Proposed Improvements to Overlay Test for Determining Cracking Resistance of Asphalt
Mixtures
by
Wangyu Ma
A thesis submitted to the Graduate Faculty of
Auburn University
in partial fulfillment of the
requirement for the Degree of
Master of Science
Auburn, Alabama
May 3, 2014
Keywords: asphalt, overlay, cracking, test
Copyright 2014 by Wangyu Ma
Approved by
Nam Tran, Chair, Associate Research Professor of Civil Engineering
Randy West, Director of National Center for Asphalt Technology
David Timm, Brasfield & Gorrie Professor of Civil Engineering
Richard Willis, Associate Research Professor of Civil Engineering
ii
ABSTRACT
There is an increasing need in evaluating the cracking resistance of asphalt mixtures as
more recycled materials are used in the mixes. A promising method that has been used to
evaluate the mixture cracking resistance is the overlay test conducted in accordance with the
Texas Department of Transportation procedure (Tex-248-F). This test can be conducted on
specimens prepared from gyratory-compacted samples or from field cores. It can be conducted in
an Overlay Tester or in the Asphalt Pavement Performance Tester (AMPT) with an Overlay Test
Kit.
The overall objective of this thesis is to evaluate and refine the overlay test conducted in
the AMPT for determining the cracking resistance of asphalt mixtures. The evaluation was
conducted using five plant-produced mixtures that were used in the bottom asphalt layers of five
test sections at the NCAT Pavement Test Track.
Key findings of this study include (1) a modified method for better determining the
number of cycles to failure (i.e., the failure point) and (2) a higher test frequency (1.0 Hz) for
reducing the testing time without significantly affecting the test result and its variability.
Furthermore, the overlay test results were compared with those of the bending beam fatigue
(BBF) test. Good correlation was found between the overlay test results and the BBF test results
determined at 800 and 400 ??.
iii
ACKNOWLEDGEMENT
First of all, I would like to acknowledge the guidance and support given to me by my
supervisor Dr. Nam H. Tran for his support and encouragement in my professional and personal
life throughout the years. Without his guidance, I could not overcome those obstacles. In my
study, Dr. Tran encouraged me to investigate many fields of my interest. Every time I had a new
idea in conducting the experiments or data analysis, I would like to talk to him at the first time.
Even though some ideas were not ready to be implemented, he was always patient and offered
invaluable suggestions for me to explore with. I have gained a lot through this process. Dr. Tran
taught me the importance of writing skill to a researcher. He provided me a great support in
developing the technical writing skill, especially during the writing process of the thesis work.
Dr. Tran is not only the teacher but also the mentor in my self-development. The most important
thing I learned from him is the way of critical thinking. He taught me how to propose question
on phenomenon, make assumptions, and find the truth based on critical analysis for the
experimental data. His tutoring made me realize only through hardworking and great efforts can
I make any progress in the career.
Next, I would like to thank all my committee members for their agreeing to serve and
also for their great help in my past studies. Dr. Randy West offered me the great opportunity to
study in Auburn University and work with those excellent engineers in NCAT. In the class of
iv
design and control of asphalt paving mixtures, he taught me the importance of paying attention to
details and listening to others. Dr. David Timm made me understand the pavement design
systematically. I benefited a lot from his great teaching in pavement design classes. I would like
to thank Dr. Richard Willis for his agreeing to serve as my committee. He provided me very
good advices for my study plan in the future.
Also, I would like to acknowledge all my colleagues in NCAT during my working. Adam
Taylor gave me tremendous support in the experimental work. He helped me to conduct the
experiments more efficiently, and to deal with the issues on AMPT facility. Without his help, I
cannot go through the hard time with the machine and software problems. I want to thank Tina
Ferguson for her assistance in my experiment. She cleaned asphalt residue on the base plates
using acetone after every test. For many times, she came back to the laboratory late evening to
check the testing machine. I would like to acknowledge Dr. Saeed Maghsoodloo for his advices
on my statistical analysis. I also would like to say thanks to Jason Moore, Brian Waller, Grant
Julian, Vickie Adams, and Pamela Turner for their unselfish help to my working in the
laboratory. Finally, I want to say thanks to all the visiting scholars, classmates, and corporate
students in NCAT. Their understandings, encouragements, and cares made my life in Auburn
happy and meaningful.
v
TABLE OF CONTENTS
ABSTRACT ................................................................................................................................... ii
ACKNOWLEDGEMENT ........................................................................................................... iii
TABLE OF CONTENTS ............................................................................................................. v
LIST OF TABLES ...................................................................................................................... vii
LIST OF FIGURES ................................................................................................................... viii
CHAPTER 1 INTRODUCTION ................................................................................................. 1
1.1 Problem Statement ................................................................................................................ 1
1.2 Objective ............................................................................................................................... 3
1.3 Organization of This Thesis .................................................................................................. 3
CHAPTER 2 LITERATURE REVIEW ..................................................................................... 6
2.1 Bending Beam Fatigue Test .................................................................................................. 6
2.1.1 Test Procedure ............................................................................................................... 6
2.1.2 Test Results .................................................................................................................... 8
2.1.3 Results of Past Studies ................................................................................................. 12
2.2 Overlay Test ........................................................................................................................ 21
2.2.1 Test Procedure ............................................................................................................. 22
2.2.2 Test Results .................................................................................................................. 26
2.2.3 Results of Past Studies ................................................................................................. 26
2.3 Summary of Literature Review ........................................................................................... 53
CHAPTER 3 LABORATORY TESTING ............................................................................... 54
3.1 Overview of Overlay Test in the AMPT............................................................................. 54
3.1.1 Displacement Measurement Method ........................................................................... 55
3.1.2 Machine Compliance in the AMPT Overlay Test ....................................................... 56
3.2 Properties of Asphalt Mixtures ........................................................................................... 58
3.3 Testing Plan ........................................................................................................................ 60
vi
3.4 Specimen Fabrication Procedure ........................................................................................ 63
3.5 Test Setup............................................................................................................................ 63
3.6 Method for Determining the Failure Point .......................................................................... 67
CHAPTER 4 RESULTS AND ANALYSIS .............................................................................. 70
4.1 Evaluation of Methods for Determining the Failure Point ................................................. 70
4.2 Overlay Test Results ........................................................................................................... 74
4.3 Evaluation of Higher Frequency in the AMPT Overlay Test ............................................. 79
CHAPTER 5 COMPARING AMPT OVERLAY TEST AND BENDING BEAM FATIGUE
TEST RESULTS ......................................................................................................................... 86
5.1 Comparing Ranking of Mixtures ........................................................................................ 86
5.1.1 Ranking Mixtures Based on BBF Test Results............................................................ 86
5.1.2 Ranking Mixtures Based on AMPT Overlay Test Results .......................................... 88
5.1.3 Comparing AMPT OT Ranking to BBF Test Ranking for Five Mixtures .................. 89
5.2 Failure Point Prediction ...................................................................................................... 92
5.2.1 BBF Test ...................................................................................................................... 92
5.2.2 AMPT Overlay Test ..................................................................................................... 94
5.2.3 Comparing Failure Point Prediction in Two Tests ...................................................... 96
CHAPTER 6 CONCLUSION AND RECOMMENDATIONS .............................................. 98
REFERENCES .......................................................................................................................... 100
APPENDICES ........................................................................................................................... 106
Appendix A AMPT Overlay Test Results of All Specimens ................................................. 107
Appendix B Peak Load Curve Labeled with Nf(NLC), Nf(Thru Crack), and Nf(93%) ......... 110
Appendix C Minitab Outputs (Two-factor ANOVA with Tukey?s Test, N11-3 mix) ........... 127
Appendix D Excel Outputs (F-test Comparing Variance at Two Frequencies, N11-3 mix) .. 131
Appendix E Minitab Outputs (T-test for Comparing the Mean of Coefficients) ................... 133
vii
LIST OF TABLES
Table 2.1 Similarities between Three Studies ............................................................................................. 43
Table 3.1 Mixture Properties ...................................................................................................................... 60
Table 3.2 Laboratory Testing Plan .............................................................................................................. 62
Table 3.3 Base Plate Dimensions ................................................................................................................ 65
Table 4.1 Summary of OT Results at Three MODs for Five Mixtures ...................................................... 75
Table 4.2 Sum of Squared Error in the Two Failure Points ........................................................................ 78
Table 4.3 Information Test Specimens with Large Squared Error (SE) in Nf(93%) .................................. 79
Table 4.4 Tukey?s Test Results ................................................................................................................... 82
Table 5.1 Summary of BBF Test Results at Three Strains for Five Mixtures ............................................ 87
Table 5.2 Ranking of Average Failure Point by BBF Test for Five Mixtures ............................................ 88
Table 5.3 Ranking of Average Failure Point by OT for Five Mixtures Based on NLC Method ................ 89
Table 5.4 Spearman?s Rank-Order Correlation Coefficients ...................................................................... 90
Table 5.5 Fitting Power Model Coefficients for the BBF Test ................................................................... 94
Table 5.6 Fitting Power Model Coefficients for the AMPT OT ................................................................. 96
viii
LIST OF FIGURES
Figure 2.1 Laboratory compacted specimen (left) and trimmed specimen (right) ........................................ 7
Figure 2.2 BBF test on IPC device ............................................................................................................... 8
Figure 2.3 Reduced energy ratio versus load cycles in controlled-stress testing model ............................. 14
Figure 2.4 Reduced energy ratio versus load cycles in controlled-strain testing model ............................. 14
Figure 2.5 Relationship between RDEC and number of load cycle............................................................ 19
Figure 2.6 Concept of Texas Overlay Tester .............................................................................................. 22
Figure 2.7 Laboratory molded specimen (left) and trimmed specimen (right) ........................................... 23
Figure 2.8 AMPT Overlay Test kit ............................................................................................................. 25
Figure 3.1 AMPT with overlay test kit ....................................................................................................... 55
Figure 3.2 External LVDT on the back of steel plates ................................................................................ 56
Figure 3.3 Maximum actuator displacements versus maximum opening displacements in AMPT Overlay
Test ............................................................................................................................................. 58
Figure 3.4 Base plates ................................................................................................................................. 64
Figure 3.5 Glue type and amount ................................................................................................................ 66
Figure 3.6 Glue curing setup ....................................................................................................................... 67
Figure 3.7 Setup of specimen glued on base plates in AMPT .................................................................... 67
Figure 3.8 Determination of failure point ................................................................................................... 69
Figure 4.1 Specimen cracking condition at three moments (0.318-mm MOD and 0.1-Hz frequency) ...... 72
Figure 4.2 Three failure points and four stages on the peak load curve (0.318-mm MOD and 0.1-Hz
frequency) .................................................................................................................................. 73
Figure 4.3 Nf(NLC) versus Nf(Thru Crack) ................................................................................................ 76
Figure 4.4 Nf(93%) versus Nf(Thru Crack)................................................................................................. 76
Figure 4.5 Comparing Nf(NLC) and Nf(93%) to Nf(Thru Crack) ............................................................... 78
Figure 4.6 Comparing overlay test results at 0.1- and 1-Hz frequencies .................................................... 80
Figure 4.7 Comparing coefficients of variation at 0.1- and 1-Hz frequencies ............................................ 83
ix
Figure 4.8 Comparing testing time at two frequencies ............................................................................... 85
Figure 5.1 Maximum tensile strains versus failure points for five mixtures from BBF test ....................... 93
Figure 5.2 Maximum opening displacements versus failure points for five mixtures by OT ..................... 95
1
CHAPTER 1 INTRODUCTION
1.1 Problem Statement
Recycled materials, including reclaimed asphalt pavement (RAP) and recycled asphalt shingles
(RAS), are used in asphalt mixtures to reduce material costs. Since the binder in RAP and RAS
is often stiffer than the virgin binder used in the mixture, cracking is one of the major concerns in
using an asphalt mixture with higher RAP and/or RAS contents. Therefore, there is an increasing
need in evaluating the resistance of the mixture to cracking before it is produced and placed in
the field.
One of the standardized test methods for determining the resistance of asphalt mixtures to
cracking is the four-point flexural bending or bending beam fatigue (BBF) test conducted in
accordance with AASHTO T321 and ASTM D7460. This test was developed to simulate the
fatigue cracking behavior at the bottom of the asphalt layer in the field. During the test, a cyclic
displacement is applied at the central third points to induce tensile strains at the bottom of the
beam, which are representative of those that occur in the field, causing cracks to initiate and
propagate to the top of the beam. The main result of the BBF test is the number of cycles to
failure (or failure point) at which macro-cracks initiate and start to propagate in the beam
specimen. Even though significant research efforts have been conducted to develop and evaluate
this test, it has not been widely implemented by transportation agencies because of two main
issues: specimen preparation and testing time. Compared to a cylindrical specimen, it is more
2
expensive and difficult to prepare a beam specimen in the laboratory or extract a beam from a
pavement section for testing. In addition, a BBF test can take up to more than 50 days depending
on the selected strain level (Prowell et al. 2010). Thus, it is not used for routine asphalt mix
design or quality assurance/quality control (QA/QC) testing, which often requires a quick
turnaround (Saadeh and Eljairi 2011).
A potential solution is to find an alternative test that does not have these issues. The overlay test
(OT) was developed in the 1970s to test an asphalt mixture?s resistance to reflective cracking,
but it has also been evaluated to determine the bottom-up fatigue cracking and the thermal
reflective cracking resistance of asphalt mixture (Tex-248-F-09, Zhou and Scullion 2003, Zhou
et al. 2007a, Zhou et al. 2007b, Zhou and Scullion 2005b). Compared to the BBF test, the OT has
a couple of advantages. First, it is easier to prepare OT specimens from gyratory-compacted
specimens or from field cores. Second, this test can be conducted in an Overlay Tester or in the
Asphalt Pavement Performance Tester (AMPT) with an Overlay Test Kit. Many transportation
departments have purchased the AMPT through pooled-fund study TPF-5(178) (Withee 2013).
Thus, if this test is proved to be effective in AMPT, it can be implemented in the future.
However, in the current TxDOT procedure (Tex-248-F), the maximum opening displacement of
0.635 mm (0.025 in.) is deemed too large for testing stiff asphalt mixtures (e.g., with higher RAP
and/or RAS contents) and the mixtures of asphalt overlay placed in different climate conditions
(i.e., smaller daily temperature variation). The OT is currently conducted at a frequency of 0.1
Hz according to the current procedure, but the OT can be conducted at a higher frequency to
reduce testing time. In the current procedure, the failure point is defined as the number of cycles
3
where 93% reduction of the initial peak load occurs. This method of determining the failure point
is not consistent with those used in other cracking tests, such as the BBF test in accordance with
ASTM D7460 procedure. Thus, additional work is needed to evaluate the maximum opening
displacement, test frequency, and method for determining the failure point specified in the
current OT procedure.
1.2 Objective
The objective of this study is to evaluate the use of overlay test in the AMPT and determine if a
smaller maximum opening displacement(s), a higher test frequency, and another method for
determining the failure point can be successfully used in the procedure for evaluating the
resistance of asphalt mixtures to cracking.
1.3 Organization of This Thesis
This thesis consists of six chapters including this chapter (Chapter 1) which offers the
background and objective of this study. Chapter 2 is the literature review focused on the past
studies on the methods of analyzing the BBF test result and the development of the overlay test
(OT) since the late 1970s. For the BBF test, general test procedures and typical testing results are
summarized, followed by several methods used to determine the number of cycles to failure. For
the OT, the literature review is focused on the testing procedure, typical testing result,
repeatability, crack propagation modeling, and relationship between laboratory test result and
field performance.
4
Chapter 3 presents the overlay test in the asphalt mixture performance tester (AMPT), followed
by discussions on the properties of applied mixtures, testing plan, and specimen fabricating
procedure. A new method for determining the failure point in the AMPT overlay test is
proposed.
Chapter 4 summarizes the AMPT overlay test results and provides the associated analysis.
Evaluation for the two failure point determining methods is provided based on the cracking
images captured from the recorded video and the peak load development during the test. Then, a
better method is selected by correlating determined failure point to the defined failure moment at
which crack was first observed to pass through the specimen. The effect of higher frequency on
the testing result is also discussed.
Chapter 5 investigates the correlation between the BBF test and OT in evaluating the fatigue
cracking resistance of asphalt mixture. The investigation is performed by comparing their
ranking for the failure points of five asphalt mixtures used in NCAT Test Track, as well as the
fitted relationships between failure points and applied maximum tensile strains (or
displacements).
Chapter 6 provides the thesis summary with a list of findings and recommendations. Also, the
planned works for the future to verify these findings are also proposed. Appendices of some
5
important information are attached afterwards. The testing data, statistical analysis outputs, and
peak load curves (relationship between peak load and number of cycles) are included.
6
CHAPTER 2 LITERATURE REVIEW
This chapter provides a review of the past studies on the bending beam fatigue (BBF) test and
the overlay test (OT). General procedures, typical results and analyzing methods of two tests are
summarized. For the OT, repeatability, crack propagation modeling and application of the test
results in predicting the fatigue life of asphalt pavements are further discussed.
2.1 Bending Beam Fatigue Test
The BBF test was designed to determine the fatigue cracking resistance of an asphalt mixture
(ASTM D7460-10). The determined number of cycles to failure can be multiplied with a shift
factor to predict the fatigue life of the asphalt pavement under repeated traffic loading. This
section briefly describes the test procedure, followed by methods for determining test results and
a summary of findings from previous studies.
2.1.1 Test Procedure
In the BBF test, the beam specimen (380 ? 6 mm long by 63 ? 2 mm wide by 50 ? 2 mm thick)
is trimmed from a laboratory or field compacted beam specimen (ASTM D7460-10). Figure 2.1
shows the laboratory-compacted and trimmed beam specimens.
7
Figure 2.1 Laboratory compacted specimen (left) and trimmed specimen (right)
The BBF test can be conducted in devices that are commercially available through Cox and IPC.
The difference between the Cox and IPC devices is that the Cox device applies load from the top
while the IPC device applies load from the bottom. Figure 2.2 shows an IPC device. The beam
specimen is held by four equal-spaced clamps (ASTM D7460-10). All contact points have free
horizontal translation and rotation. A cyclic displacement is applied at the central H-frame third
points.
8
Figure 2.2 BBF test on IPC device
The testing device is kept in an environmental chamber set at a test temperature of 20 ? 0.5?C.
The loading frequency ranges from 5 to 10 Hz. Two waveforms can be applied: one is sinusoidal
specified in AASHTO T321, and the other is haversine specified in ASTM D7460. The
maximum deflection at the center of the specimen is maintained by a closed-loop control system.
The resulting maximum strain typically ranges from 200 to 800 microstrains (AASHTO T321-
07).
2.1.2 Test Results
9
Results of the test include the failure point (number of cycles to failure) and the dissipated
energy (DE). In AASHTO T321 and ASTM D7460, the failure point is determined differently. A
description of each method follows.
In both the methods, the maximum deflection (?) in each cycle is first used to calculate the
resulting maximum tensile strain (?t) as shown in Equation 1. The maximum tensile stress (?t) is
determined using Equation 2. Then, the flexural stiffness (S) is determined using Equation 3
(ASTM D7460-10).
?t = (12?h)(3L2 ?4a2) (1)
Where,
?t = maximum tensile strain (m/m);
? = maximum deflection at center of beam (m);
a = space between inside clamps (m); and
L = length of beam between outside clamps (m).
?t = 3aPbh2 (2)
Where,
?t = maximum tensile stress (Pa);
a = center to center spacing between clamps (Cox: 0.1190 m; IPC: 0.1185
m);
10
P = load applied by actuator (N);
b = average specimen width (m); and
h = average specimen height (m).
S = ?t ?t? (3)
In AASHTO T321, the relationship between the number of loading cycles (N) and the calculated
stiffness is then determined using the exponential model shown in Equation 4. Finally, the failure
point can be calculated using Equation 5 corresponding to the 50 percent reduction of the initial
stiffness (AASHTO T321-07).
S = AebN (4)
Nf = ln(0.5?S0)? ln(A)b (5)
Where,
N = number of loading cycles;
A = regression constant;
b = regression constant; and
S0 = initial beam stiffness (modulus) estimated at 50th cycle.
However, in ASTM D7460, another method is utilized to determine the failure point using
?Normalized Stiffness ? Cycles? (NSC) as an indicator that is defined in Equation 6. The NSC
11
value is plotted against the number of loading cycles. Finally, the failure point is the number of
loading cycle corresponding to the peak NSC (ASTM D7460-10).
NSC = Si ?NiS
0 ?N0
(6)
Where,
NSC = normalized stiffness ? cycles (Pa/Pa);
Si = beam stiffness (modulus) at cycle i (Pa);
Ni = cycle number i;
N0 = cycle number (i.e., 50) at which S0 is estimated.
Dissipated energy (DE) and phase angle at loading cycle i are determined using Equations 7 and
8. The summation of dissipated energy (DE) per cycle up to the failure point is the cumulative
dissipated energy (AASHTO T321-07).
DEi = ??t?t sin? (7)
? = 360fs (8)
Where,
DEi = dissipated energy at loading cycle i (J/m3);
? = phase angle at cycle i (degree);
F = load frequency (Hz); and
S = time lag between stress and strain curve at peak value (second).
12
2.1.3 Results of Past Studies
2.1.3.1 Failure Point
In the AASHTO method, the failure point is determined based on the reduction of initial
stiffness. However, use of the 50 percent stiffness reduction as a criterion does not always
correspond to the initiation of a macro-crack in the specimen (Rowe and Bouldin 2000). In the
ASTM method, the failure point is determined based on another approach proposed by Rowe and
Bouldin (Rowe and Bouldin 2000, ASTM D7460-10). They proposed a ?reduced energy ratio?
concept modified from Hopman?s ?energy ratio? concept (Rowe and Bouldin 2000). Equations 9
and 10 are from the original concept of energy ratio. In a controlled-stress test, strain could be
calculated using Equation 11, so Equation 10 can be written as Equation 12. In Equation 12,
sin?0/sin?n is close to one. E0 is a constant that does not affect the trend of Wn. Therefore,
Equation 12 is simplified to Equation 13. Equation 13 was originally used in a controlled-stress
test to determine the failure point by Rowe and Bouldin. A plot of ?reduced energy ratio? versus
?number of cycles? is demonstrated in Figure 2.3. Then, they applied Equation 13 in a
controlled-strain test and obtained a similar curve (Figure 2.4). The number of cycles at which
peak value occurred was defined as the transition point from micro-crack to macro-crack
propagation. The ASTM standard applied a normalized ?reduced energy ratio? to eliminate the
effect of initial stiffness, which is slightly different from the method proposed by Rowe and
Bouldin (ASTMD 7460-10).
13
Wn = nw0w
n
(9)
Wn = n(??0?0sin?0)??
n?nsin?n
(10)
? = ?E (11)
Wn = n(??0
2Ensin?0)
??02E0sin?n (12)
Rn? = nEn (13)
Where,
Wn = energy ratio;
n = cycle number;
w0 = dissipated energy in first cycle;
wn = dissipated energy in nth cycle;
?0 = stress in the initial cycle;
?n = stress in nth cycle;
?0 = strain in the initial cycle;
?n = strain in nth cycle;
?0 = phase angle in the initial cycle;
?n = phase angle in nth cycle;
E0 = modulus in the initial cycle;
E? = modulus in nth cycle; and
Rn? = reduced energy ratio for controlled stress test
14
Figure 2.3 Reduced energy ratio versus load cycles in controlled-stress testing model (Rowe
and Bouldin 2000)
Figure 2.4 Reduced energy ratio versus load cycles in controlled-strain testing model (Rowe
and Bouldin 2000)
15
Another important parameter that can be determined based on the BBF test results is the mix
endurance limit, which is the strain level below which cumulative fatigue damage does not
occur. In the laboratory, the endurance limit of an asphalt mixture is the strain level
corresponding to 50 million cycles to failure (Prowell et al. 2010). Prowell et al. (2010) applied
the BBF test to verify the existence of an endurance limit for hot mix asphalt (HMA) and then
provided guidance to determine the limit for various types of asphalt mixture. The main
challenge in determining the endurance limit of an asphalt mixture is to conduct the BBF test up
to 50 million cycles, which would take up to two months for a test. Thus, they studied five
models, including the exponential model, logarithmic model, power model, Weibull Survivor
function, and rate of dissipated energy change (RDEC) model, to extrapolate the failure point of
the asphalt mixture based on the minimum laboratory testing data. They reported that the
exponential model specified in the current standard (AASHTO T 321) should not be used to
extrapolate the failure point. Also, the logarithmic and power models overestimated the failure
point (later than the actual failure point), and the RDEC method was not optimal for endurance
limit extrapolation. Instead, they demonstrated that the single-stage Weibull Survivor function
was the best among the five models for estimating long-life fatigue tests when the strain level
was near or slightly higher than the endurance limit. A discussion of the Weibull Survivor
function follows.
The Weibull Survivor function was named after Waloddi Weibull (1951) for his study on the
applicability of a statistical distribution function in many areas, including the material strength
determination. Then, Garcia-Diaz and Riggins (1984) developed a series of performance models
to predict the pavement performance using an ?S-shaped? survivor curve instead of a Weibull
16
Survivor function. Tsai (2002) simplified the general equation of Weibull Survivor function into
the form shown in Equation 14. Tsai (2002) also introduced the stiffness ratio (SR) parameter to
replace the probability of survival (S) in Equation 14 because the value of SR is equal to the
value of S. Accordingly, Equation 14 can be re-written as shown in Equation 15. The scale
parameter (?) and shape parameter (?) can be determined by a linear regression. The
corresponding curve is named the single-stage Weibull Survivor model. However, this single-
stage model usually underestimates the failure point (number of cycles to failure) (Prowell et al.
2010).
S(t) = exp(??? n?) (14)
ln(?ln(SRn)) = ln(?)+?? ln(n) (15)
Where,
S(t) = probability of survival until time t;
? = scale parameter;
? = shape parameter; and
SRn = stiffness ratio at cycle n.
Instead of fitting the model with one linear regression, Tsai et al. (2005) modified the model in
Equation 15 using three linear regressions. Each linear regression was performed on one of the
three sections indicating different damage stage in the beam specimen. The modified Weibull
function using three linear regressions was more effective to describe the initiation and
17
propagation processes of fatigue cracking. Parameters within the modified model were calculated
using a genetic algorithm.
2.1.3.2 Dissipated Energy (DE)
The application of the dissipated energy concept on fatigue analysis was started by Van Dijk
(1975). Van Dijk found a mathematical relationship between the cumulative dissipated energy
and failure point. This relationship has been proven to be unique regardless of loading mode
(stress-controlled or strain-controlled), strain level, frequency (20-50 Hz), and rest period.
However, the relationship is dependent on mixture type and testing temperature (Chiangmai
2010, Rowe 1993, Shen and Carpenter 2007, Van Dijk 1975, Van Dijk and Visser 1977).
The area under the stress-strain curve indicates the energy used for testing the material. For an
elastic material, the stress-strain curves for loading and unloading coincide. No energy is stored
in the material due to the complete recovery from deformation. For a viscoelastic material under
cyclic loading, the stress-strain curve in each cycle is a hysteresis loop due to the time delay of
deformation recovery. The area within the loop represents the dissipated energy for the current
loading cycle (Ghuzlan and Carpenter 2000). The dissipated energy could be transferred into
various forms, including plastic dissipated energy, heat, and damage (Ghuzlan and Carpenter
2000, Carpenter and Shen 2006).
Rowe (1993) performed a strain-controlled fatigue test on the asphalt mixture trapezoidal beam.
He built up a hysteresis loop based on the load-displacement relationship and calculated the
18
(cumulative) dissipated energy. The current mathematical procedure to calculate dissipated
energy is demonstrated in Equation 16 (Yoo and Al-Qadi 2010).
Dissipated Energy = ? ??i ? ?i ? sin?i (16)
Where,
?i = stress amplitude at load cycle i;
?i = strain amplitude at load cycle i; and
?i = phase angle between stress and strain at load cycle i.
The reason for applying the dissipated energy concept in the fatigue analysis is that the change of
dissipated energy can define the failure and indicate specimen behavior independent of the
loading mode (Ghuzlan and Carpenter 2000). Ghuzlan and Carpenter (2000) proposed a new
criterion based on the change of dissipated energy. They assumed that as material starts to fail at
the current cycle, a larger amount of dissipated energy would contribute to damage than the
amount of dissipated energy goes into damage in the previous cycle. Based on this assumption,
they explained the damage accumulation process in the material during loading. In each cycle,
the amount of dissipated energy excluding damage-related portion is relatively constant. If the
total dissipated energy changes dramatically, it means the portion goes into damage changes
sharply.
The change of dissipated energy is effective in indicating damage accumulation as well as
failure. Ghuzlan and Carpenter (2000) defined a ratio between the change of dissipated energy
(?DE) from cycle ?i? to cycle ?i+1? and the dissipated energy in the original cycle (DE at cycle
19
?i?). The value of ?DE/DE was named as the ratio of dissipated energy change (RDEC). This
ratio starts to decrease after a few cycles at the beginning of loading. During this stage, the
material undergoes internal microstructure rearrangement. Then, the ratio stays constant at a low
level, which indicates the stable damage accumulation rate. Finally, this ratio starts to increase
dramatically when failure occurs (Ghuzlan and Carpenter 2000, Carpenter and Shen 2006).
Figure 2.5 indicates the ratio?s development for a complete test (Shen and Carpenter 2005).
Figure 2.5 Relationship between RDEC and number of load cycle (Shen and Carpenter
2005)
This ratio can be used for both the controlled-strain and controlled-stress loading modes. The
constant value of the ratio in the stable damage accumulation stage was named the plateau value.
It has been shown that the plateau value (PV) had a unique relationship with the cycles to failure
(Nf) regardless of loading mode (Ghuzlan and Carpenter 2000, Carpenter and Janson 1997).
Shen and Carpenter (2005) investigated this PV-Nf relationship using 10 sources of mixtures
under the controlled-strain loading mode. In each source, there were several types of mixtures.
They concluded that PV-Nf relationships had no statistical difference in each source they tested.
20
Typically, the dissipated energy development in the controlled-stress test increases with loading
cycles, whereas in the controlled-strain test it decreases as cyclic loading continues (Ghuzlan and
Carpenter 2000). Therefore, the RDEC should be an absolute value in the calculation (Yoo and
Al-Qadi 2010). Because of the limitation of equipment readout, the ratio was adjusted to measure
the change within 100 cycles (Ghuzlan and Carpenter 2000). Longer intervals, such as 1,000 and
10,000 cycles, were also recommended if the dissipated energy change was too small within 100
cycles (Carpenter and Shen 2006). Carpenter and Shen (2006) suggested a calculation method to
determine plateau value in Equation 17.
Plateau Value = [1?(1 + 100N
f50
)
f
] 100? (17)
Where,
Nf50 = number of cycles to 50 percent stiffness reduction; and
f = slope of regressed DE and number of cycles relationship up to Nf50.
In addition, they used the PV-Nf relationship to indicate the existence of the endurance limit and
healing (Shen and Carpenter 2005, Carpenter and Shen 2006). The endurance limit calculated by
this relationship was compared with that determined using the Weibull function. It was
concluded that the PV-Nf relationship was able to extrapolate the long fatigue life but was not
necessarily the endurance limit. In other words, the Weibull function was a better tool to estimate
the endurance limit based on extrapolation method (Prowell et al. 2010).
2.1.3.3 Relationship between Laboratory and the Field Performance
21
There is a difference between the fatigue life determined from the BBF test and the fatigue life of
pavement in the field. This difference is due to many factors including asphalt binder aging,
traffic densification, healing, and rest period happening in the field. To mitigate this difference,
the laboratory fatigue test result is multiplied by a shift factor of 10 recommended by SHRP to
predict the fatigue life of pavement in the field (Prowell et al. 2010). Certain shift factors for
local pavement have been recommended by many researchers (Harvey et al. 1997, Pierce and
Mahoney 1996). But these researchers had proposed factors in different range and demonstrated
contrary conclusions on the relationship between shift factor and strain level. Recently, Prowell
(2010) verified a shift factor of 10 based on the performance of 2003 NCAT Test Track
structural sections and bending beam fatigue test result.
2.2 Overlay Test
Asphalt overlay is a common rehabilitation method for old asphalt and concrete pavements. A
major distress of HMA overlays is the reflective cracking occurring right above the underlying
crack or the concrete slab joint. Reflective cracking is caused by stress concentration in the
overlay due to the bending and/or shearing movements at joints and/or cracks, induced by daily
temperature and moisture cycles, or traffic loading (Hu et al. 2010).
The overlay tester was first developed by Germann and Lytton (1979) in the 1970s to predict the
reflective cracking resistance of asphalt overlay. It has been further refined by the researchers at
the Texas Transportation Institute (TTI) (Zhou and Scullion 2003, Zhou and Scullion, 2005a).
The overlay test has also been evaluated to determine the asphalt mixture resistance to fatigue
22
cracking and low temperature cracking (Zhou et al. 2007b, Walubita et al. 2011, Zhou and
Scullion 2003). While the test procedure is continuously being improved, the overlay test has
been used to evaluate the cracking resistance of asphalt mixtures in the mixture design process
and in the proposed asphalt overlay thickness design and analysis tool in Texas (Hu et al. 2011,
Hu et al. 2010, Walubita et al. 2012, Hu et al. 2008). Figure 2.6 shows the concept of the overlay
tester (Zhou et al. 2007a).
Figure 2.6 Concept of Texas Overlay Tester (Zhou et al. 2007a)
2.2.1 Test Procedure
2.2.1.1 Specimen Preparation
The test specimen (150 mm long by 76 mm wide by 38 mm high) can be trimmed from a
laboratory-molded specimen or a field core according to Tex-248-F-09 procedure (Figure 2.7).
The laboratory-molded specimen should be compacted to 150 mm (6 in.) in diameter and 115 ?
5 mm (4.5 ? 0.2 in.) in height. The size requirement for a field core is 150 ? 2 mm (6 ? 0.1 in.) in
23
diameter and at least 38 mm (1.5 in.) in height. The air voids requirement is 7 ? 1 % for the
trimmed laboratory-molded specimen. After the specimen is trimmed, it is glued on the plate
with 4.5-kg (10-pounds) weight on the top, and the test can start when the glue has been cured.
Figure 2.7 Laboratory molded specimen (left) and trimmed specimen (right)
2.2.1.2 Temperature Control
An environmental chamber is used to keep the specimen at a constant temperature. The specimen
is kept at 25 ?C (77 ?F) for at least one hour before testing. During testing, the testing temperature
is maintained at 25 ?0.5 ?C (77 ?1 ?F), which allows the test to be conducted at the room
temperature (Walubita et al. 2011).
2.2.1.3 Loading Requirement
24
The test specimen is glued on a set of two steel base plates. During the test, one plate is fixed; the
other slides horizontally until the specimen fails. The tensile load and displacement of the
moving plate are recorded every 0.1 second (Tex-248-F-09). The Texas Overlay Tester is
equipped with an electronic load cell which should have the capability to measure 25 KN (5000
pounds) load. The test is performed in controlled-displacement mode. During the test, a cyclic
saw-tooth load is applied to the moving plate to maintain the constant maximum opening
displacement (hereafter referred to as the MOD) at 0.635 mm (0.025 in.). Loading is
continuously applied with the rate controlled as 10 seconds per cycle until the peak load has been
reduced by at least 93 percent relative to the peak load at the first cycle. The test will also be
terminated if it has been conducted for 1200 cycles even though it has not reached 93-percent
reduction (Zhou and Scullion 2003, Zhou and Scullion 2005a).
Recently, a new overlay test kit for the asphalt mixture performance tester (AMPT) was designed
and manufactured by the IPC Global. Using this kit, the cyclic loading is performed vertically
different from the Texas Overlay Tester, the top plate remains fixed while a cyclic saw-tooth
load is applied to the bottom plate. The testing is also conducted in accordance with Tex-248-F-
09. Figure 2.8 illustrates the overlay test kit with specimen glued in the AMPT (IPC Global).
25
Figure 2.8 AMPT Overlay Test kit (IPC Global)
2.2.1.4 Displacement Measurement
In the Texas Overlay Tester, displacement of the plate movement is measured by a linear
variable differential transducer (LVDT) installed underneath the fixed plate. The AMPT overlay
test, there are two LVDTs: one for measuring the actuator displacement and the other for
measuring the opening displacement between two plates. During the test, a constant maximum
opening displacement (MOD) is maintained by adjusting the maximum displacement of actuator
(IPC Global).
26
2.2.2 Test Results
The number of cycle to failure is the result of the overlay test. It is recorded when the peak load
is reduced by 93 percent from the initial peak load (Tex-248-F-09).
2.2.3 Results of Past Studies
2.2.3.1 Failure Criterion in Overlay Mixture Design and Termination Point
The failure point (number of cycles to failure) in Tex-248-F-09 is determined based on a 93-
percent peak load reduction. It is interpreted as the moment when a crack has passed through the
entire thickness of the specimen (Walubita et al. 2012). The failure point determined based on
this method can be used as a pass-fail criterion in the asphalt mixture design. That is, if the
failure point (number of cycles to failure) is below the criterion, the mixture should be
redesigned. Zhou and Scullion (2005a) performed the overlay test on the field cores from
selected highway sections with known field performance in Texas. A preliminary criterion to
distinguish the reflective crack resistant mixture was suggested: at least 750 cycles for rich
bottom layer and 300 cycles for mixtures used for other layers. Zhou et al. (2007a) reported that
the preliminary criterion (300 cycles) for distinguishing the reflective cracking resistance was
also reasonable for distinguishing the fatigue cracking resistance of asphalt mixtures. In the
overlay design for joint concrete pavements, Holdt and Scullion (2006) proposed that the
minimum loading cycles to failure for crack resistant mixtures (i.e. crumb rubber mix, Strata
interlayer mix comprised of polymer modified binder and dense fine aggregate) in the overlay
27
test should be 750; for dense graded mixture, the minimum loading cycles to failure should be
300 (Holdt and Scullion 2006, Bischoff 2007).
The Tex-248-F-09 procedure specifies that the test be conducted until the peak load reaches 93-
percent reduction from its initial value or concluded at the termination point (the 1200th cycle).
Walubita et al. (2012) suggested reducing the current termination point from 1200 cycles to 1000
cycles when the 93-percent load reduction cannot be reached.
2.2.3.2 Maximum opening displacement
The maximum opening displacement (MOD) recommended in the Tex-248-F-09 procedure is
0.635 mm (0.025 in.). It was derived by evaluating asphalt mixtures used in overlays on top of
old concrete pavements in Texas and was calculated based on the thermal expansion of a 4.5-m
(15-ft) long concrete slab under a 17 ?C (30 ?F) daily temperature variation (Zhou and Scullion
2003). Two types of concrete slab with gravel and limestone aggregates were considered. The
average calculated thermal expansion of these two types of concrete slab was 0.635 mm, which
is used in the current procedure. Equation 18 shows the method for calculating the MOD in the
overlay test (Zhou and Scullion 2003). Bennert (2009) used this method to calculate the MOD in
the overlay test for determining the fatigue cracking resistance of asphalt mixture for the overlay
projects in New Jersey and Massachusetts. For the project in New Jersey, the calculated MOD
was the same as that in Tex-248-F-09 procedure. But the calculated MODs for the overlay
project in Massachusetts (0.74 mm and 0.53 mm) were different from the recommended value in
the procedure.
28
?L = ? ? Leff ? ?T?? (18)
Where,
?L = horizontal movement of slab due to temperature change (m);
? = coefficient of linear thermal expansion (10-6/m/?C);
Leff = effective PCC joint spacing (m);
?T = maximum 24-hour temperature difference (?C); and
? = PCC/ Base friction factor.
Walubita et al. (2010) performed overlay round-robin tests among six laboratories to evaluate the
repeatability and variability of testing results using the Tex-248-F procedure. One of these
laboratories applied 0.584-mm (0.023-inch) MOD due to the calibration issue of machine before
it was adjusted. Comparing the failure point at this lower MOD to the result after calibration (at
the recommended 0.635-mm MOD), the 0.051-mm (0.002-inch) difference caused a significant
difference in the overlay test result. Walubita et al. (2012) studied the effect of smaller MOD on
the testing result. Two levels of MOD were applied: one is 0.508 mm (0.020 inch), the other is
0.381 mm (0.015 inch). They did not find definitive trend of change in the result variability when
MOD decreases. However, the variability of result obtained at 0.381-mm (0.015-inch) MOD was
smaller than the variability of result at two larger MOD levels.
Zhou et al. (2009) pointed out that applying too large or too small MOD is not desirable for
determining crack development. A large displacement causes the specimen to fail much more
29
quickly. Small displacement lasts too long to perform the test. Zhou and Scullion (2005a)
provided a recommended range of the MOD based on past studies. For 77 ?F (25 ?C) testing
temperature, the MOD should be smaller than 2.0 mm (0.08 inch). For 32 ?F (0 ?C) testing
temperature, the MOD should not exceed 0.125 mm (about 0.005 inch).
2.2.3.3 Testing Temperature
Zhou and Scullion (2005a) studied the effect of temperature on the overlay test result by
performing the test at two temperatures: 25 ?C as specified in current procedure and 10?C. Three
replicates with 4.0 percent air void were used for both conditions. Maximum opening
displacement (MOD) was controlled as 0.635 mm (0.025 inch). The average failure points
obtained at two temperatures were compared, and the results at 10 ?C were much smaller. Zhou
et al. (2009) suggested that chamber of the overlay tester should have the capacity to provide the
testing temperature between -5 ?C and 35 ?C. They also proposed two desired testing
temperatures: 25 ?C and 15 ?C. At 25 ?C, they recommended using 0.635-mm (0.025-inch)
MOD in the first run. If the failure point was less than 20 cycles, the 0.381-mm (0.015-inch)
MOD should be used. At 15 ?C, a 0.381-mm (0.015-inch) MOD should be tried first. Similarly,
if fatigue life was less than 20 cycles, the MOD should be reduced based on past experiences.
Walubita et al. (2012) investigated the effect of temperature on the overlay test result and its
variability. Two types of mixtures were tried at five temperature levels between 22.8 ?C (73 ?F)
and 27.2 ?C (81 ?F). The failure point was found to increase with temperature, but the peak load
was found to decrease with temperature. However, no definitive trend was observed on the
variability of failure point or peak load due to variation of temperature.
30
2.2.3.4 Dissipated Energy
Zhou and Scullion (2005a) discussed the possibility of using dissipated energy-related failure
point determining method for the overlay test. However, they did not recommend that method to
be used in the overlay test due to two reasons. First, the energy calculation was complicated due
to non-uniform distribution of load and displacement on the cross-section of the specimen.
Second, size of specimens cannot be exactly the same, making energy calculated not comparable.
2.2.3.5 Specimen Preparation
(1) Cutting
To address the problem with wasting material in the overlay test specimen preparation, three
alternative molding methods were studied and compared to the method in Tex-248-F procedure
(Walubita et al. 2012). It was found that the current molding method which involves cutting one
specimen from a 115-mm (4.5-inch) tall molded sample yielded the most material waste. The
first alternative to prevent this waste was cutting two specimens from the 115-mm (4.5-inch) tall
molded sample; however, it had workability issues. The second alternative was cutting two
specimens from a taller sample with 127 mm (5.0 inch) in height. The third alternative was
obtaining only one specimen from a 63.5-mm (2.5-inch) tall molded sample. Comparing the
latter two alternatives, cutting two specimens from a taller sample with 127 mm (5.0 inch) in
height saved much time and enhanced the workability. However, there was no considerable
31
variation between the overlay test results obtained from the current procedure and alternative
fabricating methods. Since cutting accuracy is very important to the test result, Hu et al. (2008)
performed the other investigation of the fabrication process to examine the use of a double-blade
saw. Using the double-blade saw, the cutting procedure was automated once the thickness of
specimen was entered into the system. They cut more than 50 specimens and found that most
specimens met the size limit of ? 0.254 mm (? 0.01 inch). However, hard aggregates may push
the two blades apart leading to the problem of cutting accuracy. They recommended reducing the
blade traveling speed to minimize the accuracy issue with the hard aggregate and calibrating the
machine every time the aggregate type was changed.
(2) Drying
After the specimen is cut, the Tex-248-F procedure requires the specimen be oven-dried under
60 ?3?C (140 ?5?F) until the specimen reaches constant weight (within 0.05% change in 2
hours). Instead of the oven drying method, the TTI laboratory applied air drying overnight which
involved drying the specimen in front of a fan at room temperature. TxDOT CST laboratory
dried the specimen in an oven at 40 ?C (104 ?F) (Walubita et al. 2012). Walubita et al. (2012)
compared these two methods (air drying and oven drying at 40 ?C) and obtained similar failure
points. However, the variability of result from oven drying specimen was lower than that of the
air drying. It indicated that the oven can provide more uniform heat and constant temperature
environment than the air drying method. In addition, the use of core dryer machine was
evaluated. The evaluation showed that the core dryer method was faster but has larger variability.
32
They concluded that the best method was oven drying at 40 ?3 ?C (104 ?5 ?F) for 12 hours at
minimum.
(3) Glue
The use of two-part epoxy with required tensile strength and shear strength after 24-hour curing
time is specified in the current procedure. However, the current procedure does not suggest the
amount and the specific type of glue should be used. Walubita et al. (2012) tried three types of
two-part epoxies: Devcon plastic steel 5-min epoxy, Devcon high strength epoxy, and Devcon
two-part, two-ton epoxy S-31. The first one had workability issues (hard to spread and clean),
higher cost, and longer curing time. The second and third types both had COV values of failure
point less than 30 percent, but the second type cost much more than the third one. Therefore, the
third type (Devcon two-part, two-ton epoxy S-31) was recommended. In addition, three
quantities of epoxy (14, 16, and 18 g) were examined to find the best bond between the specimen
and plate without excess. Based on the analysis, they suggested using 16-g (?0.5-g) Devcon two-
part, two-ton epoxy to glue the specimen on the base plates.
(4) Sitting Time
The aging of HMA can be induced by several effects such as volatilization, oxidation or steric
hardening of the asphalt binder. The procedures for the overlay test from molding to testing
(molding, first bulking, cutting, second bulking, drying, gluing, curing, conditioning) take at
least three days. Thus, some specimens may take long time prior to testing. To determine the
33
aging effect on the testing result, Walubita et al. (2012) performed several overlay tests in which
the sitting time varied from 3 to 60 days. The average failure point and associated coefficient of
variation (COV) were analyzed. The failure point was found to decrease rapidly after a 7-day
sitting time and then stayed relatively steady. The COV were at the peak after a 7-day sitting
period. Walubita et al. (2012) concluded that the effect of initial oxidative aging may cause this
trend. Thus, a 3- to 5-day sitting time was recommended to minimize the effect of oxidative
aging.
(5) Air Void Content
The Tex-248-F procedure requires that the target air void content for testing specimen should be
7 ?1.0 percent. However, it is difficult to control air void contents uniformly during fabrication.
Walubita et al. (2012) investigated the effect of air void content on the variability of the overlay
test results by dividing the 5.0 to 8.5 percent air void content range into seven groups. Results
showed that two groups in which the air void contents ranged from 6.5 to 7.5 percent had COV
values in the 30 percent tolerance. However, they still recommended the 7 ?1.0 percent air void
content, since the ? 0.5 percent tolerance is difficult to obtain.
(6) Base Plate Setting
According to Tex-248-F procedure, the width of the gap between the plates is 2 mm. Also, there
is a 6.35-mm wide (0.25-inch) tape over the gap. Walubita et al. (2012) tried a new plate set with
a metal bar in the gap instead of the covered tape. This new plate set has a 6.35 mm (0.25 inch)
34
wide gap with a metal bar between the gap to avoid removing the epoxy after curing. The notch
design on the new plate set was modified to make specimen easier to glue on. Failure points and
peak loads using the new plates were compared to the old plates after testing. Even though the
test results obtained using two sets of base plates were not statistically different, they still
recommended using the new plate set without metal bar for its better workability.
2.2.3.6 Variability in Test Result
The Tex-248-F procedure does not suggest a limit for acceptable variability of the test result. The
decision to discard or redesign the mixture in the overlay test is based on the pre-determined
pass-fail criterion (certain number of loading cycles before failure). The test result below that
criterion is deemed unacceptable (Zhou and Scullion 2005a). Walubita et al. (2012) performed a
ruggedness study on several factors that may contribute to the variability of the test result and
recommended an acceptable COV limit. These factors included the number of replicates, drying
method, sitting time, air void content, gluing method, loading parameters, specimen dimension,
base plates setting, and testing temperature. Walubita et al. (2011) compared the overlay test
with other three tests including the Indirect Tensile Test (IDT), the Semi-Circular Bending Test
(SCB) and the Direct Tension (DT) test to find the best applicable method for crack resistance
characterization. The result from overlay test showed highest variability. To reduce the
variability in the overlay test, three replicates are recommended in the Tex-248-F procedure.
However, it was reported that one of three replicates had a result significantly different from
other two. Walubita et al. (2012) explored this issue and suggested selecting the best three
replicates out of five tested specimens. They tested five types of mixtures with five specimens
35
for each mixture. The groups of two, three, and four specimens with the lowest variability were
chosen as the best based on the minimum COV and then compared with the variability of all five
specimens? results. The result showed that only best of the two- and three-specimen groups had
COV in the acceptable limit (30%). However, it is possible for the two-specimen group to have
misleading result due to its small sample size. Therefore, it was not recommended, even though
the variability was the smallest.
2.2.3.7 Alternate Method to Determine the Failure Point
The current method to determine the test result (failure point) is based on the reduction of peak
tensile load during the test (Tex-248-F-09, Bennert 2009, Walubita et al. 2012, Hu et al. 2008).
Some alternative failure point determining methods including those based on 50-, 75-, and 85-
percent reduction of peak load should be well explained and validated (Walubita et al. 2012).
Walubita et al. (2012) evaluated the rate of load decrease (slope) on the plot of peak load versus
number of cycles for determining the failure point. However, they concluded that it was difficult
to find an exact point on the peak load curve where a sharp change in the slope occurs after the
peak load drops more than 50 percent from the first cycle.
2.2.3.8 Development of Testing Method
The overlay test method has been evaluated and modified since it was first developed in the
1970s. Two specimen sizes had been used: a larger one was 500 mm long by 150 mm wide; a
smaller one was 375 mm long by 75 mm wide. These two sizes were successfully used to
36
fabricate the specimen and perform reflection crack resistance study on geosynthetic materials
(Zhou and Scullion 2003). Later, an upgraded overlay tester was developed and the size
requirement was modified: (1) the length of specimen was reduced to 150 mm; (2) the width was
reduced to 75 mm; and (3) the thickness varied from 38 mm to 50 mm (Zhou and Scullion 2003,
Zhou et al. 2009). The new size requirement made the overlay test possible to be performed
routinely using laboratory-compacted specimen and field cores. The proposed length of
specimen (150 mm) was validated by finite element analysis because the tensile stress distributed
only in the mid-length of specimen. Currently, the Tex-248-F procedure specifies specimen
thickness as 38 mm and the specimen width as 76 mm. In regard to the control software, the
upgraded overlay tester was able to perform both one-phase triangle repeated loading and two-
phase mixed loading. Two-phase loading was applied by a static constant tension followed by
controlled-displacement repeated loading (Zhou and Scullion 2003). Cleveland et al. (2003)
suggested using this two-phase loading method to perform advanced mechanical analysis.
2.2.3.9 Determination of Crack Length
The completion of overlay test was considered as moment when crack has propagated through
the thickness of specimen (Walubita et al. 2012). Therefore, it is important to know the
development of crack during the test. Typically, the approaches used to obtain the crack length
during the fatigue cracking test for asphalt mixture can be categorized into two types: direct
measurement and backcalculation.
37
(1) Direct Measurement
Two common direct measurements are crack foil and digital image correlation (DIC) (21). Jacob
(1995) used crack foil measurement to determine the crack length in asphalt mixtures. However,
he did not recommend using this measurement in the calculation of the Paris? law parameters (A
and n) because the small cracks in the micro-crack zone in front of macro-crack were not
measured by the foil approach, leading to a large difference between measurement and actual
length. Instead, he suggested using crack opening displacement (COD) gauge measurements
combined with finite element analysis to determine the Paris? law coefficients.
The other direct measurement approach is DIC, which was applied by Seo et al. (2004). They
used the DIC in studying the deformation in the fracture process zone, which is a nonlinear zone
around the crack tip. They used a digital camera to capture images of a surface-painted specimen
under uniaxial tensile loading. After test, post-processing methods were applied to measure the
grayscale and compare the deformed images with the undeformed images. Displacements and
strain within the captured area were calculated. However, the measurement was still limited to
the surface image, not inside condition, of the specimen. Zhou et al. (2007a, 2009) used the DIC
approach to measure the crack growth on the overlay test specimen to verify the backcalculated
crack length. The backcalculation method is discussed in the next section. They used two digital
cameras and found that the crack growth on the two sides of specimen was different due to the
heterogeneity of specimen.
(2) Backcalculation
38
Zhou et al. (2007a, 2009) backcalculated the crack length during overlay test using maximum
tensile load at each cycle. Three assumptions were made to simplify the backcalculation
procedure. First, the macro-crack initiates at the bottom of the specimen and propagate vertically
to the top surface. Secondly, crack length development was highly correlated to the reduction of
the maximum tensile load. Third, the asphalt mixture was regarded as a quasi-elastic material
with specific modulus and Poisson?s ratio corresponding to the testing conditions (maximum
opening displacement, temperature, frequency, etc.). Jacob (1995) also applied the crack length
backcalculation approach using a relative crack opening displacement (COD) to obtain the
equivalent crack length in a 2-D finite element program. The use of relative COD instead of
absolute COD normalized the effect of gauge location in the notch on the measurement.
Equivalent crack is simulated single crack with the same COD measurement as that of the
combined existing macro-crack and micro-crack zone.
2.2.3.10 Crack Propagation Model for Asphalt Mixture
Paris and Erdogan (1963) first proposed an empirical crack propagation law named Paris? law
(also known as the Paris-Erdogan law). Germann and Lytton (1979) first applied this law in the
overlay test to determine the reflective cracking resistance of the asphalt overlay. Recently, Zhou
et al. (2007a) validated the upgraded overlay test in predicting fatigue cracking resistance of
asphalt mixture and verified the predicted result by the performance data from the FHWA-
Accelerated Loading Facility. In the prediction method, they obtained the coefficients of Paris?
law (A and n) and predicted the number of cycles to initiate and propagate macro cracks through
the asphalt layer in the field. After the J-integral was introduced in Paris? law for replacing the
39
stress intensity factor (K), viscoelastic behavior of asphalt mixture could be investigated (Zhou
and Scullion 2003). Cleveland et al. (2003) developed a modified Paris? law based on the J-
integral and the linear viscoelastic continuum damage theory to study the cracking resistance of
asphalt mixtures modified by different geosynthetic materials. Schapery (1973, 1975, 1978)
proposed a well-derived theory to determine the Paris? law parameters for viscoelastic material
using a series of simple performance tests. However, this method for general viscoelastic
material study was not directly applicable for asphalt mixture. Jacob (1995) summarized
Schapery?s method (Equation 19, 20, 21) and suggested a simplified way to estimate the
parameters for asphalt mixture. Jacob (1995) suggested that two parameters (A and n) could be
estimated using the master curve from dynamic stiffness (modulus) test and the results from
uniaxial monotonic tensile test at constant displacement rate. Equation 22, 23, 24, 25 and 26
show the recommended calculation approach. Equations 22, 23 and 24 estimate the value of ?n?.
Then, Equations 25 and 26 can be applied to estimate ?A?. The estimation using Equation 26 is
more accurate than that of Equation 25. However, his suggestion was based on many regression
coefficients for certain types of mixtures applied in the study. These coefficients may not be
valid in determining Paris? law for other mixtures.
A = ?6?
m2 l1
2[
(1 ?v2)D2
2? ]
1
m
(? w(t)ndt
?t
0
) (19)
n = {
2(1+ 1m) For load?controlled test
2
m For displacement?controlled test
(20)
(21)
40
Where,
?m = material tensile strength;
l1 = integration of stress near crack tip over the failure zone using
Barenblatt (1962) approach;
v = Poisson?s ratio;
D2,m = regression coefficient from creep compliance master curve;
? = work done to produce a unit crack surface, determined by dissipated
energy and crack length;
?t = time required to complete one cycle in the controlled-displacement
crack growth test; and
w(t) = Integral of sinusoidal ?K versus time? relationship in the period of
one cycle.
Dmix = a3 +a4logt +a5(logt)2 (22)
nest = 2(a
4 +2a5logt)CF
(23)
ln(CF) = b0 +b1Smas +b2Sbit +b3Smas ln(Sbit) (24)
logAest = aA +bAnest (25)
logAest = d?2alog(?m)?bnest2 log(2?stat)?cnest2 log(Smas) (26)
41
Where,
Dmix = creep compliance determined from the master curve in
dynamic stiffness test (10-4/MPa);
nest = estimated n-value;
a3,a4,a5 = regression coefficients from ?creep compliance versus log
(t)? relationship;
t = loading time, determined by 1/(10f) (second);
CF = correction factor;
b0,b1,b2,b3 = regression coefficients from ?CF versus Smas? relationship,
Sbit can be calculated from Smas;
Smas = mixture stiffness determined from temperature and
frequency sweep tests (MPa);
Sbit = bitumen stiffness, backcalculated from Smas by Bonnaure?s
method (MPa);
Aest = estimated A-value;
?stat = fracture energy (N?mm/mm2), determined from ?log
( ?stat?
stat,max
) versus log Sbit? relationship, ?stat,max is the
maximum fracture energy from static loading test; and
a,b,c,d = regression coefficients determined from the relationship
between Aest and other factors in Equation 26.
42
Jacob (1995) also performed a more straightforward way to determine the Paris? law parameters
for asphalt mixtures. This method started with crack length backcalculation as discussed in
section 2.2.3.9. Combining COD measurement and finite element modeling, five mathematical
relationships were obtained based on the specific material, temperature, frequency and maximum
opening displacement (Jacob 1995). This measurement-based method determining the Paris? law
parameters was also applied by Zhou et al. (2007a) in the overlay test and by Roque et al. (1999)
in the indirect tension test (IDT).
It should be noted that Jacob (1995), Zhou et al. (2007a), and Roque et al. (1999) used the same
crack growth calculation method except for the choices of factors they applied to backcalculate
the crack length. The factors they applied were all from direct measurements. Jacob (1995) used
the relative COD (or normalized COD) in an uniaxial tensile test performed on a beam-shaped
specimen (50mm?50mm?150mm). Zhou et al. (2007a) selected the normalized load in the OT.
Roque et al. (1999) reported that normalized horizontal displacement on the specimen of the
indirect tensile test (IDT) was good to use. These direct measurements (peak values within each
loading cycle) were all normalized to represent the damage process of specimen relative to its
intact state. Table 2.1 summarizes the similarities among these three studies in determining the
Paris? law parameters for asphalt mixture. ?NF? represents the normalized factors: crack opening
displacement, applied load, or horizontal displacement.
43
Table 2.1 Similarities between Three Studies
No. of Step and
Correlations Procedures
1 NF vs. Number of loading cycles (NF vs. N)
2 NF vs. Crack length (NF vs. C) (Jacob performed this procedure by
combining two correlations: NF vs. K and K vs. C)
1+2?3 Crack length vs. Number of loading cycles (C vs. N)
4 Stress intensity factor vs. Crack length (K vs. C)
3+4?5 dC/dN vs. ?K (or in log-log scale)
2.2.3.11 Application of crack propagation law in predicting fatigue life of asphalt layer
Zhou et al. (2007a) validated the application of OT in predicting traditional fatigue cracking of
asphalt mixtures. In the development of fatigue cracking, the number of loading cycles to failure
(Nf) includes the cycles required for crack initiation and propagation (Ni and NP), respectively.
The initiation stage (Ni) is the number of cycles needed for micro-cracks to coalesce to form a
macro-crack. The propagation stage (Np) is the number of cycles for a macro-crack to propagate
through the thickness of asphalt layer. Equation 27 demonstrates the correlation between the
number of cycles to failure (failure point) and the number of cycles in the two stages.
Nf = Ni +Np (27)
Where,
Nf = number of cycles to failure (failure point);
Ni = number of cycles initiate a macro-crack; and
Np = number of cycles for macro-crack to propagate through asphalt layer.
44
Crack propagation dominates crack development in the overlay test and it has strong correlation
with crack initiation. Zhou et al. (2007a) suggested that the overlay test was able to demonstrate
cracking behavior before macrocrack initiates. Typically, number of cycles for crack initiation
(Ni) was calculated by the traditional method using Equation 28. Asphalt mixture in OT was
assumed to behave like elastic material with modulus and Poisson?s ratio. This assumption made
Paris? law in linear elastic fracture mechanics applicable for analyzing OT results (Zhou et al.
2009). Thus, the number of cycles for crack propagation (Np) was calculated by Paris? law using
Equation 29. Lytton et al. (1993) suggested that the stress intensity factor (K) in Equation 29 can
be calculated by using Equation 30. Therefore, by integrating and rearranging Equation 29, the
value of Np can be determined from a function of strain as showed in Equation 31 based on
known material properties and testing conditions. Lytton et al. (1993) also pointed out that Paris?
Law was also valid to calculate the growth of microcrack in the crack initiation stage for
viscoelastic material. Therefore, Equation 28 used for calculating traditional crack initiation can
be equated to Equation 31 (Zhou et al. 2007b). After equating these two functions, the coefficient
k2 was found to equal to ?n? (Equation 33). Coefficient k1 can be determined as a function of
?A? and ?n? (Equation 32). After the Paris? law parameters were determined from the overlay
test, Equation 32 and 33 were used to calculate the parameters k1 and k2 in Equation 28 (Zhou et
al. 2007b). Entering the maximum tensile strain at the bottom of asphalt layer (?) into Equation
28, crack initiation cycles (Ni) can be obtained (Zhou et al. 2007a, Zhou et al. 2007b).
Ni = k1 ? (1 ?? )k2 (28)
45
dc dN? = A? (?K)n (29)
K = r(cd)
q
??d (30)
Np = d1
(1?n/2)
Arn(1?nq)En [1 ?(
c0
d1)
(1?nq)
](1?)
n
(31)
k1 = d1
(1?n/2)
Arn(1?nq)En [1 ?(
c0
d1)
(1?nq)
] (32)
k2 = n (33)
Where,
k1,k2,q,r = regression coefficients;
? = maximum tensile strain at the bottom of asphalt layer;
c = crack length;
c0 = initial macrocrack length;
N = number of loading cycles;
A,n = Paris? law parameters;
?K = change of stress intensity factor;
d = thickness of test specimen;
d1 = thickness of asphalt layer (the total length of crack to grow);
? = maximum stress in the specimen; and
E = asphalt layer modulus at specific frequency and temperature.
However, the method for calculating the coefficient k1 (Equation 32) seems complicated.
Therefore, Zhou et al. (2007a) simplified this method based on the relationship between
46
parameter A, n, and log E. Equation 34 shows the simplified way to obtain coefficient k1. The
coefficients (a1, a2, a3) were obtained through a regression analysis of the data from 1348
bending beam fatigue tests in other studies. With the values of log k1, k2, and log E known, the
optimized form of Equation 34 can be determined using least squares estimation.
logk1 = a1 +a2k2 +a3 logE (34)
Where,
a1,a2,a3 = regression coefficients; and
E = dynamic modulus of asphalt mixture at specific temperature and
frequency.
After the number of cycles for crack initiation (Ni) is determined, the second stage for crack
propagation needs to be considered in order to predict the fatigue life of asphalt layers using
Equation 27. In the overlay test, small crack growth could be predicted by small change of stress
intensity factor and the number of loading repetitions causing these changes (Equation 35) (Zhou
et al. 2007a). However, to predict the crack propagation in the pavement layer, the effect of
actual load on the crack propagation needs to be considered. Zhou et al. (2007a) proposed that
one axle passing the top of crack-initiated overlay had three effects on the crack propagation.
When the load was right on the top of crack tip, bending of the overlay may take place and drive
the Mode-I cracking. As the load was approaching and leaving the crack, the major driving force
for the crack propagation was shearing leading to the Mode-II cracking. Therefore, two times of
Kshearing changes along with one-time Kbending change were the result of one axle load pass. These
three changes of stress intensity factor (?Ki) should be directly reflected by the change of crack
47
length according to Paris? law. Zhou et al. (2007a) calculated these stress intensity factors using
the finite element method. It should be noted that they assumed the parameters (?A? and ?n?) for
bending and shearing to be the same based on their past studies. Equation 36 calculated the
change of crack length until the accumulated crack growth was equal to asphalt layer thickness.
Summation of the required loading passes during every small crack growth was the number of
loading cycles for crack propagation (Np) (Equation 37). According to Equation 27, Nf can be
calculated by the summation of Ni (Equation 28) and Np (Equation 37).
dc
dN =
?c
?N = A(?K)
n (35)
?c = 2A(?Kshearing)n?N+A(?Kbending)n?N
= A[2(?Kshearing)n +(?Kbending)n] ?N
(36)
Np = ??N (37)
Where,
?c = change of crack length;
?Kshearing = change of stress intensity factor induced by shearing;
?Kbending = change of stress intensity factor induced by bending; and
?N = number of load pass.
Zhou et al. (2007a) verified this prediction approach based on the Paris? law parameters from
overlay test on six FHWA-ALF test lanes. The measured fatigue life was the number of ALF
48
loading repetitions when cracking occurred on 50 percent lane area. The average ratio of the
measured fatigue life to the predicted fatigue life was equal to 1.3. In addition, Zhou et al.
(2007a) applied Miner?s law (Equation 38) to calculate the accumulated damage under certain
amount of loading repetitions. The amount of damage was entered into the crack model
(Equation 39) in the Mechanistic-Empirical Pavement Design Guide (MEPDG). They
commented that the current cracking model (Equation 39) in the MEPDG did not predict the
fatigue crack area in the field very well. Therefore, a calibration with the predicted and the
observed crack area data to determine a1, a2 in Equation 39 was recommended.
Damage = ? niN
f
T
i=1
? 100% (38)
Crack area (%) = 1001 +e(a1+a2?logdamage) (39)
Where,
T = total number of periods;
ni = actual load repetitions in ith period; and
a1,a2 = calibration coefficients (a1and a2 are functions of asphalt layer
thickness).
2.2.3.12 Correlation between overlay test and BBF test
Zhou et al. (2007b) compared BBF test results with overlay test results for three types of HMA.
In the BBF test, specimens were tested using 374 microstrain at 20 ?C. In the overlay test,
49
specimens were tested using 0.63 mm (0.025 inch) maximum opening displacement at 25 ?C.
After comparing the number of cycles to failure from two tests, they found that the ranking of
three types of HMA were the same. Therefore, Zhou et al. (2007b) proposed that the overlay test
could be an alternative for BBF test in determining the fatigue cracking resistance.
2.2.3.13 Correlation between overlay test result and field performance
Zhou and Scullion (2005a) performed a validation study on the application of the overlay tester
in differentiating asphalt overlay mixtures in terms of cracking resistance performance. Field
cores from several pavement sections on US175, US84, SH3, SH6 and IH10 in Texas were taken
and trimmed according to the size requirement of overlay test. For SPS5 sections on US175, only
the bottom asphalt layer on the core was used to fabricate the specimen. Before taking these
cores, the cracking performance of each pavement was already known. One section (SPS5) on
US175 had no reflective crack after 10-year service. Other sections demonstrated different levels
of reflective cracking distress shortly after laydown and opening to traffic. After overlay testing
was performed, results showed that virgin mixture from the section (SPS5) with no-reflective
crack on US175 had the longest reflective cracking life (number of cycles to failure): about 300
cycles. Most mixtures from other sections were tested to failure within 50 cycles. Zhou and
Scullion (2005a) also took cores from three cells (15, 18, and 20) on the MnROAD to study the
low temperature cracking resistance using the overlay tester. Two cores were taken from the
mid-lane within each cell and tested after trimming off the micro-surfacing layer. After
trimming, only the top asphalt layer was used for testing. Good correlation was found between
the observed cracking performance and the overlay test results. Accordingly, they proposed that
50
the overlay test was also good to predict low temperature cracking resistance. Zhou et al. (2007b)
also validated the overlay test result with the FHWA-ALF fatigue test results on 6 lanes where
loading was applied by a super single tire on the experimental pavement lanes. The ranking of
fatigue cracking performance for asphalt mixtures by the FHWA-ALF test was similar to the
ranking by the overlay test. The OT was adopted to conduct a reflective crack resistance control
for the very thin overlay mixes in Texas (Scullion et al. 2009). The compacted specimen should
withstand more than 750 loading cycles before failure. A half year after laydown, the overlay
performance was inspected. Some reflective transverse cracks, humps, and a longitudinal crack
due to foundation problem were found. But overall performance was good without load-related
reflective cracking issue.
2.2.3.14 Effect of mixture properties on overlay test result
Texas Transportation Institute (TTI) conducted the overlay test to study the cracking resistance
of Evotherm warm mix and compared with that of hot mix. During the tests, specimens of warm
mix lasted longer than those of hot mix before failure occurred. It was concluded that Evotherm
warm mix had better cracking resistance than hot mix (Crews 2009).
Zhou and Scullion (2005a) found that mixture properties (i.e. binder content, binder grade,
aggregate type, and aggregate gradation) significantly affect the result of the overlay test.
Mixtures with higher binder content, lower binder high-temperature performance grades, less
absorptive rock, and finer gradations tend to have more reflective crack resistance. When they
investigated the effect of aggregate absorption, they compared the crushed gravel aggregate with
51
limestone. Immediately after test, they examined the failure plane and found that gravel
aggregates with little absorption demonstrated a shining failure plane; absorptive limestone
showed a dry failure plane. Analysis of the testing data showed that the crushed gravel mixture
required more cycles to failure than that of the limestone mixture. To verify this finding, they
compared the overlay test result using three additional limestone aggregates with various
absorption levels. Controlling the asphalt type and aggregation gradation, they found that the
number of cycles to failure decreased when aggregate absorption increased.
Recently, Hu et al. (2011) investigated the effects of material properties on the overlay test
result. Seven factors (or properties) were studied, including binder grade, effective binder
content, air void content, VMA, asphalt absorption, surface area of aggregates (SA), and film
thickness of binder (FT). Two statistical methods were used to analyze the testing results. The
first one was Pearson?s correlation which was commonly used to determine the level of linear
correlation between two variables. In their analysis among the six factors (except for the binder
grade), three pairs of factors with high correlations include (1) Vbe and FT, (2) FT and VMA, and
(3) asphalt absorption and FT. After applying Pearson?s correlation method, the other statistical
method named analysis of covariance (ANCOVA) was performed to determine the regression
model between NOT and those uncorrelated factor(s). Typically, ANCOVA was an adjusted
ANOVA that can consider both quantitative and qualitative factors (Scheffe 1959). The analysis
results showed that effects of air void content and asphalt absorption were not statistically
significant on the overlay test result (i.e., failure point). Finally, three factors (binder type, film
thickness (FT), and surface area (SA)) were determined to be included in the model as shown in
Equation 40. FT and binder content (Pb) calculation methods were also proposed as shown in
52
Equation 41 and 42. The minimum asphalt content for cracking resistance can be calculated
using Equation 42 by entering the minimum FT. The recommended limit for binder content was
verified by performance examination on nine overlay sections placed on I-20 interstate highway
near Atlanta, Texas.
NOT = a1 ?e(a2?FT) ? SAa3 (40)
FT = (Pbe Gb? )(SA? P
s)
?1000 (41)
Pb = 100 ? FT? SA?Gb +1000 ? Pba1000 +FT?SA? G
b +10 ? Pba
(42)
Where,
ai = regression coefficient determined by binder type and FT
value (i=1,2,3);
FT = film thickness (?m);
SA = surface area of binder coating on aggregates (m2?kg);
Pbe = effective binder content by mass of mixture;
Gb = specific gravity of binder;
Pbe Gb? = effective binder volume;
Ps = aggregate content by mass of mixture;
Pb = binder content by mass of mixture; and
Pba = binder absorption by mass of mixture.
53
2.3 Summary of Literature Review
Generally, the bending beam fatigue (BBF) test and the overlay test (OT) are similar. Both tests
are cyclic fatigue tests and the obtained results indicate asphalt mixture?s resistance to cracking
at ambient temperature. Consistent tensile strain is applied at the bottom of specimen by
controlling the maximum displacement in each loading cycle during the test. However, some
differences need to be considered when comparing the results of two tests are as follows.
? Fabrication. Two specimens are different in size and compacted by different methods.
? Loading mode. BBF test specimen endures bending deformation while OT specimen cannot
bend due to the fixed plates on which the specimen is glued. Frequency is much higher and
tensile strain is much lower in BBF test compared to those of OT.
? Cracking behavior. Microcrack is the major damage type in the bending beam specimen
while macrocrack dominates in OT specimen.
? Failure point determining method. Failure point in BBF test is determined based on stiffness
development while peak load development is used for determining that in OT.
? Other useful test results. Dissipated energy can be obtained in BBF test and crack
propagation model coefficients (Paris? Law coefficients) can be calculated from OT result.
54
CHAPTER 3 LABORATORY TESTING
This chapter describes the overlay test in the asphalt mixture performance tester (AMPT),
followed by discussions on asphalt mixtures selected for this testing, experimental plan, and
specimen fabrication procedure. A discussion of the current method and a new method for
determining the failure point of the overlay test are also provided.
3.1 Overview of Overlay Test in the AMPT
The overlay test procedure described in the TxDOT test method (Tex-248-F-09) can be
conducted in both the Texas Overlay Tester and the AMPT using an Overlay Test Kit (IPC
Global). Figure 3.1 shows an overlay test being conducted in an AMPT. A test specimen (150
mm long, 76 mm wide and 38 mm thick) can be cut from a gyratory compacted specimen or a
field core. The test specimen is epoxied to a set of two steel plates and then loaded vertically into
the AMPT. During the test, the top plate remains fixed while a cyclic triangle-wave load is
applied to the bottom plate to maintain a constant maximum opening displacement between the
two base plates.
55
Figure 3.1 AMPT with overlay test kit
3.1.1 Displacement Measurement Method
The AMPT overlay test uses two LVDTs for measuring the actuator displacement and the
opening displacement between the two base plates. The second LVDT in the AMPT overlay test
is located on the back of the base plates, as shown in Figure 3.2. The actuator LVDT measures
the displacement of actuator in a range of ? 15 mm, and the external LVDT has a lower
measurement range of ? 0.5 mm.
56
Figure 3.2 External LVDT on the back of steel plates
In the AMPT overlay test, the MOD is measured directly by the external LVDT (Figure 3.2).
This MOD measurement is kept constant during the test by adjusting the actuator displacement
and is referred to as the target displacement. The overlay test software in the AMPT has an
Adaptive Level Control (ALC) option. With this option enabled, the external LVDT reading is
monitored during the test. If the target displacement is not achieved, the actuator displacement
will be adjusted to maintain the specified target displacement.
3.1.2 Machine Compliance in the AMPT Overlay Test
For the AMPT overlay test, the two LVDTs are expected to produce different readings because
the actuator LVDT measures the actuator displacement that consists of the specimen deformation
57
and the loading frame deformation. Equation 43 shows the relationship between two LVDT-
measured displacements. The machine compliance can be calculated using Equation 43 and 44
(Kalidindi et al. 1997).
?2 = ?1 ??3 (43)
Cm = ?2 F? (44)
Where,
?1 = displacement measured by actuator LVDT;
?2 = deformation of loading system;
?3 = deformation of specimen measured by external LVDT;
Cm = machine compliance; and
F = measured load.
Figure 3.3 shows the difference between the maximum actuator displacements measured using
the actuator LVDT and the maximum opening displacements measured by the external LVDT in
the AMPT. Results plotted in Figure 3.3 were obtained from a test conducted on a specimen at a
frequency of 0.1 Hz and using an MOD of 0.381-mm. The displacement measured by the
external LVDT is constant throughout the test except for several cycles in the beginning. The
actuator LVDT is adjusted in every loading cycle to maintain the target external displacement.
The actuator displacement increases gradually before 125th cycle, followed by a rapid increase.
Then, the actuator displacement becomes close to the external displacement to the end of the test.
58
Figure 3.3 Maximum actuator displacements versus maximum opening displacements in
AMPT Overlay Test
The difference between the two measurements is due to the machine compliance, and this
difference is varied during the test depending on stiffness of the specimen being tested and the
level of damage occurring in the specimen. Therefore, controlling the maximum opening
displacement is better than controlling the maximum actuator displacement in the AMPT overlay
test, eliminating a need for correcting the machine compliance after the test is completed.
3.2 Properties of Asphalt Mixtures
Five mixtures used in the bottom asphalt layers of the five test sections (S8-3, S10-3, S11-3,
N10-3, and N11-3) of the Group Experiment in the 2009 research cycle of the NCAT Test Track
0.36
0.365
0.37
0.375
0.38
0.385
0.39
0.395
0.4
0 50 100 150 200 250 300 350
Dis
pla
ce
men
t (mm
)
No. of Cycles
Maximum Actuator Displacement Maximum Opening Displacement (MOD)
59
were selected for this study. These mixes were chosen so that results of the laboratory evaluation
can be compared with field performance of these mixes at the Test Track in the future. The
evaluation of these mixes is still underway at the Test Track (West et al. 2012).
Table 3.1 shows the volumetric properties of all the mixtures used for preparing overlay test
specimens in this study. They were plant-produced and sampled during the construction of these
test sections. The S8-3 mixture served as the control mixture in this study was produced hot
without reclaimed asphalt pavement (RAP). The S10-3 and S11-3 mixtures, which used the same
mix design without RAP as the S8-3 mixture, were produced warm using foaming and additive
WMA, respectively. The N10-3 and N11-3 mixtures were based on a mix design with 50 percent
RAP. The N10-3 mixture was produced hot, and the N11-3 mixture was produced warm using
foaming WMA. The 50 percent RAP in the mixtures included 20 percent fine fraction RAP and
30 percent coarse fraction RAP. More information about the mixtures used in this study is
available elsewhere (Powell 2013).
60
Table 3.1 Mixture Properties
Properties Mixtures
S8-3 S10-3 S11-3 N10-3 N11-3
NMAS (mm) 19 19 19 19 19
Virgin Asphalt PG Grade 67-22 67-22 67-22 67-22 67-22
% RAP 0 0 0 50 50
WMA No Foam Additive No Foam
Design Air Voids (VTM), % 3.6 4.1 3.0 4.2 4.1
Total Combined Binder (Pb), % wt 4.9 4.7 5.0 4.7 4.6
Effective Binder (Pbe), % 4.4 4.2 4.5 4.1 4.0
Dust Proportion (DP) 1.2 1.2 1.2 1.4 1.3
Maximum Specific Gravity (Gmm) 2.532 2.533 2.522 2.537 2.544
Voids in Mineral Aggregate (VMA), % 14 14.0 13.7 13.8 13.7
Voids Filled with Asphalt (VFA), % 75 71 78 72 70
3.3 Testing Plan
As specified in the TxDOT procedure, the overlay test should be conducted using a maximum
opening displacement (MOD) of 0.635 mm (0.025 in.) and at a test frequency of 0.1 Hz. This
recommended MOD was originally applied for evaluating asphalt mixtures used in overlays on
top of old concrete pavements in Texas. The MOD was calculated based on the thermal
expansion of a 4.5-m (15-ft) long concrete slab under a 17?C (30?F) daily temperature variation.
Two types of concrete slab with gravel and limestone aggregates were considered, and the
average thermal expansion (0.635-mm) was recommended in the current TxDOT procedure
(Zhou and Scullion 2003).
61
However, if this test is used to evaluate the cracking resistance of stiff asphalt mixtures (e.g., mix
with higher RAP and/or RAS contents) and those mixes for overlays placed in other states that
have different climatic conditions (i.e., smaller daily temperature variation), the maximum
opening displacement may need to be lower (Tran et al. 2012). For this study, three MOD levels
(i.e., 0.381, 0.318, and 0.254 mm) were selected to evaluate the relationships between the MOD,
number of cycles to failure and field performance (it should be noted that the field evaluation of
these test sections is underway and thus not presented in this thesis). At the lower MOD levels,
the overlay test takes much longer, especially at the MOD of 0.254 mm. Thus, it is desirable to
evaluate the overlay test for conducting at a higher frequency (i.e., 1 Hz) to reduce the testing
time. Results of this evaluation are presented in the next chapter.
Table 3.2 shows a laboratory testing plan designed to investigate the alternative method for
determining the failure point and the use of a higher frequency (i.e., 1 Hz). Due to the
availability of plant-produced mix, the overlay test was conducted at two test frequencies (0.1
and 1 Hz) for the N11-3 mix and only at the higher frequency (1 Hz) for other mixtures. For
each mix, overlay testing was conducted at three MOD levels (i.e., 0.254, 0.318, and 0.381 mm)
and using three replicates for each testing combination. This experimental plan was designed in
the interest of time and availability of plant-produced mixes for this study.
62
Table 3.2 Laboratory Testing Plan
Section Mixture
(19 mm NMAS)
Frequency
(Hz)
Maximum Opening
Displacement
(mm)
No. of Replicates
S8-3 Control
1 0.254 3
1 0.318 3
1 0.381 3
S10-3 WMA Foam
1 0.254 3
1 0.318 3*
1 0.381 3
S11-3
WMA Additive
1 0.254 3
1 0.318 3
1 0.381 3
N10-3 50% RAP
1 0.254 3
1 0.318 3
1 0.381 3
N11-3 50% RAP + Foam
1 0.254 3
1 0.318 3
1 0.381 3
0.1 0.254 3*
0.1 0.318 3
0.1 0.381 3*
Total Number of Specimens Tested 54
Notes: Due to issues with some recorded videos, a total of 48 (instead of 54) videos were analyzed for this
study. The number in the last column labeled with ?*? indicates those tests have incomplete video
records. S10-3 mix tested at 0.318-mm MOD and 1Hz has one specimen without video record; N11-3
mix tested at 0.254-mm MOD and 0.1Hz has three; N11-3 mix tested at 0.381-mm MOD and 0.1Hz has
two. The specific number of specimen analyzed and its result are listed in the Appendix B.
63
3.4 Specimen Fabrication Procedure
1) Heated a bucket of a plant-produced mixture in an oven at compaction temperature for 4
hours.
2) Splitted the heated mixture into the appropriate sample size for compaction.
3) Reheated the samples until the mixture temperature reached the compaction temperature.
4) Compacted each sample using the gyratory compactor to the height of 115 mm.
5) Cooled down the molded samples and determined the bulk specific gravity.
6) Cut each compacted sample to prepare one overlay test specimen.
7) Dried each test specimen in front of a fan overnight and determined the bulk specific gravity
and the specimen air void content.
8) If the air void content is within 7.0 ? 1.0 percent, dry the specimen in front of a fan overnight
and measured the size (length, width, and thickness).
9) Sealed each test specimen with a wrap if it is to be tested more than two weeks later.
3.5 Test Setup
To monitor the development of cracks on each specimen during overlay testing, a rectangular
area was painted white on one side of each specimen, and a 2 mm ? 2 mm black grid was then
drawn on the painted surface before the specimen was glued on the base plates. The development
of cracks on the painted side was monitored using a high definition camcorder for analysis later
in the study. The following steps were taken to prepare specimens for testing.
64
In the first step, the two base plates were aligned and bolted on a mounting jig. A small gap was
left between two plates, and a tape (6.09 mm wide) is placed over the gap. Figure 3.4 (a) shows
the setup of the two base plates for the AMPT overlay test. Figure 3.4 (b) shows a smaller set of
base plates used in the AMPT overlay test and a larger set of base plates used in the Texas
Overlay Tester. The steel base plates are grooved to increase the bond between the test specimen
and the base plate after they were glued together. Table 3.3 shows the dimensions of the base
plates.
(a) AMPT base plates (b) Overlay tester and AMPT base plates
Figure 3.4 Base plates
65
Table 3.3 Base Plate Dimensions
Dimension AMPT Overlay Test (mm) Texas Overlay Tester (mm)
Plate Dimension
Length 92.01 108.09
Width 119.95 120.74
Height 18.07 17.90
Gap width 1.85 2.10
Gap tape width 6.09 6.09
Groove Dimension
Groove width 3.10 3.16
Groove depth 1.73 1.68
Groove interval 4.90 4.75
In the second step, glue (DEVCON 2-ton Epoxy in Figure 3.5(a)) was applied on the bottom side
of the specimen. Glue amount measurements on 45 specimens showed that the average amount
for each specimen in this study was 8.3 g, and the standard deviation was 1.1 g. Figure 3.5(b)
shows the glue was uniformly applied on the specimen, and Figure 3.5(c) shows the residual glue
after the specimen was removed at the end of testing. In this study, a glue amount of 9.0 g was
enough to provide good bonding between a specimen and base plates. It was observed that it may
be excessive if a glue amount of 10 g is used.
66
(a) Glue type
(b) Glue uniformly applied on specimen
(c) Residual glue after specimen removed (9.0-g glue applied)
Figure 3.5 Glue type and amount
In the final step, the specimen with uniformly applied glue was placed on the top of the base
plates. Then, the glue was cured overnight as shown in Figure 3.6. The specimen was then
conditioned in an environmental chamber at 25 ?C for at least 1 hour before testing. After
conditioning, the test specimen with the base plates was set up in the AMPT (Figure 3.7).
67
Figure 3.6 Glue curing setup
Figure 3.7 Setup of specimen
glued on base plates in AMPT
3.6 Method for Determining the Failure Point
The TxDOT procedure defines the failure point (i.e., the number of cycles to failure) as the
number of cycles at which the applied peak load is reduced by 93 percent compared to the
applied peak load measured at the beginning of the test (hereafter referred to as the 93%
reduction method). Based on this method, cracks are often seen propagated through the entire
thickness of the specimen long before the applied load is reduced by 93 percent of the initial
load.
An alternative method, referred to as the ?normalized load ? cycle? or NLC, was evaluated in
this study for use in the overlay test. The NLC method is developed based on the ?normalized
stiffness ? cycle? method described in the ASTM D7460 standard (a description of this method
68
was presented in the previous chapter). The ?normalized stiffness ? cycle? method was modified
from the ?reduced energy ratio? method/theory (Rowe 1993, Rowe and Bouldin 2000) to
determine the failure point for the BBF test. In the BBF test, failure point is defined as the
transition point from micro-crack to macro-crack propagation, and as described in ASTM
D7460, it is the number of cycles at which the curve of ?normalized stiffness ? cycle? versus
number of cycles reaches the maximum value.
For the alternative method, the ?normalized stiffness? term is replaced with the ?normalized
load? term. The failure point or the number of cycles to failure for the overlay test can be
determined in three steps. First, the ?normalized load ? cycle? is determined using Equation 45
for each load cycle. Then, the NLC is plotted against the number of cycles. Finally, the failure
point is determined corresponding to the peak of the NLC curve. Figure 3.8 illustrates how the
failure point can be determined for an overlay test. In this study, the alternative method for
determining the failure point was evaluated. Results of this evaluation are presented in the next
chapter.
NLC = Pi ? NiP
1 ? N1
(45)
Where,
NLC = normalized load ? cycles (kN/kN);
Pi = peak load at cycle number i (kN);
P1 = peak load at 1st cycle (kN);
Ni = cycle number i; and
N1 = cycle number at which P1 is estimated.
69
Figure 3.8 Determination of failure point
0
10
20
30
40
50
60
70
0
0.2
0.4
0.6
0.8
1
1.2
0 200 400 600 800 1000 1200
No
rmali
ze
d Lo
ad
x C
yc
le
(kN/
kN)
No
rm
ali
zed
Lo
ad
(Pi/
P0)
No. of Cycles
Normalized Load Normalized Load x Cycle
Failure
Point
70
CHAPTER 4 RESULTS AND ANALYSIS
This chapter summarizes the results of overlay testing in the AMPT and analysis. First, the
proposed ?normalized load ? cycle? (NLC) method and the 93-percent load reduction method for
determining the failure point in the overlay test are evaluated using the video recorded during
testing and the relationship of peak load versus the number of cycles. Second, the failure points
determined by both methods are obtained and compared to the moment of failure when crack
was first visually observed to propagate through the specimen. After that, the effect of higher
frequency on the testing result is discussed.
4.1 Evaluation of Methods for Determining the Failure Point
For each specimen, still images capturing the specimen cracking conditions corresponding to the
failure points determined according to NLC and 93-percent reduction methods were extracted
from the video being recorded during the test. Figure 4.1 include three images showing cracking
conditions at the two failure points and at the moment when the crack was first observed to
propagate through the specimen. A brief discussion of these images follows.
? Figure 4.1(a) shows the cracking condition at the number of cycles determined as the
failure point based on the NLC method (Nf(NLC)). At this failure point, the crack
typically has not visually propagated through the specimen thickness.
71
? Figure 4.1(c) shows the specimen condition at the number of cycles determined as the
failure point determined based on the 93% reduction method (Nf(93%)). At this failure
point, the crack typically has propagated through the specimen long before the test ends
at the 93% reduction of the peak load.
? Figure 4.1(b) shows the specimen condition when the crack was first visually observed to
propagate through the specimen (Nf(Thru Crack)). The number of cycles corresponding
to this moment was determined for each specimen for analysis. Of 48 specimens with
good recoded videos, four specimens (# 86, 88, 89 and 121) had multiple cracks captured
in the video, and the number of cycles when the first continuous crack propagates
through the thickness was determined as Nf(Thru Crack). Other seven specimens (# 26,
40, 74, 75, 110, 111, and 123) had multiple short cracks throughout the thickness of the
specimen, but those cracks were not connected even after the peak load had reached the
93% reduction of the initial value. For these seven specimens, the Nf(Thru Crack) was
determined as the first number of cycles at which the shapes of the cracks remained
unchanged through the end of the test. Further investigation of the test data and recorded
videos of these 11 specimens did not find any unusual behaviors, so they were included
in the analysis.
72
(a) Nf(NLC)
(b) Nf(Thru Crack)
(c) Nf(93%)
Figure 4.1 Specimen cracking condition at three moments (0.318-mm MOD and 0.1-Hz
frequency)
The numbers of cycles corresponding to the three specimen conditions shown in Figure 4.1 are
plotted on the curve of peak load versus number of cycles in Figure 4.2. As shown in Figure 4.2,
the peak load versus number of cycles curve typically has four different stages as follows:
1. In Stage I, the peak load decreased sharply.
2. In Stage II, the peak load decreased at an approximately constant rate. The failure point
determined based on the NLC method was approximately at the end of Stage II. Even
though the crack was not visually observed to propagate though the thickness of the
specimen at the Nf(NLC), micro-cracking may have occurred in the portion of the
specimen that did not have visible cracks. Thus, the crack was able to propagate through
this portion of the specimen quicker.
73
3. In Stage III, the load started to decrease at a higher rate after the Nf(NLC) failure point.
For most specimens tested, the failure point corresponding to the moment the crack was
first observed to propagate through the specimen in the video was near the end of this
stage (Of 48 specimens with good recorded videos, 32 specimens exhibit this trend).
4. In Stage IV, the peak load started to decrease at a much lower rate. It took a lot more
cycles before the peak load reached the 93-percent reduction of the initial peak load. The
Nf(93%) failure point was also set as the end of the overlay test.
Figure 4.2 Three failure points and four stages on the peak load curve (0.318-mm MOD
and 0.1-Hz frequency)
In the field, cracks are reported once they are observed on the pavement surface or when they
propagate through the asphalt layer. Therefore, the number of cycles corresponding to the
moment when the crack is first observed to propagate through the specimen in the video is
0
0.5
1
1.5
2
2.5
0 500 1000 1500 2000
Pea
k l
oa
d (
KN
)
No. of Cycles
Nf(NLC)
Nf(ThruCrack) Nf(93%)
III III IV
74
considered to best represent the way cracks are reported in the field. However, the determination
of this failure point cannot be done quickly or accurately based on the recorded video. Thus,
further analysis is conducted to determine if another method (either the NLC method or the 93%
reduction method) that can be easily determined based on measured testing data instead of a
recorded video may be used. The method recommended for future use should yield the failure
point closer to the Nf(Thru Crack).
4.2 Overlay Test Results
For each mix, the numbers of cycles to failure were determined based on both the failure point
determination methods (the NLC and the 93% reduction methods). The number of cycles when
crack was first observed to propagate through the specimen (Nf(Thru Crack)) was also
determined by analyzing the recorded video of crack propagation during testing. The average
(Avg.), standard deviation (Std. Dev.), and coefficient of variation (COV) of results from three
replicates are summarized in Table 4.1.
75
Table 4.1 Summary of OT Results at Three MODs for Five Mixtures
Mix Freq. (Hz) MOD (mm)
Nf(NLC) Nf(93%) Nf(Thru Crack)
Avg. Std. Dev. COV Avg. Std. Dev. COV Avg. Std. Dev. COV
S8-3
1 0.381 762 119 16% 1363 418 31% 937 223 24%
1 0.318 1718 371 22% 2986 762 26% 1947 467 24%
1 0.254 7346 1665 23% 9967 2344 24% 8334 2018 24%
S10-3
1 0.381 885 196 22% 1400 83 6% 1211 193 16%
1 0.318 2029 329 16% 2946 817 28% 2048 154 7%
1 0.254 4416 1051 24% 5916 1117 19% 5303 979 18%
S11-3
1 0.381 1037 297 29% 1619 665 41% 1237 450 36%
1 0.318 2794 828 30% 4291 1516 35% 3215 885 28%
1 0.254 4770 629 13% 7287 1354 19% 5800 571 10%
N10-3
1 0.381 140 99 71% 380 259 68% 210 108 51%
1 0.318 348 104 30% 1130 83 7% 497 130 26%
1 0.254 1611 598 37% 5107 2343 46% 1888 707 37%
N11-3
1 0.381 520 26 5% 1143 258 23% 622 60 10%
1 0.318 674 139 21% 2390 702 29% 851 166 19%
1 0.254 4262 1225 29% 8756 3726 43% 4769 1182 25%
0.1 0.381 156 64 41% 355 123 35% 221 N/A N/A
0.1 0.318 1463 521 36% 2821 837 30% 1969 839 43%
0.1 0.254 4264 1741 41% 8848 97 1% N/A N/A N/A
Note: 1. The average and standard deviation with the unit of cycle are rounded up to the nearest integer.
2. ?N/A? means only one or none of Nf(Thru Crack) was recorded due to issue of video.
Further analysis was performed to evaluate the two methods ? NLC and 93-percent
determination methods. The failure points determined by the NLC method and the 93%
76
reduction method were plotted against the Nf(Thru Crack) failure points in Figure 4.3 and Figure
4.4, respectively, to evaluate the correlation. The results from the 48 specimens with good
recorded videos were used. A trendline and a line of equality were added in each plot for
comparison. The difference between two correlating parameters in each plot can be graphically
represented by the difference between the corresponding trendline and the line of equality.
Figure 4.3 Nf(NLC) versus Nf(Thru Crack)
Figure 4.4 Nf(93%) versus Nf(Thru Crack)
y = 0.8724x - 67.756
R? = 0.9914
0
2000
4000
6000
8000
10000
12000
14000
0 2000 4000 6000 8000 10000 12000 14000
Nf(N
LC
)
Nf(Thru Crack)
Equality
y = 1.2186x + 581
R? = 0.8562
0
2000
4000
6000
8000
10000
12000
14000
0 2000 4000 6000 8000 10000 12000 14000
Nf(9
3%)
Nf(Thru Crack)
Equality
77
As shown in Figure 4.3, the slope and intercept of the trendline are 0.8724 and -67.756,
respectively. This means the overall difference between the Nf(NLC) and Nf(Thru Crack) is
approximately 13%. Also, the R2 value is 99.1%, which means the Nf(Thru Crack) varies closely
with the Nf(NLC).
In Figure 4.4, the slope, intercept and R2 value of the trendline are 1.2186, 581 and 85.6%,
respectively. This indicates the overall difference between Nf(93%) and Nf(Thru Crack) is
approximately larger than 21%. In this case, correlation coefficient (r) is equal to the square root
of R2 value. Their correlation coefficient (r = 0.925) is smaller than that between the Nf(NLC)
and Nf(Thru Crack) (r = 0.995). However, better correlation (indicated by larger coefficient
coefficient) is not sufficient to determine if the NLC method yields the failure point closer to the
observed moment of failure than the 93% load reduction method.
Figure 4.5 compares the failure points determined by two methods (Nf(NLC) and Nf(93%)) to
the visually observed moment of failure (Nf(Thru Crack)) which is ranked from the smallest to
the largest following a non-decreasing curve. The horizontal axis is the number of specimens (or
number of observations). The Nf(NLC) curve is much closer to the Nf(Thru Crack) curve with
less variations. The Nf(93%) curve has more variations or departures from the Nf(Thru Crack)
curve. Mathematically, the variation from the Nf(Thru Crack) can be regarded as the error. The
sum of squared error (SSE) of Nf(NLC) versus Nf(93%) indicates their overall departure from the
?observed? failure point (Nf(Thru Crack)). Table 4.2 summarizes the calculated SSE for the two
failure point determination methods. The SSE in Nf(93%) is more than 10 times of that in
Nf(NLC).
78
Figure 4.5 Comparing Nf(NLC) and Nf(93%) to Nf(Thru Crack)
Table 4.2 Sum of Squared Error in the Two Failure Points
Failure Point SSE
Nf(NLC) by NLC method 1.33E+07
Nf(93%) by 93% load reduction method 1.40E+08
In Figure 4.5, the Nf(93%) curve has several local peaks (indicated by ???) where the variation
from Nf(NLC) is quite large. The contribution of error from these peak points to the total error
should be considered. Table 4.3 provides the information of test specimens and associated
conditions corresponding to these peak points (from the left to the right in Figure 4.5). In the last
column, the contribution of individual error to the total error is indicated by the ratio of SE to
0
2000
4000
6000
8000
10000
12000
14000
0 10 20 30 40 50 60
No
. o
f c
yc
les
to
fa
ilu
re
(N
f)
No. of specimens
Nf(Thru Crack) Nf(NLC) Nf(93%)
79
SSE. The largest contribution can be 34% from a single test. More importantly, the specimens in
Table 4.3 are all fabricated using the mixes with 50% RAP. It indicates that the 93% load
reduction method may not be able to determine the failure point of high RAP mix in the overlay
test very well.
Table 4.3 Information Test Specimens with Large Squared Error (SE) in Nf(93%)
Section
No. Mix Type
MOD
(mm) Freq. (Hz) SE SE/SSE
N11-3 50%RAP+WMA Foam 0.318 1 2.79E+06 2%
N11-3 50%RAP+WMA Foam 0.318 1 4.80E+06 3%
N10-3 50%RAP+HMA 0.254 1 1.67E+06 1%
N10-3 50%RAP+HMA 0.254 1 1.85E+07 13%
N10-3 50%RAP+HMA 0.254 1 1.65E+07 12%
N11-3 50%RAP+WMA Foam 0.254 1 4.82E+07 34%
N11-3 50%RAP+WMA Foam 0.254 1 1.32E+07 9%
As mentioned before, the Nf(Thru Crack) is the moment of failure when the crack was first
observed to propagate through the specimen. The above analysis shows the NLC method would
be a better alternative for defining the moment of failure. Therefore, it determines the number of
cycles to failure in the overlay test more accurately.
4.3 Evaluation of Higher Frequency in the AMPT Overlay Test
Another improvement for the overlay test is to increase the test frequency. Since the overlay test
may be conducted at lower MOD levels for other material and climate conditions in the future, it
is desirable in these cases to conduct the overlay test at a higher frequency to shorten testing
80
time. Practically, for a specimen that requires 10,000 cycles of testing prior to failure, the
difference in testing time is approximately 25 hours (approximately 3 hours for a 1-Hz test
versus approximately 28 hours for a 0.1-Hz test). Due to the availability of the plant-produced
mix, overlay testing was conducted at both 0.1- and 1-Hz frequencies for the N11-3 mixture only
to evaluate the overlay test at 1 Hz (instead of 0.1 Hz as specified in the TxDOT procedure). The
failure point for each N11-3 test specimen was determined based on two failure point
determination methods?the NLC and 93% reduction methods.
Figure 4.6 compares the average and associated standard deviation of the test results determined
at 0.1- and 1-Hz frequencies for the three MOD levels based on the NLC and 93% reduction
methods. The results are very similar, especially at the lowest MOD level.
(a) NLC method
0
1000
2000
3000
4000
5000
6000
7000
0.381 0.318 0.254
Av
era
ge
Fa
ilu
re
Po
int
MOD (mm)
0.1 Hz 1 Hz
81
(b) 93% reduction method
Figure 4.6 Comparing overlay test results at 0.1- and 1-Hz frequencies
The test results determined at the two frequencies are also compared statistically using a two-
factor Analysis of Variance (ANOVA) (significance level ??= 0.05). The two factors analyzed
are frequency and MOD. First, three assumptions of ANOVA (normality, homogeneity of
variance, and independency) were checked to make sure the analysis result was valid (PROPHET
StatGuide 1997). The variance was found not homogenous. Therefore, the logarithmic
transformation (to base 10) was performed to stabilize the variance (Nettleton 2004). The
ANOVA based on the transformed data shows that (1) the interaction effect of two factors and
the MOD effect are statistically significant (p-value < 0.05); (2) the frequency effect is not
statistically significant (p-value > 0.05) (Montgomery 2009).
Further analysis using Tukey?s test was conducted to make pairwise comparison for each MOD.
Since Tukey?s test has the same assumptions as the ANOVA, the analysis here still uses the
0
2000
4000
6000
8000
10000
12000
14000
0.381 0.318 0.254
Av
era
ge
Fa
ilu
re
Po
int
MOD (mm)
0.1 Hz 1 Hz
82
transformed data in ANOVA (Coble 2014). Table 4.4 summarizes Tukey?s test results for the
NLC and 93% reduction methods. Based on the grouping information shown in the last column
of Table 4.4, two testing conditions that share the same letter are considered statistically the
same. Thus, at lower MOD level (0.254 and 0.318 mm), the overlay test conducted at 0.1 and 1
Hz would not yield statistically different results. However, at the highest MOD level (0.381
mm), test results at 0.1 and 1 Hz are statistically different (Montgomery 2009).
Table 4.4 Tukey?s Test Results
Frequency
(Hz)
Maximum Opening
Displacement (mm)
No. of
Replicates
Mean Failure
Point (Cycle)
Grouping
Tukey?s Test Results for the NLC Method
0.1 0.254 3 4264 A
1.0 0.254 3 4262 A
0.1 0.318 3 1463 B
1.0 0.318 3 674 B C
0.1 0.381 3 156 D
1.0 0.381 3 520 C
Tukey?s Test Results for the 93% Reduction Method
0.1 0.254 2 8848 A
1.0 0.254 3 8756 A
0.1 0.318 3 2821 B
1.0 0.318 3 2390 B
0.1 0.381 3 355 C
1.0 0.381 3 1143 B
The next step of the evaluation process was determining the test variability at the two
frequencies. The coefficient of variation (COV) and F-test were used for comparing the
83
variability. Figure 4.7 shows the coefficients of variation of the overlay testing results
determined at the two frequencies. As shown, the overlay test results determined at 0.1 Hz have
higher COVs (or larger variation) than the test results determined at 1 Hz, except for the 93%
reduction method at the 0.254-mm MOD level.
(a) NLC method
(b) 93% reduction method
Figure 4.7 Comparing coefficients of variation at 0.1- and 1-Hz frequencies
41%
36%
41%
5%
21%
29%
0%
10%
20%
30%
40%
50%
0.381 0.318 0.254
Co
effic
ien
t o
f v
ari
ati
on
Maximum Opening Displacement (mm)
0.1 Hz 1 Hz
35%
30%
1%
23%
29%
43%
0%
10%
20%
30%
40%
50%
0.381 0.318 0.254
Co
effic
ien
t o
f v
ari
ati
on
Maximum Opening Displacement (mm)
0.1 Hz 1 Hz
84
Then, F-test was performed to compare the variance of the overlay test results at the two
frequencies. First, the test results are grouped only by frequency (0.1 and 1 Hz), regardless of the
MOD level. F-test shows the variances from two groups (each has 9 data points) are not
statistically different a significance level of 0.05. Second, the test results are grouped by both
frequency and MOD level into six groups (each has 3 data points) in order to test the equality of
variances at different MOD levels (0.254, 0.318, and 0.381 mm). The F-test results show that the
variances at two frequencies are not statistically different at higher MOD levels (0.381 and 0.318
mm) for either Nf (NLC) or Nf (93%) results. At the lowest MOD level (0.254 mm), the
variances at two frequencies are not statistically different for the Nf (NLC) results but are
statistically different for the Nf (93%) results. The detailed F-test results are included in
Appendix D. The small samples sizes (especially for groups of 3 data points) make it difficult to
check the normality assumption of F-test, and also diminish its power (PROPHET StatGuide
1997). More overlay test results are required to validate these F-test results in the future.
In addition, Figure 4.8 compares the average testing time (in minutes) required for conducting
the overlay test at the two frequencies for the NLC and 93% reduction methods. The 1-Hz test
requires much shorter testing time, especially at lower MOD levels (0.318 and 0.254 mm). At the
0.254-mm MOD level, the overlay test can take more than 24 hours at 0.1 Hz but approximately
2.5 hours at 1 Hz (Figure 4.8(b)).
85
(a) NLC method
(b) 93% reduction method
Figure 4.8 Comparing testing time at two frequencies
Based on the above analysis, the overlay test may be conducted at 1 Hz to reduce the testing time
without significantly affecting the test variability. While the ANOVA showed that the two
frequencies could be used interchangeably without statistically affecting the test results at
smaller MOD levels (0.254 and 0.318 mm), only one frequency should be used to evaluate
different mixes in a project.
26
244
711
9 12 72
0
200
400
600
800
1000
0.381 0.318 0.254Av
era
ge
Te
sti
ng
Ti
me
(mi
nu
te)
Maximum Opening Displacement (mm)
0.1 Hz 1 Hz
60
471
1475
20 40 146
0
200
400
600
800
1000
1200
1400
1600
1800
0.381 0.318 0.254Av
era
ge
Te
sti
ng
Ti
me
(mi
nu
te)
Maximum Opening Displacement (mm)
0.1 Hz 1 Hz
86
CHAPTER 5 COMPARING AMPT OVERLAY TEST AND BENDING BEAM FATIGUE TEST
RESULTS
In this study, the proposed ?normalized load ? cycle? (NLC) failure point determining method in
the AMPT overlay test was derived from the ?normalized stiffness ? cycle? method in bending
beam fatigue test (ASTM D7460). The two tests were designed to determine the cracking
resistance of asphalt mixture. Therefore, it is desirable to determine the correlation between the
results of the two tests because the BBF test results have been determined for these mixes in
another study. This chapter compares results of the two tests using the ranking of mixtures and
the relationship between failure point and applied maximum strain (or displacement).
5.1 Comparing Ranking of Mixtures
In this section, the five asphalt mixtures were ranked based on the average bending beam fatigue
(BBF) test and the AMPT overlay test (OT) results. Then, correlation of rankings between two
tests was analyzed.
5.1.1 Ranking Mixtures Based on BBF Test Results
This section summarized the testing results and ranking of the average BBF test failure points for
the five mixtures. These results were obtained from another project and summarized in Table
87
5.1. The number of cycles to failure or failure point (Nf) was determined according to ASTM
D7460 based on the peak ?normalized stiffness ? cycle? value.
Table 5.1 Summary of BBF Test Results at Three Strains for Five Mixtures
Mixture Strain (??)
Number of Cycles to Failure/Failure Point
Average (Cycle) Std. Dev. (Cycle) COV
N11-3
800 2,587 501 19%
400 124,094 22,542 18%
200 37,367,084 28,471,254 76%
S8-3
800 9,887 6,874 70%
400 186,194 39,659 21%
200 5,038,040 2,533,496 50%
N10-3
800 2,317 1,430 62%
400 52,524 52,825 101%
200 9,441,897 5,943,834 63%
S10-3
800 9,147 6,881 75%
400 184,737 66,911 36%
200 5,333,954 1,660,846 31%
S11-3
800 10,494 3,682 35%
400 199,847 93,486 47%
200 3,710,114 1,703,150 46%
Note: the average and standard deviation with the unit of cycle are rounded up to the nearest
integer.
As shown in Table 5.2, the average number of cycles to failure (failure point) at each strain level
is ranked from the largest to the smallest. The ranking at 800 and 400 ?? are the same. But the
88
ranking at 200 ?? is much different from those of the other two strain levels, since the mixtures
with 50 percent RAP (N11-3 and N10-3) rank higher than the WMA and control mixes. Based
on the properties of five mixtures, the mixes with 50 percent RAP should be stiffer than hot and
warm mixes without RAP due to higher content of aged binder. Therefore, the failure point of
N10-3 and N11-3 mixes should be lower regardless of strain level. The reason for the ranking
difference at different strain levels will be discussed later in Section 5.2.1.
Table 5.2 Ranking of Average Failure Point by BBF Test for Five Mixtures
Mixture Processing Information
Maximum Tensile Strain (??)
800 400 200
N10-3 50%RAP+HMA 5th 5th 2th
N11-3 50%RAP+WMA Foam 4th 4th 1th
S8-3 0%RAP+HMA (Control) 2th 2th 4th
S10-3 WMA Foam 3th 3th 3th
S11-3 WMA Additive 1th 1th 5th
5.1.2 Ranking Mixtures Based on AMPT Overlay Test Results
The overlay test has been verified as an alternative to determine the fatigue cracking resistance
of asphalt mixture (Zhou et al. 2007a). Since the BBF test is currently used as a typical test
characterizing the fatigue cracking resistance, the ranking of five plant-mixes from the NCAT
test track regarding the average failure point by OT should be similar to the ranking by BBF test.
Since the proposed NLC method can better define the moment of failure, only the results based
on NLC method were discussed in the analysis.
89
Table 5.3 ranks the average failure points of five mixtures in descending order for each MOD
based on the NLC determination method. The rankings at 0.381- and 0.318-mm MOD are the
same, but the rankings for the S8-3, S10-3, and S11-3 mixtures are different for the 0.254-mm
MOD. In addition, at each MOD, the asphalt mixtures with 50 percent RAP (N11-3 and N10-3
mixes) ranks lower than the two warm mixes and HMA without RAP. It is reasonable because
the aged binder in the RAP makes the N11-3 and N10-3 mixes much stiffer.
Table 5.3 Ranking of Average Failure Point by OT for Five Mixtures Based on NLC
Method
Mixture Processing Information
Maximum Opening Displacement (mm)
0.381 0.318 0.254
N10-3 50%RAP+HMA 5th 5th 5th
N11-3 50%RAP+WMA Foam 4th 4th 4th
S8-3 0%RAP+HMA 3th 3th 1th
S10-3 WMA Foam 2th 2th 3th
S11-3 WMA Additive 1th 1th 2th
5.1.3 Comparing AMPT OT Ranking to BBF Test Ranking for Five Mixtures
Spearman?s Rank-Order Correlation Coefficient (rs) was calculated to determine the strength and
direction of correlation (or similarity) among six rankings from Table 5.2 and 5.3. The closer rs
to zero, the weaker the correlation is. The positive or negative sign of rs shows whether or not the
two rankings are in the same direction (Royal Geographical Society). Table 5.4 shows the
90
correlation coefficient matrix among these six rankings. This matrix compares the ranking at
each overlay test MOD to the ranking at each BBF maximum tensile strain. Also, it gives the
correlations among three rankings within each test.
Table 5.4 Spearman?s Rank-Order Correlation Coefficients
OT
@0.381
mm
OT
@0.318
mm
OT
@0.254
mm
BBFT
@800
??
BBFT
@400
??
BBFT
@200
??
OT @0.381 mm 1 1 0.7 0.9 0.9 -0.8
OT @0.318 mm 1 0.7 0.9 0.9 -0.8
OT @0.254 mm 1 0.9 0.9 -0.8
BBFT @800?? 1 1 -0.9
BBFT @400?? 1 -0.9
BBFT @200?? 1
A hypothesis test was performed to determine if the ranking correlation truly existed (in this
case, the average failure points of five mixes were ranked). For a significance level of 0.05, the
critical value for rs is 0.9. That is, the correlation would occur at 95 percent chance if the
coefficient is equal or above 0.9 (Gauthier 2001). As shown in Table 5.4, the rankings of the
mixes tested at three overlay test MOD levels correlated well (rs = 0.9) with the rankings of the
mixes tested at 800 ?? and 400 ?? in the BBF test. However, the rankings of the mixes based on
the OT results were almost apposite (rs = -0.8) compared to those based on the BBF test results at
200 ??.
The rankings of the mixes for the three OT MOD levels are very similar (rs ? 0.7). Even though
0.7 is smaller than the critical value of 0.9, it still indicates a positive correlation. However, the
91
BBF test rankings at 200 ?? are in a reversed order compared to those at the other strain levels.
Overall, the OT rankings at each MOD based on the NLC method is similar to the BBF test
rankings at 800 ?? and 400 ?? but different from those at 200 ??. The good correlations between
the two tests indicate the potential use of overlay test to characterize fatigue cracking resistance
of asphalt mixtures.
92
5.2 Failure Point Prediction
5.2.1 BBF Test
Figure 5.1 illustrates the relationship between maximum tensile strain and BBF test number of
cycles to failure for five asphalt mixtures. Trendlines are fitted to the testing data for each
mixture. In the log-log scale, each trendline is linear. The slopes of trendlines for S8-3, S10-3,
and S11-3 mixtures are different from those of N11-3 and N10-3 mixtures. The failure point of
high RAP mixes is higher at the smallest strain level (200 ??) but lower at the largest strain level
(800 ??) compared to other three mixes. Therefore, Table 5.2 shows the different failure point
rankings of the mixes at 200 ?? and at 800 ?? in BBF test. A possible explanation of this
difference is that high RAP mixes tend to be more elastic at lower strain, but more brittle at
higher strain than other mixes. Field cracking performance should be investigated in the future
study to verify this explanation.
93
Figure 5.1 Maximum tensile strains versus failure points for five mixtures from BBF test
The failure point (or the number of cycles to failure) at certain maximum tensile strain in the
BBF test can be determined by a fatigue transfer function shown in Equation 46 (Huang, 1993).
Table 5.5 includes the power model coefficients determined by fitting Equation 46 to the BBF
test data for the five mixtures.
Nf = ?1 (1?)
?2
(46)
100
1000
100 1,000 10,000 100,000 1,000,000 10,000,000100,000,000
Maxi
mu
m Te
nsi
le
Str
ain
(m
icr
ostr
ain
)
Failure Point/ Number of Cycle to Failure
S11-3-WMA-Additive
S10-3-WMA-Foam
S8-3-Control
N11-3-RAP-WMA
N10-3-RAP-HMA
S11-3-WMA-Additive
S10-3-WMA-Foam
S8-3-Control
N11-3-RAP-WMA
N10-3-RAP-HMA
94
Table 5.5 Fitting Power Model Coefficients for the BBF Test
Mixture
Type
Processing Information
Power Law Regression Coefficients
?1 ?2 R2
S11-3 WMA Additive 1?1016 4.1923 0.9743
S10-3 WMA Foam 4?1017 4.7140 0.9753
S8-3 0%RAP+HMA (Control) 1?1017 4.5321 0.9686
N11-3 50%RAP+WMA Foam 3?1022 6.5846 0.9600
N10-3 50%RAP+HMA 4?1020 6.0192 0.9288
5.2.2 AMPT Overlay Test
Figure 5.2 shows the maximum opening displacement (MOD) versus the OT number of cycles to
failure determined based on the NLC method for the five mixtures. All the failure points were
determined at 1-Hz. The power model (Equation 47) was used to fit the data. As shown in Figure
5.2, the slopes of S10-3, and S11-3 trendlines are different from the slopes of the S8-3, N10-3,
and N11-3 mixes. As MOD level changes, the rate of change of failure point for high RAP mixes
and control mix is higher than that of warm mixes. This is similar to the result of BBF test
showed in Figure 5.1. Probably, high RAP mixes and control mix tend to be more sensitive than
warm mixes to the change of MOD level.
95
Figure 5.2 Maximum opening displacements versus failure points for five mixtures by OT
Equation 47 shows the fitted power-model relationship between failure point and the reciprocal
of MOD (1/MOD). The fitted model can be used to predict the failure point at the desired
maximum opening displacement. Table 5.6 summarizes the model coefficients ??1? and ??2? for
five mixtures. All the R2 values are larger than 0.80 which indicates good fitting.
Nf(NLC) = ?1 ( 1MOD)
?2
(47)
Coefficient ??1? is a scaling factor moving the trendline up or down (i.e. larger ??1? moves the
trendline up). Coefficient ??2? governs the rate of growth or decline of the trendline (i.e. smaller
0.1
1
10 100 1000 10000
MOD (
mm
)
Nf(NLC)
S11-3-WMA-Additive
S10-3-WMA-Foam
S8-3-Control
N11-3-RAP-WMA
N10-3-RAP-HMA
S11-3-WMA-Additive
S10-3-WMA-Foam
S8-3-Control
N11-3-RAP-WMA
N10-3-RAP-HMA
96
absolute value of ??2? corresponds to lower changing rate). The mixture with smaller absolute
value of ??2? in the fitted model is less sensitive to MOD change.
Table 5.6 Fitting Power Model Coefficients for the AMPT OT
Mixture Type Processing Information
Power Law Regression Coefficients
?1 ?2 R2
S11-3 WMA Additive 29.956 3.760 0.87
S10-3 WMA Foam 20.478 3.934 0.93
S8-3 0%RAP+HMA (Control) 3.158 5.601 0.96
N11-3 50%RAP+WMA Foam 2.595 5.233 0.85
N10-3 50%RAP+HMA 0.269 6.286 0.87
5.2.3 Comparing Failure Point Prediction in Two Tests
Comparing the overlay test and BBF test by plotting the maximum tensile strain (or maximum
opening displacement) versus the failure point, the power model can be used to fit both
relationships (as shown in Equations 46 and 47). Using these relationships, the failure point at
any maximum tensile strain (or maximum opening displacement) of interest within the tested
range can be interpolated.
Also, both of the ??2? column in Table 5.5 and the ??2? column in Table 5.6 indicate the rate of
change of mix?s failure point to the change of tensile strain. The coefficients of warm mixes
(S10-3 and S11-3) are smaller than those of high RAP mixes (N10-3 and N11-3). Obviously, the
97
coefficients ??2? and ??2? have similar range (4.192 < ?2 < 6.585, 3.760 < ?2 < 6.286). Therefore,
independent-t test was performed to test the equality of the means of two coefficients for five
mixes (the Minitab output is summarized in Appendix E). It shows that the mean of ??2? and the
mean of ??2? are statistically no different at significance level of 0.05 (p-value = 0.724). Even
though the assumption of equal variances is met (as shown in Appendix E), the power of t test is
weakened due to small sample size (n=5). In order to draw a reliable conclusion from t-test, more
mixture types need to be tested in the future (Montgomery 2009).
98
CHAPTER 6 CONCLUSION AND RECOMMENDATIONS
Based on the results of this study, the following conclusions and recommendations can be
offered:
? The current TxDOT procedure determines the failure point once the applied load is
reduced by 93 percent of the initial applied load. However, cracks are often seen to
propagate through the test specimen long before the applied load reaches this criterion,
especially at lower MOD levels. The NLC method presented in this study may be used to
better determine the failure point (shortly before the visible crack propagates through the
test specimen). The regression analysis shows that the failure point determined based on
the NLC method (Nf(NLC)) is approximately 13% lower than the failure moment
determined when the crack was first observed to propagate through the specimen
(Nf(Thru Crack)).
? The Nf(Thru Crack) values vary closely with those of the Nf(NLC) (R2 = 99.1%). Also,
the overall difference (the sum of squared error (SSE)) between the Nf(Thru Crack)
values and the Nf(NLC) value is 10 times less than the overall difference between the
Nf(Thru Crack) values and the Nf(93%) values. Hence, the NLC method is recommended
for determining the failure point for overlay test.
? The TxDOT procedure specifies that the overlay test be conducted using an MOD of
0.635 mm (0.025 in.) and at a test frequency of 0.1 Hz for evaluating asphalt mixtures
used in overlays on top of old concrete pavements in Texas. However, this test may be
99
conducted at lower MOD levels for other stiff materials (e.g., mix with high RAP and/or
RAS contents) and climate conditions (i.e., small daily temperature variation) in the
future. At the lower MOD levels, the overlay test takes much longer. As shown in the
analysis, the overlay test may be conducted at 1 Hz to reduce testing time without
significantly affecting the test variability. Also, the test results conducted at 0.1 and 1 Hz
were not statistically different.
? The BBF and AMPT overlay tests have similar rankings of the five asphalt mixtures
based on the number of cycles to failure. The power model used in the BBF test can also
be used to determine the relationship between the number of cycles to failure and
maximum opening displacement (MOD) for overlay test. Based on the relationships for
both the BBF and overlay tests, the warm mixes were less sensitive to the change of
maximum tensile strain or MOD than the high RAP mixes.
? To further evaluate the AMPT overlay test in determining the cracking resistance of
asphalt mixture, correlation between laboratory test results and field cracking
performance at the test track should be investigated in the future. Also, further testing
conducted at the 0.635-mm MOD specified in the TxDOT procedure should be
performed and compared with the results conducted at the smaller MOD used in this
study. More mixes with various binders and aggregates should also be tested to verify the
application of overlay test at higher frequency (1Hz).
100
REFERENCES
American Association of State Highway Transportation Officials (AASHTO) (2007) AASHTO T 321-07:
Standard Method of Test for Determining the Fatigue Life of Compacted Hot Mix Asphalt (HMA)
Subjected to Repeated Flexural Bending. AASHTO, Washington, D.C.
American Society for Testing and Materials (ASTM) (2010). ASTM D7460-10: Standard Test Method
for Determining Fatigue Failure of Compacted Asphalt Concrete Subjected to Repeated Flexural
Bending, ASTM International, West Conshohocken, PA.
Barenblatt, G. I. (1962). The mathematical theory of equilibrium cracks in brittle fracture. Advances in
applied mechanics, 7(1), 55-129.
Bennert, T. A. (2009). A rational approach to the prediction of reflective cracking in bituminous overlays
for concrete pavements. Doctoral dissertation, The State University of New Jersey, Rutgers, NJ.
Bischoff, D. (2007). Evaluation of Strata? Reflective Crack Relief System, Report FEP-01-07, Wisconsin
Department of Transportation.
Carpenter, S. H., & Jansen, M. (1997). Fatigue behavior under new aircraft loading conditions. In
Aircraft/Pavement Technology In the Midst of Change, 259-271.
Carpenter, S. H., & Shen, S. (2006). Dissipated energy approach to study hot-mix asphalt healing in
fatigue. Transportation Research Record: Journal of the Transportation Research Board, 1970(1), 178-
185.
Chiangmai, C. N. (2010). Fatigue-fracture Relation on Asphalt Concrete Mixtures. Master?s Thesis,
University of Illinois at Urbana-Champaign, IL.
Cleveland, G. S., Lytton, R. L., & Button, J. W. (2003). Reinforcing benefits of geosynthetic materials in
asphalt concrete overlays using pseudo strain damage theory. In Pre-Print CD-ROM, 82nd Annual
Meeting of the Transportation Research Board, National Research Council, National Academies,
Washington, D.C.
Crews, E. (2009). MWV EvothermTM pavement durability: result of laboratory and field testing. MWV
Specialty Chemical Report. Retrieved from
http://www.meadwestvaco.com/mwv/groups/content/documents/document/mwv024063.pdf.
Coble, D. W. (2014) Week 6 Lecture: Multiple Comparison Tests (Chapter 11)
Retrieved from
http://www.faculty.sfasu.edu/cobledean/Biostatistics/Lecture6/MultipleComparisonTests.PDF
101
Garcia-Diaz, A., & Riggins, M. (1984). Serviceability and distress methodology for predicting pavement
performance. Transportation Research Record: Journal of the Transportation Research Board, 997, 56-
61.
Gauthier, T. D. (2001). Detecting trends using Spearman's rank correlation coefficient. Environmental
Forensics, 2(4), 359-362.
Germann, F. P., & Lytton, R. L. (1979). Methodology for predicting the reflection cracking life of asphalt
concrete overlays. Interim Report, Sep. 1974-Mar. 1979 Texas A&M University, College Station.
Ghuzlan, K. A., & Carpenter, S. H. (2000). Energy-derived, damage-based failure criterion for fatigue
testing. Transportation Research Record: Journal of the Transportation Research Board, 1723(1), 141-
149.
Harvey, J. T., Deacon, J. A., Taybali, A. A., Leahy, R. B., & Monismith, C. L. (1997). A reliability-based
mix design and analysis system for mitigating fatigue distress. In Eighth international conference on
asphalt pavements (Vol. I), 301-323.
Hu, S., Zhou, F., & Scullion, T. (2010). Reflection cracking-based asphalt overlay thickness design and
analysis tool. Transportation Research Record: Journal of the Transportation Research Board, 2155(1),
12-23.
Hu, S., Zhou, F., & Scullion, T. (2011). Factors that affect cracking performance in hot-mix asphalt mix
design. Transportation Research Record: Journal of the Transportation Research Board, 2210(1), 37-46.
Hu, X., Zhou, F., & Scullion T. (2008) Pilot implementation of the overlay tester and double-blade saw
(FHWA/TX-08/5-4467-01-1) Texas Transportation Institute, Texas A&M University System.
Huang, Y. H. (1993). Pavement Analysis and Design, Prentice Hall, Inc., New Jersey.
IPC Global? (2012), AMPT Overlay Test Kit. Retrieved from http://instrotek.com/wordpress/wp-
content/uploads/AMPT-Overlay-Test-Kit.pdf.
Jacob, M. M. J. (1995). Crack Growth in Asphalt Mixes. Doctoral dissertation, Delft University of
Technology, Delft, Netherlands.
Kalidindi, S. R., Abusafieh, A., & El-Danaf, E. (1997). Accurate characterization of machine compliance
for simple compression testing. Experimental mechanics, 37(2), 210-215.
Lytton, R. L., Uzan, J., Fernando, E. G., Roque, R., Hiltunen, D., & Stoffels, S. M. (1993). Development
and validation of performance prediction models and specifications for asphalt binders and paving mixes
(Vol. 357). Strategic Highway Research Program.
102
Montgomery, D. C. (2009) Design and Analysis of Experiments: 7th Edition, John Wiley & Sons, Inc.,
New York.
Nettleton, D. (2004) Checking Model Assumptions
Retrieved from http://www.public.iastate.edu/~dnett/S402/wassumptions.pdf
Paris, P. C., & Erdogan, F. (1963). A critical analysis of crack propagation laws. Journal of Basic
Engineering, 85, 528.
Pierce, L. M., & Mahoney, J. P. (1996). Asphalt concrete overlay design case studies. Transportation
Research Record: Journal of the Transportation Research Board, 1543(1), 3-9.
Powell, R. B. (2013) NCAT Pavement Test Track: Construction.
Retrieved from http://www.pavetrack.com/construction.htm.
Prowell, B. D. (2010). Estimate of fatigue shift factors between laboratory tests and field performance.
Transportation Research Record: Journal of the Transportation Research Board, 2181(1), 117-124.
Prowell, B. D., Brown, E. R., Anderson, R. M., Daniel J. S., Swamy A. K., Quintus, H. V., ?
Maghsoodloo, S. (2010). Validating the fatigue endurance limit for hot mix asphalt (Vol. 646). National
Academies Press.
PROPHET StatGuide (1997) Do your Data Violate F-test Assumptions?
Retrieved from http://www.basic.northwestern.edu/statguidefiles/ftest_ass_viol.html
Roque, R., Zhang, Z., & Sankar, B. (1999). Determination of crack growth rate parameter of asphalt
mixtures using the Superpave IDT. Journal of the Association of Asphalt Paving Technologists, 68, 404-
433.
Rowe, G. M. (1993) Performance of asphalt mixtures in the trapezoidal fatigue test. Association of
Asphalt Paving Technologist, 62, 344.
Rowe, G. M., & Bouldin, M. G. (2000). Improved techniques to evaluate the fatigue resistance of
asphaltic mixtures. In 2nd Eurasphalt & Eurobitume Congress Barcelona (Vol. 2000).
Royal Geographical Society. Spearman?s Rank Correlation Coefficient - Excel Guide.
Retrieved from http://www.rgs.org/NR/rdonlyres/4844E3AB-B36D-4B14-8A20-
3A3C28FAC087/0/OASpearmansRankExcelGuidePDF.pdf.
Saadeh, S. & Eljairi, O. (2011). Development of a quality control test procedure for characterizing
fracture properties of asphalt mixtures, Final Report of Project No. 10-24, California State University,
Long Beach.
103
Schapery, R. A. (1973). A theory of crack growth in visco-elastic media, Report No. MM 2764-73-1,
Mechanics and Materials Research Center, Texas A&M University.
Schapery, R. A. (1975). A theory of crack initiation and growth in viscoelastic media. International
Journal of Fracture, 11(1), 141-159.
Schapery, R. A. (1978). A method for predicting crack growth in nonhomogeneous viscoelastic media.
International Journal of Fracture, 14(3), 293-309.
Scheffe, H. (1959). The analysis of variance, John Wiley & Sons, Inc., New York.
Scullion, T., Zhou, F., Walubita, L., & Sebesta, S. (2009). Design and performance evaluation of very
thin overlays in Texas (FHWA/TX-09/0-5598-2). Texas Transportation Institute, Texas A&M University
System.
Seo, Y., Kim, Y. R., Schapery, R. A., Witczak, M. W., & Bonaquist, R. (2004). A study of crack-tip
deformation and crack growth in asphalt concrete using fracture mechanics. Journal of the Association of
Asphalt Paving Technologists, 73, 200-228.
Shen, S., & Carpenter, S. H. (2005). Application of the dissipated energy concept in fatigue endurance
limit testing. Transportation Research Record: Journal of the Transportation Research Board, 1929(1),
165-173.
Shen, S., & Carpenter, S. H. (2007). Dissipated energy concepts for HMA performance: fatigue and
healing. COE Report No.29. Department of Civil and Environmental Engineering, University of Illinois
at Urbana-Champaign, Advanced Transportation Research and Engineering Laboratory.
Texas Department of Transportation (TxDOT) (2009) Tex-248-F: Test Procedure for Overlay Test.
Tran, N. H., Taylor, A. J., & Willis, J. R. (2012) Effect of rejuvenator on performance properties of HMA
mixtures with high RAP and RAS contents, Report 12-05, National Center for Asphalt Technology,
Auburn University, AL.
Tsai, B. W. (2001). High temperature fatigue and fatigue damage process of aggregate-asphalt mixes.
Doctoral dissertation. University of California, Berkeley.
Tsai, B. W., Harvey, J. T., & Monismith, C. L. (2005). Using the three-stage Weibull equation and tree-
based model to characterize the mix fatigue damage process. Transportation Research Record: Journal of
the Transportation Research Board, 1929(1), 227-237.
Van Dijk, W. & Visser, W. (1977) Energy approach to fatigue for pavement design, In Proceeding of
Annual Meeting of the Association of Asphalt Paving Technologist, 46, 1-40.
104
Van Dijk, W. (1975). Practical fatigue characterization of bituminous mixes. Journal of the Association of
Asphalt Paving Technologists, 44, 38-72.
Von Holdt, C., & Scullion, T. (2006). Methods of reducing joint reflection cracking: field performance
studies (FHWA/TX-06/0-4517-3). Texas Transportation Institute, Texas A&M University System.
Walubita, L. F., Faruk, A. N., Das, G., Tanvir, H. A., Zhang, J., & Scullion, T. (2012). The overlay tester:
a sensitivity study to improve repeatability and minimize variability in the test results (FHWA/TX-12/0-
6607-1). Texas Transportation Institute, Texas A&M University System.
Walubita, L. F., Jamison, B. P., Das, G., Scullion, T., Martin, A. E., Rand, D., & Mikhail, M. (2011).
Search for a laboratory test to evaluate crack resistance of hot-mix asphalt. Transportation Research
Record: Journal of the Transportation Research Board, 2210(1), 73-80.
Walubita, L. F., Umashankar, V., Hu, X., Jamison, B., Zhou, F., Scullion, T., ... Dessouky, S. H. (2010).
New generation mix-designs: laboratory testing and construction of the APT test sections (FHWA/TX-
10/0-6132-1). Texas Transportation Institute, Texas A&M University System.
Weibull, W. (1951). A statistical distribution function of wide applicability. Journal of applied
mechanics, 18(3), 293-297.
West, R. C., Timm, D. H., Willis, J. R., Powell, R. B., Tran, N. H., Watson, D. E., ? Nelson, J. (2012)
Phase IV NCAT pavement test track findings. Report 12-10, National Center for Asphalt Technology,
Auburn University, AL.
Withee, J. (2013). Implementation of the asphalt mixture performance tester (AMPT) for Superpave
validation, TPF-5(178) Project Quarterly Report (1st Quarter), Federal Highway Administration.
Yoo, P. J., & Al-Qadi, I. L. (2010). A strain-controlled hot-mix asphalt fatigue model considering low
and high cycles. International Journal of Pavement Engineering, 11(6), 565-574.
Zhou, F., & Scullion, T. (2003). Upgraded overlay tester and its application to characterize reflection
cracking resistance of asphalt mixtures (FHWA/TX-04/0-4467-1). Texas Transportation Institute, Texas
A&M University System.
Zhou, F., & Scullion, T. (2005a). Overlay tester: a rapid performance related crack resistance test
(FHWA/TX-05/0-4467-2). Texas Transportation Institute, Texas A&M University System.
Zhou, F., & Scullion, T. (2005b). Overlay tester: a simple performance test for thermal reflective cracking
(with discussion and closure). Journal of the Association of Asphalt Paving Technologists, 74.
105
Zhou, F., Hu, S., & Scullion, T. (2007a). Development and verification of the overlay tester based fatigue
cracking prediction approach (FHWA/TX-07/9-1502-01-8). Texas Transportation Institute, Texas A&M
University System.
Zhou, F., Hu, S., & Scullion, T. (2009). Overlay tester: a simple and rapid test for HMA fracture property.
Road Pavement Material Characterization and Rehabilitation selected papers from the 2009 GeoHunan
International Conference. 65-73.
Zhou, F., Hu, S., Chen, D. H., & Scullion, T. (2007b). Overlay tester: simple performance test for fatigue
cracking. Transportation Research Record: Journal of the Transportation Research Board, 2001(1), 1-8.
106
APPENDICES
107
Appendix A
AMPT Overlay Test Results of All Specimens
Table A.1 N11-3 Mixture (50%RAP+WMA Foam)
Mix No. of specimen Frequency (Hz) Maximum Opening Displacement (MOD) (mm) Nf (NLC) Nf (93%)
Nf
(Thru
Crack)
N11-3
6 0.1 0.381 116 330 221
3 0.1 0.381 123 246 N/A
2 0.1 0.381 229 487 N/A
117 0.1 0.318 885 1871 1021
40 0.1 0.318 1894 3446 2273
41 0.1 0.318 1608 3146 2612
8 0.1 0.254 2280 N/A N/A
33 0.1 0.254 4980 8916 N/A
34 0.1 0.254 5532 8780 N/A
26 1 0.381 512 1433 690
24 1 0.381 548 941 594
23 1 0.381 499 1054 581
45 1 0.318 530 2332 661
49 1 0.318 686 1718 964
116 1 0.318 806 3118 927
112 1 0.254 4948 12204 5258
114 1 0.254 4988 9260 5628
124 1 0.254 2848 4804 3421
108
Table A.2 S8-3 Mixture (0%RAP+HMA)
Mix No. of specimen Frequency (Hz) Maximum Opening Displacement (MOD) (mm) Nf (NLC) Nf (93%)
Nf
(Thru
Crack)
S8-3
69 1 0.381 895 1837 1190
53 1 0.381 669 1202 772
54 1 0.381 722 1049 849
55 1 0.318 1672 2432 1822
61 1 0.318 2108 3854 2463
62 1 0.318 1372 2672 1555
64 1 0.254 5756 7740 6689
67 1 0.254 7204 9748 7727
68 1 0.254 9076 12412 10584
Table A.3 N10-3 Mixture (50%RAP+HMA)
Mix No. of specimen Frequency (Hz) Maximum Opening Displacement (MOD) (mm) Nf (NLC) Nf (93%)
Nf
(Thru
Crack)
N10-3
73 1 0.381 96 291 178
74 1 0.381 71 177 122
75 1 0.381 253 670 329
76 1 0.318 276 1036 379
79 1 0.318 301 1192 475
80 1 0.318 467 1161 636
81 1 0.254 936 2404 1110
70 1 0.254 1824 6364 2063
72 1 0.254 2072 6552 2490
109
Table A.4 S10-3 Mixture (WMA Foam)
Mix No. of specimen Frequency (Hz) Maximum Opening Displacement (MOD) (mm) Nf (NLC) Nf (93%)
Nf
(Thru
Crack)
S10-3
85 1 0.381 1110 1385 1296
86 1 0.381 761 1326 991
88 1 0.381 784 1489 1346
90 1 0.318 1876 2532 1939
91 1 0.318 2406 3886 N/A
92 1 0.318 1804 2418 2156
93 1 0.254 5520 6932 6241
89 1 0.254 3428 4720 4289
95 1 0.254 4300 6096 5379
Table A.5 S11-3 Mixture (WMA Additive)
Mix No. of specimen Frequency (Hz) Maximum Opening Displacement (MOD) (mm) Nf (NLC) Nf (93%)
Nf
(Thru
Crack)
S11-3
101 1 0.381 1372 2382 1756
105 1 0.381 807 1168 975
107 1 0.381 931 1307 979
108 1 0.318 2028 2632 2256
110 1 0.318 2680 4636 3390
111 1 0.318 3672 5604 3999
121 1 0.254 4044 5732 5198
122 1 0.254 5132 8204 5867
123 1 0.254 5132 7924 6334
110
Appendix B
Peak Load Curve Labeled with Nf(NLC), Nf(Thru Crack), and Nf(93%)
(48 figures in total for the specimens with good video recorded)
Figure B.1
Figure B.2
111
Figure B.3
Figure B.4
Figure B.5
112
Figure B.6
Figure B.7
Figure B.8
113
Figure B.9
Figure B.10
Figure B.11
114
Figure B.12
Figure B.13
Figure B.14
115
Figure B.15
Figure B.16
Figure B.17
116
Figure B.18
Figure B.19
Figure B.20
117
Figure B.21
Figure B.22
Figure B.23
118
Figure B.24
Figure B.25
Figure B.26
119
Figure B.27
Figure B.28
Figure B.29
120
Figure B.30
Figure B.31
Figure B.32
121
Figure B.33
Figure B.34
Figure B.35
122
Figure B.36
Figure B.37
Figure B.38
123
Figure B.39
Figure B.40
Figure B.41
124
Figure B.42
Figure B.43
Figure B.44
125
Figure B.45
Figure B.46
Figure B.47
126
Figure B.48
127
Appendix C
Minitab Outputs (Two-factor ANOVA with Tukey?s Test, N11-3 Mix)
C.1 Analysis result using Nf(NLC) failure points
General Linear Model: Nf1 versus frequency, MOD
Factor Type Levels Values
frequency fixed 2 0.1, 1.0
MOD fixed 3 0.254, 0.318, 0.381
Analysis of Variance for Nf1, using Adjusted SS for Tests
Source DF Seq SS Adj SS Adj MS F P
frequency 1 0.02857 0.02857 0.02857 1.32 0.273
MOD 2 4.07261 4.07261 2.03630 94.26 0.000
frequency*MOD 2 0.57048 0.57048 0.28524 13.20 0.001
Error 12 0.25923 0.25923 0.02160
Total 17 4.93090
S = 0.146979 R-Sq = 94.74% R-Sq(adj) = 92.55%
Unusual Observations for Nf1
Obs Nf1 Fit SE Fit Residual St Resid
7 3.35793 3.59935 0.08486 -0.24141 -2.01 R
R denotes an observation with a large standardized residual.
Grouping Information Using Tukey Method and 95.0% Confidence
frequency MOD N Mean Grouping
1.0 0.254 3 3.6 A
0.1 0.254 3 3.6 A
0.1 0.318 3 3.1 B
1.0 0.318 3 2.8 B C
1.0 0.381 3 2.7 C
0.1 0.381 3 2.2 D
Means that do not share a letter are significantly different.
Tukey 95.0% Simultaneous Confidence Intervals
Response Variable Nf1
All Pairwise Comparisons among Levels of frequency*MOD
frequency = 0.1
MOD = 0.254 subtracted from:
frequency MOD Lower Center Upper --------+---------+---------+--------
0.1 0.318 -0.859 -0.456 -0.053 (---*---)
128
0.1 0.381 -1.831 -1.428 -1.025 (---*---)
1.0 0.254 -0.387 0.016 0.419 (---*---)
1.0 0.318 -1.180 -0.777 -0.374 (---*---)
1.0 0.381 -1.287 -0.884 -0.481 (---*---)
--------+---------+---------+--------
-1.0 0.0 1.0
frequency = 0.1
MOD = 0.318 subtracted from:
frequency MOD Lower Center Upper
0.1 0.381 -1.375 -0.9721 -0.5691
1.0 0.254 0.069 0.4721 0.8752
1.0 0.318 -0.724 -0.3212 0.0819
1.0 0.381 -0.831 -0.4282 -0.0251
frequency MOD --------+---------+---------+--------
0.1 0.381 (---*---)
1.0 0.254 (---*---)
1.0 0.318 (---*---)
1.0 0.381 (---*---)
--------+---------+---------+--------
-1.0 0.0 1.0
frequency = 0.1
MOD = 0.381 subtracted from:
frequency MOD Lower Center Upper --------+---------+---------+--------
1.0 0.254 1.0412 1.4442 1.8473 (---*---)
1.0 0.318 0.2478 0.6509 1.0540 (----*---)
1.0 0.381 0.1409 0.5440 0.9471 (---*---)
--------+---------+---------+--------
-1.0 0.0 1.0
frequency = 1.0
MOD = 0.254 subtracted from:
frequency MOD Lower Center Upper
1.0 0.318 -1.196 -0.7933 -0.3902
1.0 0.381 -1.303 -0.9002 -0.4972
frequency MOD --------+---------+---------+--------
1.0 0.318 (---*---)
1.0 0.381 (---*---)
--------+---------+---------+--------
-1.0 0.0 1.0
frequency = 1.0
MOD = 0.318 subtracted from:
frequency MOD Lower Center Upper
1.0 0.381 -0.5100 -0.1069 0.2961
frequency MOD --------+---------+---------+--------
1.0 0.381 (---*---)
--------+---------+---------+--------
-1.0 0.0 1.0
129
C.2 Analysis result using Nf(93%) failure points
General Linear Model: N1(93%) versus Frequency, MOD
Factor Type Levels Values
Frequency fixed 2 0.1, 1.0
MOD fixed 3 0.254, 0.318, 0.381
Analysis of Variance for N1(93%), using Adjusted SS for Tests
Source DF Seq SS Adj SS Adj MS F P
Frequency 1 0.20118 0.07877 0.07877 3.88 0.074
MOD 2 3.43494 3.49224 1.74612 86.08 0.000
Frequency*MOD 2 0.31766 0.31766 0.15883 7.83 0.008
Error 11 0.22313 0.22313 0.02028
Total 16 4.17691
S = 0.142424 R-Sq = 94.66% R-Sq(adj) = 92.23%
Grouping Information Using Tukey Method and 95.0% Confidence
Frequency MOD N Mean Grouping
0.1 0.254 2 3.9 A
1.0 0.254 3 3.9 A
0.1 0.318 3 3.4 B
1.0 0.318 3 3.4 B
1.0 0.381 3 3.1 B
0.1 0.381 3 2.5 C
Means that do not share a letter are significantly different.
Tukey 95.0% Simultaneous Confidence Intervals
Response Variable N1(93%)
All Pairwise Comparisons among Levels of Frequency*MOD
Frequency = 0.1
MOD = 0.254 subtracted from:
Frequency MOD Lower Center Upper
0.1 0.318 -0.954 -0.511 -0.0680
0.1 0.381 -1.858 -1.415 -0.9714
1.0 0.254 -0.478 -0.035 0.4079
1.0 0.318 -1.024 -0.581 -0.1382
1.0 0.381 -1.339 -0.896 -0.4528
Frequency MOD ---------+---------+---------+-------
0.1 0.318 (----*---)
0.1 0.381 (----*---)
1.0 0.254 (----*---)
1.0 0.318 (---*----)
1.0 0.381 (---*---)
---------+---------+---------+-------
-1.0 0.0 1.0
Frequency = 0.1
130
MOD = 0.318 subtracted from:
Frequency MOD Lower Center Upper
0.1 0.381 -1.300 -0.9034 -0.5070
1.0 0.254 0.080 0.4759 0.8722
1.0 0.318 -0.467 -0.0702 0.3262
1.0 0.381 -0.781 -0.3848 0.0115
Frequency MOD ---------+---------+---------+-------
0.1 0.381 (---*---)
1.0 0.254 (---*---)
1.0 0.318 (---*---)
1.0 0.381 (---*---)
---------+---------+---------+-------
-1.0 0.0 1.0
Frequency = 0.1
MOD = 0.381 subtracted from:
Frequency MOD Lower Center Upper
1.0 0.254 0.9829 1.3792 1.7756
1.0 0.318 0.4369 0.8332 1.2296
1.0 0.381 0.1222 0.5186 0.9149
Frequency MOD ---------+---------+---------+-------
1.0 0.254 (---*---)
1.0 0.318 (---*---)
1.0 0.381 (---*---)
---------+---------+---------+-------
-1.0 0.0 1.0
Frequency = 1.0
MOD = 0.254 subtracted from:
Frequency MOD Lower Center Upper
1.0 0.318 -0.942 -0.5460 -0.1497
1.0 0.381 -1.257 -0.8607 -0.4643
Frequency MOD ---------+---------+---------+-------
1.0 0.318 (---*---)
1.0 0.381 (---*---)
---------+---------+---------+-------
-1.0 0.0 1.0
Frequency = 1.0
MOD = 0.318 subtracted from:
Frequency MOD Lower Center Upper
1.0 0.381 -0.7110 -0.3147 0.08169
Frequency MOD ---------+---------+---------+-------
1.0 0.381 (---*---)
---------+---------+---------+-------
-1.0 0.0 1.0
131
Appendix D
EXCEL Outputs (F-test for Comparing Variances at Two Frequencies, N11-3 Mix)
D.1 For Nf(NLC) failure points D.2 For Nf(93%) failure points
Regardless of MOD Regardless of MOD
Variable 1 Variable 2 Variable 1 Variable 2
Mean 1960.778 1818.333 Mean 3402.75 4096
Variance 4129641 3741189 Variance 12804751 16116281
Observations 9 9 Observations 8 9
df 8 8 df 7 8
F 1.103831 F 0.794523
P(F<=f) one-tail 0.446151 P(F<=f) one-tail 0.387303
F Critical one-tail 3.438101 F Critical one-tail 0.268404
MOD = 0.381 mm MOD = 0.381 mm
Variable 1 Variable 2 Variable 1 Variable 2
Mean 156 519.6667 Mean 354.3333 1142.667
Variance 4009 644.3333 Variance 14964.33 66412.33
Observations 3 3 Observations 3 3
df 2 2 df 2 2
F 6.221935 F 0.225325
P(F<=f) one-tail 0.138467 P(F<=f) one-tail 0.18389
F Critical one-tail 19 F Critical one-tail 0.052632
MOD = 0.318 mm MOD = 0.318 mm
Variable 1 Variable 2 Variable 1 Variable 2
Mean 1462.333 674 Mean 2821 2389.333
Variance 270434.3 19152 Variance 699375 492465.3
Observations 3 3 Observations 3 3
df 2 2 df 2 2
F 14.12042 F 1.420151
P(F<=f) one-tail 0.066136 P(F<=f) one-tail 0.413197
F Critical one-tail 19 F Critical one-tail 19
132
(Continued)
D.1 For Nf(NLC) failure points D.2 For Nf(93%) failure points
MOD = 0.254 mm MOD = 0.254 mm
Variable 1 Variable 2 Variable 1 Variable 2
Mean 4264 4261.333 Mean 8848 8756
Variance 3028368 1498533 Variance 9248 13880512
Observations 3 3 Observations 2 3
df 2 2 df 1 2
F 2.020888 F 0.000666
P(F<=f) one-tail 0.331028 P(F<=f) one-tail 0.018249
F Critical one-tail 19 F Critical one-tail 0.005013
133
Appendix E
Minitab Output (T-test for Comparing the Means of Coefficients, ??2? and ??2?)
Test and CI for Two Variances: ?2 (BBF), ?2 (OT)
Method
Null hypothesis Sigma(?2 (BBF)) / Sigma(?2 (OT)) = 1
Alternative hypothesis Sigma(?2 (BBF)) / Sigma(?2 (OT)) not = 1
Significance level Alpha = 0.05
Statistics
Variable N StDev Variance
?2 (BBF) 5 1.035 1.072
?2 (OT) 5 1.088 1.184
Ratio of standard deviations = 0.951
Ratio of variances = 0.905
95% Confidence Intervals
CI for
Distribution CI for StDev Variance
of Data Ratio Ratio
Normal (0.307, 2.948) (0.094, 8.694)
Continuous ( *, 4.666) ( *, 21.770)
Tests
Test
Method DF1 DF2 Statistic P-Value
F Test (normal) 4 4 0.91 0.925
Levene's Test (any continuous) 1 8 0.02 0.893
Two-Sample T-Test and CI: ?2 (BBF), ?2 (OT)
Two-sample T for ?2 (BBF) vs ?2 (OT)
N Mean StDev SE Mean
?2 (BBF) 5 5.21 1.04 0.46
?2 (OT) 5 4.96 1.09 0.49
Difference = mu (?2 (BBF)) - mu (?2 (OT))
Estimate for difference: 0.246
95% CI for difference: (-1.303, 1.795)
T-Test of difference = 0 (vs not =): T-Value = 0.37 P-Value = 0.724 DF = 8
Both use Pooled StDev = 1.0620