conditions.
99
FIGURE 5.9 Strain Pulse Near Neutral Axis.
5.4.2 Effect of Depth on Strain Pulse Duration
To determine the general relationship between strain pulse duration and depth,
measured strain pulse durations were plotted against gage depth. Figure 5.10 displays
the expected trend of increasing duration with increased depth for a single axle at 35
mph. The same trend was also observed for the remaining axle types and speeds tested.
Attaching a line of best fit and its associated regression equation and coefficient of
determination showed that the strain pulse duration is a function of the natural logarithm
of the gage depth, described by Equation 5-4 for all axle types and speeds. Although
only the equation for the data measured on April 6, 2007 is shown, data measured on the
remaining dates also illustrated close fitting equations, with similarly high R2 values.
khjt += )ln( (5-4)
where:
t = strain pulse load duration (sec)
h = depth (in)
Baseline
= 20??
Time (sec)
Vo
lta
ge
(V
)
Tension
Compression
100
j, k = regression coefficients
In looking at Figure 5.10, if the trend lines were extended linearly towards the x-
axis, it is evident that at some depth the strain pulse durations would reach zero. This is
an indication that the neutral axis has been reached and at the x-intercept zero tensile
strain exists. Therefore, at depths shallower than the x-intercept, only compressive strain
is experienced. Also, it should be noted that the x-intercept is not the same for each date
tested, which may be an indication that temperature is a factor.
Strain Pulse Load Duration by Depth (Single Axle at 35mph)
y = 0.115Ln(x) - 0.195
R2 = 0.91
0
0.02
0.04
0.06
0.08
0.1
0.12
0 2 4 6 8 10 12 14 16
Depth (in)
Du
ra
tio
n (
se
c)
06-Apr-07
10-Apr-07
25-Apr-07
FIGURE 5.10 Strain Pulse Duration by Gage Depth.
5.4.3 Effect of Speed on Strain Pulse Duration
The relationship between speed and strain pulse duration was determined by
plotting measured strain pulse durations against vehicle speed. Rather than using the
target speeds of the trucks, the actual vehicle speed was calculated from the known
distance between gages and the times at which an axle passed over the gages. This was
101
done to ensure an accurate relationship. Figure 5.11 displays the strain pulse durations
with vehicle speed at a gage depth of 11.0 inches for a single axle. As was found with
strain levels, increasing vehicle speed resulted in decreased strain pulse durations. It was
found that by attaching a trend line that the strain pulse duration is related to the vehicle
speed by a power function of the form listed in Equation 5-5. Although only the
regression equation for the first test date is shown, Equation 5-5 was found to represent
the remaining dates with very high R2 values. Furthermore, plots at the remaining gage
depths showed that Equation 5-5 represents the relationship between strain pulse
duration and speed regardless of axle type and gage depth.
mlvt = (5-5)
where:
t = strain pulse load duration (sec)
v = vehicle speed (mph)
l, m = regression coefficients
102
Strain Pulse Load Duration at 11.0 in. Deep by Speed
(For Single Axle)
y = 1.74x-0.856
R2 = 0.98
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0 10 20 30 40 50 60
Speed (mph)
Du
ra
tio
n
(se
c) 06-Apr-07
10-Apr-07
25-Apr-07
02-May-07
FIGURE 5.11 Effect of Speed on Strain Pulse Duration.
5.4.4 Effect of Temperature on Strain Pulse Duration
The effect of pavement temperature on strain pulse duration was assessed by
developing plots for each axle type. To be consistent with the evaluation of field
measured strain levels, the mid-depth pavement temperatures were utilized for this
analysis as well. Figure 5.12 shows that at the bottom of the HMA layers, the strain
pulse duration decreases slowly with an increase in pavement temperature. A power
function is shown to fit the data very well for a target vehicle speed of 45 mph. The
remaining target speeds can also be fitted with a power function of the same form;
however the correlations to the measured data, indicated by the R2 values, are not as
close (at 15 mph, R2 = 0.71). This was also the case for the remaining gage depths. It is
evident however; that there is a definite trend, although it might be slight, that the strain
103
pulse duration decreases with an increase in mid-depth pavement temperature. This
trend was evident regardless of axle type or depth in the pavement, and can be described
by a power function. Therefore, the power function relationship shown in Equation 5-5
was utilized to characterize strain pulse duration with temperature (rather than speed).
Load Pulse Duration at bottom of Pavement by Mid-depth
Pavement Temperature For Single Axle
y = 0.7439x-0.5454
R2 = 0.9409
0
0.05
0.1
0.15
0.2
0.25
50 55 60 65 70 75 80 85 90 95 100 105
Temperature (F)
Lo
ad
P
ul
se
D
ur
at
io
n
(s
ec
)
15 mph
25 mph
35 mph
45 mph
FIGURE 5.12 Effect of Temperature on Strain Pulse Duration.
5.4.5 Modeling Strain Pulse Duration for Field Conditions
Once the individual effects of depth, speed and temperature were evaluated for
the measured strain pulse durations, the combined effect of all three variables was
quantified. A model was developed using DataFit to account for all three variables by
pooling all strain pulse duration measurements regardless of axle type. The resulting
model is listed in Equation 5-6 and is a linear combination of the previous relationships,
104
listed in Equations 5-4 and 5-5. The same process as was discussed in section 5.3.4 to
determine the most appropriate model was again followed, in which multiple models
were first defined, then based on the statistical output by DataFit, a final model was
selected:
rTvhnt qp +++= ln (5-6)
where:
t = strain pulse load duration (sec)
h = depth (in)
v = vehicle speed (mph)
T = mid-depth temperature (?F)
n, p, q, r = regression coefficients
Equation 5-6 was selected for its strong correlation (R2 value of 83.74%) to the
measured data which is displayed in Figure 5.13. Note the measured data clustered
around the line of equality in Figure 5.13. Additionally, each of the regression
coefficients was found to be statistically significant, evident by the reported p-value,
also shown in Figure 5.13.
In Equation 5-6, coefficient ?n? adjusts for HMA depth. As previously
discussed, increased depth translates to increased load duration, and therefore a positive
coefficient is logical. It was found that increasing vehicle speed resulted in decreased
load duration, which is accurately represented in the model by a negative exponent,
coefficient ?p?. Similarly, increases in mid-depth temperature induced shorter load
durations which are explained by a negative exponent, coefficient ?q,? in the model.
105
Using equations of the same form listed in Equation 5-6, individual models were
developed by axle type: steer, tandem, and single. Small improvements in correlation to
the measured data were found, with R2 values of 88.83%, 87.62%, and 86.34%
respectively. The improvements were slight, and therefore do not suggest that the load
duration is heavily dependent on axle type.
By developing a model for strain pulse duration as a function of depth, speed and
temperature, predictions can be made for the N9 test section for a set of given
conditions. Furthermore, such a model also enables comparisons to be drawn with load
durations computed by mechanistic-empirical design procedures, specifically the
MEPDG.
Measured Strain Pulse Load Duration Compared to Predicted Strain Pulse Load Durations
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
Measured Duration (sec)
Mo
de
led
D
ur
ati
on
(s
ec
)
All Axles
FIGURE 5.13 Goodness of Fit of Predicted Strain Pulse Durations.
Regression
coefficients
Value p-value
n 0.1131 0
p -0.0807 0
q -0.0628 0.00001
r -1.7241 0
106
5.5 SUMMARY
A field investigation into strain levels and strain pulse durations was completed
on section N9 at the NCAT Test Track. Strain pulse traces were recorded by strain gages
embedded at multiple depths under live traffic at various speeds and temperatures. From
the recorded strain pulse traces the strain levels at the bottom of the HMA layers were
evaluated to quantify the effect of speed, and temperature on tensile strain. The strain
pulse durations were determined from the recorded traces and utilized to model the
effect of pavement depth, vehicle speed, and temperature.
It was found that tensile strain levels at the bottom of the HMA layers are most
influenced by mid-depth pavement temperatures. Tensile strain was found to be a
function of the natural logarithm of vehicle speed and the exponent of mid-depth
pavement temperature. Given the varying weights of the axle groups, the tensile strain
levels were found to be heavily dependent on axle type. Additionally, tensile strains in
the longitudinal direction were more significant than those in the transverse direction.
Given these findings, models were developed separately for tensile strain in the
longitudinal and transverse directions to account for vehicle speed, and mid-depth
pavement temperature. Furthermore, a model for tensile strain in each direction was
developed for each axle type, tallying six models.
Strain pulse durations were defined by the time that the HMA layers experienced
only tensile strain under dynamic loading. From the recorded longitudinal strain pulse
traces, the durations were measured and related to three variables: pavement depth,
vehicle speed, and mid-depth pavement temperature. It was found that strain pulse
durations increase with the natural logarithm of pavement depth, and decrease with a
107
power function of vehicle speed and pavement temperature. Unlike, strain levels, strain
pulse durations were not found to be heavily dependent on axle type. One model was
developed to account for critical strain pulse durations.
Although the models developed are specific for the N9 test section, it offers a
field-measured data set by which to make comparisons to established pavement design
procedures that estimate strain levels and load durations. Specifically, comparisons can
be made between pavement responses predicted by various methods of computing
material properties and the field-measurements. From these comparisons, conclusions
can be made on methods of computing material properties, particularly E*, and the
quality of these design procedures.
108
CHAPTER SIX
MEPDG EVALUATION
6.1 INTRODUCTION
It is imperative that the quality of the MEPDG be evaluated in first
characterizing material properties and second, in designing against critical distresses,
such as fatigue cracking. The mechanism behind fatigue cracking, as mentioned
previously, is tensile strain at the bottom of the HMA. To evaluate the quality of the
MEPDG, both a field investigation and an investigation into the internal workings of the
MEPDG are necessary. The field investigation was completed, and results were
discussed in Chapter Five regarding the factors affecting tensile strain at the bottom of
the HMA and load durations at various points in the structure. Following the completion
of the field investigation, the next step in validating the MEPDG was to follow its
procedure to compute load duration which in turn can be used to assess E* predictions
and ultimately strain predictions. E* values are computed en route to computing load
durations in the method prescribed by the MEPDG. Using these load durations and E*
values computed by the MEPDG, results were compared with field measurements and
evaluated to determine its usefulness as a design mechanism for state DOTs.
6.2 EVALUATION OF MEPDG LOAD DURATION PROCEDURE
In characterizing the material property, E*, of HMA layers, the MEPDG
considers two factors to be the most important: temperature and rate of loading (Eres,
109
2003). The temperature is determined internally within the program from an enhanced
integrated climatic model (EICM) which is calibrated for different regions from
historical data (Eres, 2003). The rate of loading, however, is much more complex, due to
its direct relationship with time of loading which is influenced by vehicle speed, axle
configuration, and properties of the pavement structure (Eres, 2003). Thus, to evaluate
the quality of E* estimates, it is necessary to take a detailed look into the procedure to
determine the time of loading, as defined by the MEPDG.
6.2.1 MEPDG Load Duration Procedure
The MEPDG uses an iterative procedure to compute the load duration under
dynamic loading, shown conceptually in Figure 6.1. The MEPDG assumes the load
duration as the length of time for one complete haversine stress pulse in the longitudinal
direction for an applied load (Eres, 2003). In following the MEPDG procedure, the load
duration is heavily dependent on the pavement structure. Within the procedure, the
pavement structure is transformed following Odemark?s transformation procedure for
layered systems (Eres, 2003). In doing so, the height of each layer is transformed into an
effective height based on the ratio of the modulus of that layer to the modulus of the
subgrade and the layer height. The effective heights of each layer are used to compute
the effective depth, Zeff, of the stress pulse given any point within the structure. The
effective depth is the sum of the effective heights of the layers above the point in
interest, plus the effective height of the layer where said point resides. Figure 6.1 shows
a two layer system in which the point of interest is at the mid-point of the bottom layer.
To compute the effective depth, the modulus of each HMA layer is required; however,
the modulus of each HMA layer is a function of the time of loading. Since, the time of
110
FIGURE 6.1 MEPDG Load Duration Procedure (Eres, 2003).
Subgrade Modulus,
ESG
Layer height,
hi
Initial loading
time, t
3 223 11 *2
1
SGSG
eff E
Eh
E
EhZ +=
)(2 effceff ZaL +=
Vehicle speed,
vs
s
eff
v
Lt
6.17=
f = 1/t Has Ei* converged? NO YES Time of loading = t
Temperature, T
Ei* = fn(f, T)
f = 1/t
Leff =
111
loading has yet to be computed, it must be assumed initially from which rate of loading
is then computed.
In addition to the pavement structure, the time of loading is dependent on the
axle configuration. Configurations are taken into account in the computation of the
effective length of the stress pulse. Figure 6.1 illustrates the effective length for a single
axle in which the effective length of the stress pulse is a function of the contact radius,
ac, and effective depth. This illustrates the assumption that the stress pulse is distributed
throughout the pavement structure at a 45 degree angle from the edge of the contact at
the surface (Eres, 2003). This assumption is held for all axle types. For tandem, tridem,
and quad axles, the axle spacing must be known to determine the amount of overlap at
the effective depth. Further discussion on axle types other than single axles are excluded
because in the field, strain pulses under the tandem axles did not exhibit overlap at the
deepest point measured (13.92 inches), and were therefore treated as two single axles.
Vehicle speed is taken into account in the determination of time of loading.
Shown in Figure 6.1, load duration is inversely proportional to the vehicle speed and
directly proportional to the effective length of the stress pulse. Given that this is an
iterative process, and that E* is dependent on time of loading, the resulting load duration
must be used in the time-frequency relationship to help compute E*. The entire
procedure must be repeated several times until the HMA modulus of each layer has
converged.
6.2.2 N9 E* Regression Analysis
In order to follow the MEPDG procedure, a means to estimate E* from
temperature and loading frequency must first be established. It is prescribed in the
112
method that the frequency is inversely proportional to time, as described by Equation 6-
1 (Eres, 2003).
tf
1= (6-1)
where:
f = loading frequency (Hz)
t = time of loading (sec)
The MEPDG uses one of three methods to determine E* via the construction of a master
curve, in which the method depends on the selected level of complexity in design. In
two of the three methods an equation is utilized to compute E* from various volumetric
properties and binder information. For the most complex level of design, the MEPDG
requires E* laboratory test results to construct the master curve. E* laboratory testing
was completed for the N9 section, at three temperature: 40, 70, and 100 ?F, and seven
frequencies: 0.5, 1, 2, 5, 10, 20, and 25Hz. E* testing was discussed in more detail in
Chapter Four. Given that the majority of the temperatures experienced in the field were
within the range tested in the laboratory, a regression analysis was completed to develop
a model to determine E* for each of the HMA layers in N9. The model, shown in
Equation 6-2, was selected based on the very high coefficients of determination, and
significance of each regression coefficient. Table 6.1 lists the coefficients for the
regression equation by the HMA lift, as well as the coefficient of determination.
Although the p-values are not listed, all coefficients were found to be significant with a
p-value of less than 0.0001. It should be noted that the HMA lifts are numbered from the
top down, with number one being the surface layer. Furthermore, the regression
113
coefficients for lifts three and four are the same because they were constructed of the
same mix.
cT fabE =* (6-2)
where:
E* = dynamic modulus of HMA (psi)
T = Temperature (?F)
f = loading frequency (Hz)
a, b, c = regression coefficients
TABLE 6.1 E* Regression Coefficients by Lift
HMA Lift Type Thickness (in) a b c R2
1 SMA 2.16 3,445,000 0.9719 0.1551 0.97
2 76-28 3.84 4,546,000 0.9712 0.1464 0.98
3 64-22 2.76 4,637,000 0.9740 0.1313 0.97
4 64-22 2.28 4,637,000 0.9740 0.1313 0.97
5 Rich Bottom 2.88 3,342,000 0.9692 0.1734 0.99
6.2.3 Load Duration Computation
To draw direct comparisons with the field measured load durations, the MEPDG
method for computing was followed, utilizing the exact same conditions as experienced
in the field. For each time of loading measured, the load duration was calculated for the
same gage depth, pavement temperatures, and vehicle speed. To compute the E* of the
necessary layers, in-situ pavement temperatures recorded by probes T7, T9, T11, T13
and T15 were employed. Probes in each layer were not consistently located at the mid-
point of the layer, therefore, probes located closet to the gage depth were used, and
hence the selection of the aforementioned probes. Table 6.2 lists the depth of the
114
embedded temperature probes used for this analysis, as well as the associated pavement
layer.
TABLE 6.2 Location of Temperature Probes
Temperature Probe Depth (in) Lift
T7 2.02 1
T9 5.41 2
T11 8.38 3
T13 10.81 4
T15 14.08 5
To compute E*, an initial loading time was required to determine the loading
frequency through Equation 6-1, for use in Equation 6-2. The seed value for time of
loading was calculated following the equation developed by Brown (1973):
log (t) = 0.5d ? 0.2 ? 0.94log(v) (6-3)
where:
d = depth (m)
v = vehicle speed (km/hr)
According to Brown, the loading time should be an average of the stress pulses in all
three directions: vertical, radial, and tangential (Brown, 1973). As illustrated in Equation
6-3, Brown found that the time of loading was a function of the depth within the
pavement and the vehicle speed. The vehicle speed calculated from the known axle
spacing and time at which the axle passed a gage was utilized in the application of
Equation 6-3. From this calculation an initial HMA modulus of each layer was
determined. Due to the iterative process used in the MEPDG, any shortcomings of this
equation are quickly resolved by successive iterations, and in reality any value could be
used.
115
The calculated HMA modulus was then used to compute an effective depth of
the stress pulse at the gage depth according to (Eres, 2003):
3
1
1
3
SG
n
n
n
i SG
i
ieff E
Eh
E
EhZ +
???
?
???
?= ??
=
(6-4)
where:
hn = height of the bottom layer (at depth in question)
hi = height of layer i (above the bottom layer)
Ei = Dynamic modulus of layer i (psi)
ESG = Modulus of subgrade (psi)
En = Dynamic modulus of bottom layer (psi)
The average modulus of the underlying Track soil subgrade was utilized for use in
Equation 6-4. As described in Chapter Three, the N9 structure consisted of 39.2 inches
of soft Seale subgrade sandwiched between two layers of Track soil, an 8.4-inch base,
and a deep subgrade. Backcalculation revealed very low moduli values for the Track soil
as a base material, inconsistent with laboratory testing (Taylor, 2008). It was likely due
to the soft Seale subgrade. Due to the fact that the Seale subgrade layer was thin relative
to the deep underlying layer of the Track soil, it was elected to use the resilient modulus
of the Track soil subgrade. To remain on the conservative side, the average resilient
modulus value of 28,335 psi found in the laboratory (Taylor, 2008) was used rather than
the larger resilient modulus found in the field through backcalculation.
Once the effective depth was computed, the effective length of the stress pulse
was calculated for each time of loading measured. The effective load duration was
calculated using Equation 6-5, given the desired depth within the pavement structure.
116
The contact radius was calculated for each tire, using the known axle weights for each
truck (Table 3-4) and a tire pressure of 100 psi. The Leff was calculated for only one of
the tire loads on each axle, such that, for a single axle, the axle weight was considered to
be equally distributed over 4 tires, resulting in four equal radii, of which only one was
selected for the computation.
)(2 effceff ZaL += (6-5)
where:
Leff = effective length of load pulse (in.)
ac = radius of tire contact area (in.)
Lastly, the time of loading was calculated following Equation 6-6, using the
calculated vehicle speed. Once the load duration was calculated, it was used to compute
frequency to begin the second iteration. The final load duration was taken once the
HMA modulus of each layer converged. For this investigation a total of nine iterations
were completed, although the moduli converged at iteration seven. An example of the
convergence is shown in Figure 6.2.
s
eff
v
Lt
6.17= (6-6)
where:
t = duration of stress pulse (sec)
vs = vehicle speed (mph)
117
Convergence on E* values
0
100,000
200,000
300,000
400,000
500,000
600,000
700,000
800,000
0 2 4 6 8 10
Iteration
E*
(p
si)
E*1
E*2
E*3
E*4
E*5
FIGURE 6.2 Example of E* Convergence.
6.2.4 Load Duration Comparisons
The load durations computed by the aforementioned MEPDG procedure were
compared with the strain pulse durations measured during the field investigation. A
direct comparison could be drawn because the field conditions (in-situ temperatures,
calculated vehicle speed, and gage depth) for each measured time of loading were
utilized to calculate a corresponding time of loading through the MEPDG procedure.
Figure 6.3 illustrates the difference in the measured and calculated load durations for all
gage depths, by plotting measured versus theoretical (MEPDG). It is evident that the
MEPDG procedure consistently over-predicts the load durations as every data point on
the plot is above the line of equality. Attaching a regression equation to the data,
illustrates that this over-prediction is approximately 68% greater than the measured load
durations. It should be noted that the measured load durations represent the tensile strain
118
pulse durations in the longitudinal direction, while the theoretical durations represent the
duration of stress pulses in the longitudinal direction assumed to be at 45 degree angles
to the horizontal. These differences may account in part for the over-prediction by the
MEPDG procedure. However, it should be expected that better agreement exists
regardless of strain or stress measurements.
y = 1.6768x + 0.0284
R2 = 0.7905
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
Measured Load Pulse Duration (sec)
Th
eo
re
tic
al
Lo
ad
P
uls
e D
ur
ati
on
(s
ec
)
FIGURE 6.3 Measured Load Duration Versus Theoretical.
6.3 Effect of MEPDG Load Duration Calculations
It is imperative that the MEPDG be evaluated on its ability to characterize
material properties because material properties directly influence pavement responses
and ultimately pavement performance. As noted previously, one such property, E*,
significantly influences tensile strain. Furthermore, tensile strain at the bottom of the
119
HMA is the controlling factor for the development of fatigue cracking. The MEPDG
determines E* en route to computing load duration, both of which are dependent on each
other. To assess the accuracy of the MEPDG, strain levels were predicted from these
values using layered elastic analysis for comparison with strain values determined in the
field, following Figure 6.4.
FIGURE 6.4 Evaluation of MEPDG by Pavement Response.
6.3.1 Strain Predictions Based on MEPDG Load Durations
The MEPDG neither outputs strains levels, nor is any process used to compute
strain discussed in the associated appendices. Therefore, to assess the E* values
computed through the method for determining load duration, strain values must be
E*, h
Pavement Structure
LEA ?t
VS.
?t
Pavement Response,
Measured
Pavement Response,
Predicted
120
predicted by another means. In this case, layered elastic analysis, specifically the
software program WESLEA for Windows (version 3.0), was utilized.
WESLEA is capable of computing pavement responses provided a few material
properties of each layer: modulus, Poisson?s ratio, and layer height. The program is
however limited to only three HMA layers atop a base layer and subgrade. Additionally,
the program requires that axle configurations be defined, as well as tire load. Using
layered elastic theory and the user defined inputs, pavement responses at critical
locations are predicted.
To use WESLEA, the eight-layered pavement structure of N9 was converted to a
five-layered structure. Doing so required that the heights and material properties of three
layers of HMA be transformed into one, and the Track Soil base layer be combined with
the Seale Subgrade layer. In order to do so, knowledge of the aforementioned properties
of each of the eight layers were required. Thus, computation of the HMA modulus of
each layer was necessary. First, a set of conditions was selected, listed in Table 6.3. To
simplify the procedure, the in-situ pavement temperatures at all depths were considered
equal. This eliminated the need to model the temperature gradient across the five HMA
layers in the N9 structure. Using these conditions, the MEPDG?s method for
determination of time of loading was followed, as described previously, again using the
E* regression equations listed in Equation 6-2 and Table 6.1.
121
TABLE 6.3 Conditions for Strain Predictions
Speed, mph Temp, ?F
15 60
15 80
15 110
25 60
25 80
25 110
45 60
45 80
45 110
Because tensile strain at the bottom of the HMA is critical to fatigue cracking, only load
durations at the bottom of the HMA (13.9 inches) were computed. To ensure accuracy,
nine iterations were completed, from which the resulting E* values were used to
describe each HMA layer, listed in Table 6.4. Although the exact calculated values are
listed in this table, much less precision exists.
TABLE 6.4 Computed E* Values for N9 HMA Layers
Speed
(mph) Temp (?F) E1* (psi) E2* (psi) E3* (psi) E4* (psi) E5* (psi)
15 60 968,585 1,058,003 1,169,592 1,129,741 614,110
15 80 554,358 601,895 705,472 681,703 337,579
15 110 239,461 257,795 330,112 319,260 137,448
25 60 1,046,470 1,136,962 1,247,353 1,204,823 668,494
25 80 599,042 646,893 752,429 727,048 367,496
25 110 258,830 277,125 352,129 340,529 149,646
45 60 1,143,832 1,235,113 1,343,234 1,297,401 737,049
45 80 654,912 702,834 810,331 782,961 405,212
45 110 283,055 301,160 379,280 366,757 165,026
Next, three HMA layers of the structure were transformed into one layer,
illustrated by Figure 6.5. The first layer, a stone matrix-asphalt (SMA) mix, with PG 76-
28 binder and the fifth, a rich bottom layer designed for 2% air voids and composed of
PG 64-22 binder, were left as independent layers due to their uniqueness. The second,
third and fourth HMA layers were combined into one. Given that the third and fourth
layers were constructed of the same mix, combining these two was logical. The second
122
lift was also combined with this pair because the HMA moduli for the varying
conditions were very similar to those in the third and fourth layers and because they
were all standard mixes. The HMA modulus of the transformed second layer was
calculated using a weighted average dependent on layer height, described by Equation 6-
6. The resulting HMA moduli of the transformed structure are listed in Table 6.5; again
much less precision in these values exists.
( )
?
?=
n
nn
T h
hEE ** (6-6)
where:
ET* = HMA Modulus of Transformed layer
En* = HMA Modulus of nth layer
hn = height of nth layer
FIGURE 6.5 Transformation of Structure for Use in WESLEA.
Track Soil, MR-SG Track Soil, MR-SG
SMA, E1*, 2.16?
PG 76-22, E2*, 3.84?
PG 64-22, E3*, 2.76?
PG 64-22, E4*, 2.28?
RBL, E5*, 2.88?
Track Soil, MR-GB, 8.4?
Seale Soil, MR-SG, 39.2?
SMA, E1*, 2.16?
RBL, E3*, 2.88?
Combined E2,T*, 8.88?
Combined Base,
MR,T, 47.6?
Original N9 Structure Transformed N9 Structure
123
TABLE 6.5 HMA Moduli for Transformed N9 Structure
Speed
(mph)
Temp
(?F) h1 (in.) E*1 (psi) h2 (in.) E*2T (psi) h3 (in.) E*3 (psi)
15 60 2.16 968,585 8.88 1,111,105 2.88 614,110
15 80 2.16 554,358 8.88 654,579 2.88 337,579
15 110 2.16 239,461 8.88 296,053 2.88 137,448
25 60 2.16 1,046,470 8.88 1,188,697 2.88 668,494
25 80 2.16 599,042 8.88 700,275 2.88 367,496
25 110 2.16 258,830 8.88 316,716 2.88 149,646
45 60 2.16 1,143,832 8.88 1,284,711 2.88 737,049
45 80 2.16 654,912 8.88 756,818 2.88 405,212
45 110 2.16 283,055 8.88 342,283 2.88 165,026
Next, the Track soil base layer was combined with the Seale soil subgrade layer,
to create a transformed base layer 47.6 inches thick. These unbound materials were
characterized in the laboratory through a previous investigation at the Test Track
(Taylor, 2008). From this investigation the stress-sensitive resilient moduli were found
to be described by Equation 6-7 (Taylor, 2008). The associated regression coefficients
for each material are listed in Table 6.6.
32
1
k
a
d
k
a
aR pppkM ???
?
???
?
???
?
???
?= ??
(6-7)
where:
MR = resilient modulus of unbound material
pa = atmospheric pressure = 14.696 psi
? = bulk stress, psi
?d = deviatoric stress, psi
k1, k2, k3 = regression coefficients
TABLE 6.6 Regression Coefficients for MR (Taylor, 2008)
Unbound Material k1 K2 k3
Seale Subgrade 225.09 0.3598 -0.7551
Track Soil 1095.43 0.5930 -0.4727
124
The resilient modulus is dependent on the states of stress within each layer. The state of
stress within the base layer and subgrade layer are further dependent on the ability of the
HMA layers above to disperse the applied load. Therefore, the properties of the
transformed HMA layers, listed in Table 6.5 were used in WESLEA to determine the
induced stresses in the transformed base layer and subgrade layer. Induced stresses, ?x,
?y, and ?z, were used to determine the states of stress, bulk stress and deviatoric stress,
for each layer independently. Through an iterative process the MR of the transformed
base layer and Track soil subgrade layer were determined.
To complete this iterative process, the bulk (?) and deviatoric (?d) stresses were
further defined by Equations 6-8 and 6-9.
? = ?1 + ?2 + ?3 (6-8)
?d = ?1 - ?3 (6-9
where:
?1 = total axial stress, psi
?2, ?3 = confining pressure, psi
The total axial stress, ?1, is the sum of the principal stress, ?1p, in the vertical direction
and the induced stress in the vertical direction, ?z, as determined from WESLEA. In this
case, the principal vertical stress is due to the overburden stress of the overlying layers,
computed by Equation 6-10.
1728/)...( 22111 iip hhh ???? +++= (6-10)
where:
?1p = principal vertical stress, psi
125
?i = unit weight of ith layer, pcf
hi = height of ith layer, in.
The critical location where induced stresses were predicted in WESLEA for the
determination of the base MR was the mid-point of the base layer (37.7 inches deep)
directly beneath the tire load. For the subgrade MR, the critical location was the interface
of the base and subgrade layers (61.5 inches deep), also directly beneath the tire load. To
determine the principal vertical stress for either layer the unit weight of the base layer
was required. Previous laboratory investigations for the 2006 Test Track reported a
value of 126.9 pcf (Timm, 2008). The unit weight of each HMA layer was the product
of the bulk specific gravity, Gmb, in the field and the unit weight of water. The percent
compaction of the laboratory determined maximum specific gravity, Gmm, was recorded
during construction. From this, the bulk specific gravity and unit weight of each HMA
layer were computed using Equation 6-11 and the values listed in Table 6.7. To ensure
accuracy, the properties of all five HMA layers in the original N9 pavement structure
were used to compute the vertical principal stress for each the base and subgrade layer.
mbwmb G?? = (6-11)
where:
?mb = bulk unit weight of layer, pcf
?w = unit weight of water, pcf = 62.4
Gmb = bulk specific gravity = %Gmm * Gmm
126
TABLE 6.7 Unit Weight by HMA Layer (Timm, 2008)
Lift %Gmm Gmm Gmb ?mb (pcf)
1 93 2.397 2.229 139.1
2 92.9 2.496 2.319 144.7
3 95.1 2.503 2.380 148.5
4 93.9 2.507 2.354 146.9
5 94.4 2.424 2.288 142.8
The confining pressures, ?2 and ?3, were equivalent due to the defined critical
location, directly beneath the tire load, and the assumption that the materials were
homogenous and isotropic. Confining pressure is further defined as the summation of
the horizontal principal stress, ?3p, and the induced horizontal stress, ?x, determined in
WESLEA. The horizontal principal stress is dependent on the at-rest lateral earth
pressure, and was computed using Equation 6-12.
pp k 103 ?? = (6-12)
where:
?3p = horizontal principal stress, psi
k0 = coefficient of at rest lateral earth pressure
?1p = vertical principal stress, psi (see Equation 6-10)
The coefficient of at rest lateral earth pressure, k0, is dependent on the angle of internal
friction of the soil. Using Equation 6-13 to compute k0, the angle of internal friction was
assumed to be 40? to be consistent with the previous investigation into the
characteristics of these unbound materials (Taylor, 2008).
?sin10 ?=k (6-13)
where:
? = angle of internal friction, assumed to be 40?
127
To begin the iterative process of determining the resilient modulus of each base
and subgrade layer, an initial MR value of each was assumed. Again referring to prior
research (Taylor, 2008) conducted on the unbound materials used at the Test Track, the
initial values were selected based on representative states of stress. For a stress state
with 25 psi of bulk stress and 7 psi of deviatoric stress, the resilient modulus of the
transformed base layer was approximately 6,500 psi (Taylor, 2008). The transformed
base layer was a combination of both the Track soil and Seale subgrade, therefore a
slightly higher value of 10,000 psi was selected to account for the much stiffer Track
soil. At the same state of stress used to select the base layer, the MR value for the Track
soil was approximated at 30,000 psi.
Once the initial values were selected, the MR of the base layer was determined
first. Using the HMA properties from the original N9 8-layer structure, the vertical and
horizontal principal stresses were computed. Then using WESLEA, and the
aforementioned seed values of the base and subgrade, the maximum stresses induced at
the mid-point of the 47.6 inch deep transformed base layer were predicted. Table 6.8
lists the defined properties necessary to complete the analysis in WESLEA. It should be
noted that to simplify the analysis, it was assumed that the pavement was under the load
of a 20,000 lb single axle with single tires. Additionally the layer heights for each HMA
layer are shown in Figure 6.5 for the original structure. The base layer height used was
the height of the transformed base layer, 47.6 inches deep, also shown in Figure 6.5.
128
TABLE 6.8 Properties Defined for WESLEA
Property Value
Poisson?s Ratio ? HMA 0.35
Poisson?s Ratio ? Transformed Base 0.45
Poisson?s Ratio ? Subgrade 0.45
Slip 1: Full adhesion
Axle Steer
Tire Load 10,000 lb
Tire Pressure 100 psi
The resulting stresses, ?x, ?y, and ?z, found at the mid-point of the base layer were then
used to compute the bulk and deviatoric stresses. From these values, the resilient
modulus of the transformed base layer was computed. Throughout the process, the
resilient modulus of the subgrade was kept constant at 30,000 psi. The new base layer
resilient modulus was then substituted into WESLEA to replace the initial seed value,
starting the second iteration. This process was repeated until the resilient modulus of the
transformed base layer converged (about 4 iterations). Following this process the
resilient moduli of the transformed base layer was determined for the nine conditions
listed in Table 6.3.
The same iterative process was also employed to determine the MR values for the
subgrade layer. The final MR values for the base layer were kept constant in determining
the resilient moduli values of the subgrade layer under the varying conditions. The final
MR values for the base and subgrade layers are listed in Table 6-9 for each condition.
TABLE 6.9 Final Resilient Moduli Values
Speed (mph) Temp (?F) Base MR (psi) Subgrade MR (psi)
15 60 9,253 25,301
15 80 8,825 25,615
15 110 8,154 26,082
25 60 9,282 25,254
25 80 8,869 25,569
25 110 8,223 25,993
45 60 9,349 25,227
45 80 8,947 25,498
45 110 8,294 25,969
129
Once, the moduli of each layer in the transformed structure (Tables 6.9 and 6.5)
were established, WESLEA was again employed to estimate pavement responses. The
properties defined in Table 6.8 were once again used; however, the analysis was
completed for a 20,000 lb single axle with dual tires, which thereby reduced the tire load
to 5,000 lbs. The maximum tensile strain was selected among two critical locations at
the bottom of the HMA (13.9 inches deep). The first of the two critical locations was
directly beneath the center of the outside tire load, and the second was located directly
beneath the edge of the outside tire load, 6.75 inches from the center of the tire. The
resulting maximum strain values are listed in Table 6.10 for the nine conditions
investigated.
TABLE 6.10 Tensile Strain Based on MEPDG Load Durations
Speed (mph)
Temp
(?F) ?t (??)
15 60 50.95
15 80 77.8
15 110 158.01
25 60 47.82
25 80 76.23
25 110 149.07
45 60 44.41
45 80 70.94
45 110 139.35
6.3.2 Strain Predictions Based on Field-Modeled Load Duration
To assess the ability of the MEPDG to estimate those strain levels experienced in
the field, two comparisons were drawn. The first was a comparison with the strain levels
resulting from load durations modeled after field measurements. A procedure similar to
130
the procedure previously discussed for strain predictions from MEPDG load durations
was used, with the only difference being the means to quantify load duration.
First, the load durations were calculated at the mid-depth of each of the five
original HMA layers following Equation 5-6. This equation represents the load duration
for tensile strain pulses at various points in the HMA layers of the N9 pavement
structure. However, as was noted in Chapter Five, this equation results in negative
values for pavement depths less than the depth to the neutral axis. This is an indication
that the strain pulses are compressive in nature above the neutral axis. Depending on the
conditions (speed and temperature), load durations were found to be negative as deep as
the mid-point of the third HMA layer. The load durations at the mid-point of each HMA
layer were necessary to compute the HMA modulus following the regression equation
listed in Equation 6-2. Time of loading cannot be negative, and if only tensile strain
durations were used, some HMA moduli values would be zero. Thus, in order to
calculate the HMA moduli, some assumptions about the induced strain pulses were
necessary.
It was assumed that above the neutral axis the critical response was compressive
strain. At the surface the tensile strain can be assumed to be equal to zero, and it is
assumed that the amount of tensile strain slowly increases with pavement depth.
However, regardless of the amount of tensile strain, the pavement is still under loading
and a strain pulse is still induced. Based on this, it was assumed that strain pulses were a
function of the depth, vehicle speed and in-situ temperature regardless of the depth
relative to the neutral axis. To further investigate the trends, Equation 5-6 was used to
describe the load durations at the mid-point of all five HMA layers for a speed of 45
131
mph and in-situ temperatures equal to 60?F. The results were plotted in Figure 6.6.
Although negative, the strain pulse durations near the surface of the pavement were
found to be longer than the durations near the bottom. The strain pulse durations
illustrated account for the time that the pavement was in its dominant strain mode only,
either compressive or tensile. As discussed in Chapter Five, measuring the duration of
an entire pulse, which included the strain reversal from compressive to tensile or vice
versa, was nearly impossible. Thus, in measuring the duration of only the dominant
strain mode (relative to the neutral axis), Equation 5-6 does so accurately. Thus, it was
assumed that Equation 5-6 appropriately modeled strain pulse duration for either
compressive or tensile strain as long as the absolute value of the duration is taken.
Equation 5-6 is rewritten in Equation 6-14, taking into account these assumptions,
allowing the strain pulse duration to be calculated regardless of the dominant strain
mode.
7241.1ln1131.0 0628.00807.0 ?++= ?? Tvht (6-14)
The HMA moduli were calculated for the five layers of the original N9 pavement
structure following Equation 6-2 from the regression analysis on the laboratory-
determined E* values. The strain pulse durations were used to determine frequency
following the assumption that they are inversely proportional, described by Equation 6-
1. After the HMA moduli were determined, the resilient moduli of the transformed base
and subgrade layers were determined following the same iterative procedure previously
discussed. In following this iterative procedure, it was necessary to transform the
original structure into a five-layered structure for evaluation in WESLEA. Equation 6-6
132
was again employed to transform the previously determined HMA moduli values for the
transformed structure shown in Figure 6.5. The moduli of the transformed layers are
listed in Table 6.11.
0
1
2
3
4
5
6
7
8
9
10
11
12
13
-0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1
Strain Pulse Duration (sec)
De
pt
h (
in)
FIGURE 6.6 Field Modeled Strain Pulse Duration at 45 mph and 60 ?F.
TABLE 6.11 Moduli of Layers in Transformed Structure from Field Modeled
Load Durations
Speed (mph) Temp (?F) E*1 (psi) E*2T (psi) E*3 (psi) Base MR (psi) Subgrade MR (psi)
15 60 844,846 1,393,909 718,772 9,304 24,522
15 80 470,434 921,451 391,194 8,927 24,909
15 110 196,955 353,125 156,270 8,227 25,562
25 60 817,700 1,388,683 752,887 9,304 22,894
25 80 456,549 793,798 412,233 8,902 24,958
25 110 191,614 355,927 166,099 8,243 25,562
45 60 793,979 1,428,555 808,598 9,327 24,553
45 80 444,203 885,195 448,899 8,961 24,894
45 110 186,787 362,866 185,070 8,258 25,593
Next, the moduli values of the transformed structure were input in WESLEA to
predict the tensile strain at the bottom of the pavement. The critical locations were
133
exactly as defined for the analysis of strain for MEPDG load durations. Just as was the
case for the previous analysis, the values listed in Table 6.8 were defined in WESLEA,
with the exception of the axle configuration and tire load. Rather then using a 20,000 lb
steer axle, a 20,000 lb single axle was used to predict the strain values. The maximum
tensile strains at the bottom of the HMA were predicted from WESLEA and are listed in
Table 6.12.
TABLE 6.12 Tensile Strain Based on Field Modeled Load Durations
Speed (mph) Temp (?F) ?t (??)
15 60 45.15
15 80 69.05
15 110 145.44
25 60 44.78
25 80 72.31
25 110 142.92
45 60 43.24
45 80 67.61
45 110 137.82
6.3.3 Strain Predictions Based on Field Modeled Tensile Strain
The second comparison with the strain predictions due to the MEPDG load
durations was drawn with the strain values predicted from measured tensile strain. In
Chapter Five Equation 5-3 was developed to characterize the tensile strain at the bottom
of the HMA layers for varying vehicle speed and in-situ pavement temperatures. For a
single axle in the longitudinal direction, the developed equation is re-written in Equation
6-15. For the nine conditions listed in Table 6.3, the tensile strain at the bottom of the
HMA was directly computed with results listed in Table 6.13.
67.206ln57.40 053.0 ++?= Tt ev? (6-15)
134
TABLE 6.13 Tensile Strain Based on Field Modeled Tensile Strain
Speed (mph) Temp (?F) ?t (??)
15 60 120.98
15 80 166.72
15 110 440.55
25 60 100.26
25 80 145.99
25 110 419.83
45 60 76.41
45 80 122.14
45 110 395.98
6.3.4 Comparison among Strain Predictions
Comparisons were drawn among the three aforementioned methods to predict
strain for the evaluation of the MEPDG?s method for determining load duration. The
first comparison was drawn between the strain predicted from the MEPDG load duration
method and the strain predicted from the field modeled strain pulse duration. Shown in
Figure 6.7 are the strain predictions by temperature and speed.
The process to predict strain in both cases was identical, aside from the method
to determine load duration, t. Both load duration computations produced strains that
increased with temperature and decreased with speed, consistent with findings in the
field investigation. Strain predictions as a result of the method prescribed by the
MEPDG (labeled ?MEPDG t? in Figure 6.7) were slightly higher than the predictions
resulting from the load durations modeled after field measurements (labeled ?Modeled
t?).
135
0
20
40
60
80
100
120
140
160
180
60 80 110 60 80 110 60 80 110
15 15 15 25 25 25 45 45 45
Temperature (oF)
Speed (mph)
St
ra
in
( ?
???????)
Modeled t
MEPDG t
FIGURE 6.7 Predicted Strains by Temperature and Speed.
Over-prediction of load duration, as was found with the MEPDG method, would
be expected to result in lower E* values, due to the inverse relationship with frequency
and time, and the direct relationship between E* and frequency. This was found to be
the case, in looking at Equation 6-2, and the resulting E* values in Tables 6.5 and 6.10,
E* decreases with longer load durations. Illustrated in Tables 6.5 and 6.10, E* values
were greater for surface mixes where the MEPDG estimated shorter load durations than
Equation 5-6. Further down in the pavement structure, E* values were lower where load
durations were over-predicted by the MEPDG. Although the MEPDG grossly over-
predicted load duration deeper in the pavement relative to the model developed from
field measurements, the E* values were not as greatly influenced. E* values in the
bottom layer of the transformed structure differed by only 20,000-100,000 psi,
approximately. The higher strain predictions for the MEPDG determination of load
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durations could be attributed to the fact that E* values were overall found to be lower
than those based on the field measured model for load duration.
Strain was also estimated utilizing the regression equation (6-15) developed in
Chapter Five, characterizing tensile strain at the bottom of the HMA by speed and
temperature. Figure 6.8 displays the strains simulated in WESLEA from both the
MEPDG computed load durations, and the model from field measured load durations
compared with the results from Equation 6-14. The modeled strains resulted from a
regression analysis in which Equation 6-14 fit the measured strain values very well with
a coefficient of determination of 0.983. The highest mid-depth pavement temperature
recorded during the field investigation was 99.47?F, at which a strain of 308 ?? was
recorded at 15 mph, shown in Figure 5.6. Based on this, the strain predicted from the
regression equation may be slightly higher than expected. This maybe an indication of
the limits of the equation, as 110?F is outside the range of measured mid-depth
temperatures. But overall, the strain values in the field have been shown to be most
accurately predicted by Equation 6-15.
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0
50
100
150
200
250
300
350
400
450
500
60 80 110 60 80 110 60 80 110
15 15 15 25 25 25 45 45 45
Temperature (oF)
Speed (mph)
St
ra
in
( ?
???????) Modeled t
MEPDG t
Modeled strain
FIGURE 6.8 Simulated Strains Compared with Modeled Strains.
It is evident that the two strain simulations that were based on load durations
underpredict the strain likely to be experienced at the conditions investigated. Looking
at the results of all three strain predictions in Table 6.14, these simulations are nearly
half of those predicted by the regression equation. The strain based on MEPDG load
durations were closest to those from Equation 6-15, with percent differences ranging
from 42% to 65%. Although these two simulations returned relatively close values,
neither represented values likely to occur in the field under these conditions. Both
simulations utilized the same procedure aside from the determination of load duration.
The large discrepancies in the strain predictions relative to Equation 6-14 may
not be a result of the load duration calculations. The MEPDG overpredicted the load
durations measured in the field. As discussed earlier, longer load durations lead to lower
E* values and ultimately higher strain values. Although this was the case, the gross
138
overprediction of load duration only resulted in strain values that were at best 58% of
those based on measured values. The other simulation was based on field measured load
durations and still resulted in strain estimates that were a fraction of those modeled from
field measured strain. Some of these errors may be a result of the assumption that the
regression equation for load durations could be applied to pavement depths less than the
neutral axis. However, following this assumption resulted in longer load durations at
shallower depths which then produced higher strain values. Therefore, it is unlikely that
either procedure to determine load duration was the major cause for the gross under-
predictions of tensile strain levels.
TABLE 6.14 Resulting Strain Predictions
Based on Load Durations
Speed
(mph)
Temp
(?F)
MEPDG t
?t (??)
Modeled t
?t (??)
Modeled
?t (??)
15 60 50.95 45.15 120.98
15 80 77.8 69.05 166.72
15 110 158.01 145.44 440.55
25 60 47.82 44.78 100.26
25 80 76.23 72.31 145.99
25 110 149.07 142.92 419.83
45 60 44.41 43.24 76.41
45 80 70.94 67.61 122.14
45 110 139.35 137.82 395.98
Both simulations did however use the same E* regression analysis to predict
HMA moduli from load durations. In computing E* for both load duration methods, the
time-frequency relationship (f = 1/t) was utilized. Regardless of how load duration was
computed, it was found that the resulting strain was nearly half of the strain determined
from field measurements. Since the time-frequency relationship was consistent among
strain predictions from load durations, it is possible that the large differences between
measured strain and predicted strain are a result of this time-frequency relationship. In
139
order for the MEPDG to construct a master curve from E* laboratory results, both cold
and warm temperatures are required. It is difficult to obtain accurate and reliable results
at such extreme temperatures. Due to the lack of data at these extreme temperatures, the
regression equation developed from the results that were obtained was used instead. The
coefficients of determination for Equation 6-2 were very high (0.97-0.99) suggesting
that it may be an acceptable alternative to a master curve. However, given that Equation
6-2 was used in both the simulations that returned poor correlation to modeled strains
from field measurements, it is a possible source of error. Equation 6-2 was a product of
the temperature in the layer in question. Although, in the simulations, it was assumed
that a temperature gradient did not exist, and that all layers experienced the same
temperature. The strain values modeled from field measurements however were
dependent on mid-depth pavement temperature. Thus, the failure to account for a
temperature gradient may have also contributed to the low strain values in both
simulations. Also, the maximum temperature, 110?F that was investigated was 10?F
beyond the highest temperature tested in the laboratory.
6.4 SUMMARY
The MEPDG?s method for computing load duration was investigated relative to
field measured load durations. Additionally, the effects of such computations were
assessed based on strain predictions. The strain and load durations measured in the field
investigation of test section N9 were used for comparison and evaluation of the
MEPDG.
First, the method prescribed by the MEPDG for the computation of load duration
was followed. The MEPDG method is an iterative procedure to determine the time of
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loading modeled by a haversine stress pulse dependent on vehicle speed, depth in the
pavement and HMA moduli. Although the MEPDG constructs a master curve to
characterize E*, it was elected to use E* laboratory test results to develop a regression
equation for each mix in the N9 test section. The resulting equations were a function of
loading frequency and in-situ pavement temperature. The use of a regression equation
seemed appropriate given the very high coefficients of determination (0.97-0.99) and the
temperatures experienced in the field were almost all within the range tested in the
laboratory. The procedure was completed for the exact same conditions at which
measurements were made in the field enabling a direct comparison. The resulting load
durations were found to over-predict measured strain pulse durations by approximately
68%. The difference in load duration definition was cited as a possible cause for the
gross over-prediction. The durations measured in the field were of strain pulses in
tensile strain only. However, regardless of whether stress or strain was measured, a
better correlation should be expected.
A set of conditions were defined, representative of the conditions experienced in
the field, to assess how the MEPDG load durations affected strain levels. The MEPDG
itself does not output strain predictions directly. Therefore, strain levels at the bottom of
the HMA were predicted using a separate layered elastic analysis program, WESLEA.
To utilize WESLEA, the 8-layered structure of N9 was transformed into a 5-layer
structure, in which the three middle HMA layers were combined into one, and the Track
soil base layer was combined with the Seale subgrade layer. Using the regression
equation developed for field measured strain pulse durations, strain predictions were
also made through WESLEA for the same conditions and transformed structure. Both
141
simulations resulted in very similar tensile strain values, in which the maximum absolute
difference was found to be 12.57 ??. Further comparisons were made with strain
calculated directly from vehicle speed and temperature using the regression equation
developed from field measured tensile strain at the bottom of the HMA under a single
axle. The strain simulated from the MEPDG load durations did display the expected
trend of increased strain with an increase in load duration. However, the strain levels
poorly replicated the strain calculated from the regression equation, with simulated
levels at best 58% of the calculated levels. Overall, it was found that the over-prediction
of the load durations by the MEPDG did not result in an over-prediction of strain levels.
Contrary to theory, the elongated durations grossly under estimated the strain levels in
the field. Such large differences in predicted strain and strain determined from field
measurements could indicate that the time-frequency relationship utilized is inaccurate.
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CHAPTER SEVEN
CONCLUSIONS AND RECOMMENDATIONS
7.1 SUMMARY
This thesis investigated the viscoelastic nature of HMA in an M-E pavement
design framework, specifically the MEPDG, by means of E* predictive equations and
measurable pavement responses under field conditions. To meet the objectives set forth
in Chapter One of this thesis, a literature review was first completed on E* laboratory
test procedures and results, E* predictive equations, load durations and tensile strain. An
evaluation of three E* predictive equations, the Witczak 1-37A, the Witczak 1-40D, and
the Hirsch, was completed for HMA mixes from the 2006 Test Track structural study. A
field study was also conducted for one pavement section in the Test Track structural
study, in which vehicle speeds were varied from 15-55 mph and varying pavement
temperatures were recorded. During the field study, horizontal tensile strain pulses were
recorded at multiple depths within the HMA layers, including the most critical point, the
bottom of the HMA. The recorded strain pulses enabled an evaluation of tensile strain at
the bottom of the HMA, as well as an evaluation of strain pulse durations at various
depths. The MEPDG prescribed method for determining load duration was followed to
offer comparisons with field measured strain pulse durations. Furthermore, field-
measured and MEPDG load durations were utilized to predict E* and ultimately tensile
strain at the bottom of the HMA using a layered-elastic analysis program. These
143
strains were then compared with measured strains, thus linking the time-element of E*
to pavement response. Findings from these evaluations are further summarized in the
following section.
7.2 CONCLUSIONS
7.2.1 Evaluation of E* Predictive Equations
To determine the most appropriate E* predictive model for HMA mixtures of the
2006 Test Track structural study, three equations were analyzed: the Witczak 1-37A, the
Witczak 1-40D and the Hirsch E* predictive models. The dynamic moduli of these
mixtures were determined in the laboratory at seven frequencies and three temperatures.
Following the Witczak 1-37A model, E* was estimated for three temperatures
(40, 70, and 100?F) and seven frequencies (0.1, 1, 2, 5, 10, 20, and 25 Hz). E* was also
estimated using the Witczak 1-40D and Hirsch E* predictive models for two
temperatures (70, and 100?F) and three frequencies (1, 10, 25 Hz). In comparing the
predicted dynamic moduli to measured dynamic moduli it was found that the Hirsch
model predicted E* most accurately. The Witczak 1-37A model was the least precise for
the mixtures tested, with large amounts of scatter on either side of the line of equality.
The Witczak 1-40D model consistently grossly over estimated measured E* values by at
most 5.6 times the measured values. When plotted against measured E* values, it was
found that both the Witczak 1-40D and the Hirsch models flattened out at extreme
values, rather than increasing with frequency as did the measured values. Therefore,
neither model accurately captured the time-dependency of HMA at the extremes.
However, this trend was more predominant in the Hirsch model at moduli values
predicted at 70?F. Despite this flaw, the Hirsh model consistently hovered around the
144
line of equality, producing the highest coefficient of determination (0.707 in log scale)
of the three models for its associated linear regression equation. Furthermore, the Hirsch
model was very accurate for low moduli values (250,000-700,000 psi). Due to the large
scatter resulting from the Witczak 1-37A predictions, and gross over predictions made
by the Witczak 1-40D model, the Hirsch model is the most accurate and reliable
predictive equation for the HMA mixtures evaluated.
The effect of mixture parameters on the accuracy of the models was investigated
as well. Plots were developed comparing measured moduli to predicted moduli for each
mixture type, binder type, grade, and NMAS included in the study. It was found that
although these parameters influence the magnitude of measured and predicted moduli,
none of these parameters were found to significantly affect the accuracy of the
predictions made by these three models.
7.2.2 Evaluation of Field Measured Strain and Strain Pulse Durations
One pavement section at the Test Track was selected for a field study in which
live traffic was applied to the N9 test section at a minimum of four different speeds (15,
25, 35, 45, and 55 mph) on four test dates. During the testing, embedded strain gages
captured horizontal strain pulses at four depths while temperature probes recorded in-
situ pavement temperatures. From these measurements tensile strain at the bottom of the
HMA was characterized by mid-depth temperature and vehicle speed. Additionally,
strain pulse durations were characterized by layer mid-depth temperature, vehicle speed,
and pavement depth.
Tensile strains were found to vary by direction and axle type, with the highest
strains recorded in the longitudinal direction and under single axles. In characterizing
145
tensile strain at the bottom of the HMA, it was found to be a function of the natural
logarithm of vehicle speed and the exponent of the mid-depth temperature.
Strain pulse durations were defined by the time in which the pavement was in
tensile strain when under dynamic loading. Strain pulse durations were characterized
based on measurements at 8.76?, 11.04? and 13.92? deep in the HMA structure.
Increases in vehicle speed resulted in shortened strain pulse durations, while load
durations elongated deeper in the pavement. As mid-depth pavement layer temperatures
increased, the strain pulses were found to shorten in length.
7.2.3 Evaluation of the MEPDG?s Method for Determining Load Duration
The MEPDG?s method for computing load duration was investigated relative to
field measured load durations. Additionally, the effects of such computations on strain
predictions were assessed. The strain and load durations measured in the field for test
section N9 were used for comparison and evaluation of the MEPDG.
The iterative procedure outlined in the MEPDG for the determination of load
duration of a haversine stress pulse was followed for conditions identical to those in the
field investigation. Comparing the load durations computed by the MEPDG and the
measured strain pulse durations in the field, it was found that the MEPDG load durations
were approximately 68% greater than those measured in the field.
For a set of given conditions, load durations were calculated by the MEPDG and
by the model developed from field measured strain pulse durations, from which E* was
calculated. Since the MEPDG does not output actual strain predictions, a separate
layered elastic analysis program, WESLEA was employed to predict strain at the bottom
146
of the HMA for both load duration procedures. In comparing these strain predictions it
was found that despite the 68% difference in load durations, there was little difference in
strain levels. The maximum absolute difference between these strain predictions was
only 12.57 ??. Both procedures exhibited the expected trend of increased strain with an
increase in load duration.
For the same set of conditions, tensile strain was computed by the regression
equation developed from measured tensile strain from the field investigation. When
compared with the strains simulated in WESLEA from MEPDG load durations and load
durations based on field measurements, strains estimated from field measurements were
nearly double the simulated strains. It should be noted that the strains simulated in
WESLEA from either definition of load duration were dependent on the time-frequency
relationship. It can be concluded from these findings that it is not the definition of load
duration that is most influential in predicting strain from E*, but rather the relationship
between load duration and frequency.
7.3 RECOMMENDATIONS
For the State DOTs from which the mixtures herein originated, the Hirsch E*
model may be used to predict E* in the absence of E* laboratory testing. However, it
should be used with caution given the discrepancies found at high frequencies and
moderate temperatures. If the MEPDG is being utilized for design, Hirsch E* model
estimates may be substituted in a Level One design for laboratory E* results, following
extrapolation to colder temperatures. Furthermore, if the MEPDG is to be used in its
current format it is recommended that calibration be completed both regionally and
147
nationally for the Witczak 1-40D model prior to implementation of the software
program as the primary design tool.
Given the advancement in pavement design and global push towards
mechanistic-empirical pavement design, characterizing the viscoelastic nature of HMA
is imperative to successful designs. Therefore, based on the comparisons of load
duration, it is recommended that further investigation in defining the load duration
throughout the HMA be completed. Due to the under estimation of strain from either
load duration definition, it is suggested that the time-frequency relationship is inaccurate
and thus needs further refinement. Lastly, at the current state of the MEPDG, the output
is in the form of pavement distresses which are predicted from estimated strain levels.
Findings from this thesis identified the possible under estimation of strain based on
procedures outlined within the MEPDG; therefore further investigation into the accuracy
of the predicted distresses should be completed. Also, further refinement of the strain
predictions, possibly by accurately characterizing the time-frequency relationship,
should be completed before implementation of the program for design purposes.
148
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