CHARACTERISTICS AND PREDICTION OF THE LOW TEMPERATURE INDIRECT
TENSILE STRENGTHS OF MICHIGAN ASPHALT MIXTURES
By
Michael Krcmarik

A THESIS
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
Civil Engineering – Master of Science
2013

ABSTRACT
CHARACTERISTICS AND PREDICTION OF THE LOW TEMPERATURE INDIRECT
TENSILE STRENGTHS OF MICHIGAN ASPHALT MIXTURES
By
Michael Krcmarik
Thermal cracking is the predominant flexible pavement distress in northern climates,
causing transverse cracking perpendicular to the direction of traffic. The indirect tensile (IDT)
strength test is currently the most widely used method to characterize thermal cracking
susceptibility and is an input to the Pavement ME Design software (formerly known as the
Mechanistic- Empirical Design Guide (MEPDG). In Pavement ME Design when laboratory IDT
strength testing data is not available to designers it is predicted using mixture volumetrics and
performance grade (PG) of the binder. The purpose of this research is to examine the IDT
strength characteristics of flexible pavement mixtures commonly used by the Michigan
Department of Transportation (MDOT) and to develop improved prediction methods for IDT
strength. Laboratory testing of 62 unique MDOT mixtures showed Pavement ME Design
software generally over predicted IDT strength. Three models were developed to improve the
accuracy of IDT strength prediction. The first model consists of local calibration of the current
IDT strength Pavement ME Design predictive model for MDOT mixes. The second model
consists of a new statistical model developed based on job mix information to predict low
temperature IDT strength. The third model consists of an artificial neural network developed to
predict low temperature strength from job mix information. All three models showed increased
prediction performance when compared to Pavement ME Design IDT strength prediction. With
these models, a more accurate low temperature prediction of IDT strength is available to
pavement

designers

in

Michigan

using

readily

available

job

mix

information.

TABLE OF CONTENTS
LIST OF TABLES .......................................................................................................................... v
LIST OF FIGURES ....................................................................................................................... vi
1. INTRODUCTION ...................................................................................................................... 1
1.1 Objective................................................................................................................................ 3
1.2 Outline ................................................................................................................................... 3
2. LITERATURE REVIEW ........................................................................................................... 4
2.1 Motivation ............................................................................................................................. 4
2.2 Background of the Indirect Tensile Strength Test ................................................................ 4
2.3 Current Indirect Tensile Strength Testing Procedure ............................................................ 7
2.4 Calculation of Indirect Tensile Strength According to AASHTO T-322 ........................... 10
2.5 Calculation of Indirect Tensile Strength without Deformation Monitoring........................ 11
2.6 Determination of Fracture Work from Indirect Tensile Strength Testing........................... 12
2.7 Relevance of Indirect Tensile Strength to Pavement ME Design ....................................... 14
2.8 Pavement ME Design IDT Strength Prediction .................................................................. 16
2.9 Factors Affecting Mixture Indirect Tensile Strength .......................................................... 17
3. METHODS ............................................................................................................................... 19
3.1 Introduction ......................................................................................................................... 19
3.2 Mixtures Used ..................................................................................................................... 19
3.3 Specimen Preparation .......................................................................................................... 23
3.4 Indirect Strength Testing Procedures .................................................................................. 24
3.4.1 Testing Temperature ..................................................................................................... 24
3.4.2 Use of LVDTs .............................................................................................................. 24
3.4.3 Environmental Chamber ............................................................................................... 25
4. RESULTS OF LABORATORY INDIRECT TENSILE TESTING ........................................ 27
4.1 Indirect Tensile Strength of Michigan Mixtures ................................................................. 27
4.2 Fracture Work of Michigan Mixtures ................................................................................. 30
4.3 MDOT Mix Designation and IDT Strength ........................................................................ 38
4.4 Superpave PG and IDT Strength ......................................................................................... 40
4.5 Warm Mix Asphalt IDT Properties ..................................................................................... 44
5. INDIRECT TENSILE STRENGTH PREDICTION MODELS............................................... 47
5.1 Introduction to Indirect Tensile Strength Prediction for Pavement ME Design ................. 47
5.2 Model Evaluation ................................................................................................................ 49
5.3 Local Calibration of Pavement ME Design Strength Prediction Model ............................. 50
5.4 Linear Strength Prediction Model ....................................................................................... 55
5.5 Artificial Neural Network Prediction Model ...................................................................... 62
5.5.1 Structure of the IDT Strength ANN ............................................................................. 63
5.5.2 Overview of IDT Strength Prediction with the ANN ................................................... 63
iii

5.5.2 Training of the IDT Strength ANN .............................................................................. 65
5.5.3 Testing of the IDT Strength ANN ................................................................................ 68
6. CONCLUSIONS AND RECOMMENDATIONS ................................................................... 70
APPENDICES .............................................................................................................................. 72
APPENDIX A: MIX PROPERTIES AND VOLUMETRICS OF MIXTURES TESTED ...... 73
APPENDIX B: IDT STRENGTH, FRACTURE WORK, AND VOLUMTERICS OF
SPECIMENS TESTED ............................................................................................................. 85
REFERENCES ........................................................................................................................... 102

iv

LIST OF TABLES
Table 1 HMAs tested for IDT strength ......................................................................................... 20
Table 2 HMAs tested for IDT strength (GGSP and LVSP Mixtures) .......................................... 22
Table 3 HMAs tested for IDT strength (SUPERPAVE) – Mixtures that do not follow MDOT
specifications but are permitted to be used ................................................................................... 23
Table 4 HMAs tested for IDT strength (GGSP and LVSP Mixtures) - Mixtures that do not follow
MDOT specifications but are permitted to be used ...................................................................... 23
Table 5 Summary of IDT strength values for the State of Michigan asphalt mixtures ................ 28
Table 6 Summary of total work values for the State of Michigan asphalt mixtures .................... 31
Table 7 Summary of pre fracture work values for the State of Michigan asphalt mixtures ......... 33
Table 8 Summary of post fracture work values for the State of Michigan asphalt mixtures ....... 35
Table 9 Binder and Mixture Properties of 36 MDOT Mixtures used in Michigan Calibration of
the Pavement ME Design Strength Prediction Model Developed by Witczak ............................ 51
Table 10 Comparison of the original and Michigan calibrated Pavement ME Design IDT strength
Model Calibration Coefficients..................................................................................................... 52
Table 11 Comparison of model performance evaluation parameters measured for Original
Pavement ME Design and Calibrated IDT strength prediction models for 36 MDOT asphalt
mixtures......................................................................................................................................... 55
Table 12 MDOT JMF parameters found to be significantly correlated with measured IDT
strength using a Pearson Correlation analysis. Correlation significance, either at the .01 or .05
level, and the relationship of the parameter, either positive (+) or negative (-), is also listed ...... 56
Table 13 Comparison of performance criteria for the original Pavement ME Design and linear
IDT strength prediction models for commonly used MDOT asphalt mixtures ............................ 61
Table 14 Overview of specimens used and correlation coefficients for each stage of IDT ANN
development .................................................................................................................................. 69
Table 15 Mixture properties and volumterics of mixtures tested ................................................. 74
Table 16 IDT Strength, Fracture Work, and Air Voids of Specimens Tested .............................. 86
v

LIST OF FIGURES
Figure 1 Examples of typical thermal cracking distress in flexible pavements evidenced by
transverse cracking in the direction perpendicular to travel. For interpretation of the references to
color in this and all other figures, the reader is referred to the electronic version of this thesis. ... 1
Figure 2 Development of stress in a diametrically loaded specimen during the IDT strength test 5
Figure 3 IDT strength test specimen at failure................................................................................ 6
Figure 4 Overview of the IDT strength specimen fabrication and testing process ......................... 9
Figure 5 Typical (Y-X) versus time curve depicting first peak time ............................................ 10
Figure 6 Typical IDT stress versus strain curve depicting pre and post energy ........................... 13
Figure 7 IDT test system consisting of an axial loading device with external environmental
chamber ......................................................................................................................................... 26
Figure 8 Total fracture work versus IDT strength relationship .................................................... 38
Figure 9 Laboratory measured IDT strength for MDOT Mix ESAL designation categories for
leveling and top course pavement layers ...................................................................................... 39
Figure 10 Laboratory measured total fracture work for MDOT Mix ESAL designation categories
for leveling and top course pavement layers................................................................................. 40
Figure 11 IDT strength versus Low Temperature PG relationship............................................... 41
Figure 12 IDT strength for high PG characterization of Michigan asphalt mixtures ................... 41
Figure 13 Fracture work for low temperature Superpave PG characterization of Michigan asphalt
mixtures......................................................................................................................................... 42
Figure 14 Fracture work for high temperature Superpave PG characterization of Michigan
asphalt mixtures ............................................................................................................................ 43
Figure 15 IDT strength for comparable WMA and HMA mixtures ............................................. 44
Figure 16 IDT fracture work for comparable WMA and HMA mixtures .................................... 45
Figure 17 IDT post fracture work for comparable WMA and HMA mixtures ............................ 46
vi

Figure 18 Effect of IDT strength input in Pavement ME Design Level 3 thermal cracking
analysis for a 4”, PG 58-22 flexible pavement constructed in Detroit, Michigan. ....................... 48
Figure 19 Original Pavement ME Design IDT Strength Model for 36 MDOT mixtures with
respect to the LOE ........................................................................................................................ 53
Figure 20 Michigan Calibrated Pavement ME Design IDT Strength Model for 36 MDOT
mixtures with respect to the LOE ................................................................................................. 54
Figure 21 IDT strength predicated by Pavement ME Design software versus laboratory measured
IDT strength for commonly used State of Michigan asphalt mixtures ......................................... 59
Figure 22 IDT strength predicated during calibration by newly developed linear model versus
laboratory measured IDT strength for commonly used State of Michigan asphalt mixtures ....... 60
Figure 23 IDT strength predicated during testing by newly developed linear model versus
laboratory measured IDT strength for commonly used State of Michigan asphalt mixtures ....... 60
Figure 24 IDT strength predicated for all specimens by newly developed linear model versus
laboratory measured IDT strength for commonly used State of Michigan asphalt mixtures ....... 61
Figure 25 Structure of the ANN model developed for prediction of IDT strength for Michigan
asphalt mixtures ............................................................................................................................ 63
Figure 26 Reduction in mean squared error of laboratory measured and ANN predicted IDT
strength values during training, validation, and testing stages of ANN development .................. 66
Figure 27 ANN predicted IDT strength versus measured IDT strength (base 10) for the training,
validation, testing, and all data used in ANN development .......................................................... 67
Figure 28 ANN Predicated versus measured IDT strength values for all mixtures used in ANN
development .................................................................................................................................. 68

vii

1. INTRODUCTION
Thermal cracking is the predominant pavement distress in the northern United States and
Canada. At low temperatures, cooling of a flexible pavement causes contraction of the aggregate
and asphalt binder, creating thermal stresses which manifest as transverse cracking perpendicular
to the direction of travel (Figure 1). Thermal cracking leads to additional pavement deterioration
mechanisms including water seeping into the base/subbase, pumping, frost heave, and ultimately
deterioration of the road leading to premature maintenance.

Figure 1 Examples of typical thermal cracking distress in flexible pavements evidenced
by transverse cracking in the direction perpendicular to travel. For interpretation of
the references to color in this and all other figures, the reader is referred to the
electronic version of this thesis.

The identification and evaluation of mix design factors than can increase thermal cracking
resistance is of extreme interest to state agencies seeking to improve pavement performance. The
low temperature indirect tensile (IDT) strength is one measure of an asphalt mixture’s resistance
to thermal cracking and is measured by the IDT strength test. The IDT strength test is currently
the most widely used thermal cracking mixture characterization method.

1

The low temperature IDT strength test is conducted by applying displacement controlled
loading along the direction of diameter in a cylindrical specimen until failure. The stress at
failure is taken as the low temperature IDT strength. Low temperature IDT strength is directly
related to the expected thermal cracking pavement performance in the field. Based on this
concept the Pavement ME Design software (i.e., M-E PDG) utilizes semi-mechanistic and semiempirical models to predict pavement distresses over time, such as thermal cracking.
As a result of research under NCHRP Project 1-37A, the Pavement ME Design software is
the most recently developed design guide for newly constructed and rehabilitated pavement
designs. The Pavement ME Design software requires traffic, climate, and material inputs to
predict pavement distresses and accurate measurement of these inputs is necessary for successful
prediction. For thermal cracking prediction in flexible pavements, the Pavement ME Design
software requires material inputs of mixture IDT strength and creep compliance values to predict
thermal cracking per unit length over time. The IDT strength and creep compliance
characterization of the asphalt mixture is required for Levels 1, 2, and 3. Inputs into the
Pavement ME Design are classified according to a three level system (Levels 1, 2, and 3), which
allow pavement engineers to select the level of design accuracy. A Level 1 analysis requires the
most detailed characterization of material inputs and can generally be thought to predict
pavement distresses most accurately. A Level 3 analysis requires the least detailed
characterization of material inputs; as a result the accuracy of the distress predictions can be low.
Many state transportation agencies, including the Michigan Department of Transportation
(MDOT), do not have testing programs to measure the required Pavement ME Design Level 1
material inputs for thermal cracking analysis and they are instead predicted by Pavement ME
Design using predictive equations at the expense of accuracy.
2

1.1 Objective
The first objective of this study was to characterize the IDT strength and fracture work of
asphalt mixtures commonly used in the State of Michigan. It is important to understand the low
temperature fracture properties and if they can be predicted from or are related to current
pavement design frameworks, such as Superpave Performance Grading or MDOT mix
designation.
The second objective was to examine the accuracy of the predictive equations used by the
Pavement ME Design software in predicting low temperature IDT strength and develop
improved prediction equations/models if necessary. This is important for accurate prediction of
asphalt thermal cracking distress and subsequently successful implementation of the Pavement
ME Design software by MDOT.
1.2 Outline
This thesis is organized as follows: Chapter 2 presents a literature review on the
background of the IDT creep and strength tests and prediction of IDT strength in Pavement ME
Design software. Second, a discussion on the relevance of IDT strength to the Pavement ME
Design software and how it is used in thermal cracking prediction is given. Finally, Chapter 2
also reviews current research on mix design factors and volumetrics influencing IDT strength.
Chapter 3 presents the materials used in this research and the testing protocol followed. Chapters
4 and 5 present the results of the IDT strength laboratory testing and development of IDT
strength predictive models, respectively. Chapter 6 presents the conclusions of this study and
recommendations for future work.

3

2. LITERATURE REVIEW
2.1 Motivation
Thermal cracking is the predominant asphalt pavement distress in northern climates such
as the State of Michigan. As the Pavement ME Design becomes state of the practice for the
design of new and rehabilitated pavements it is in the best interest of transportation agencies to
accurately characterize material inputs in order to successfully predict pavement distresses such
as thermal cracking. Review of literature on asphalt mixtures used in the State of Michigan
showed a need for low temperature mixture characterization for use in pavement design.
Additionally preliminary analysis of Pavement ME Design IDT strength prediction showed poor
prediction performance for Michigan mixtures. This study aims to characterize the low
temperature strength properties of Michigan asphalt mixtures. Secondly this study aims to
predict these low temperature strength properties. Accurate prediction of material properties such
as IDT strength is important for successful thermal cracking distress prediction and subsequent
successful implementation of the Pavement ME Design software.

2.2 Background of the Indirect Tensile Strength Test
A material’s IDT strength is a measure of its tensile strength when loaded diametrically
across a circular specimens’ cross-section. Figure 2 illustrates the loading scheme and resulting
stress distribution within the IDT strength test sample.

4

Load
Load

Compression
Compression

Tension
Tension

Y
σσ
Xx

σσyY
X

X

Y
Stress distribution
acrossdiameter
diameter
Stress distribution
across
Load

Load

Figure 2 Development of stress in a diametrically loaded specimen during the IDT strength
test

Loading applied along the circular specimens’ diameter causes tensile forces to develop
perpendicular to the direction of loading, ultimately resulting in a tensile failure (Figure 3). The
IDT strength test was first used to determine the tensile strength of wood and rock materials in
what is commonly known as the Brazilian Test [26]. In 1943 Carneiro [13] applied the IDT
strength test to concrete and it is still used as the primary method to determine concrete tensile
strength today. In the early 1990’s work began by Roque [8] to apply the IDT test to asphalt
mixtures and as a result the first procedure for low temperature IDT creep and strength
5

characterization of asphalt mixtures was developed under the first Strategic Highway research
Program (SHRP) [7][8].

As a result of this work the procedure was then codified as an

AASHTO standard, AASHTO T-322, “Standard Method of Test for Determining the Creep
Compliance and Strength of Hot-Mix Asphalt (HMA) Using the Indirect Tensile Test Device”
[1]. In the late 1990’s the IDT strength test underwent further examination by the Federal
Highway Administration (FHWA) during the development of Superpave mix design protocol.
Due to its accuracy and durability, the IDT strength and creep test was identified as a simple
performance test for low temperature cracking in HMA mix design. The IDT strength and creep
was then also selected as a materials characterization test in NCHRP Project 1-37A due to its
ability to predict a mixture’s resistance to thermal cracking as evidenced by its good correlation
to field thermal cracking data [10].

Figure 3 IDT strength test specimen at failure

6

Today the IDT strength test is still the most widely used strength test to characterize a
mixture’s resistance to thermal cracking. Other tests exist to characterize the thermal cracking
resistance of asphalt mixtures each with their own advantages and disadvantage and include the
Thermal Stress Restrained Specimen Test (TSRST) [21], Semi-Circular Bend (SCB) Test [24],
Modified IDT, and Disk-Shaped Compact Tension (DCT) Test [27]. These methods also
measure mixture tensile strength to characterize thermal cracking resistance, but differ mostly in
specimen geometry, deformation monitoring methods, and loading application in an attempt to
rectify perceived shortcomings in the IDT creep and strength test [27]. Yet currently the IDT
creep and strength tests are still considered the most promising parameters for predicting the low
temperature performance of asphalt mixtures [10].
2.3 Current Indirect Tensile Strength Testing Procedure
The standard test method for the IDT strength is the AASHTO T-322 “Determining the
Creep Compliance and Strength of Hot-Mix Asphalt (HMA) Using the Indirect Tensile Test
Device.” The AASHTO T-322 contains detailed procedures to determine tensile creep
compliance, tensile strength, and Poisson’s ratio of an HMA mixture [1]. The summary of the
method to determining the tensile strength, commonly known as the IDT strength, is as follows:
Bulk laboratory molded specimens are compacted from loose mixture in a Superpave Gyratory
Compactor (SGC). Cylindrical specimens are then cut from the SGC compacted specimens to a
diameter of 150

9 mm and to a height of 38 to 50 mm (Figure 4). Bulk Specific Gravity and

air voids of each specimen are determined and only specimens meeting air voids of 7

.5% are

selected for testing. Once specimens are fabricated to geometric and volumetric criteria two
linear variable differential transducers (LVDTs) are attached to each of the two specimen’s faces
with the use of mounting gauges and epoxy (Figure 4). Specimens are then conditioned in an
7

environmental chamber at the test temperature for 3

1 hours prior to testing. A test temperature

of 0°C or less is used for thermal cracking analysis, however if the analysis is used for
Superpave design, test temperatures of 0, -10, and -20°C are recommended.
After conditioning, the specimen is placed into a testing frame located inside an Indirect
Tensile Test System (Figure 4, Step 3). The IDT Test System consists of an axial loading device,
environmental chamber, and a control and data acquisition system. At the test temperature, load
is applied to the specimen at a rate of 12.5 mm of vertical ram movement per minute. During
load application vertical and horizontal deformations on both faces of the specimen and the load
magnitude are recorded. Displacement controlled loading is applied until the load starts to
decrease, at which point strength test is complete. The desired failure mode consists of a vertical
crack running along the length of the specimen’s diameter in line with the direction of loading
(Figure 3 and Figure 4).

8

Step 1) Bulk specimens are
compacted from loose mixture
samples using the SGC

Step 2) Compacted specimens
are cut to dimension and
volumetric properties measured

Step 3) Specimens are mounted
with LVDTs and conditioned at
the testing temperature

Step 4) Load is applied until
failure (LVDTs removed for
display purposes)

Figure 4 Overview of the IDT strength specimen fabrication and testing
process

9

2.4 Calculation of Indirect Tensile Strength According to AASHTO T-322
AASHTO T-322 defines failure as the point when vertical deformations (Y) minus
horizontal deformations (X) (as measured by the LVDTs) reach a maximum value. This time is
called first peak time and the load at this time is called the first failure load (Figure 5).

Determination of peak failure time

50

Side 1

Y-X (μm)

40

Side 2

Side 2 Y-X
peaks first

30
20
10

t

0

0

1

2
Time (seconds)

3

peak

4

Figure 5 Typical (Y-X) versus time curve depicting first peak time

The failure load is then used along with specimen geometry to determine the tensile strength.
The procedure is as follows.
1. Determine failure time, tf, for both faces of the specimen, defined as the time
when vertical deformation minus horizontal deformation reaches a maximum
value. Take the shortest tf.
2. Obtain the failure load, Pf, at time tf.
3. Calculate the IDT strength, St.
(1)

10

Where,
bn = average thickness of the specimen
Dn = average diameter of the specimen

2.5 Calculation of Indirect Tensile Strength without Deformation Monitoring
Under NCHRP 530 report [10] AASHTO T-322 was thoroughly examined in an effort to
first validate and secondly determine possible improvements to the test. One of the suggested
improvements proposed in NCHRP 530 report was IDT strength testing without the use of
LVDTs to monitor deformations. LVDTs were initially incorporated into AASHTO T-322
because the precise moment of failure during the IDT test is difficult to determine due to the
often slow specimen failure and ability of the specimen to carry significant load even after cracks
become visible along the specimen face. Despite the accuracy and precision of the exact failure
moment determination with the LVDTs testing at state agencies, the FHWA, and regional
Superpave Centers reported feasibility issues with using the LVDTs. LVDTs were found to be
difficult to keep in place and due to the sometimes explosive nature of specimen failure, the
expensive and delicate LVDTs were at risk to be damaged during testing, potentially
jeopardizing overall reliability and accuracy of the IDT strength test. As a result of feedback
from testing centers, an empirical relationship was found between the true (corrected) and
unninstrumented (uncorrected) strength values and evaluated in NCHRP 530 report [10]
(Equation 2). The empirical equation relating corrected and uncorrected IDT strength values was
found to be accurate and able to predict true strength reasonably well from uninstrumented IDT
strength as compared to LVDT instrumented testing. For practical purposes the IDT strength
testing that serves at the basis of this thesis did not employ LVDTs during testing and Equation
11

2, developed by NCHRP-530 researchers, was used to estimate the true strength (instrumented)
from the uninstrumented strength. The strength at maximum load is termed the uncorrected
strength (Equation 2).
True Tensile Strength (psi) = [0.781 x Uncorrected IDT Strength (psi)] + 38

(2)

2.6 Determination of Fracture Work from Indirect Tensile Strength Testing

The IDT strength test can also be used to measure a mixture’s fracture energy [22] [25]
and fracture work [39]. Fracture energy of a mixture is defined as the area under the stress versus
strain curve while similarly fracture work is the area under the load versus horizontal
displacement curve. Total fracture energy consists of pre-peak energy (fracture energy measured
until failure), and post-peak fracture energy (fracture energy measured after failure) depicted in
Figure 6 [40].

12

Typical pre and post fracture ernergies

450

Specimen
Failure

400
Pre Fracture
Energy

350
Stress (psi)

300

250

Post Fracture
Energy

200
150
100

50
0
0

400

800
1200
Strain (με)

1600

2000

2400

Figure 6 Typical IDT stress versus strain curve depicting pre and post energy

Pre-peak fracture energy is associated with crack initiation while post-peak fracture
energy is associated with crack propagation [40]. High pre-peak fracture energy would be
indicative of greater resistance to thermal cracking initiation, while high post-peak fracture
energy would be associated with a lower rate of thermal cracking propagation. A mixture high in
fracture energy, pre or post, would generally be expected to exhibit lower rates of thermal
cracking compared to a mixture with lower fracture energy.
In this thesis fracture work was used to characterize mixture thermal cracking resistance
instead of fracture energy. Fracture work measured by the IDT test has been shown to correlate
well with field performance whereas fracture energy has been shown not to correlate well with
field performance [39]. This is in part due to fracture work’s ability to capture the entire postpeak behavior whereas fracture energy often cannot due to limits in the range of LVDT
13

measurements. Another advantage of fracture work is the elimination of LVDT instrumentation
during testing. Vertical ram movement has been shown to be no different that LVDT measured
horizontal displacement [39]. This enables rapid testing and eliminates LVDT damage. For these
reasons the use of fracture work was used in this thesis as an additional method to characterize
thermal cracking susceptibility of Michigan mixtures.

2.7 Relevance of Indirect Tensile Strength to Pavement ME Design
Pavement ME Design is the latest pavement design guide developed as a result of
research completed under NCHRP 1-37A. In the Pavement ME Design distresses are predicted
over a design period based on material properties, climate, traffic, and design geometry.
Pavement engineers input a design pavement cross section and can predict pavement distresses
over time and modify their design accordingly.
Pavement ME Design predicts thermal cracking in flexible pavements using the Thermal
Cracking (TC) Model first developed by Hiltunen and Roque [17] [36]. The TC Model takes into
account material inputs, climate, and design geometry to predict the amount of thermal cracking
per length of pavement over time. For example, a typical MDOT HMA pavement constructed in
Northern Michigan may be predicted to exhibit thermal cracking distress of 500 feet per mile
after 20 years. The amount of thermal cracking in the TC Model is predicted in three steps. First
thermal stress distribution due to cooling is calculated. Second, crack propagation is modeled.
And lastly the amount of cracking visible on the pavement surface is calculated [28] [40].
Mixture IDT strength is used as an input into the calculation of crack propagation portion of the
TC Model and is discussed subsequently.
14

Crack growth rate in the TC Model is governed using the Paris Law, given by the
following equation [28]:

n

ΔC = A(ΔK)

(3)

where:
ΔC = change in crack length
ΔK = change in the stress intensity factor
A, n = regression parameters

The change in the stress intensity factor, ΔK, is determined through a subroutine program called
CRACKTIP, a finite element program used to calculate the stress at the tip of a single vertical
thermal crack [17]. A and n are regression parameters originally derived by Schapery [35] for
nonlinear viscoelastic materials and related to creep compliance, IDT strength, and fracture work
[35]. A and n can be empirically related to mixture strength, IDT strength, and creep compliance
through the following relationships [35].
(4)
Where:
E = mixture stiffness, psi
σm = mixture IDT strength, psi
n=

m = slope of the linear portion of the log compliance-log
time relationship determined from the IDT creep test
15

In summary, the IDT strength is directly used as an input into calculating the A parameter
and used in calculation of crack propagation in the Pavement ME Design TC Model. The
accuracy of the thermal cracking model is therefore directly dependent on the accuracy of the
models used for estimating creep compliance and tensile strength, which is the subject of this
thesis.

2.8 Pavement ME Design IDT Strength Prediction
In the TC Model subroutine of Pavement ME Design, IDT strength at -10°C is a direct
input in Level 1 and Level 2 analysis, often measured by universities or private testing facilities
as most state agencies do not have their own testing programs in place. For Level 3 analysis IDT
strength at -10°C is still required but is estimated from the binder PG and mixture volumterics.
Initially IDT strength was predicated based solely on binder PG, i.e. any mixture containing PG
58-28 would have an IDT strength of 400 psi while any mixture containing PG 64-34 would
have an IDT strength of 475 psi. This initial predictive model was found to provide a biased
estimate and high variance in predicting IDT strength [6]. Final modification and revision of the
TC Model by Witczak et al [6] under NCHRP 9-19 revised the IDT strength prediction
subroutine of the TC Model based on correlations with PG and volumetric and mixture
properties [6]. IDT strength was found to correlate well with air voids, voids filled with asphalt
(VFA), the Penetration at 77°F, and the A intercept of the RTFO conditioned binder temperatureviscosity relationship. Based on these relationships, the following empirical equation was
developed.

16

2

2

St = 7416.712 – 114.016Va – 0.304Va -122.592VFA + 0.704VFA + 405.71log (Pen77)
- 2039.296log(ARTFO)

(5)

Where:

St = Indirect tensile strength at -10°C (psi)
Va = Air Voids, %
VFA = Voids Filled with Asphalt, %
Pen77 = Penetration at 77°F
ARTFO = Intercept of RTFO conditioned binder Viscosity-Temperature relationship

Binder material parameter ARTFO is not directly input into Pavement ME software, instead it is
predicted from binder PG. Pen77 is also not required and is predicted from binder PG.
Global calibration of the IDT strength subroutine in the TC Model was completed using
31 data points. Goodness of fit statistics Se/Sy (standard error of estimate/standard deviation),
2

and correlation coefficient (R ) were 0.68 and 0.62, respectively [6].

2.9 Factors Affecting Mixture Indirect Tensile Strength
Much work has been done on low temperature characterization of asphalt binder, while
less work has been done on low temperature characterization of the asphalt mixture. Relatively
few studies have examined the effects of mixture properties and volumetric influences on the low
temperature IDT strength. Because of the use of IDT strength in thermal cracking resistance

17

characterization in Pavement ME Design it is important to understand the mixture and
volumetric properties that affect IDT strength and thus directly impact thermal cracking
susceptibility. NCHRP 530 reported IDT strength values correlated well with voids filled with
asphalt (VFA). Low temperature cracking research by Zborowsk and Kaloush [40] showed that
crumb rubber modified mixtures exhibited a lower IDT strength and higher fracture energy
values as compared to conventional HMA mixtures. In 2011 the National Asphalt Pavement
Association in their Warm Mix Asphalt (WMA) best practices report hypothesized that as a
result of lower production and placement temperatures WMA mixtures would be softer and thus
lead to greater resistance to thermal cracking regardless of their respective WMA additive [16].
Li et al. [25] examined the effect of binder type, binder, modifier, aggregate type, asphalt
content, and air voids on the fracture work and fracture toughness of 28 asphalt mixtures as
measured by the IDT strength test. Aggregate type, air voids, and high PG for a constant PG low
limit were found to have a significant impact on both fracture work and toughness, while an
increase in percent binder was not found to be a significant factor. Fracture work was found to
increase as test temperature increased while fracture toughness was found to decrease as test
temperature increases [25]. In a 2011 study on the effect of Reclaimed Asphalt Pavement (RAP)
on IDT strength values Huang et al. reported that generally increasing the percentage of RAP in
an HMA mixture resulted in greater IDT strengths and lower toughness indices as did increasing
the long term aging of a mixture [18].

18

3. METHODS
3.1 Introduction
This study was part of a larger comprehensive research effort to characterize asphalt
mixtures commonly used in the State of Michigan, for MDOT implementation of Pavement ME
Design. In this study 62 different asphalt mixtures were characterized using the IDT strength test
to determine IDT strength, total fracture work, pre-peak fracture work, and post-peak fracture
work.
3.2 Mixtures Used
Mixtures used in this study consisted of 58 unique HMA and 4 unique WMA mixtures
obtained as loose mixture samples by MDOT personal from MDOT pavement projects across the
State of Michigan (North, Grand, Bay, Southwest and University Regions, Metro Region, and
Superior Region). Mix design volumetrics and aggregate gradations were also provided by
MDOT for each mixture. A description of mixtures tested in this thesis is shown in Table 1
through Table 4, where mixtures tested are highlighted in grey.

19

M
HS
M
HS
M
HS

E30
E30
E50
E50
E10
E10

Top

North, Grand, Bay, Southwest and University Regions (NGBSU)
64-22 1 64-22 2A 70-28P
3
70-28P
4
70-28P
64-22 1 64-22 2B
76-28P
6
76-28P
7
76-28P
64-22 9 64-22
10
70-28P 11 70-28P 12 70-28P
64-22 9 64-22
10
76-28P 14 76-28P 15 76-28P
58-22 17 58-22 18A
64-28
19
64-28
20
64-28
58-22 17 58-22 18B 70-28P 22 70-28P 23 70-28P

20

HMA#

Leveling/Top

Binder
PG

Leveling

HMA#

Base

Binder
PG

Base

HMA#

5

Binder
PG

4

HMA#

3

Binder
PG

3

HMA#

2

Binder
PG

Mix
Type

Layer:

Mix No:

Table 1 HMAs tested for IDT strength

5
8
13
16
21
24

M
HS
M
HS
M
HS
M
HS
M
HS
M
HS
M
HS
M
HS
M
HS
M
HS
M
HS
M
HS

North, Grand, Bay, Southwest and University Regions (NGBSU)
E3 58-22 25 58-22 26A 64-28 27 64-28
28
64-28
E3 58-22 25 58-22 26B 70-28P 30 70-28P 31 70-28P
E03 58-22 33 58-22
34
58-28 35 58-28
36
58-28
E03 58-22 33 58-22
34
64-28 38 64-28
39
64-28
E1 58-22 41 58-22
42
58-28 43 58-28
44
58-28
E1 58-22 41 58-22
42
64-28 46 64-28
47
64-28
Metro Region
E30 64-22 1
64-22 2A 70-22P 89 70-22P 90 70-22P
E30 64-22 1
64-22 2B 76-22P 92 76-22P 93 76-22P
E50 64-22 9
64-22
10 70-22P 95 70-22P 96 70-22P
E50 64-22 9
64-22
10 76-22P 98 76-22P 99 76-22P
E10 58-22 17 *58-22 18A 64-22 101 64-22 102 64-22
E10 58-22 17 58-22 18B 70-22P 104 70-22P 105 70-22P
E3 58-22 25 58-22 26A 64-22 107 64-22 108 64-22
E3 58-22 25 58-22 26B 70-22P 110 70-22P 111 70-22P
E03 58-22 33 58-22
34
58-22 113 58-22 114 58-22
E03 58-22 33 58-22
34
64-22 116 64-22 117 64-22
E1 58-22 41 58-22
42
58-22 119 58-22 120 58-22
E1 58-22 41 58-22
42
64-22 122 64-22 123 64-22
Superior Region
E10 58-28 53 58-28
54
58-34 55 58-34
56
58-34
E10 58-28 53 58-28
54 64-34P 58 64-34P 59 64-34P
E3 58-28 61 58-28
62
58-34 63 58-34
64
58-34
E3 58-28 61 58-28
62 64-34P 66 64-34P 67 64-34P
E03 58-28 69 58-28
70
58-34 71 58-34
72
58-34
E03 58-28 69 58-28
70 64-34P 74 64-34P 75 64-34P

21

HMA#

Top
Binder
PG

Leveling/Top
HMA#

Leveling

Binder
PG

Base

HMA#

Lay
er:

Base

Binder
PG

5

HMA#

4

Binder
PG

3

HMA#

3

Binder
PG

2

Mix
Type

Mi
x
N
o:

Table 1 (cont’d)

29
32
37
40
45
48
91
94
97
100
103
106
109
112
115
118
121
124
57
60
65
68
73
76

M E1 58-28 77
HS E1 58-28 82
Note: M=Mainline,
HS=High Stress

58-28
58-28

Superior Region
78
58-34
79
83 64-34P 84

58-34
64-34P

80
85

58-34
64-34P

81
86

Binder
PG

HMA#

Top

Binder
PG

Leveling/Top

HMA#

Leveling

Binder
PG

Base

HMA#

Base

HMA#

5

Binder
PG

4

HMA#

3

Binder
PG

Mix No:

3

Mix
Type:

2

Layer:

Table 1 (cont’d)

Table 2 HMAs tested for IDT strength (GGSP and LVSP Mixtures)

HMA Type

Layer:
Region:

Leveling/Top
North, Grand, Bay,
Southwest and
University Regions
(NGBSU)

Mix
Binder PG
Type
M
GGSP
70-28P
HS
GGSP
76-28P
M
LVSP
58-28
HS
LVSP
64-28
Note: M=Mainline, HS=High Stress

Metro

Superior

HMA#

Binder PG

HMA#

Binder PG

HMA#

49
50
51
52

70-22P
76-22P
58-22
64-22

125
126
127
128

-

-

58-34
64-34P

87
88

22

Table 3 HMAs tested for IDT strength (SUPERPAVE) – Mixtures that do not follow
MDOT specifications but are permitted to be used
HMA
Type

Mix No:
2
3
Layer:
Base
Base
Mix
Binder
Binder
HMA#
HMA#
Type
PG
PG
M
E10
58-28
200
HS
E10
HS
E30
M
E3
58-28
205
M
E1
M
E1
Note: M=Mainline, HS=High Stress

4
Leveling/Top
Binder
HMA#
PG

5
Top
Binder
HMA#
PG

70-22P

64-22
70-22P

202
204

64-22
64-22

206
207

203

Table 4 HMAs tested for IDT strength (GGSP and LVSP Mixtures) - Mixtures that do not
follow MDOT specifications but are permitted to be used
HMA
Type:

Layer:
Leveling/Top
Region:
NGBSU
Metro
Superior
Mix
Binder HMA# Binder HMA# Binder HMA#
Type
M
ASCRL 64-28
201
Note: M=Mainline
3.3 Specimen Preparation
All specimens where compacted according to AASHTO PP60, “Preparation of
Cylindrical Performance Test Specimens Using the Superpave Gyratory Compactor (SGC)”, to
an air void value of 7

.5%, as determined according to the AASHTO T 166-11 “Bulk Specific

Gravity of Compacted Hot Mix Asphalt (HMA) Using Saturated Surface-Dry Specimens.” For
each unique mixture 3 replicates were generally prepared. A limited number of mixtures had
more or less than 3 replicates due to limits in amount of loose mixture available and variability
when reaching the target air void content. Each specimen was wet sawed to dimensions of
approximately 150 mm diameter and 38 mm height and checked for correct air void content. A
23

total of 204 specimens were tested with the IDT strength test method for this study. Exact
specimens dimensions, air void contents, and number of replicates for each mixture are listed in
Appendix A.
3.4 Indirect Strength Testing Procedures
Each specimen was tested for IDT strength in accordance with AASHTO T-322. Due to
testing recommendations described in NCHRP 530 and equipment constraints, a few important
changes were made in this study and they are listed in the subsequent sections.
3.4.1 Testing Temperature
IDT testing in this study was conducted at -10°C, which is the test temperature required
for IDT strength input into Pavement ME Design but differs from AASHTO T-322 requirements.
Testing temperature in AASHTO T-322 is recommended based on low temperature PG, PGXX28 and PG XX-22 are recommended at -10°C while PG XX-16 and stiffer binders are
recommended at 0°C. In Pavement ME Design the -10°C testing temperature was selected to
represent the undamaged tensile strength of an asphalt mixture in Pavement ME Design as
testing in SHRP A-005 showed that peak strength always occurred at temperatures lower than 10°C [6]. Thus testing at -10°C may be considered an accurate and conservative measure of a
mixture’s “undamaged” tensile strength. The term “undamaged” herein corresponds to the newly
constructed asphalt mixture (i.e. no aging or damaged has yet occurred).
3.4.2 Use of LVDTs
As per recommendations put forth in NCHRP 530 and discussed previously, LVDTs
were not used in this study. The corrected, or LVDT instrumented, strength of each specimen
24

was determined using Equation 2, an empirical relationship found to estimate reasonably well
corrected strength using uncorrected (uninstrumented) strength [10].
3.4.3 Environmental Chamber

The final modification, actually a limitation, is that specimens were tested in an IDT Test
System without an environmental chamber. Due to the IDT Test System chamber inability to
maintain a stable test temperature specimens were conditioned and held in an external chamber
placed immediately next to the IDT Test System (Figure 7). At the time of testing, each
specimen was immediately transferred from the external environmental chamber to the IDT Test
System loading frame and loaded to failure in less than 60 seconds from leaving the external
environmental chamber. In order to minimize temperature loss during the 60 second transfer
process, a dummy specimen with an internal thermocouple was transferred from the external
chamber to the testing area. It was observed that the dummy specimen did not lose more than
1°C during this process.

25

Figure 7 IDT test system consisting of an axial loading device with external environmental
chamber

26

4. RESULTS OF LABORATORY INDIRECT TENSILE TESTING
4.1 Indirect Tensile Strength of Michigan Mixtures
An overview of the average laboratory measured IDT strength for the 62 MDOT asphalt
mixtures

tested

at

-10°C

as

a

part

of

27

this

study

is

shown

in

Table

5.

Table 5 Summary of IDT strength values for the State of Michigan asphalt mixtures
Mix No:
3
4
5
Layer:
Base
Leveling/Top
Top
IDT Strength, -10°C
IDT Strength, -10°C
IDT Strength, -10°C
Traffic HMA # Strength
HMA # Strength
HMA# Strength
SD
CV
SD
CV
SD
CV
(psi)
(psi)
(%)
(psi)
(psi)
(%)
(psi)
(psi)
(%)
E30
E30
E10
E10
E10
E10
E3
E3
E3
E3
E3
E3
E1
E1

2A
2B
18A
18B
200

477
362
343
463

22
21
49
30

5
6
14
7

26A
26B
26C
62

400
338
346
413

19
29
12
19

5
9
3
5

4

483

18

4

20A
20C
23

452
395
462

32
23
15

7
6
3

28A
28B
31A
31B
64
67
44
47

483
416
442
470
388
402
405
433

15
20
36
11
45
20
27
4

3
5
8
2
12
5
7
1

E03

28

20B
21
24A
24B
29A
29B
32A
32B
65

448
454
372
498
399
426
460
453
362

19
19
27
16
12
22
19
8
10

4
4
7
3
3
5
4
2
3

45
48

346
422

34
21

10
5

37

455

20

4

Table 5 (cont’d)
Mix No:
Layer:
Mix
GGSP
GGSP
LVSP
LVSP
LVSP
LVSP
ASCRL
2E3
LVSP

Miscellaneous
Miscellaneous
IDT Strength, -10°C
HMA
Strength SD
CV
#
(psi)
(psi)
(%)
49A
49C
51A
51B
51C
127
201
205
208

387
336
347
405
379
389
276
321
425

14
16
40
14
12
40
7
37
18

4
5
12
4
3
10
3
12
4

Mix No:
Layer:
Traffic
E50
E30
E30
E10
E10
E10
E10
E3
E3
E3
E1
E1
E1

4
Leveling/Top
IDT Strength, -10°C

HMA
Strength
#
(psi)

SD
(psi)

CV
(%)

90A
203
102
105

455
451
487
449

0
13
17
32

0
3
4
7

67
108
111
80
85

402
467
512
409
403

20
15
10
15
11

5
3
2
4
3

29

5
Top
IDT Strength, -10°C
HMA# Strength
(psi)

SD
(psi)

CV
(%)

97
204

508
560

5
12

1
2

103
202
209A
209B
68
109
112
81
86
206

427
512
453
419
410
480
533
357
417
468

70
8
9
31
24
28
9
0
16
22

16
2
2
7
6
6
2
0
4
5

The average IDT strength of all mixtures was 426 psi. The lowest recorded IDT strength
was 276 psi, measured from mix 201 an Asphalt Stabilized Crack Relief Layer (ASCRL)
mixture. The highest IDT strength recorded was 560 psi, measured from mix 204 a MDOT
designated 5E30 High Stress mixture.
Major state and highway mixtures used in the State of Michigan are designated using a
two part nomenclature system. The first part of the designation details the location in the
pavement system in which the mix will be used (base, leveling, leveling/top, or top course). The
second part of the designation is termed the mix type and details the expected design traffic value
in millions of ESALs. For instance a mix designated 5E30 would be used as a top course and is
designed to withstand 30 million ESALs. The IDT strength values for each of the ESAL design
categories was examined to investigate the use of the MDOT mixture classification systems
ability to be used as a thermal cracking resistance parameter during design. In Table 5 mixtures
with greater IDT strength are generally designated as Mix No. 4 and 5 while mixtures with the
lower IDT strength are generally designated as Mix No. 2 and 3, GGSP, and LVSP.

4.2 Fracture Work of Michigan Mixtures
It is recalled that fracture work of a mixture is defined as the area under the load versus
vertical deformation curve and can be reported as total fracture work (Figure 6), which consists
of pre-peak work (fracture work measured until failure), and post-peak fracture work (fracture
work measured after failure). Measured total, pre, and post fracture work for the mixtures tested
in this study are given in Table 6.

30

Table 6 Summary of total work values for the State of Michigan asphalt mixtures
Base
Leveling/Top
Top
Total Work, -10°C
Total Work, -10°C
Total Work, -10°C

Layer:
Traffic

HMA #

Total
Work
(lb*in.)

SD
(lb*in.)

CV
(%)

HMA #

Total
Work
(lb*in.)

SD
(lb*in.)

CV
(%)

E30
E30
E10
E10
E10
E10
E3
E3
E3
E3
E3
E3
E1
E1
E03

2A
2B
18A
18B
200

280
419
365
273
242

75
92
164
87
11

27
22
45
32
5

4

415

53

13

20A
20C
23

269
362
446

61
86
63

23
24
14

26A
26B
26C
62

412
430
349
508

0
11
63
97

0
3
18
19

28A
28B
31A
31B
64
67
44
47

225
185
281
283
246
522
226
245

45
33
72
32
77
85
45
42

20
18
26
11
31
16
20
17

31

HMA#

Total
Work
(lb*in.)

SD
(lb*in.)

CV
(%)

20B
21
24A
24B
29A
29B
32A
32B
65

341
281
527
459
280
202
327
406
324

24
42
68
84
11
23
42
79
40

7
15
13
18
4
12
13
20
12

45
48
37

323
213
515

40
48
154

12
22
30

Table 6 (cont’d)
Mix
No:
Layer:

Miscellaneous
Miscellaneous
Total Work, -10°C

Mix

HMA
#

GGSP
GGSP
LVSP
LVSP
LVSP
LVSP
ASCRL
LVSP

49A
49C
51A
51B
51C
127
201
208

Total
SD
Work
(lb*in.)
(lb*in.)
499
1014
544
215
294
307
232
174

141
258
130
47
27
98
83
22

Mix
No:
Layer:

CV
(%)

Traffic

28
25
24
22
9
32
36
13

E50
E30
E30
E10
E10
E10
E10
E3
E3
E3
E1
E1
E1

4

5

Leveling/Top
Total Work, -10°C
HMA
#

Total
SD
Work
(lb*in.)
(lb*in.)

CV
(%)

90A
203
102
105

182
337
343
312

0
60
81
58

0
18
23
19

67
108
111
80
85

522
302
338
514
622

85
65
9
96
147

16
22
3
19
24

32

Top
Total Work, -10°C
HMA#

Total
Work
(lb*in.)

SD
(lb*in)

CV
(%)

97
204

258
383

28
70

11
18

103
202
209A
209B
68
109
112
81
86
206

333
185
200
196
405
241
238
193
538
178

212
21
41
52
40
46
20
0
116
20

64
11
20
27
10
19
8
0
22
11

Table 7 Summary of pre fracture work values for the State of Michigan asphalt mixtures
Mix
No:
Layer:

3

4

5

Base

Leveling/Top

Top

Pre Work, -10°C

Pre Work, -10°C

Pre Work, -10°C
Traffic

HMA #

Pre
Work
(lb*in.)

SD
(lb*in.)

CV
(%)

HMA #

Pre
Work
(lb*in.)

SD
(lb*in.)

CV
(%)

E30
E30
E10
E10
E10
E10
E3
E3
E3
E3
E3
E3
E1
E1
E03

2A
2B
18A
18B
200

275
261
228
244
242

68
29
36
47
11

25
11
16
19
5

4

300

30

10

20A
20C
23

264
247
320

53
33
4

20
14
1

26A
26B
26C
62

247
220
247
265

0
17
23
36

0
8
9
14

28A
28B
31A
31B
64
67
44
47

225
183
254
279
202
253
226
245

45
29
38
28
42
35
45
42

20
16
15
10
21
14
20
17

33

HMA#

Pre
Work
(lb*in.)

SD
(lb*in.)

CV
(%)

20B
21
24A
24B
29A
29B
32A
32B
65

263
281
287
335
260
198
291
275
274

37
42
17
17
24
20
20
37
8

14
15
6
5
9
10
7
13
3

45
48
37

252
213
254

2
48
56

1
22
22

Table 7 (cont’d)
Mix No:

Miscellaneous

Layer:

Miscellaneous

Mix
No:
Layer:

Pre Work, -10°C

4

5

Leveling/Top

Top

Pre Work, -10°C
HMA
#

Pre Work, -10°C

Mix

HMA
#

Pre
Work
(lb*in.)

SD
(lb*in.)

CV
(%)

Traffic

GGSP

49A

260

13

5

E50

GGSP

49C

200

24

12

E30

90A

182

0

0

LVSP

51A

226

29

13

E30

203

289

60

21

LVSP

51B

215

47

22

E10

102

297

28

LVSP

51C

236

24

10

E10

105

297

35

LVSP

127

243

37

15

ASCRL

201

180

20

LVSP

208

174

22

HMA#

Pre
Work
(lb*in.)

SD
(lb*in.)

CV
(%)

97

258

28

11

204

377

60

16

9

103

218

41

19

12

202

185

21

11

E10

209A

200

41

20

11

E10

209B

192

47

24

13

E3

67

253

35

14

68

292

26

9

E3

108

298

58

19

109

241

46

19

E3

111

321

19

6

112

238

20

8

E1

80

294

32

11

81

193

0

0

E1

85

254

31

12

86

287

33

12

206

178

20

11

E1

34

Pre
Work
(lb*in.)

SD
(lb*in.)

CV
(%)

Table 8 Summary of post fracture work values for the State of Michigan asphalt mixtures
Mix
No:
Layer:

3
Base
Post Work, -10°C

4

5

Leveling/Top
Post Work, -10°C

Top
Post Work, -10°C

Traffic

HMA #

Post
Work
(lb*in.)

SD
(lb*in.)

CV
(%)

HMA #

Post
Work
(lb*in.)

SD
(lb*in.)

CV
(%)

E30
E30
E10
E10
E10
E10
E3
E3
E3
E3
E3
E3
E1
E1
E03

2A
2B
18A
18B
200

5
158
137
30
0

9
77
144
46
0

173
49
105
155
0

4

115

32

28

20A
20C
23

5
115
125

8
96
61

173
83
49

26A
26B
26C
62

165
210
102
243

0
8
49
130

0
4
48
54

28A
28B
31A
31B
64
67
44
47

0
2
27
4
43
269
0
0

0
5
37
7
50
108
0
0

0
200
136
173
116
40
0
0

35

HMA#

Post
Work
(lb*in.)

SD
(lb*in.)

CV
(%)

20B
21
24A
24B
29A
29B
32A
32B
65

78
0
240
123
20
4
35
131
50

27
0
78
90
35
5
41
43
49

35
0
32
73
173
122
116
32
98

45
48
37

71
0
261

41
0
210

58
0
80

Table 8 (cont’d)
Mix No:

Miscellaneous

Mix No:

4

5

Layer:

Miscellaneous

Layer:

Leveling/Top

Top

Post Work, -10°C
Mix

HMA
#

GGSP

49A

239

GGSP

49C

LVSP

Post
SD
Work
(lb*in.)
(lb*in.)

Post Work, -10°C
HMA
#

Post
SD
Work
(lb*in.)
(lb*in.)

Post Work, -10°C

CV
(%)

Traffic

144

60

E50

813

247

30

E30

90A

0

0

0

51A

318

157

49

E30

203

49

49

101

LVSP

51B

0

0

0

E10

102

46

53

LVSP

51C

59

14

25

E10

105

15

31

LVSP

127

64

67

106

ASCRL

201

52

63

LVSP

208

0

0

CV
(%)

HMA#

Post
SD
Work
(lb*in.)
(lb*in.)

CV
(%)

97

0

0

0

204

6

11

173

116

103

115

193

168

200

202

0

0

0

E10

209A

0

0

0

123

E10

209B

4

7

173

0

E3

67

269

108

40

68

112

48

43

E3

108

4

7

200

109

0

0

0

E3

111

16

28

173

112

0

0

0

E1

80

221

123

56

81

0

0

0

E1

85

367

178

48

86

251

148

59

206

0

0

0

E1

36

The average total fracture work of all mixtures was 340 lb*in. The lowest total fracture
work was 174 lb*in., measured from mix 208 a Low Volume Superpave (LVSP) mixture. The
highest total fracture work recorded was 1014 lb*in., measured from mix 49C a Gap Graded
Superpave (GGSP) mixture.
A comparison of the pre and post fracture work for all 62 mixtures tested in this study is
depicted in Table 7 and Table 8. The average pre fracture work was 250 lb*in and the average
post fracture work was 91 lb*in. The greatest pre fracture work was 377 lb*in., measured from
mix 204 (5E30 High Stress). The lowest pre fracture work recorded was 174 lb*in, measured
from mix 208 (LVSP). The highest post fracture work recorded was 813 lb*in., measured from
mix 49C (GGSP). The lowest post fracture work recorded was 0 lb*in. Post fracture work of a
mixture was generally less than pre fracture work and 16 of the 62 mixtures tested in this study
had no measured post fracture work.
The relationship between total fracture work and IDT strength is shown in Figure 8.
While there is high scatter in the data, a general trend exists as IDT strength increases total
fracture work decreases. This trend is reasonable as softer mixes can generally be expected to
exhibit greater fracture work and lower IDT strength, while stiffer mixes have greater IDT
strength and lower fracture work.

37

Total Fracture Work (lb*in)

Total Fracture Work versus IDT Strength
1200
1000
800
600
400
200
0
0

100

200

300

400

500

600

IDT Strength (psi)
Figure 8 Total fracture work versus IDT strength relationship

4.3 MDOT Mix Designation and IDT Strength
The IDT strength values for each of the ESAL design categories was examined to
investigate the use of the MDOT mixture classification systems ability to be used as a thermal
cracking resistance parameter during design. Figure 9 shows the relationship between ESAL and
IDT strengths of the asphalt mixtures tested. As shown, the IDT strength generally increases with
the design ESAL of the mixtures. However a clear relationship is not visible. Some of the
mixtures designated with ESAL of 1 million have higher IDT strength than mixtures designated
with ESALs of 10, 30, and 50 million. This is meaningful because besides ESAL, there are many
other factors affecting the IDT strength. A clear trend should not be anticipated since there are
many variables (e.g., aggregate gradation, PG, VMA, VFA...etc.) that play a role in IDT
strength.

38

IDT Strength of MDOT Mix Designation ESAL's
IDT Strength (psi)

600
500
400
300
200
100
0
0

10

20
30
40
50
MDOT Mix ESAL Designation

60

Figure 9 Laboratory measured IDT strength for MDOT Mix ESAL designation categories
for leveling and top course pavement layers
Figure 10 shows the relationship between MDOT Mix ESAL designation and total
fracture work. As shown, even though there is significant scatter in the data, a general decrease
in fracture work is observed with increasing ESAL. As was seen with mixture IDT strength a
clear trend should not be anticipated since there are many variables (e.g., aggregate gradation,
PG,

volumetrics)

that

affect

a

39

mixture’s

fracture

work.

Total Fracture Work (lb*in.)

Total Fracture Work of MDOT Mix
Designation ESAL's
700
600
500
400
300
200
100
0
0

10

20

30

40

50

60

MDOT Mix ESAL Designation
Figure 10 Laboratory measured total fracture work for MDOT Mix ESAL designation
categories for leveling and top course pavement layers

4.4 Superpave PG and IDT Strength
Superpave performance grading (PG) is a binder characterization system developed to
relate binder performance to the climatic conditions in which it will be utilized. For the PG
grading process, binder undergoes a battery of tests including Rolling Thin Film Oven (RTFO),
Pressure Aging Vessel (PAV), Rotational Viscometer (RV), Dynamic Shear Rheometer (DSR),
Bending Beam Rheometer (BBR), and Direct Tension Tester (DDT). Based on the results of
these tests, a PG is determined consisting of a high grade; the average seven-day maximum
pavement temperature (°C), and a low grade; the minimum expected pavement temperature (°C)
likely to be experienced. For instance, in the northern US, a binder graded PG 58-40 would be
expected to outperform a PG 58-16 binder in regards to thermal cracking due to its greater low
40

PG classification. The IDT strength of the Michigan mixtures used in this study are depicted as a
function their low PG (-22, -28, or -34) and their high PG (58, 64, or 70) in Figure 11 and Figure
12, respectively.

IDT Stregnth (psi)

IDT Strength at Superpave Low PG
600
500
400
300
200
100
0
16

22

28

34

40

Low PG (-)
Figure 11 IDT strength versus Low Temperature PG relationship

IDT Strength at Superpave High PG
IDT Strength (psi)

600
500
400
300
200
100
0
52

58

64

70

76

High PG
Figure 12 IDT strength for high PG characterization of Michigan asphalt mixtures
41

As shown, while there is scatter in the data, IDT strength generally decreases with an
increase in low PG. This is somewhat meaningful since as low PG increases, the binder becomes
softer (and less brittle). Soft binder perhaps leads to low IDT strength. Figure 12 shows the
relationship between the high PG and IDT strength, where an increase in IDT strength is
observed with increasing high PG. This is consistent with the trend with low PG where stiffer
binder (higher the high PG) results in higher IDT strength.
The relationship between total fracture work and low and high PG is shown in Figure 13
and Figure 14, respectively. As low PG increases total fracture work generally increases,
although there is significant scatter in the data. This is somewhat expected as at a greater low PG
the softer binder (less brittle) should exhibit greater fracture work. There is no clear relationship
between high PG and total fracture work, as little difference is seen in total fracture work for

Total Fracture Work (lb*in)

different high PG (Figure 14).

Total Fracture Work at Superpave Low PG
1200
1000
800
600
400
200
0
16

22

28
Low PG (-)

34

40

Figure 13 Fracture work for low temperature Superpave PG characterization of Michigan
asphalt mixtures

42

Total Fracture Work (lb*in)

Total Fracture Work at Superpave High PG
1200
1000
800
600
400
200

0
52

58

64
High PG

70

76

Figure 14 Fracture work for high temperature Superpave PG characterization of Michigan
asphalt mixtures

This is evidence of two important characteristics of low temperature performance
characterization of asphalt mixtures. Firstly, although the Superpave PG system is an
improvement upon binder classification methods binders can still have significantly different
performance characteristics within a PG designation. Secondly IDT strength of an asphalt
mixture is not a function of solely the type of binder used in mixture design. IDT strength cannot
be evaluated based on PG or MDOT mix designation alone. Other mixture components such as
aggregate source and gradation, volumetric, and mixture properties must be considered when
examining the IDT strength of an asphalt mixture. Pavement engineers should use caution when
anticipating increased IDT strength as a result of increasing the low temperature PG magnitude
and should instead utilize laboratory testing or IDT strength prediction models to examine the
effect of mixture design on thermal cracking resistance.

43

4.5 Warm Mix Asphalt IDT Properties
A number of warm mix asphalt (WMA) mixtures where characterized with the IDT
strength test in this study. A comparison of their IDT strength and total fracture work is shown in
Figure 15 and Figure 16. Comparison of WMA and HMA mixtures was made between mixtures
having similar PG, percent binder, and gradations, i.e. mixture 2A (HMA) was compared with
mixture 2B (WMA) and mixture 209A (HMA) was compared to mixture 209B
(WMA)(Appendix A). Mixture 208 (WMA) was not examined in this analysis, as it did not have
a comparable HMA mixture.

IDT Strength (psi)

Comparison of WMA and HMA IDT
Strength
500
400
300

HMA

200

WMA

100
0
51

2
Mixture

209

Figure 15 IDT strength for comparable WMA and HMA mixtures

As shown in Figure 15, the WMA mixtures had lower IDT strength values as compared
to their similar HMA mixtures. Figure 16 shows a comparison of total fracture work for the
similar WMA and HMA mixtures. Generally it is shown that WMA mixtures tested in this study
have higher total fracture work as compared to their similar HMA mixtures.
44

Total Fractrue Work (lb*in.)

Comparison of WMA and HMA Total
Fracture Work
500
400

HMA
HMA

300

WMA
WMA

200
100
0
51

2
Mixture

209

Figure 16 IDT fracture work for comparable WMA and HMA mixtures

A comparison of post fracture work for WMA and HMA mixtures is shown in Figure 17.
It is shown that all WMA mixtures have a greater post fracture work as compared to their similar
HMA mixtures. It is noted that all HMA mixtures where shown to have zero or nominal post
fracture work, a property that correlates to crack growth and propagation. When compared to
tested HMA mixtures similar WMA mixtures tested in this study may be thought to exhibit
slower rates of thermal cracking growth.

45

Post Fractrue Work (lb*in.)

Comparison of WMA and HMA Post
Fracture Work
500
400

HMA
HMA

300

WMA
WMA

200
100
0
51

2
Mixture

209

Figure 17 IDT post fracture work for comparable WMA and HMA mixtures

46

5. INDIRECT TENSILE STRENGTH PREDICTION MODELS
5.1 Introduction to Indirect Tensile Strength Prediction for Pavement ME Design
In Pavement ME Design thermal cracking distress prediction directly depends on
accurate material characterization, i.e. IDT strength at -10°C and creep compliance. Over
prediction of IDT strength in Level 3 analysis of the Pavement ME Design can lead to higher
thermal cracking rates while under prediction can lead to over designed pavements, both costly
to state transportation agencies. Figure 18 depicts a preliminary sensitivity analysis of IDT
strength input on thermal cracking prediction in Pavement ME Design. For a scenario of a 4”
flexible pavement lift (PG 58-22) constructed in Detroit, MI the amount of thermal cracking was
determined as a function of different IDT strength values. An IDT strength of 100 psi was used
as it is the lower boundary limit of IDT strength input into Pavement ME Design while an IDT
strength of 500 psi was used as it was generally a typical upper limit of IDT strength of the
mixtures tested in this study. In Figure 18 it is shown that the amount of thermal cracking varies
with IDT strength and thermal cracking prediction is dependent on the IDT strength value input
into Pavement ME Design software. To successfully predict thermal cracking in Pavement ME
Design it is necessary to accurately determine material inputs such as IDT strength. If testing is
not possible or feasible, an accurate predictive equation for IDT strength is necessary to improve
the predictions of Pavement ME Design.

47

Impact of IDT Strength on Pavement ME Design
Level 3 Thermal Cracking Prediciton
Thermal Cracking (ft/mi)

100 psi Tensile Strength

500 psi Tensile Strength

1800
1600
1400
1200
1000
800
600
400
200
0
0

5

10
Time (yrs)

15

20

Figure 18 Effect of IDT strength input in Pavement ME Design Level 3 thermal cracking
analysis for a 4”, PG 58-22 flexible pavement constructed in Detroit, Michigan.

In this study three models were developed to improve IDT strength prediction for
Michigan mixtures; (i) a locally calibrated Pavement ME Design IDT strength model, (ii) a
newly developed linear IDT strength model, and (iii) an artificial neural network (ANN) based
model. The development of each IDT model is explained and then evaluated for prediction
performance with respect to current Pavement ME Design IDT strength prediction. Increased
IDT strength prediction performance has the potential to firstly increase Level 3 thermal
cracking prediction accuracy with the use of more accurate material inputs. Secondly calibration
or development of a model with adequate prediction performance could be utilized to predict
IDT strength for Level 1 and 2 Pavement ME Design analyses, which are currently measured by
laboratory testing. Lastly development of a model that utilizes inputs readily obtainable by

48

pavement designers and does not require costly and time consuming laboratory testing would be
advantageous to state agencies.

5.2 Model Evaluation
The performance of a Michigan calibrated Pavement ME Design IDT strength model and
a newly developed IDT linear regression model were evaluated using goodness-of-fit statistics,
visual inspection with respect to the line of equality (LOE), and local bias statistics. Goodness2

of-fit statistics include Se/Sy and R and are calculated as follows.

∑

̂

∑

̅

√
√

(6)

(7)

( )
Where:
Se = Standard error of estimate,
Sy = Standard deviation,
2

R = Correlation coefficient,
y = Measured IDT strength,
̂ = Predicted IDT strength,
̅ = Mean value of measured IDT strength,
49

(8)

n = Sample size
k = Number of independent variables in the model

Se/Sy is a measure of prediction improvement over the empirical model, a smaller Se/Sy
2

ratio is indicative of improved prediction by the model. The R is a measure of model accuracy,
a value closer to 1 indicates better estimation by the model [31]. Evaluation by visual inspection
is accomplished by examining the plotted measured versus predicted values with respect to the
LOE. If the plotted values are fairly equally distributed around the LOE then the empirical model
will generally exhibit good correlation to the measured data [30]. Slope and intercept are a
measure of local bias in the empirical models and were calculated by fitting an unconstrained
line of best fit to the measured versus predicted data in Microsoft Excel. Local bias statistics can
indicate patterns of over prediction or under prediction by the empirical model that may not be
discerned by either goodness-of-fit statistics or visual inspection [30].
5.3 Local Calibration of Pavement ME Design Strength Prediction Model

The first effort to improve Pavement ME Design IDT strength prediction performance
was local calibration of the original IDT equation developed by Witczak et al [6] (Equation 5)
for calculation of IDT strength in the TC Model. 36 of the 62 MDOT mixtures tested in this
study were used in the local calibration process since only 36 of the binders where available for
Penetration testing. It is noted that Penetration testing is an input to the Pavement ME IDT
strength predictive model. Also, only these 36 mixtures had available binder characterization
data, ARTFO and VTS, a required input into the Pavement ME Design IDT strength predictive
50

model. Air void and Penetration Grade values for the 36 mixtures used in the local calibration
are listed inTable 9. ARTFO and VTS binder properties, measured as part of a larger material
characterization project at Michigan State University, are listed in Table 9.
Table 9 Binder and Mixture Properties of 36 MDOT Mixtures used in Michigan
Calibration of the Pavement ME Design Strength Prediction Model Developed by Witczak
Sample
ID
2A
4
18B
20B
21
26A
26B
28B
29B
31A
31B
32A
37
44
45
47
48
49A
62
65
67
68
86
102
103
108
109
111
112
127
200
202

Pen77
Average
(0.1 mm)
55.3
61.7
42.3
55.0
68.7
63.0
74.7
49.3
69.7
74.3
52.0
49.7
67.3
66.7
111.3
63.0
51.3
77.3
67.0
141.0
103.3
80.3
129.7
49.7
56.0
50.7
58.0
55.0
40.3
53.3
58.0
33.3

ARTFO

VFA
(%)

Va (+-.5)
(%)

9.550
7.519
9.935
8.201
8.604
10.265
9.697
9.926
10.207
7.783
8.146
7.819
9.817
8.494
11.701
8.170
9.066
7.553
10.039
10.220
7.540
7.795
7.611
9.540
9.978
9.709
9.605
7.616
7.904
10.162
8.720
9.903

71.98
70.01
70.51
68.66
68.30
68.40
68.56
69.32
68.31
68.62
68.91
67.36
68.60
69.82
68.27
69.86
68.30
69.37
72.39
67.98
71.82
70.35
68.44
70.49
70.03
70.58
70.59
70.10
69.47
69.63
69.89
67.96

7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00

51

Table 9 (cont’d)
Sample
ID
204
205
206

Pen77
Average
(0.1 mm)
33.3
71.0
36.7

ARTFO

VFA
(%)

Va (+-.5)
(%)

8.017
10.119
9.388

68.49
70.85
71.14

7.00
7.00
7.00

For local calibration coefficients of the original Pavement ME Design IDT strength
model (Equation 5) were varied using Microsoft Excel Solver package to reduce the sum of the
squares between measured and Pavement ME Design predicted IDT strengths. Coefficient
labeling of the original Pavement ME Design IDT strength model is shown in Equation 9.
2

2

St = C1 + (C2)Va + (C3)Va + (C4)VFA + (C5)VFA + (C6)log (Pen77)
+ (C7)log(ARTFO)

(9)

Values of the original Pavement ME Design IDT strength model coefficients before and after
Michigan calibration are listed in Table 10.
Table 10 Comparison of the original and Michigan calibrated Pavement ME Design IDT
strength Model Calibration Coefficients

Coefficient
C1
C2
C3
C4
C5
C6
C7

IDT Prediction Model
Michigan
Original Pavement
Calibrated Witczak
ME Design Witczak
Pavement ME
Design
7416.7120
6377.5873
-114.0160
-112.9216
-0.3040
-0.3039
-122.5920
-122.5112
0.7040
0.8589
405.7100
-246.1319
-2039.2960
-346.4313

52

It is of note that the coefficient assigned to the Pen77 parameter changes both sign and magnitude
(Table 10) in local calibration with the Michigan mixes. This is reasonable as softer binders are
generally expected to have higher penetration and lower IDT strength. Thus the higher Pen 77 in
the Michigan calibrated model the lower predicted IDT strength will be. Comparison of the
measured versus predicted IDT strength values for the original and Michigan calibrated IDT
strength models are plotted in Figure 19 and Figure 20, respectively. Visual inspection of the
original Pavement ME Design IDT strength model shows points are poorly distributed with
respect to the LOE while after calibration points are fairly well distributed along the LOE.

Predicted IDT Strength (psi)

600

Uncalibrated Pavement ME Design IDT
Strength Model

500
400
300
200
100
0
0

200
400
Measured IDT Strength (psi)

600

Figure 19 Original Pavement ME Design IDT Strength Model for 36 MDOT mixtures with
respect to the LOE

53

Michigan Calibrated Pavement ME
Design IDT Strength Model

Predicted IDT Strength (psi)

600
500
400
300
200
100
0
0

200
400
Measured IDT Strength (psi)

600

Figure 20 Michigan Calibrated Pavement ME Design IDT Strength Model for 36 MDOT
mixtures with respect to the LOE
Table 11 overviews the performance evaluation criteria before and after local calibration.
The Michigan calibrated Pavement ME Design model shows increased performance with a lower
standard error of estimate/standard deviation, Se/Sy = 0.0598, and higher correlation coefficient,
2

R = 0.663, as compared to the original Pavement ME Design model. Local bias statistics,
unconstrained slope and intercept, of the Michigan calibrated model are 0.5939 and 178.48,
respectively, indicating a tendency of the calibrated model to under predict IDT strength.
54

Comparison of the original Pavement ME Design model before and after calibration shows
substantially increased distribution around the LOE.

Table 11 Comparison of model performance evaluation parameters measured for Original
Pavement ME Design and Calibrated IDT strength prediction models for 36 MDOT
asphalt mixtures
Model Performance
Measure
R

IDT Prediction Model
Original

Calibrated

0.000

0.598

4.436

0.663

Poorly
distributed
-0.0402
283.87

Well
distributed
0.5939
178.48

2

Se/Sy
Visual Inspection (LOE)
Unrestrained Slope
Unrestrained Intercept
5.4 Linear Strength Prediction Model

The second effort to improve Pavement ME Design IDT strength prediction performance
was development of new model using linear regression techniques. IBM

©

SPSS

©

Statistics

software (SPSS) was used to perform a statistical analysis on variables with a potential impact on
IDT strength. The purpose of the statistical analysis was to firstly determine if there was a
relationship between measured IDT strength and mix design properties and volumetrics.
Secondly, determine if the relationship is positive or negative. And thirdly determine the strength
of the relationship between the two variables. Once the relationship of the mix design and
volumetric variables to IDT strength was determined, linear regression was performed with
parameters that significantly correlated to IDT strength to develop a linear model. In addition to
a possible increase in IDT prediction performance, the advantage of such a model is the ease of
55

obtaining the input parameters. All inputs are readily obtainable by engineers via a MDOT Job
Mix Formulas (JMFs) and do not require costly and often time consuming laboratory testing. A
JMF is a document provided to the paving contractor containing detailed mix design information
including mixture properties, volumetrics, gradation, compaction and placement temperatures,
and other important mix information.
A Pearson correlation analysis was performed using SPSS to determine which JMF
variables where significantly correlated to IDT strength. When determining significant
relationships, the p-value statistic was used. If the p-value is less than 0.05 then the correlation
coefficient is considered to be significant at the 0.05 level and if the p-value is less than 0.01 then
the correlation coefficient is considered to be significant at the 0.01 level. JMF parameters
having a significance at least 0.05 were used in construction of a linear IDT strength model for
this study. Table 12 summarizes the JMF parameters that correlated significantly with laboratory
measured IDT strength, their respective p-values, and type of relationship (positive or negative).
Table 12 MDOT JMF parameters found to be significantly correlated with measured IDT
strength using a Pearson Correlation analysis. Correlation significance, either at the .01 or
.05 level, and the relationship of the parameter, either positive (+) or negative (-), is also
listed
Correlated JMF
Variable
Polymer Modified
High PG
Low PG
Fines/Asphalt Ratio
Angularity
% Passing 1/2"
% Passing 3/8"
% Passing #4
% Passing #8
% Passing #100
% Passing #200
% Air Voids

Correlation
Significance
0.01
0.01
0.01
0.05
0.01
0.01
0.01
0.01
0.05
0.05
0.05
--56

Relationship
+
+
+
+
+
+
+
+
---

It is of note that laboratory measured IDT strength correlated with not only asphalt binder
parameters (Polymer Modification, High and Low PG), but also with aggregate parameters (%
Passing 1/2”, 3/8”, #4, #8, #100, and #200 sieves and the Fines/Asphalt Ratio). This is evidence
that aggregate gradation is also a significant factor influencing low temperature IDT strength in
addition to asphalt binder properties.
For development of a linear Pavement ME Design IDT strength predictive equation,
significantly correlated JMF parameters (Table 12) were assigned coefficients (Equation 10) and
then varied using Microsoft Excel Solver package to reduce the sum of the squares between
laboratory measured and linear model predicted IDT strengths. Due to the small range of air
voids tested in this study, 6.5 – 7.5%, air voids were not found to be significantly correlated to
IDT strength. However the importance of accounting for the effect of air voids on IDT strength
is recognized and thus is included as a parameter in the linear strength predictive equation.
St = C1 + C2PM + C3PGHigh + C4PGLow + C5ANG + C6FAR +
C7P1/2” + C8P3/8” + C9P#4 + C10P#8 + C11P#100 + C12P#200 + C13AV
(10)

The value of the parameter coefficients and the resulting linear model is shown in
Equation 11.
St = -9.901 + 20.737PM + 2.674PGHigh - 6.407PGLow + .669ANG + 356.593FAR +
1.027P1/2” + 2.517P3/8” – 3.768P#4 + 5.151P#8 + 3.452P#100 – 62.733P#200
- .017AV
(11)

57

Where:
PM = Polymer Modification Factor, either 1 for polymer modified or 0
for unmodified binder
PGHigh = Magnitude of high PG
PGLow = Magnitude of low PG
ANG = Angularity, %
FAR = Fines/Asphalt Ratio
P1/2” = Percent passing the 1/2” sieve
P3/8” = Percent passing the 3/8” sieve
P#4 = Percent passing the #4 sieve
P#8 = Percent passing the #8 sieve
P#100 = Percent passing the #100 sieve
P#200 = Percent passing the #200 sieve
AV = Percent Air Voids

Comparison of the measured versus predicted IDT strength values for the original
Pavement ME Design and linear IDT strength models are plotted in Figure 21 and Figure 24,
respectively. It is noted that predicted Pavement ME Design IDT strength in Figure 21 is the
software output IDT strength, as opposed to prediction by the original IDT equation developed
by Witczak et al [6] used in the previous section. The main difference is that binder properties,

58

ARTFO and Pen77, are predicted from PG. For output of IDT strength prediction in Pavement
ME Design the PG, design air voids (%), and effective binder content, Pbe (%) are entered into
the design guide software and IDT strength is immediately calculated.
Visual inspection of the original Pavement ME Design IDT strength model shows points
are poorly distributed with respect to the LOE while for the linear IDT strength model points are
fairly well distributed along the LOE.

Predicted IDT Stregnth (psi)

Prediction of IDT Strength by Pavement ME
Design Software
1000
900
800
700
600
500
400
300
200
100
0
0

200

400
600
800
Measured IDT Strength (psi)

1000

Figure 21 IDT strength predicated by Pavement ME Design software versus laboratory
measured IDT strength for commonly used State of Michigan asphalt mixtures

Development of a linear IDT strength predictive model was accomplished using all
specimens tested in this study (202 mixtures). A comparison of measured versus predicted IDT
strengths for calibration, testing, and all stages is shown in Figure 22, Figure 23, and Figure 24
respectively.
59

Predicted IDT Strength (psi)

Linear Calibration, R2 = 0.679
600
500
400
300
200
100
0
0

100

200

300

400

500

600

Measured IDT Strength (psi)
Figure 22 IDT strength predicated during calibration by newly developed linear model
versus laboratory measured IDT strength for commonly used State of Michigan asphalt
mixtures

Predicted IDT Strength (psi)

Linear Testing, R2 = 0.509
600
500
400
300
200
100
0
0

100

200

300

400

500

600

Measured IDT Strength (psi) (psi)

Figure 23 IDT strength predicated during testing by newly developed linear model versus
laboratory measured IDT strength for commonly used State of Michigan asphalt mixtures

60

Predicited IDT Stren(lb*in)

Linear All, R2 = .648
600
500
400
300
200
100
0
0

100

200
300
400
Measured IDT Strength (psi)

500

600

Figure 24 IDT strength predicated for all specimens by newly developed linear model
versus laboratory measured IDT strength for commonly used State of Michigan asphalt
mixtures
A comparison of model performance evaluation criteria for the original Pavement ME Design
and linear IDT strength models are listed in Table 13 along with the number of unique sample
used for each stage of development.
Table 13 Comparison of performance criteria for the original Pavement ME Design and
linear IDT strength prediction models for commonly used MDOT asphalt mixtures

Model
Performance
Measure
Unique
Samples
R

2

Se/Sy

IDT Predictive Equation
Pavement
ME

Cal.

Test

All

62

161

40

201

0.006

0.679

0.509

0.648

6.954

0.594

0.887

0.615

61

The linear IDT strength model shows increased performance with a lower standard error
2

of estimate/standard deviation, Se/Sy = 0.615, and higher correlation coefficient, R = 0.648, as
compared to the original Pavement ME Design model. Local bias statistics, unconstrained slope
and intercept, of the Michigan calibrated model are 0.69 and 130.24, respectively, indicating a
trend of the calibrated model to under predict IDT strength as was seen in the Michigan
calibrated Pavement ME Design IDT strength model discussed previously.

5.5 Artificial Neural Network Prediction Model
The third effort to improve Pavement ME Design IDT strength prediction performance
was development of an Artificial Neural Network (ANN) using the strength and mix design
properties and volumetrics data in this study. An ANN can most simply be defined as a
computational model used to predict a desired output from a set of inputs. Unlike regression
techniques, the ANN concept is modeled after living neural networks, giving it the capability to
learn and recognize patterns. Inputs into an ANN are assigned weights and thresholds which are
varied by functions in a network of layers within the ANN. Ultimately the ANN adjusts the
weights and thresholds within the layers to predict a desired output. First used in the field of
computer science ANNs are now used widely in the field of civil engineering [5], including
pavement engineering. In the pavement engineering field ANNs have been employed to
successfully estimate pavement layer thickness [15], IDT strength [14], reflective cracking [9],
base layer moduli [33], roughness and permeability [11] [32], and rutting and fatigue distresses
[19]. Notably, ANN modeling techniques have also been employed in the Pavement ME Design
[6].

62

5.5.1 Structure of the IDT Strength ANN
The ANN developed for the prediction of IDT strength in this study consists of a feed
forward (back propagation) network of one hidden layer and one output layer (Figure 25). This
structure was determined through a trial and error using the readily available MATLAB neural
network toolbox [12].

Figure 25 Structure of the ANN model developed for prediction of IDT strength for
Michigan asphalt mixtures

5.5.2 Overview of IDT Strength Prediction with the ANN
Forward computation of IDT strength, y, in this ANN model was determined from the
following 15 inputs hereby referred to as p, a 15 x1 input vector. Inputs into the ANN developed
as part of this study were the following:

63

PM = Polymer Modification Factor, either 1 for polymer modified
binder or 0 for unmodified binder
PGHigh = Magnitude of high PG
PGLow = Magnitude of low PG
ANG = Angularity, %
FAR = Fines/Asphalt Ratio
P1/2” = Percent passing the 1/2” sieve
P3/8” = Percent passing the 3/8” sieve
P#4 = Percent passing the #4 sieve
P#8 = Percent passing the #8 sieve
P#16 = Percent passing the #16 sieve
P#30 = Percent passing the #30 sieve
P#100 = Percent passing the #100 sieve
P#200 = Percent passing the #200 sieve
RAP = Percent Recycled Asphalt Pavement (RAP)
AV = Percent Air Voids

The process of forward computation in an ANN is completed according to the following steps.
H

Step 1) The output of the hidden layer, a a 15 x 1 vector, is computed using Equations
12 and 13.
H

H

H

n =W p+b
64

(12)

H

H

a = tansig(n )

(13)

Where:
(14)

And:
H

W = The matrix weight vector, 12 x 14
H

b = The bias vector of the hidden layer, 12 x 1
H

Step 2) With the output hidden layer, a , the output of the output layer, y, is computed
using Equation 15 and 16.

o

o H

o

n =W a +b

o

y = purelin(n )

(15)
(16)

Where:

o

W = The matrix weight vector, 1 x 12
o

b = The bias constant of the output layer, 12 x 1
5.5.2 Training of the IDT Strength ANN
The ANN was then trained with laboratory measured IDT strength data gathered from
testing of all 62 unique MDOT mixtures used in this study. To increase training accuracy,
65

individual IDT strength tests, generally 3 replicates for each mixture, were used in the ANN
training procedure resulting in a total of 183 data points. For the training procedure, weights and
biases are varied randomly and repeatedly until the predicted output (i.e. IDT strength)
approaches the measured IDT strength, such that difference between the two is minimized. Error
minimization is measured as the mean square error between measured and predicted IDT
strength and decreases as the number of repetitions increases (Figure 26).

Figure 26 Reduction in mean squared error of laboratory measured and ANN predicted
IDT strength values during training, validation, and testing stages of ANN development

66

Figure 27 ANN predicted IDT strength versus measured IDT strength (base 10) for the
training, validation, testing, and all data used in ANN development

2

Performance of the trained ANN was evaluated with the goodness-of-fit statistic, R , and
2

visual inspection with respect to the LOE. R for the trained IDT strength ANN was 0.828 and
data points were fairly well distributed around the LOE (Figure 27).

67

5.5.3 Testing of the IDT Strength ANN
Final validation of the IDT strength ANN was completed using 20 individual IDT
strength tests set aside from the original 201 strength tests used in the training and validation
steps. These 20 tests were input into the IDT ANN feed forward computation model and the
predicted versus measured IDT strength values where evaluated (Figure 27). The IDT strength
2

2

ANN showed an acceptable correlation coefficient, R = 0.806, for testing (Figure 27). R for all
IDT strength ANN data was 0.835 and data points were fairly well distributed around the LOE
(Figure 28). A summary of specimens used and correlation coefficients for each step of ANN

ANN Predicted IDT Strength (psi)

development and is shown in Table 14.

Measured Versus ANN Predicted IDT Strength,
R2 = 0.835
600
500
400
300
200
100
0
0

100

200
300
400
Measured IDT Strength (psi)

500

600

Figure 28 ANN Predicated versus measured IDT strength values for all mixtures used in
ANN development

68

Table 14 Overview of specimens used and correlation coefficients for each stage of IDT
ANN development

ANN Development Stage

# Unique
Tests

R

Training

160

0.828

Validation

21

0.904

Testing

20

0.806

All

201

0.835

69

2

6. CONCLUSIONS AND RECOMMENDATIONS
Accurate low temperature material characterization is critical for successful design of flexible
pavements such that they resist thermal cracking in the field. The indirect tensile (IDT) strength of an
asphalt mixture is an important parameter used in characterization of its thermal cracking resistance.
This research investigated the IDT strength characteristics of numerous asphalt mixtures commonly
used in the State of Michigan. The research program also included investigation of the ability of
Pavement ME Design Guide in predicting IDT strength of the asphalt mixtures from the constituent
properties in Level 3 analysis. In an effort to improve IDT strength prediction for use in Pavement
ME Design Guide, new IDT strength predictive models were developed. First, the current Pavement
ME Design Guide IDT strength predictive model was locally calibrated with the Michigan mixtures
tested in this study. Second a new IDT strength predictive model was developed using linear
regression techniques. Lastly, an Artificial Neural Network (ANN) was trained and validated using
the Michigan mixtures. All inputs in the newly developed and ANN IDT strength models can easily
be obtained by designers from mix design Job Mix Formulas (JMFs). Based on the foregoing, the
following major conclusions were drawn:


In 62 different Michigan mixtures tested, a wide variety of IDT strength and fracture
work values were observed. The IDT strength and fracture work were affected by
factors such as the aggregate gradation, binder PG, and aggregate angularity of the
asphalt mixtures.



Direct relationship between the IDT strength as well as fracture work to binder
Performance Grade (PG) and MDOT mixture designation was not observed.
Generally, stiff binders resulted in higher low temperature IDT strength and lower
fracture work.

70



Level 3 IDT strength predictions of Pavement ME Design Guide were very poor for
the Michigan asphalt mixtures. All three predictive models developed in this study
showed improved IDT strength prediction performance as compared to Pavement ME
Design Guide Level 3 IDT strength prediction.

It is recommend that pavement designers in the State of Michigan exercise caution when relying on
low PG or MDOT mix designation as a method to increase or decrease IDT strength and when using
the IDT strength predictive equation in Pavement ME Design Guide Level 3 thermal cracking
analysis. To determine mixture low temperate IDT strength, the models developed in this study
should be used instead (depending on the inputs available).

71

APPENDICES

72

APPENDIX A: MIX PROPERTIES AND VOLUMETRICS OF MIXTURES TESTED

73

Table 15 Mixture properties and volumterics of mixtures tested
Measured
Corrected
Peak
Sample
Tensile
Tensile
ID
Strength
Strength
(psi)
(psi)
2A
562
477
2B
414
362
(WMA)
4
570
483
18A
391
343
18B
544
463
20A
530
452
20B
524
448
20C
457
395
21
533
454

Polymer
FE
Modified
Post
(1-yes, 0(lb*in)
no)

PG
High
Grad
e

PG
Low
Grad
e

RAP
(%)

Mix Type

Pb (%)
(JMF)

0

64

22

17

3E30

4.90

158

0

64

28

17

3E30

4.90

300
228
244
255
263
247
281

115
137
30
3
78
115
0

1
0
0
0
0
0
0

70
58
58
64
64
64
64

28
22
22
28
28
28
28

16
19
19
18
20
20
21

4E30
3E10
3E10
4E10
5E10
4E10
5E10
4E10 High
Stress
5E10
5E10
3E3
3E3
3E3
4E3
4E3
5E3
5E3
4E3
4E3
5E3
5E3 High
Stress

5.31
5.20
5.04
5.23
5.53
5.58
6.01

FE
Total
(lb*in)

FE Pre
(lb*in)

280

275

5

419

261

415
365
273
258
341
362
281

23

542

462

446

320

125

1

70

28

16

24A
24B
26A
26B
26C
28A
28B
29A
29B
31A
31B
32A

428
589
463
384
394
570
484
462
496
518
553
540

372
498
400
338
346
483
416
399
426
442
470
460

527
459
412
430
349
225
185
280
202
281
283
327

287
335
247
220
247
225
183
260
198
254
279
291

240
123
165
210
102
0
2
20
4
27
4
35

0
1
0
0
0
0
0
0
0
1
1
1

70
70
58
58
58
64
64
64
64
70
70
70

28
28
22
28
28
28
28
28
28
28
28
28

16
19
19
24
28
21
19
16
21
19
21
16

32B

531

453

406

275

131

1

70

28

22

74

4.94
6.29
5.78
5.60
5.30
5.43
5.40
5.43
5.99
5.92
5.62
5.40
5.99
6.08

Table 15 (cont’d)
Measured
Corrected
Peak
Sample
Tensile
Tensile
ID
Strength
Strength
(psi)
(psi)
44
470
405
45
395
346

Polymer
FE
Modified
Post
(1-yes, 0(lb*in)
no)

FE
Total
(lb*in)

FE Pre
(lb*in)

226
323

226
252

0
71

PG
High
Grad
e

PG
Low
Grad
e

RAP
(%)

0
0

58
58

28
28

25
24

Mix Type

Pb (%)
(JMF)

47

506

433

245

245

0

0

64

28

25

48

491

422

213

213

0

0

64

28

30

49A
49B
51A
51B
51C
(WMA)
62
64
65

447
382
396
470

387
336
347
405

499
1014
544
215

260
200
226
215

239
813
318
0

1
1
0
0

70
70
58
58

28
28
28
28

0
0
15
30

4E1
5E1
4E1 High
Stress
5E1 High
Stress
GGSP
GGSP
LVSP
LVSP

437

379

294

236

59

0

58

28

15

LVSP

5.60

480
448
415

413
388
362

508
246
324

265
202
274

243
43
50

0
0
0

58
58
58

28
34
34

10
19
20

4.89
5.40
6.00

67

466

402

522

253

269

1

64

34

15

68

476

410

405

292

112

1

64

34

17

80
81
85

474
409
467

409
357
403

537
193
622

295
193
254

241
0
367

0
0
1

58
58
64

34
34
34

21
20
17

86

486

417

538

287

251

1

64

34

21

90

534

455

182

182

0

1

70

22

18

3E3
4E3
5E3
4E3 High
Stress
5E3 High
Stress
4E1
5E1
4E1 HS
5E1 High
Stress
4E30

75

5.35
5.98
5.29
5.91
6.18
6.12
6.24
5.36

5.10
5.46
5.45
5.66
5.48
6.14
4.98

Table 15 (cont’d)
Measured
Corrected
Peak
Sample
Tensile
Tensile
ID
Strength
Strength
(psi)
(psi)
102
575
487
103
498
427

Polymer
FE
Modified
Post
(1-yes, 0(lb*in)
no)

FE
Total
(lb*in)

FE Pre
(lb*in)

343
333

297
218

46
115

PG
High
Grad
e

PG
Low
Grad
e

RAP
(%)

0
0

64
64

22
22

20
19

Mix Type

Pb (%)
(JMF)

105

526

449

312

297

15

1

70

22

14

108
109

549
566

467
480

302
241

298
241

4
0

0
0

64
64

22
22

20
18

111

607

512

338

321

16

1

70

22

20

112

634

533

238

238

0

1

70

22

19

127
200
201
202

450
570
304
606

389
483
276
512

307
242
232
185

243
242
180
185

64
0
52
0

0
0
0
0

58
58
64
64

22
28
28
22

23
25

203

529

451

337

289

49

1

70

22

14

204

668

560

383

377

6

1

70

22

15

205
206
208
WMA
209
HMA
209
WMA

363
551

321
468

178

178

0

0
0

58
64

28
22

25
15

4E10
5E10
4E10 High
Stress
4E3
5E3
4E3 High
Stress
5E3 High
Stress
LVSP
3E10
ASCRL
5E10
4E30 High
Stress
5E30 High
Stress
2E3
5E1

496

425

174

174

0

0

64

22

30

LVSP

5.60

532

453

200

200

0

0

64

22

21

5E10

6.21

487

419

196

192

4

0

64

22

21

5E10

6.21

76

21

5.20
5.60
5.08
5.21
5.50
5.31
5.80
5.43
5.20
3.30
6.03
4.99
5.80
4.90
5.40

Table 15 (cont’d)
Sample
ID
2A
2B
(WMA)
4
18A
18B
20A
20B
20C
21
23
24A
24B
26A
26B

VMA

Angulari
VFA % Air
ty

13.9
4
14.0
2
15.0
4
14.1
6
13.5
2
15.0
5
14.9
7
14.8
3
16.3
4
14.4
0
16.0
4
15.9
4
14.1
7
13.8
0

78.4
7
78.6
7
73.5
1
78.8
1
77.8
1
73.4
9
73.2
8
76.4
0
75.5
8
75.6
9
75.0
6
78.0
4
78.8
3
78.1
7

Gmm

Gmb

Gb

Gse

Gsb

Pbe

Fines/
Asphalt
Ratio

Crushed
Face 1

1-1/2"

3.00

46.00

2.545

2.469

1.027

2.755

2.728

4.55

1.100

99.60

100.00

3.00

46.00

2.508

2.433

1.029

2.708

2.691

-

0.960

98.30

100.00

4.00

45.30

2.510

2.410

1.025

2.732

2.686

4.70

1.040

94.90

100.00

3.00

46.00

2.534

2.458

1.018

2.760

2.715

4.62

1.130

99.70

100.00

3.00

41.30

2.502

2.427

1.023

2.710

2.665

-

0.990

92.30

100.00

4.00

45.20

2.506

2.406

1.029

2.722

2.684

4.72

1.000

85.90

100.00

4.00

45.00

2.485

2.386

1.029

2.710

2.651

4.73

1.230

92.30

100.00

3.50

45.20

2.489

2.402

1.032

2.715

2.663

-

0.940

92.70

100.00

4.00

45.30

2.481

2.382

1.029

2.727

2.676

5.33

1.010

94.80

100.00

3.50

46.00

2.578

2.488

1.030

2.796

2.763

-

0.950

92.70

100.00

4.00

45.40

2.426

2.329

1.031

2.668

2.599

5.33

1.090

95.50

100.00

3.50

45.00

2.531

2.422

1.030

2.779

2.737

-

1.070

86.60

100.00

3.00

45.00

2.538

2.462

1.018

2.785

2.708

4.62

1.130

99.50

100.00

3.00

42.10

2.490

2.415

1.020

2.709

2.653

4.55

0.960

96.90

100.00

77

Table 15 (cont’d)
Sample
ID
28A
28B
29A
29B
31A
31B
32A
32B
37
44
45
47
48
49A

VMA

Angulari
VFA % Air
ty

14.7
5
15.0
6
15.7
4
16.0
7
15.2
7
14.7
1
15.7
1
16.2
0
16.5
2
15.0
7
16.2
2
14.8
8
16.0
2
17.5
9

72.8
7
73.4
4
74.5
9
75.1
1
73.7
6
72.8
1
74.5
4
75.3
1
75.7
8
73.4
6
75.3
8
73.1
2
75.0
3
77.3
5

Gmm

Gmb

Gb

Gse

Gsb

Pbe

Fines/
Asphalt
Ratio

Crushed
Face 1

1-1/2"

4.00

41.20

2.471

2.372

1.028

2.686

2.632

4.66

1.160

90.40

100.00

4.00

41.70

2.490

2.390

1.028

2.711

2.661

4.76

1.070

90.40

100.00

4.00

43.40

2.457

2.359

1.028

2.696

2.632

5.12

1.060

90.60

100.00

4.00

43.00

2.463

2.364

1.028

2.700

2.650

5.24

0.930

76.60

100.00

4.00

41.20

2.471

2.372

1.017

2.701

2.642

4.83

0.970

95.00

100.00

4.00

41.20

2.472

2.373

1.031

2.686

2.632

4.66

1.160

90.40

100.00

4.00

43.40

2.458

2.360

1.031

2.696

2.632

5.12

1.060

90.60

100.00

4.00

41.70

2.450

2.352

1.017

2.696

2.636

5.27

0.950

94.80

100.00

4.00

42.60

2.494

2.395

1.032

2.743

2.696

5.39

1.090

93.80

100.00

4.00

42.10

2.475

2.376

1.020

2.692

2.648

4.75

0.930

88.50

100.00

4.00

42.40

2.454

2.356

1.020

2.695

2.644

5.29

1.020

97.20

100.00

4.00

42.60

2.504

2.404

1.029

2.722

2.675

4.66

1.140

85.50

100.00

4.00

41.90

2.474

2.375

1.029

2.713

2.661

5.21

1.170

92.80

100.00

4.00

48.90

2.535

2.434

1.025

2.808

2.771

5.72

1.430

100.00

100.00

78

Table 15 (cont’d)
Sample
ID
51A
51B
51C
(WMA)
62
64
65
67
68
80
81
85
86
90
97

VMA

Angulari
VFA % Air
ty

16.5
1
14.7
2
15.3
7
14.1
7
15.0
0
16.1
0
15.4
0
15.7
8
15.2
0
16.1
1
15.2
0
16.0
0
14.7
3
15.9

75.8
0
76.2
2
77.3
3
78.8
2
73.3
0
75.2
0
74.1
0
75.6
5
73.7
0
75.2
0
77.0
0
81.2
0
76.2
3
74.8

Gmm

Gmb

Gb

Gse

Gsb

Pbe

Fines/
Asphalt
Ratio

Crushed
Face 1

1-1/2"

4.00

-

2.474

2.375

1.032

2.727

2.667

5.44

0.860

98.90

100.00

3.50

-

2.483

2.396

1.024

2.701

2.659

-

1.080

74.70

100.00

3.50

-

2.468

2.382

1.024

2.693

2.657

-

0.880

95.40

100.00

3.00

42.90

2.589

2.512

1.032

2.807

2.783

4.59

0.760

98.40

100.00

4.00

41.00

2.462

2.364

1.023

2.679

2.629

4.74

0.950

75.30

100.00

4.00

43.20

2.468

2.369

1.023

2.712

2.655

5.24

0.910

81.80

100.00

4.00

42.10

2.565

2.463

1.026

2.789

2.764

4.75

1.050

96.30

100.00

4.00

42.80

2.537

2.436

1.026

2.773

2.734

4.96

1.050

94.70

100.00

4.00

41.80

2.511

2.411

1.026

2.740

2.688

4.77

1.170

89.30

100.00

4.00

42.80

2.523

2.422

1.026

2.765

2.724

5.13

1.130

88.80

100.00

3.50

43.20

2.497

2.410

1.033

2.721

2.686

-

1.080

87.70

100.00

3.50

42.50

2.471

2.397

1.033

2.718

2.678

-

1.020

75.00

100.00

3.50

47.00

2.547

2.458

1.023

2.763

2.739

-

1.200

97.00

100.00

4.00

46.00

2.537

2.436

1.023

2.776

2.738

1.240

99.80

100.00

79

Table 15 (cont’d)
Sample
ID
102
103
105
108
109
111
112
127
200

VMA
14.9
6
16.0
6
15.2
3
15.0
5
16.0
8
15.0
9
16.3
9
15.2
3
13.7
0

201
202
203
204
205

16.1
9
14.8
5
15.7
7
13.2
3

Angulari
VFA % Air
ty
73.2
5
75.1
0
73.7
4
73.4
3
75.1
2
73.5
0
75.5
9
73.7
4
78.2
2
75.3
6
73.0
7
74.6
3
77.3
2

Gmm

Gmb

Gb

Gse

Gsb

Pbe

Fines/
Asphalt
Ratio

Crushed
Face 1

1-1/2"

4.00

46.00

2.550

2.448

1.027

2.776

2.729

4.60

1.220

99.50

100.00

4.00

45.00

2.498

2.398

1.027

2.730

2.697

5.17

1.160

92.30

100.00

4.00

46.00

2.536

2.434

1.025

2.753

2.726

4.73

1.160

95.50

100.00

4.00

46.00

2.541

2.439

1.027

2.765

2.722

4.65

1.220

97.90

100.00

4.00

45.00

2.493

2.393

1.027

2.719

2.695

5.18

1.240

98.60

100.00

4.00

46.00

2.544

2.443

1.025

2.775

2.724

4.66

1.220

99.20

100.00

4.00

45.00

2.489

2.389

1.025

2.729

2.692

5.31

1.150

99.80

100.00

4.00

-

2.522

2.421

1.022

2.754

2.701

4.74

1.180

93.50

100.00

3.00

43.20

2.513

2.438

1.024

2.731

2.678

4.50

1.130

82.00

100.00

-

3.30

2.734

1.026

2.835

2.775

2.54

1.090

100.00

100.00

4.00

45.60

2.482

2.383

1.031

2.728

2.672

5.29

1.140

95.20

100.00

4.00

47.00

2.510

2.410

1.025

2.717

2.689

4.62

1.190

99.30

100.00

4.00

47.00

2.524

2.423

1.025

2.774

2.710

4.98

1.230

99.80

100.00

3.00

42.10

2.502

2.427

1.020

2.704

2.660

4.31

1.052

95.90

100.00

80

Table 15 (cont’d)
Sample
ID
206
208
WMA
209
HMA
209
WMA

VMA

Angulari
VFA % Air
ty

16.0
8
14.7
5
15.8
9
15.8
9

75.1
3
76.2
7
77.9
7
77.9
7

Gmm

Gmb

Gb

Gse

Gsb

Pbe

Fines/
Asphalt
Ratio

Crushed
Face 1

1-1/2"

4.00

45.00

2.503

2.403

1.027

2.727

2.709

5.16

1.250

97.90

100.00

3.50

-

2.461

2.375

1.034

2.680

2.630

-

0.920

85.00

100.00

3.50

45.00

2.476

2.389

1.209

2.730

2.664

-

0.920

95.00

100.00

3.50

45.00

2.476

2.389

1.209

2.730

2.664

-

0.920

95.00

100.00

81

Table 15 (cont’d)
Sample
ID
2A
2B
(WMA)
4
18A
18B
20A
20B
20C
21
23
24A
24B
26A
26B
26C
28A
28B
29A
29B
31A
31B
32A
32B
37
44
45
47

1/2"

3/8"

No. 4

No. 8

No. 16 No. 30 No. 50

No.
100

No.
200

100.00 100.00

83.00

72.30

47.30

34.90

26.00

18.20

9.30

6.10

5.00

100.00 100.00

88.10

77.10

57.60

40.90

27.70

19.50

12.70

7.50

4.50

100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00

98.80
84.50
88.80
98.80
93.40
93.20
100.00
91.60
100.00
100.00
88.10
89.80
86.10
98.90
90.10
100.00
100.00
93.90
98.90
100.00
100.00
100.00
93.70
100.00
93.50

88.60
73.40
84.30
89.50
90.40
88.60
99.20
83.00
95.70
97.80
78.40
80.70
80.70
89.60
84.40
97.90
96.90
87.80
89.60
97.90
96.70
92.50
86.20
96.60
87.10

73.20
49.40
65.80
71.10
83.40
73.50
83.60
68.30
80.10
86.80
52.60
63.60
63.30
71.50
71.20
80.30
77.40
72.00
71.50
80.30
77.80
70.10
73.30
77.40
76.40

56.30
34.70
46.20
53.50
56.20
54.00
66.30
50.00
58.00
61.80
33.00
46.30
49.00
57.00
55.70
59.60
59.00
56.70
57.00
59.60
58.20
58.60
54.80
57.80
57.20

38.00
25.70
33.90
36.30
36.70
40.70
46.50
35.90
39.90
44.30
22.10
35.60
41.40
46.30
44.20
44.90
46.40
43.90
46.30
44.90
45.10
50.30
41.80
45.10
41.30

25.20
20.20
25.50
23.50
25.60
30.80
31.20
25.60
28.70
32.30
15.60
26.60
32.60
35.90
32.20
32.90
33.20
32.60
35.90
32.90
34.20
41.10
30.60
34.40
29.90

14.70
11.50
16.30
13.10
15.80
19.40
17.30
14.40
16.20
18.30
10.90
13.90
14.20
15.60
16.10
15.20
16.10
16.30
15.60
15.20
191.00
21.90
16.10
18.60
16.60

7.80
6.90
7.40
7.40
8.40
8.60
8.70
6.80
7.70
9.00
7.20
6.50
6.20
7.00
7.40
7.20
7.10
6.90
7.00
7.20
7.40
8.70
6.60
8.00
8.00

4.90
5.20
4.40
4.70
5.80
4.60
5.40
4.30
5.80
5.60
5.20
4.40
4.50
5.40
5.10
5.40
4.90
4.70
5.40
5.40
5.00
5.90
4.40
5.40
5.30

1"

3/4"

100.00
100.00
98.10
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00

82

Table 15 (cont’d)
Sample ID

1"

3/4"

1/2"

3/8"

No. 4

No. 8

No. 16 No. 30 No. 50

48
49A
49B
51A
51B
51C (WMA)
62
64
65
67
68
80
81
85
86
90
97
102
103
105
108
109
111
112
127
200
201
202
203

100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00

100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
99.90
96.00
100.00
100.00

100.00
94.60
96.10
94.80
91.90
91.20
86.50
95.00
100.00
95.90
100.00
98.20
100.00
93.70
100.00
98.20
100.00
98.50
100.00
99.30
98.70
100.00
98.90
100.00
92.50
88.90
59.50
100.00
96.40

99.70
70.00
79.70
83.20
84.80
85.70
76.10
86.90
97.40
84.30
95.40
89.90
97.40
84.40
97.00
85.60
99.70
88.60
99.90
88.30
87.30
99.60
87.60
99.90
86.80
82.60
30.20
99.70
87.10

83.30
26.60
31.80
58.70
72.40
71.40
56.90
72.50
75.20
64.80
73.60
69.30
75.20
66.40
80.20
63.60
77.70
65.10
75.90
63.00
65.10
75.60
66.50
75.80
79.20
65.00
14.70
84.10
52.30

63.00
20.50
22.10
44.60
57.20
56.70
45.40
56.70
56.70
56.20
59.90
54.00
56.40
53.50
62.20
44.20
53.90
45.00
54.70
42.20
46.50
51.40
47.30
54.90
58.50
48.40
11.50
66.70
33.60

49.80
16.60
17.80
35.90
45.40
43.90
34.40
43.50
42.50
45.00
47.80
41.10
43.60
42.60
47.80
31.00
37.20
30.30
39.10
28.10
32.30
36.50
33.90
39.20
43.20
34.10
9.10
46.80
22.40

83

36.70
13.00
14.40
27.40
35.50
30.80
23.10
32.20
31.10
30.90
33.90
30.00
31.00
26.90
33.80
22.00
26.20
21.50
29.50
19.40
23.30
27.40
24.40
29.10
32.60
22.50
7.20
31.50
15.90

20.00
10.40
11.80
14.00
19.50
14.80
14.60
15.50
15.50
20.10
21.60
18.60
16.80
11.20
18.20
14.00
14.80
13.50
18.00
12.90
14.90
17.60
15.80
18.20
20.90
12.00
6.00
16.60
10.90

No.
100
9.20
8.90
9.70
7.10
7.90
7.30
6.10
6.20
6.60
8.20
8.80
8.40
8.60
7.00
8.20
7.50
9.10
7.80
9.80
7.70
8.10
9.60
8.20
8.40
10.30
7.30
4.60
8.70
7.10

No.
200
6.10
8.20
8.10
4.70
5.20
4.50
3.50
4.50
4.80
5.00
5.20
5.60
5.80
5.40
5.70
5.60
6.20
5.60
6.00
5.50
5.70
6.40
5.70
6.10
5.60
5.10
3.60
6.00
5.50

Table 15 (cont’d)
Sample ID

1"

205
206
208 WMA
209 HMA
209 WMA

100.00
100.00
100.00
100.00
100.00

3/4"

1/2"

90.00 73.50
100.00 100.00
100.00 94.20
100.00 100.00
100.00 100.00

3/8"

No. 4

No. 8

No. 16 No. 30 No. 50

69.70
99.70
86.10
97.80
97.80

57.40
78.00
65.20
77.60
77.60

44.50
53.90
48.70
52.70
52.70

35.30
38.60
39.40
37.40
37.40

84

25.50
29.10
32.40
25.90
25.90

12.60
18.00
15.60
14.20
14.20

No.
100
5.90
9.60
6.40
7.30
7.30

No.
200
4.40
6.40
4.50
4.90
4.90

APPENDIX B: IDT STRENGTH, FRACTURE WORK, AND VOLUMTERICS OF
SPECIMENS TESTED

85

Table 16 IDT Strength, Fracture Work, and Air Voids of Specimens Tested

Mix

2A
2B

4

18A

18B

20A

20B

Sample
2A-1-A
2A-3-A
2A-1-B
2B-2-A
2B-3-B
2B-2-C
4-1-A
4-3-A
4-1-B
4-3-B
18-2-2
18-1-B
18-1-C
18-3-C
18B-2A
18B-1B
18B-2B
18B-3B
20A-3A
20A-1B
20A-3B
20B-1A
20B-3A
20B-1B
20B-3B

VA
(%)
7.6
7.3
7.2
6.6
7.4
7.1
7.1
7.1
7.1
6.9
7.4
7.4
6.4
6.6

IDT
IDT
Strength
Strength
Average
(psi)
(psi)
452.5
495.9
477
482.2
380.5
365.8
362
338.5
497.2
459.5
483
478.0
497.3
276.8
338.1
343
368.4
388.8

6.7

450.4

6.4

466.8

SD
(psi)

CV
(%)

22.19

4.65

21.28

5.88

18.13

3.75

48.81

14.2
3

Total
FE
(lb*in.)
291.0
349.2
201.0
392.7
521.7
343.6
359.5
419.0
466.1
387.6
191.2
516.5

Total FE
Average
(lb*in)

Total
FE
SD
(lb*in)

280

74.63

419

91.98

415

53.42

365

163.8
5

273

87.41

269

60.82

341

23.58

387.2
290.3
463

30.26

6.54

7.3

431.2

232.5

7.4

502.6

183.8

7.0

454.5

338.7

7.1

418.4

7.1

482.8

240.4

6.6

438.8

336.0

7.4

469.5

452

32.24

7.14

227.5

309.1
448

19.15

4.28

6.8

456.2

361.1

7.0

425.9

356.0

86

Table 16 (cont’d)

Mix

20C

21

23

24A

24B

26A

Sample
20C-1A
20C-3A
20C-3B
21-3-B
21-1-B
21-1-D
23A-1A
23A-2A
23A-3A
24-1-B
24-3-B
24A-1A
24A-3A
24B-3A
24B-1A
24B-1B
24B-3B
26A-1A
26A-1B

VA
(%)

IDT
IDT
Strength
Strength
Average
(psi)
(psi)

SD
(psi)

CV
(%)

Total
FE
(lb*in.)

7.4

369.6

7.4

401.6

7.2

413.1

391.0

7.4
7.3
7.2

472.0
456.4
433.8

301.6
309.1
232.7

6.7

459.0

7.5

448.6

6.7

477.3

391.4

6.6
6.8

343.4
367.3

565.6
602.9

6.6

408.3

6.9

368.9

462.8

7.1

483.2

441.6

7.0

490.2

403.2

7.5

520.9

407.3

6.9

499.1

582.3

7.7

413.1

412.0

7.4

386.1

Total FE
Average
(lb*in)

Total
FE
SD
(lb*in)

362

86.00

281

42.12

446

63.20

527

68.00

459

84.25

412

0.00

430.2
395

22.55

454

19.19

5.71

4.23

265.6

430.2
462

14.50

372

26.90

498

16.39

400

19.05

3.14

7.23

515.0

477.1

3.29

4.77
-

87

Table 16 (cont’d)

Mix

26B

26C

28A

28B

29A

Sample
26B-1B
26B-3B
26B-2C
26B-3C
26C-1A
26C-2A
26C-3A
28A-1A
28A-1B
28A-3B
28B-1A
28B-3A
28B-1B
28B-3B
29A-3A
29A-3B
29A-1B

IDT
Strength
Average
(psi)

VA
(%)

IDT
Strength
(psi)

7.5

315.6

7.7

359.2

7.3

309.8

7.7

367.3

443.0

7.2

347.0

417.5

7.2

333.4

6.5

356.8

335.4

7.5

492.4

192.1

7.2

490.7

7.3

465.4

276.1

7.1

429.6

192.8

7.5

416.7

7.4

430.1

7.2

387.1

182.3

7.4

410.7

276.5

7.3

387.5

7.3

397.4

SD
(psi)

CV
(%)

Total
FE
(lb*in.)

Total FE
Average
(lb*in)

Total
FE
SD
(lb*in)

430

11.29

349

62.66

225

44.97

185

32.71

280

11.20

435.0
29.4
8

338

11.7
7

346

15.1
1

483

20.1
6

416

11.6
5

399

418.6
8.72
422.4

3.40

3.13

294.5

206.3

222.7
4.85
143.6

2.92

292.3
270.7

88

Table 16 (cont’d)

Mix

29B

31A

31B

32A

32B

37

Sample
29B-1A
29B-2A
29B-1B
29B-3B
31A-1A
31A-2A
31A-3A
31B-3A
31B-1A
31B-1B
32A-1A
32A-2A
32A-1B
32A-3B
32B-1A
32B-3A
37-3-B
37-2-1A
37-1-B

IDT
Strength
Average
(psi)

VA
(%)

IDT
Strength
(psi)

6.7

454.5

7.3

402.1

6.9

418.5

7.2

427.9

223.7

6.6

475.1

210.7

7.1

404.3

6.5

447.2

354.4

6.9

474.9

307.5

7.4

478.4

7.2

457.4

294.6

7.0

449.8

316.4

7.7

445.5

6.9

486.7

7.0

456.3

372.1

7.1

458.6

350.0

6.9

447.1

7.4
7.1
7.6

431.8
465.4
466.4

SD
(psi)

CV
(%)

Total
FE
(lb*in.)

Total FE
Average
(lb*in)

Total
FE
SD
(lb*in)

202

23.31

281

71.88

283

31.62

327

41.99

406

79.50

515

153.9
2

169.5
21.9
4

426

35.6
7

442

11.2
5

470

18.6
1

460

453

8.15

212.2
5.15
202.2

8.07

2.39

279.3

247.4

345.0
4.05
273.9

1.80
462.4

19.7
2

455

89

4.34

603.9
603.9
337.3

Table 16 (cont’d)

Mix

44

45
47
48

49A

49C

51A

Sampl
e
44A-1C
44A-3C
44A-2C
45-3-A
45-1-A
45-1-B
47-1-A
47-2-A
48-1-A
48-3-A
49A-2A
49A-3A
49A-1B
49A-3B
49C-2A
49C-3A
49C-1B
49C-3B
51A-1A
51A-3A
51A-2A

IDT
Strength
Average
(psi)

VA
(%)

IDT
Strength
(psi)

6.6

387.2

6.7

435.4

7.5

392.1

7.6
7.1
6.8
6.7
7.6
7.3
7.3

325.7
327.6
385.0
436.2
429.9
436.4
406.6

7.5

367.9

6.7

388.7

6.4

401.1

7.1

391.5

687.2

7.0

332.8

1295

6.6

346.9

7.4

350.6

7.4

315.5

956.5

7.5

305.0

692.1

7.2

384.7

7.5

351.3

SD
(psi)

CV
(%)

Total
FE
(lb*in.)

Total FE
Average
(lb*in)

Total
FE SD
(lb*in)

226

44.80

323

39.73

245

41.76

213

47.67

499

140.70

1014

257.63

544

130.05

200.2
26.5
5

405

6.56

200.3
277.8

346

33.7
1

9.74

433

4.45

1.03

422

21.1
0

5.01

319.2
364.6
285.5
215.0
274.1
179.1
246.5
414.3

14.0
1

387

15.9
4

336

40.0
2

347

371.4
3.62
521.4

4.74
789.4

11.5
3

450.1
488.7

90

Table 16 (cont’d)

Mix

51B

51C

62

64

65

76

68

Sample
51B-2A
51B-1B
51B-3B
51C-1A
51C-3A
51C-1B
51C-3B
62-1-A
62-3-A
62-2- B
64-3-1
64A-1E
64A-3E
64A-1D
65-1-A
65-2-A
65-3-A
67-1/41A
67-1/43
67-1/42
68-3-B
68-1-B
68-1-D
68-3-D

IDT
Strength
Average
(psi)

VA
(%)

IDT
Strength
(psi)

7.2

402.1

7.1

421.0

6.6

393.0

191.1

7.6

376.9

321.4

7.3

391.2

7.1

364.0

7.0

385.8

6.4
7.0
7.3
7.6

390.4
425.3
422.0
423.3

6.6

421.6

6.6

379.6

7.5

326.9

6.9
7.5
7.0

371.0
351.1
363.9

6.6

415.6

6.7

411.6

7.4

379.0

7.5
7.2
7.1
7.5

402.1
444.8
393.2
398.6

SD
(psi)

CV
(%)

Total
FE
(lb*in.)

Total FE
Average
(lb*in)

Total
FE
SD
(lb*in)

215

47.31

294

26.60

508

96.68

246

76.78

324

40.40

522

85.32

405

40.21

270.0
14.2
8

405

11.8
9

379

3.52

185.4

304.5
3.13
258.5
293.1

19.2
7

413

4.67

434.5
617.5
472.0
163.0
208.5

45.3
7

388

11.7
0

339.4
271.8

10.1
0

362

2.79

369.2
291.4
311.4
451.4

20.0
9

402

5.00

498.2
616.9

23.6
8

410

91

5.78

370.4
373.9
454.6
420.2

Table 16 (cont’d)

Mix

80
81

85

86

90A

97

102

Sample
80-1-A
80-2-A
80-1-B
80-3-B
81-1-1
85A-3A
85A-1B
85A-3B
86A-1A
86A-3A
86A-2B
86A-3B
90A-1B
97A-1A
97A-2A
97A-3A
102A-3B
102A-1C
102A-3C

IDT
Strength
Average
(psi)

VA
(%)

IDT
Strength
(psi)

6.4
7.1
7.1
7.1
7.4

428.8
400.0
409.1
396.4
357.4

7.5

407.2

6.8

411.0

7.4

390.9

787.9

7.6

432.6

490.0

7.4

423.4

SD
(psi)

CV
(%)

409

14.5
2

3.55

357

0.00

0.00

Total
FE
(lb*in.)
552.7
628.7
463.4
413.0
192.9

Total FE
Average
(lb*in)

Total
FE
SD
(lb*in)

514

95.58

193

0.00

622

147.4
8

538

116.3
5

182

0.00

258

28.31

343

80.52

506.5
10.6
8

403

16.0
7

417

2.65

570.7

411.8
3.85

6.8

418.4

565.8

6.8

394.9

6.4

455.3

6.8

511.9

7.8

502.9

7.1

508.2

269.3

6.4

470.8

281.0

6.5

505.4

6.8

485.1

685.1
455

0.00

0.00

181.6
225.8

508

4.53

17.4
0

487

0.89

3.57

278.9

314.0
434.0

92

Table 16 (cont’d)

Mix

103

105

108

109

111

112

Sample
103A-1B
103A-2B
103A-3E
103A-1E
105A-2B
105A-3B
105A-1C
105A-3C
108-1-B
108A-1B
108A-2B
108A-3B
109-4/2
109-1-A
109-3-A
111A-1B
111A-2B
111A-3B
112-1-A
112-3-A
112-1-B
112-3-B

VA
(%)

IDT
Strength
(psi)

6.7

364.9

7.1

368.8

IDT
Strength
Average
(psi)

SD
(psi)

CV
(%)

Total
FE
(lb*in.)

Total FE
Average
(lb*in)

Total
FE
SD
(lb*in)

333

211.6
4

312

58.18

302

64.87

241

46.34

338

9.25

238

19.56

634.1
70.1
6

427

16.4
4

326.0

7.6

500.1

7.6

473.7

171.7

7.5

409.0

387.9

6.5

486.6

7.1

444.7

7.4

456.5

325.5

7.4

476.7

272.4

6.5

475.6

32.1
2

449

200.2

255.4
7.15
280.2

297.1
15.3
3

467

3.29

7.3

470.0

393.1

7.2

444.0

7.6
6.9
7.3

449.0
504.1
486.3

6.5

509.7

7.5

523.2

6.7

502.9

347.9

7.0
7.2
7.1
7.5

545.2
535.4
527.1
525.6

211.4
252.0
234.6
253.3

243.5
28.0
9

480

5.85

206.8
222.4
293.7
330.0

10.3
7

512

533

9.03

93

2.03

1.69

334.7

Table 16 (cont’d)

Mix

127

200

201

202

203

204

205
206

Sample

VA
(%)

127-1-B 7.3
127-3-B 7.4
127-17.3
C
200-1-A 7.0
200-3-A 7.3
200-1-B 7.2
201A-110.8
A
201A-211.6
A
201A-310.6
A
202A-26.6
A
202A-37.2
A
202A-16.6
B
202A-37.0
B
203-1-A 7.3
203-3-A 7.4
203A-17.0
A
203A-37.1
A
204-1-3 7.3
204-1-1 7.3
204A-37.5
A
205-2-1 7.0
205-2-2 7.1
205-2-3 7.5
206-1-A 7.3
206-3-A 7.0
206-1-B 7.5

IDT
Strength
(psi)
432.7
354.8

IDT
Strength
Average
(psi)

39.7
2

389

380.5
506.6
475.0
468.2

SD
(psi)

20.4
6

483

CV
(%)
10.2
0
4.23

271.4
271.6

Total
FE
(lb*in.)
200.8
393.2
252.9
242.5
230.2

276

7.29

2.65

163.0

513.1

172.6

500.2

194.9
512

8.40

1.64

512.2

162.8

520.5

209.3

447.7
464.9

272.9
311.3
13.3
1

451

2.95

434.1

97.67

242

11.39

232

82.95

185

21.12

353.3

337

59.69

383

70.27

-

-

178

20.35

412.2
11.7
0

2.09

321

37.4
9

11.6
7

468

21.5
2

4.60

560

566.7
359.0
284.0
320.7
483.4
477.9
443.7

307

323.7

207.9

566.8
546.5

Total
FE
SD
(lb*in)

326.5

284.1

457.5

Total FE
Average
(lb*in)

94

366.4
322.6
460.1
201.3
167.7
164.6

Table 16 (cont’d)

Mix

208

209
A

209
B

Sample
208A-1A
208A-2A
208A-3A
209A-3A
209A-1B
209A-3B
209B-1B
209B-1A
209B-3B

IDT
Strength
Average
(psi)

VA
(%)

IDT
Strength
(psi)

6.6

431.9

7.3

439.4

7.0

405.0

189.7

7.1

463.6

154.5

7.2

449.3

7.4

446.4

233.4

6.8

418.7

244.3

7.6

387.4

7.3

449.5

SD
(psi)

CV
(%)

Total
FE
(lb*in.)

Total FE
Average
(lb*in)

Total
FE
SD
(lb*in)

174

22.21

200

40.93

196

51.92

158.3
18.0
9

425

453

9.23

31.0
6

419

4.25

2.04

7.42

-

212.7

141.0
202.0

95

Table 16 (cont’d)

Mix

Total
FE
CV
(%)

2A

26.62

2B

21.94

4

12.88

18A

44.88

18B

31.96

20A

22.62

20B

6.92

20C

23.74

21

14.98

23

14.19

24A

12.90

Pre FE
(lb*in.)
291.0
333.8
201.0
281.9
274.3
227.5
282.4
284.0
334.5
262.1
191.2
230.1
290.7
268.6
232.5
183.8
324.9
227.5
240.4
236.7
235.3
263.9
315.3
216.3
242.5
282.7
301.6
309.1
232.7
323.7
321.0
316.0
300.6
263.3
298.7
284.1

Pre FE
Average
(lb*in)

Pre
FE
SD
(lb*in)

Pre
FE
CV
(%)

275

67.79

24.63

261

29.47

11.28

300

29.64

9.87

228

35.52

15.59

244

46.69

19.14

264

52.91

20.02

263

37.40

14.23

247

33.44

13.53

281

42.12

14.98

320

3.92

1.23

287

17.22

6.01

96

Post Post FE Post
FE
Average FE SD
(lb*in.) (lb*in)
(lb*in)
0.0
15.3
0.0
110.8
247.4
116.1
77.1
135.0
131.6
125.5
0.0
286.5
96.4
21.7
0.0
0.0
13.8
0.0
0.0
99.3
73.9
97.2
40.7
213.9
23.1
108.3
0.0
0.0
0.0
106.5
194.0
75.4
265.0
339.6
178.4
178.6

Post
FE CV
(%)

5

8.84

173.21

158

77.35

48.92

115

32.47

28.35

137

143.59 104.58

30

45.76

154.93

5

7.96

173.21

78

27.24

35.03

115

95.59

83.04

0

0.00

0.00

125

61.48

49.07

240

77.69

32.32

Table 16 (cont’d)
Total
FE
CV
(%)

Pre FE
(lb*in.)

24B

18.37

320.4
328.3
360.2
332.6

26A

0.00

26B

2.63

26C

17.95

28A

20.00

28B

17.65

29A

4.00

29B

11.54

31A

25.53

31B

11.17

32A

12.85

32B

19.57

Mix

246.7
221.7
210.9
205.1
243.1
258.0
220.3
261.6
192.1
206.3
276.1
192.8
213.6
143.6
182.3
276.5
231.6
270.7
169.5
212.2
195.6
212.9
210.7
267.1
284.3
296.0
247.4
294.6
316.4
275.9
273.9
299.6
249.0
301.2

Pre FE
Average
(lb*in)

Pre FE
SD
(lb*in)

Pre
FE
CV
(%)

335

17.31

5.16

247

0.00

0.00

220

16.73

7.60

247

22.92

9.29

225

44.97

20.0
0

183

29.38

16.0
5

260

24.41

9.40

198

20.33

10.2
9

254

38.48

15.1
5

279

27.64

9.90

291

20.34

6.98

275

36.93

13.4
2

97

Post
FE
SD
(lb*in)

Post
FE
CV
(%)

123

89.72

72.81

165

0.00

0.00

210

7.51

3.58

102

49.36

48.16

0

0.00

0.00

2

4.56

200.0
0

20

35.03

173.2
1

4

5.30

122.1
8

27

37.48

136.5
0

4

6.65

173.2
1

35

40.90

115.5
3

131

42.57

32.47

Post
Post FE
FE
Average
(lb*in.)
(lb*in)
121.2
74.9
47.0
249.7
165.3
213.3
207.7
217.3
200.0
159.5
74.2
73.8
0.0
0.0
0.0
0.0
9.1
0.0
0.0
0.0
60.7
0.0
0.0
0.0
6.6
10.8
0.0
12.2
70.2
11.5
0.0
0.0
0.0
69.1
0.0
72.5
101.0
161.2

Table 16 (cont’d)

Mix

Total
FE
CV
(%)

37

29.89

44

19.82

45

12.29

47

17.07

48

22.40

49A

28.22

49C

25.42

51A

23.92

51B

21.96

51C

9.04

62

19.03

64

31.25

Pre FE
(lb*in.)
221.5
221.5
318.1
200.2
200.3
277.8
250.8
251.0
254.4
215.0
274.1
179.1
246.5
249.4
277.1
251.6
261.4
220.4
206.8
173.2
193.9
234.1
249.6
270.0
185.4
191.1
262.2
249.5
215.4
215.2
302.8
230.9
259.8
163.0
208.5
258.1
180.3

Pre FE
SD
(lb*in)

Pre
FE
CV
(%)

254

55.79

21.9
9

226

44.80

19.8
2

252

2.04

0.81

245

41.76

213

47.67

260

12.63

4.86

200

24.30

12.1
4

226

28.75

12.7
3

215

47.31

21.9
6

236

23.97

10.1
7

265

36.18

13.6
8

202

41.52

20.5
1

Pre FE
Average
(lb*in)

98

17.0
7
22.4
0

Post
FE
SD
(lb*in)

Post
FE
CV
(%)

261

209.7
0

80.26

0

0.00

0.00

71

41.35

58.18

0

0.00

0.00

0

0.00

0.00

239

144.1
1

60.37

813

247.4
0

30.41

318

156.7
2

49.33

0

0.00

0.00

59

14.46

24.58

243

130.3
1

53.52

43

50.06

115.8
6

Post
Post FE
FE
Average
(lb*in.)
(lb*in)
382.4
382.4
19.1
0.0
0.0
0.0
68.5
113.7
31.1
0.0
0.0
0.0
0.0
164.9
94.2
269.9
425.8
1074.6
582.6
783.2
498.2
215.9
239.0
0.0
0.0
0.0
59.2
55.0
43.1
77.9
131.7
386.6
212.1
0.0
0.0
81.4
91.5

Table 16 (cont’d)

Mix

Total
Pre
FE CV
FE
(%)
(lb*in.)

65

12.47

76

16.34

68

9.93

80

18.58

81

0.00

85

23.72

86

21.62

90A

0.00

97

10.97

102

23.48

103

63.56

105

18.63

264.7
280.5
278.0
245.2
291.2
223.0
287.4
313.1
311.3
257.7
299.5
248.3
322.3
304.2
192.9
273.1
270.8
219.0
293.7
316.8
298.3
239.0
181.6
225.8
278.9
269.3
281.0
280.7
329.4
233.4
267.0
200.2
171.7
326.3
255.4
280.2
325.5

Pre FE
Average
(lb*in)

Pre FE
SD
(lb*in)

Pre
FE
CV
(%)

274

8.47

3.09

253

34.81

13.7
5

292

25.93

8.87

294

31.73

10.8
1

193

0.00

0.00

254

30.63

12.0
5

287

33.48

11.6
7

182

0.00

0.00

258

28.31

10.9
7

297

28.01

9.43

218

41.22

18.9
0

297

35.05

11.8
1

99

Post
FE
SD
(lb*in)

Post
FE
CV
(%)

50

48.84

98.45

269

108.1
5

40.20

112

48.28

42.97

221

123.0
1

55.70

0

0.00

0.00

367

177.7
0

48.37

251

147.9
0

58.87

0

0.00

0.00

0

0.00

0.00

46

53.45

116.3
2

115

192.5
3

167.5
4

15

30.78

200.0
0

Post
Post FE
FE
Average
(lb*in.)
(lb*in)
104.5
10.9
33.5
206.2
207.0
393.9
82.9
60.8
143.3
162.5
253.2
380.3
141.1
108.8
0.0
233.4
299.9
569.0
196.3
95.1
267.5
446.0
0.0
0.0
0.0
0.0
0.0
33.2
104.6
400.7
59.0
0.0
0.0
61.6
0.0
0.0
0.0

Table 16 (cont’d)

Mix

Total
FE
CV
(%)

108

21.51

109

19.23

111

2.74

112

8.22

127

31.83

200

4.71

201

35.82

202

11.42

203

17.69

204

18.35

206

11.44

Pre FE
(lb*in.)
272.4
297.1
378.4
243.5
206.8
222.4
293.7
330.0
334.7
299.2
211.4
252.0
234.6
253.3
200.8
258.8
270.4
252.9
242.5
230.2
201.3
163.0
175.3
172.6
194.9
162.8
209.3
272.9
209.6
338.8
332.8
366.4
322.6
441.9
201.3
167.7
164.6

Pre FE
Average
(lb*in)

Pre FE
SD
(lb*in)

Pre
FE
CV
(%)

298

57.98

19.4
6

241

46.34

19.2
3

321

19.30

6.01

238

19.56

8.22

243

37.26

15.3
1

242

11.39

4.71

180

19.57

10.8
8

185

21.12

11.4
2

289

60.45

20.9
5

377

60.36

16.0
1

178

20.35

11.4
4

100

Post
FE
SD
(lb*in)

Post
FE
CV
(%)

4

7.38

200.0
0

0

0.00

0.00

16

28.10

173.2
1

0

0.00

0.00

64

67.47

106.2
3

0

0.00

0.00

52

63.40

122.6
8

0

0.00

0.00

49

49.29

100.8
3

6

10.53

173.2
1

0

0.00

0.00

Post
Post FE
FE
Average
(lb*in.)
(lb*in)
0.0
0.0
14.8
0.0
0.0
0.0
0.0
0.0
0.0
48.7
0.0
0.0
0.0
0.0
0.0
134.3
56.2
0.0
0.0
0.0
122.4
0.0
32.6
0.0
0.0
0.0
0.0
0.0
101.7
14.5
79.4
0.0
0.0
18.2
0.0
0.0
0.0

Table 16 (cont’d)

Mix

Total
FE
CV
(%)

208

12.76

209
A

20.44

209
B

26.52

Pre FE
(lb*in.)
158.3
189.7
154.5
212.7
233.4
232.8
141.0
202.0

Pre FE
SD
(lb*in)

Pre
FE
CV
(%)

174

22.21

12.7
6

200

40.93

20.4
4

192

46.76

24.3
6

Pre FE
Average
(lb*in)

101

Post
FE
(lb*in.)
0.0
0.0
0.0
0.0
0.0
11.4
0.0
0.0

Post FE
Average
(lb*in)

Post
FE
SD
(lb*in)

Post
FE
CV
(%)

0

0.00

0.00

0

0.00

0.00

4

6.58

173.2
1

REFERENCES

102

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106