RECALIBRATION OF THE ASPHALT LAYER COEFFICIENT
Except where reference is made to the work of others, the work described in this thesis
is my own or was done in collaboration with my advisory committee. This thesis does
not include proprietary or classified information.
_________________________
Kendra Peters Davis
Certificate of Approval:
_______________________
Rod E. Turochy
Associate Professor
Civil Engineering
David H. Timm, Chair
Associate Professor
Civil Engineering
_______________________ _______________________________
Randy C. West George T. Flowers
Director Dean
National Center for Asphalt Graduate School
Technology
RECALIBRATION OF THE ASPHALT LAYER COEFFICIENT
Kendra Peters Davis
A Thesis
Submitted to
the Graduate Faculty of
Auburn University
in Partial Fulfillment of the
Requirements for the
Degree of
Masters of Science
Auburn, Alabama
August 10, 2009
iii
RECALIBRATION OF THE ASPHALT LAYER COEFFICIENT
Kendra Peters Davis
Permission is granted to Auburn University to make copies of this thesis at its discretion,
upon requests of individuals or institutions and at their expense. The author reserves all
publication rights.
_________________________
Kendra Peters Davis
_________________________
Date of Graduation
iv
VITA
Kendra Peters Davis, daughter of Anthony and Debbie (Miller) Peters, was born
January 21, 1984 in Decatur, Alabama. She graduated from Speake High School as
Valedictorian in May 2002. She attended Auburn University from where she graduated
magna cum laude in December, 2007 with a Bachelor?s of Science in Civil Engineering.
As an undergraduate student she participated in the Co-operative Education Program,
working for Turner Universal Construction. She entered into graduate school at Auburn
University in January 2008, where she specialized in the pavements and materials field
of civil engineering.
v
THESIS ABSTRACT
RECALIBRATION OF THE ASPHALT LAYER COEFFICIENT
Kendra Peters Davis
Master of Science, August 10, 2009
(B.S.C.E., Auburn University, 2007)
112 Typed Pages
Directed by David H. Timm
The Alabama Department of Transportation (ALDOT) currently uses the 1993
DARWin version of the 1986 American Association of State Highway and
Transportation Officials (AASHTO) Guide for the Design of Pavement Structures when
designing flexible pavements. The AASHTO design methodology is based on
information obtained at the AASHO Road Test, which was performed from 1958 to
1960 near Ottowa, Illinois. This road test provided an empirical correlation between
pavement thickness and traffic loadings. However, the results stemming from the road
test are limited to the pavement materials utilized, applied traffic and the climate of
vi
Illinois. Using the results of the AASHO Road Test, a flexible pavement design
equation was developed and introduced in the 1986 AASHTO Guide for Design of
Pavement Structures that includes inputs of soil resilient modulus, traffic, structural
capacity (structural number), reliability, variability, and ride quality (change in
serviceability). The structural number is calculated using the layer thicknesses, material
drainage properties and layer coefficients, which are used to express the relative strength
contribution of each pavement layer to the overall pavement structure. In this study,
these inputs were analyzed to determine the relative influence of each on the resulting
hot mix asphalt (HMA) thickness. It was found that the HMA layer coefficient, resilient
modulus and traffic inputs are by far the most influential parameters. Since the soil
modulus and traffic are generally given parameters for a particular design, it was
decided that the layer coefficient be recalibrated to provide the greatest potential savings
in HMA thickness. Furthermore, the layer coefficient has not been updated to account
for advancements made in construction methods, gradation requirements, and paving
materials since the AASHTO Road Test, and therefore should be reanalyzed.
The recalibration was performed using traffic and performance data collected for
the structural sections of the 2003 and 2006 National Center for Asphalt Technology
(NCAT) Test Track cycles. These data were used in conjunction with traffic equations
developed from the AASHO Road Test as well as the AASHTO flexible pavement
design equation to find both the calculated and predicted equivalent single axle loads
(ESALs). Once these values were found for each section, a least squares regression was
performed to determine new HMA layer coefficients. The resulting average layer
coefficient was 0.54 for all sections, with a standard deviation of 0.08. Using this
vii
parameter instead of the AASHTO recommended coefficient of 0.44 results in an
approximate HMA thickness savings of 18%. From these results, it is recommended
that ALDOT adopt this value as their new layer coefficient for flexible pavement
designs.
viii
ACKNOWLEDGEMENTS
I would like to thank my husband, Brandon, for his unending love, support and
patience during the writing of this thesis and in all my other endeavors. I would also
like to thank my friends and family their constant words of encouragement and love. I
am eternally grateful to my advisor, Dr. David Timm for his understanding, guidance
and patience in the writing of this thesis, and throughout my graduate career. I am also
for grateful for the guidance and support offered by my advisory committee, Dr. Randy
West and Dr. Rod Turochy. I would like to acknowledge the Alabama Department of
Transportation for their commitment of financial support for this project.
ix
Style used: MLA Handbook for Writers of Research Papers (5
th
edition)
Computer software used: Microsoft Word, Microsoft Excel
x
TABLE OF CONTENTS
LIST OF TABLES ...........................................................................................................xiii
LIST OF FIGURES.......................................................................................................... xiv
CHAPTER 1: INTRODUCTION ....................................................................................... 1
Background......................................................................................................................1
Objectives ........................................................................................................................ 3
Scope... ............................................................................................................................ 4
Organization of Thesis..................................................................................................... 4
CHAPTER 2: LITERATURE REVIEW ............................................................................ 6
Introduction ..................................................................................................................... 6
AASHO Road Test .......................................................................................................... 7
Overview and Limitations ........................................................................................ 7
Results....................................................................................................................... 9
Origins of the Layer Coefficient............................................................................. 10
AASHTO Traffic Equations.......................................................................................... 13
AASHTO Flexible Pavement Design............................................................................ 14
Fundamental Equations .......................................................................................... 14
PSI and IRI ............................................................................................................. 17
xi
Structural Number .................................................................................................. 20
Minimum Thickness ............................................................................................... 21
Sensitivity to Inputs ................................................................................................ 22
ALDOT Practice............................................................................................................ 22
Past Calibration Efforts ................................................................................................. 25
Summary........................................................................................................................ 33
CHAPTER 3: SENSITIVITY ANALYSIS ...................................................................... 34
Introduction ...................................................................................................................34
Methodology.................................................................................................................. 34
Fundamental Equations .......................................................................................... 34
Inputs ...................................................................................................................... 35
Results and Discussion .................................................................................................. 37
Input Trends............................................................................................................ 37
Input Dependency................................................................................................... 42
Summary........................................................................................................................ 45
CHAPTER 4: RECALIBRATION OF LAYER COEFFICIENTS .................................. 47
Introduction ...................................................................................................................47
Test Facility ................................................................................................................... 50
Overview................................................................................................................. 50
Structural Experiment............................................................................................. 51
Performance Monitoring......................................................................................... 54
Methodology.................................................................................................................. 55
IRI Data .................................................................................................................. 55
xii
Predicted ESALs..................................................................................................... 58
Calculated ESALs................................................................................................... 62
Regression............................................................................................................... 68
Results and Discussion .................................................................................................. 69
Regressed Layer Coefficients................................................................................. 69
Trends ..................................................................................................................... 77
Impact of Changing Layer Coefficient ................................................................... 78
Minimum Thickness ............................................................................................... 78
Summary........................................................................................................................ 79
CHAPTER 5: CONCLUSIONS AND RECOMMENDATIONS .................................... 81
Summary........................................................................................................................ 81
Conclusions ................................................................................................................... 81
Recommendations ......................................................................................................... 83
REFERENCES.................................................................................................................. 84
APPENDIX A: PSI VERSUS TIME GRAPHS FOR EACH TEST SECTION .............. 88
APPENDIX B: REGRESSION STATISTICS FOR EACH TEST SECTION ................ 95
xiii
LIST OF TABLES
Table 2. 1 HMA Layer Coefficients from AASHO Road Test (after HRB, 1962) ......... 11
Table 2. 2 Minimum Thicknesses (after AASHTO, 1993)............................................... 21
Table 2. 3 Recommended Design Values (after Holman, 1990). .................................... 24
Table 3. 1 Value Ranges Used for Flexible Design Equation Inputs............................... 36
Table 3. 2 Correlation between HMA Thickness and Other Inputs............................... 372
Table 4. 1 Thickness Data for the Test Track Sections.................................................... 60
Table 4. 2 Resilient Modulus Data (after Taylor, 2008) .................................................. 61
Table 4. 3 Serviceability Data for Section N1 (2003 Test Track).................................... 61
Table 4. 4 Predicted ESALs Applied for Section N1 (2003 Test Track)......................... 62
Table 4. 5 Axle Weights for 2003 Test Track (after Priest and Timm, 2006) ................. 64
Table 4. 6 Axle Weights for 2006 Test Track (Taylor, 2008) ......................................... 65
Table 4. 7 Average Axle Weights for 2003 Test Track ................................................... 65
Table 4. 8 Average Axle Weights for 2006 Test Track ................................................... 65
Table 4. 9 Section N1 (2003 Test Track) Traffic Calculation Results............................. 66
Table 4. 10 Calculated ESALs for Section N1 (2003 Test Track)................................... 67
Table 4. 11 ESAL Differences Assuming a
1
= 0.44 for Section N1 (2003 Test Track) .. 68
Table 4. 12 Regression Statistics for Section N1 (2003 Test Track) ............................... 70
Table 4. 13 Regressed HMA Layer Coefficients ............................................................. 72
xiv
LIST OF FIGURES
Figure 2. 1 AASHO Road Test Vehicles (Smith et al., 2004). .......................................... 8
Figure 2. 2 4th Power Relationship between Axle Weight and Pavement Damage (after
HRB, 1962). ...................................................................................................................... 10
Figure 2. 3 Determining a
1
Based on HMA Modulus (after AASHTO, 1993)................ 12
Figure 2. 4 AASHTO Flexible Design Nomograph (AASHTO, 1993)........................... 16
Figure 2. 5 Relationship between IRI and PSR for All Pavement Types (Al-Omari and
Darter, 1994). .................................................................................................................... 19
Figure 3. 1 General Trend of HMA Thickness with Layer Coefficient (a
1
). ................... 39
Figure 3. 2 General Trend of HMA Thickness with Traffic (W
18
).................................. 39
Figure 3. 3 General Trend of HMA Thickness with Resilient Modulus (M
R
)................. 40
Figure 3. 4 General Trend of HMA Thickness with Reliability (R)................................ 40
Figure 3. 5 General Trend of HMA Thickness with Serviceability (?PSI)..................... 41
Figure 3. 6 General Trend of HMA Thickness with Variability (S
o
)............................... 41
Figure 3. 7 Resulting HMA Thickness from Changing Layer Coefficient (a
1
). .............. 42
Figure 3. 8 Resulting HMA Thickness from Changing Resilient Modulus (M
R
)............ 43
Figure 3. 9 Resulting HMA Thickness from Changing Serviceability (?PSI)................ 43
Figure 3. 10 Resulting HMA Thickness from Changing Variability (So)....................... 44
Figure 3. 11 Resulting HMA Thickness from Changing Reliability (R)......................... 44
Figure 4. 1 Recalibration Procedure Illustration. ........................................................... 483
xv
Figure 4. 2 Layout of the NCAT Test Track.................................................................. 505
Figure 4. 3 2003 Test Track Structural Sections (Timm et. al, 2004)............................ 527
Figure 4. 4 2006 Test Track Structural Sections (Timm, 2009). ..................................... 69
Figure 4. 5 ARAN Inertial Profiler at NCAT Test Track. ............................................... 70
Figure 4. 6 PSI Data from Section N1 (2003 Test Track)................................................ 72
Figure 4. 7 PSI Data from Section N3 (2003 and 2006 Test Track Cycles).................... 73
Figure 4. 8 Triple Trailer Truck at NCAT Test Track. .................................................... 79
Figure 4. 9 Box Trailer Truck at NCAT Test Track. ....................................................... 79
Figure 4. 10 Sample of Detailed Axle Data. .................................................................... 82
Figure 4. 11 Calculated vs. Predicted ESALs. ................................................................. 86
Figure 4. 12 Regressed Layer Coefficients. ..................................................................... 88
Figure 4. 13 Trench Showing Signs of Debonding in Section N10................................. 89
Figure 4. 14 Trench Showing Delamination of HMA Lifts in Section N10.................... 90
Figure 4. 15 Calculated vs. Predicted ESALs Using a
1
= 0.54. ................................... 7691
Figure 4. 16 Calculated vs. Predicted ESALs Using a
1
= 0.44. ....................................... 91
Figure 4. 17 Change in Resulting HMA Thickness from a
1
= 0.44 to a
1
= 0.54.............. 94
1
CHAPTER 1
INTRODUCTION
BACKGROUND
The Alabama Department of Transportation (ALDOT) currently uses the 1993
DARWin version of the 1986 American Association of State Highway and
Transportation Officials (AASHTO) Guide for the Design of Pavement Structures when
designing flexible pavements. The AASHTO design method is based on information
obtained at the AASHO Road Test, which was performed from 1958 to 1960 near
Ottowa, Illinois. This road test provided an empirical correlation between pavement
thickness and traffic loadings. Equations were developed from the road test to
determine the pavement thickness required for a particular design, and although they
have been modified somewhat, are still in use today. Through the road test research and
the developed equations, the structural number (initially termed the thickness index) was
introduced to define the overall structural capacity of a pavement cross section. The
structural number for flexible pavement design is mathematically defined by the
following equation (AASHTO, 1993):
33322211
mDamDaDaSN ++= (1.1)
Where a
i
is the empirically based layer coefficient that represents the structural
capacity of the material used in the i
th
layer, the m coefficients are used to describe the
2
drainage properties of each layer, and the D terms are the thicknesses of each respective
layer. The structural number can also represent the capacity of each individual layer in
the pavement cross section. For example, the structural number for the HMA can be
expressed as:
111
DaSN = (1.2)
The same concept can be used to calculate the SN for other pavement layers.
The structural numbers for each layer in the pavement cross section can be summed to
equal the total structural number for the pavement as expressed in Equation 1.1. While
the respective layer thicknesses and drainage conditions are relatively easy to quantify,
the layer coefficients are not so straightforward. No direct method exists for
establishing new layer coefficients as new HMA mix types are created, and they are
dependent upon many different parameters including material stiffness, tensile strength,
compressive strength, moisture conditions and even the layer?s position within the
pavement cross section.
The recommended layer coefficient for dense graded HMA mixes (a
1
) is 0.44,
which comes from the results of the AASHO Road Test (HRB, 1962; AASHTO, 1993).
ALDOT uses this value for designing flexible pavements, as do many other
transportation agencies. This coefficient is based on the limited parameters used at the
road test. The trucks had only bias-ply tires with pressures of around 70 psi. No triple
or quad axles were utilized, and no super singles tires were used. Additionally, only 2
million equivalent single axle loads (ESALs) were applied over the course of the road
test. Only a limited number of cross sections were tested, one soil type was used as the
subgrade, one type of gravel was used as the base material, and one type of HMA was
3
used. The thickest HMA pavement was 6 inches. The entire road test only lasted two
years. All the results from the road test are a product of the climate in northern Illinois.
Furthermore, no Superpave mixes, open-graded friction courses, stone-matrix asphalts
or other advanced paving materials were available at the time. These new mixes provide
better performance against rutting, fatigue cracking and other distresses, and therefore it
seems logical that these improved asphalt mixes would have a higher structural capacity
(SN). Since there are only two inputs needed to calculate the structural number of the
HMA as shown in Equation 1.2, this implies that the layer coefficient should be higher
for these new mixes. If a new, and presumably higher, layer coefficient were
established for these improved mixes, then the required HMA thicknesses would
decrease. Consequently, this would result in lower material and construction costs and
an overall more efficient pavement structure.
Due to this reasoning, it was concluded that there is a need to analyze the current
recommended value for the HMA layer coefficient of 0.44. It should be updated to
reflect the changes and improvements that have occurred in HMA materials and
construction over the last 50 years. In addition, while a savings in HMA thickness is
expected, the magnitude of that savings is uncertain; therefore, the sensitivity of the
layer coefficient on the resulting HMA thickness should be analyzed as well.
OBJECTIVES
There were two primary objectives of this investigation. One was to determine
the sensitivity of the layer coefficient (a
1
) on the resulting HMA thickness using the
1993 AASHTO method for flexible pavement design. The second objective was to
4
recalibrate the layer coefficient for newer mixes, and compare that value to the currently
used layer coefficient of 0.44.
SCOPE
The sensitivity analysis was performed using the 1993 AASHTO Design Guide
flexible pavement design equation to create a large database of resulting HMA
thicknesses from changing individual inputs to the equation. This database allowed easy
viewing of the trends and relative influences of each of the inputs, including the HMA
layer coefficient.
The primary objective of this investigation was to recalibrate the layer
coefficients for current asphalt mixes. Data from the structural sections of the 2003 and
2006 National Center for Asphalt Technology (NCAT) Test Track cycles were utilized
to achieve this objective. The Test Track provides unique opportunities for such
research: accelerated traffic is applied to create accelerated levels of pavement damage
in a relatively short period of time, which was very useful for this investigation.
Detailed traffic and performance data collected over the course of the test cycles were
used to perform a least squares regression to arrive at new layer coefficients for each test
section and recommendations were made for the use of a new HMA layer coefficient.
ORGANIZATION OF THESIS
A literature review is provided in Chapter 2 that further describes the AASHTO
design method, ALDOT?s pavement design procedure, and the origins of the layer
coefficient. Additionally, Chapter 2 contains information on past research efforts
5
regarding the HMA layer coefficient. Chapter 3 provides details on the sensitivity of the
flexible pavement design equation to the required inputs, and ranks their influence on
the resulting HMA thickness. Chapter 4 provides a description of the test facility and
the cross sections used in this study, and details the recalibration procedure and the
resulting layer coefficients for each test section. Trends in layer coefficients are
discussed in Chapter 4, as well as the impact of changing the layer coefficient. Chapter
5 presents conclusions and recommendations.
6
CHAPTER 2
LITERATURE REVIEW
INTRODUCTION
The current flexible pavement design methodology used by the Alabama
Department of Transportation (ALDOT) is derived from the results of the American
Association of State Highway Officials (AASHO) Road Test conducted in the late
1950?s. A basic nomograph and equation were developed from the road test results that
includes inputs of soil modulus, traffic, ride quality (serviceability), reliability,
variability, and the capacity of the pavement structure (structural number). Using the
aforementioned flexible pavement design equation or nomograph in conjunction with
these inputs, the designer arrives at a design thickness for the hot mix asphalt (HMA).
To find the structural number of the entire pavement cross section or its
respective layers, the layer thicknesses, drainage properties, and layer coefficients are
needed. Layer coefficients, also called structural coefficients, are used to quantify a
particular layer?s relative ability to function and perform within the pavement cross
section. For dense graded HMA mixes, the AASHTO recommended layer coefficient is
0.44, and this value is used by ALDOT for all plant mix designs (AASHTO, 1993;
ALDOT, 2004). Recommended layer coefficients for other materials are listed in
Chapter 2. This value is based on results from the very limited test conditions of the
7
AASHO Road Test, and has not been recalibrated for newer pavement types and other
variables.
AASHO ROAD TEST
Overview and Limitations
The AASHO Road Test was conducted from 1958 to 1960 near Ottowa, Illinois.
The primary purpose of the road test was to determine the effect of various axle loadings
on pavement behavior. Both flexible and rigid pavements were tested in the study,
along with several short span bridges. Six two-lane test loops were created for
trafficking, including four large loops and two small loops. Hot mix asphalt (HMA) and
base thicknesses were varied within each test loop to determine the effect of axle
loadings on different pavement cross sections. Individual lanes were subjected to
repeated loadings by a specific type and weight of vehicle. Single and tandem axle
vehicles were used for trafficking. Bias-ply tires were used with pressures of
approximately 70 psi. Only 2 million equivalent single axle loads (ESALs) were
applied over the course of the test. The test vehicles ranged in gross weight from 2,000
lb to 48,000 lb, and are shown in Figure 2.1. The improved paving materials that are
used today such as Superpave mixes, stone matrix asphalts and open graded friction
courses were not available during the road test. Within the pavement cross section, only
one type of HMA, granular base material and subgrade soil were used. The thickest
HMA pavement was 6 inches. All results from the road test are a product of the climate
of northern Illinois within a two-year period (HRB, 1962).
8
Figure 2. 1 AASHO Road Test Vehicles (Smith et al., 2004).
9
Results
The results of the AASHO Road Test were used to develop the first pavement
design guide, known as the AASHO Interim Guide for the Design of Rigid and Flexible
Pavements. This design guide was issued in 1961, and had major updates in 1972, 1986
and 1993. The 1993 AASHTO Design Guide is essentially the same as the 1986 Design
Guide for the design of new flexible pavements, and is still used today by many
transportation agencies, including ALDOT.
The primary objective for the AASHO Road Test was to determine the
relationship between pavement loading and deterioration. Using replicate cross sections
in different test loops (that were loaded with different axle weights), researchers at the
road test were able to view the differences in pavement distresses such as rutting,
cracking and slope variance, that were caused by increasing axle loads. The relationship
found was an approximate fourth power relationship: a unit increase in axle weight
causes increased damage to the fourth power. To put this relationship into context, if the
axle weight is doubled, it causes approximately sixteen times more damage to the
pavement. Figure 2.2 illustrates the general relationship between loading and damage
found at the road test.
10
Axle Weight
Relat
i
ve Damage
Figure 2. 2 4th Power Relationship between Axle Weight and Pavement Damage
(after HRB, 1962).
Origins of the Layer Coefficient
It was from this fourth-power relationship that the concept of pavement capacity
was derived. Knowing the expected traffic that will load a pavement and its associated
damage, the pavement must have a certain capacity to withstand said traffic and
resulting damage. The researchers at the AASHO Road Test developed an equation
termed the ?thickness index? (similar to the structural number), which can be
mathematically expressed as (HRB, 1962):
332211
DaDaDaD ++= (2.1)
Where the a terms are the layer coefficients, the D terms are the thicknesses of each
layer, and the subscripts 1, 2 and 3 represent the HMA, base, and subbase pavement
layers, respectively. If the layer coefficients are all equal to one, then the thickness
11
index is simply the total thickness of the pavement cross section. However, for the
AASHO Road Test investigation, these parameters were allowed to vary so that each
pavement layer could have a certain capacity per unit thickness (HRB, 1962). These
parameters were varied because, for example, a four inch HMA layer contributes
considerably more to pavement capacity than a four inch subbase layer. From this
concept stems the general definition of the layer coefficient: an empirical relationship
between the layer thickness and structural number that expresses a layer?s relative
contribution to the performance of the pavement structure (AASHTO, 1993). The layer
coefficient depends upon many variables, including the resilient modulus, layer
thickness, underlying support, position in the pavement structure, and stress state
(AASHTO, 1993; Pologruto, 2001).
Using the thickness index equation, several analyses of variance were conducted
on the data from the AASHO Road Test to determine the layer coefficients for each
pavement sublayer. Table 2.1 shows the HMA layer coefficients (a
1
) found from those
analyses, the number of test sections in each loop used to find those coefficients, and the
model R
2
values. Loop 1 is not included in the table because it was never trafficked; it
was used to evaluate environmental impacts on pavements.
Table 2. 1 HMA Layer Coefficients from AASHO Road Test (after HRB, 1962)
Loop Layer Coefficient (a
1
) Test Sections R
2
2 0.83 44 0.80
3 0.44 60 0.83
4 0.44 60 0.90
5 0.47 60 0.92
6 0.33 60 0.81
Based upon this table and other details from the results, the value of 0.44 was
recommended for use as the HMA layer coefficient (HRB, 1962). According to the
12
authors, a weighted average was taken to arrive at this recommended value. However, it
is uncertain how these values were weighted.
In 1972, a relationship was created that linked the layer coefficient to the elastic
modulus (E) of the HMA at 70?F, and is shown in Figure 2.3. This graph can only be
used if the modulus is between 110,000 and 450,000 psi. The AASHO Road Test
recommended layer coefficient of 0.44 corresponds to a modulus of 450,000 psi
(AASHTO, 1993). In 2006, Priest and Timm found a relationship relating temperature
and stiffness for all the structural sections in the 2003 Test Track cycle. Using their
relationship, the average HMA modulus was calculated as 811,115 psi. If the curve in
Figure 2.3 were extrapolated out to this modulus value, the resulting layer coefficient
would equal 0.54.
0
0.1
0.2
0.3
0.4
0.5
012345
HMA Elastic Modulus at 70
o
F (10
5
psi)
Struc
t
ural Coe
f
fi
cient
(
a
1
)
Figure 2. 3 Determining a
1
based on HMA Modulus (after AASHTO, 1993).
13
AASHTO TRAFFIC EQUATIONS
Using the fourth-power relationship found at the AASHO Road Test, equations
were derived to relate axle loading to pavement damage. Replicate cross sections were
constructed in different test loops to apply varying repeated axle loads on the same
pavement structure. This allowed the researchers at the road test to view the damage
caused by heavier axles, and create mathematical relationships based upon that damage.
The resulting pavement damage was quantified using Equivalent Axle Load
Factors (EALFs), which are used to find the number of ESALs. An EALF is used to
describe the damage done by an axle per pass relative to the damage done by a standard
axle per pass. This standard axle is typically an 18-kip single axle, as defined in the
road test. From the AASHO Road Test results, the EALF can be expressed in the
following form according to Huang (2004):
tx
t
W
W
EALF
18
= (2.2)
Where W
tx
is the number of x axle load applications at time t, and W
t18
is the number of
18 kip axle load applications at time t.
The EALFs for each axle load group are used to find the total damage done
during the design period, which is defined in terms of passes of the standard axle load,
as shown in the following equation (Huang, 2004):
?
=
=
m
i
ii
nEALFESAL
1
(2.3)
Where m is the number of axle load groups, EALF
i
is the EALF for the ith axle load
group, and n
i
is the number of passes of the ith axle load group during the design period.
14
These basic traffic equations can be used in conjunction with the following
equations that were also developed from the AASHO Road Test to characterize traffic
for a given flexible pavement design (Huang, 2004):
?
?
?
?
?
?
?
?
=
5.12.4
2.4
log
t
t
p
G (2.4a)
()
()
23.3
2
19.5
23.3
2
1
081.0
40.0
LSN
LL
x
x
?+
+?
+=? (2.4b)
()
18
22
18
log33.4log79.41252.6log
??
t
x
t
x
t
tx
GG
LLL
W
W
?+++?=
?
?
?
?
?
?
(2.4c)
Where G
t
is the log of the ratio of loss of serviceability (ride quality) at some time t to
the potential loss of serviceability at terminal serviceability (p
t
) = 1.5. The initial
serviceability is assumed to be 4.2; this value was typical for flexible pavements at the
AASHO Road Test, and is used as the initial value for ALDOT pavement designs as
well. ?
x
is a function of design and load variables, L
x
is the axle group load in kips, L
2
is
the axle code (1 for single, 2 for tandem and 3 for tridem), SN is the structural number,
W
tx
is the number of x axle load applications at time t, W
t18
is the number of 18 kip axle
load applications at time t, and ?
18
is the value of ?
x
when L
x
is equal to 18 and L
2
is
equal to one.
AASHTO FLEXIBLE PAVEMENT DESIGN
Fundamental Equations
The 1993 AASHTO Design Guide is the current standard used for designing
flexible pavements for many transportation agencies. In the AASHTO design
15
methodology, the subgrade resilient modulus (M
R
), applied ESALs (W
18
), reliability
(with its associated normal deviate, Z
R
), variability (S
o
), change in serviceability (?PSI)
and structural number (SN) are used in the nomograph in Figure 2.4 and the following
corresponding equation to design flexible pavements (AASHTO, 1993):
07.8log32.2
)1(
1094
4.0
5.12.4
log
20.0)1log(36.9log
19.5
018
?+
+
+
?
?
?
?
?
?
?
?
+?++=
R
R
M
SN
PSI
SNSZW
(2.5)
The reliability level selected is typically based upon the predicted traffic level. A
low volume road (defined as less than 500 ESALs per day traveling in both directions)
requires 85% reliability, medium volume (between 500 and 1750 ESALs per day)
requires and high volume (greater than 1750 ESALs per day) requires 95% (Holman,
1990). The reliability level selected corresponds to a standard normal deviate, Z
R
, which
is calculated using the following equation (Huang, 2004):
0
1818
loglog
S
WW
Z
t
R
?
= (2.6)
Where W
t18
is the number of single-axle load applications to cause the reduction of
serviceability to the terminal level (p
t
). The standard normal deviates needed for design
are typically tabulated and do not need to be calculated for individual designs.
The standard deviation, S
o
, is typically assumed to be 0.49 for flexible pavements
based upon previous research (AASHTO, 1993).
16
90%,
Figure 2. 4 AASHTO Flexible Design Nomograph (AASHTO, 1993).
17
The M
R
of the subgrade soil seen in the equation has been adjusted to account for
seasonal changes, and is termed the effective M
R
. The AASHTO Design Guide (1993)
recommends taking an annual average for backcalculated resilient modulus data and
dividing it by three to obtain the effective modulus. This is done to account for
differences in testing procedures from the road test and the current testing method using
the falling weight deflectometer (FWD). At the road test, screw driven laboratory
devices were used to determine the soil stiffness. Due to the slow response time of such
devices, the apparent stiffness of the soil was very low (around 3,000 psi). With the
much more rapid loading of FWD testing, the moduli are typically around three times
higher, and therefore are divided by three to arrive at similar numbers to those used at
the road test.
PSI and IRI
The change in serviceability (?PSI) seen in Equation 2.5 is the difference
between the initial serviceability rating of the pavement when opened to traffic and the
terminal serviceability that the pavement will reach before rehabilitation, resurfacing or
reconstruction is required. The present serviceability index (PSI), also known as the
present serviceability rating (PSR), is a subjective measure by the road user of the ride
quality, ranging from zero (impassible) to five (perfect ride). Studies conducted at the
AASHO Road Test found that for a newly constructed flexible pavement, the initial
serviceability (p
o
) was approximately 4.2 (AASHTO, 1993). For the selection of a
terminal serviceability (p
t
), the AASHTO Design Guide recommends selection based
upon the same traffic levels used for reliability selection: for low traffic, 2.5, for medium
18
traffic, 3.0, and for high traffic, 3.5. To demonstrate the subjectivity of the
measurement, studies from the AASHO Road Test found that an average of 12% of road
users believe that a pavement receiving a rating of 3.0 is unacceptable for driving while
55% of road users believe that 2.5 is unacceptable (AASHTO, 1993).
Due to the subjective nature of serviceability measurements, most current road
roughness measurements are now standardized to the international roughness index
(IRI). This index provides a measure of the longitudinal wavelengths in the pavement
profile in inches per mile or meters per kilometer. These measurements are taken by
inertial profilers, and can be closely replicated from machine to machine (Sayers and
Karamihas, 1998). This removes the subjectivity of assessing the ride quality, and
therefore is a more accurate measurement. However, since the AASHTO flexible
pavement design procedure still requires serviceability levels as inputs, a conversion
must be made from IRI to PSI.
In 1990, an in-house study was conducted by Holman at ALDOT to relate IRI to
PSI. The derived relationship can be expressed as:
()0016027.00051118.0
5
???
=
IRI
ePSI (2.7)
Al-Omari and Darter (1994) studied the relationships between serviceability, IRI
and pavement distresses. Plots were created that relate IRI to serviceability (PSR) as
shown in Figure 2.5. The data in this graph comes from the states of Louisiana,
Michigan, New Jersey, New Mexico, and Indiana, and include flexible and rigid
pavements, as well as combinations of the two. The equation shown in the figure is for
all pavement types and for units of mm/m, and is recommended by the National
Highway Institute (NHI) for use if no state-specific data is available (Holman, 2003).
19
Based upon only the flexible pavement data from their study, Al-Omari and Darter
developed an equation that converts IRI (in/mile) measurements to PSI:
()IRI
ePSI
??
=
0038.0
5 (2.8)
Figure 2. 5 Relationship between IRI and PSR for All Pavement Types (Al-Omari
and Darter, 1994).
A study conducted in 1994 by Gulen et al. stated that the equation developed by
Al-Omari and Darter was biased and not statistically correct because it was forced to
pass through an IRI value of zero when PSR was equal to 5. The authors developed
their own relationships relating IRI and PSI for the state of Indiana and recommended
that the selection of a model be based upon the needs of the end user (Gulen et al.,
1994).
20
In 1999, Hall and Munoz developed relationships for relating IRI and PSI for
both asphalt and concrete pavements. They analyzed data from the AASHO Road Test
that included parameters of slope variance (SV) and PSI, and then developed a
correlation between SV and IRI for a broad range of road roughness levels. Their
findings for flexible pavements can be expressed mathematically as:
xxxxPSI 5803.14045.1771.12397.05
234
??+?= (2.9a)
)1log( SVx += (2.9b)
2
)(2704.2 IRISV = (2.9c)
Based upon the similarity of the Al-Omari/Darter and Holman equations, it was
decided to focus on those relationships for this study. Since the equation developed by
Al-Omari and Darter is the result of a much larger performance database and is
recommended by the NHI, it was determined that their equation would be optimal for
converting the IRI data to present serviceability values.
Structural Number
As seen in the nomograph in Figure 2.4, the designer arrives at a structural
number for a given set of inputs. This structural number is used to find the design HMA
thickness (D
1
) for a given base and subbase thickness (D
2
and D
3
, respectively) from the
following relationship (AASHTO, 1993):
33322211
mDamDaDaSN ++= (2.10)
This equation is very similar to the thickness index presented in Equation 2.1.
However, Equation 2.10 accounts for the drainage properties present in the base and
subbase layers with the m
2
and m
3
coefficients, respectively.
21
While the structural number is found directly from the nomograph, it cannot be
solved for directly using Equation 2.5. Therefore, an iterative procedure must be used to
arrive at the appropriate structural number for a given design. A seed value for the SN
must be input into the equation, and the resulting calculated ESALs must be compared
to the design ESALs. From there, the SN is adjusted, and the process is repeated.
However, it is not expected that the design ESALs will perfectly match the calculated
ESALs due to the effect of taking the logarithm (base-10) of such large numbers. For
example, the logarithm of 5 million equals 6.70, and the logarithm of 6 million equals
6.78. Due to this logarithm effect, there can be very similar answers to the logW
18
term
using the iterative procedure, yet these answers can result in large differences between
the calculated ESAL values (W
18
).
Minimum Thickness
When designing flexible pavements, minimum thickness values should be used
to prevent impractical or uneconomical designs. The 1993 AASHTO Design Guide
recommends the minimum thicknesses shown in Table 2.2 for asphalt concrete and
aggregate base layers based upon the traffic level (ESALs) of the design.
Table 2. 2 Minimum Thicknesses (after AASHTO, 1993)
Traffic (ESALs) Asphalt Concrete (in) Aggregate Base (in)
Less than 50,000 1.0 (or surface treatment) 4
50,001-150,000 2.0 4
150,001-500,000 2.5 4
500,001-2,000,000 3.0 6
2,000,001-7,000,000 3.5 6
Greater than 7,000,000 4.0 6
22
Sensitivity to Inputs
A search was conducted to find the relative influence of each of the inputs in the
flexible pavement design equation on the resulting HMA thickness. Very little
information was available for this topic. Therefore, it was concluded that research
should be conducted to determine the sensitivity of these inputs.
Some information can be inferred from the design nomograph shown in Figure
2.4. For example, looking at the far left of the nomograph, the reliability scale changes
as the value increases. This means that at lower reliability levels (50 to 70%), changing
the design reliability by a single percentage has little effect on the resulting HMA
thickness. However, at higher levels (90 to 99%), a unit change will have a more
apparent affect on the HMA thickness. This trend of changing scales is also seen on the
standard deviation, resilient modulus and structural number, though the scales change at
varying degrees. The traffic level does not demonstrate the same trend because it is on a
log scale between the two turning lines. In other words, for traffic, it is the order of
magnitude that is critical rather than relatively small differences within an order of
magnitude.
ALDOT PRACTICE
To design flexible pavements in the state of Alabama, ALDOT currently follows
the 390 Procedure (ALDOT, 2004). This procedure provides guidance for conducting
pavement designs according to the 1993 AASHTO Design Guide, and includes
additional information for materials testing and obtaining traffic information. The end
result of the 390 procedure is a ?materials report? that contains traffic data, materials test
23
results, and printouts detailing the pavement structural design from the DARWin
TM
software, which is the embodiment of the 1993 AASHTO Design Guide. The traffic
data and materials test results are inputs to the DARWin software, and the output
obtained from the software is the pavement structural design.
ALDOT also has another pavement design guidance document, Guidelines for
Flexible Pavement Design in Alabama that describes how to determine each of the
inputs for the flexible pavement design equation to be entered into the DARWin
software. Further details can be obtained from the original document (Holman, 1990).
The current ALDOT flexible pavement design procedure, employed through
DARWin, utilizes Equation 2.5 and the corresponding nomograph shown in Figure 2.4.
ALDOT currently uses default recommended values for the layer coefficients, change in
serviceability, reliability and variability inputs (Holman, 1990). These values are
summarized in Table 2.2. The remaining inputs of drainage coefficients, traffic and
subgrade resilient modulus, are calculated on a project-by-project basis. The traffic
ranges used for reliability and serviceability are the same as those discussed previously.
24
Table 2. 3 Recommended Design Values (after Holman, 1990).
Input Recommended Values
HMA layer coefficient (a
1
)*
414 and 416 mixes (plant mix) 0.44
411 mixes 0.30
Base layer coefficient (a
2
)*
Granular base 0.14
Bituminous treated base 0.30
Cement or lime treated base 0.23
Subbase layer coefficient (a
3
)*
Granular subbase 0.11
Terminal Serviceability (p
t
)
Low Traffic 2.5
Medium Traffic 3.0
High Traffic 3.5
Reliability (R)
Low traffic 85%
Medium traffic 90%
High traffic 95%
Variability (S
o
)
Flexible pavements 0.49
* Note: Layer coefficients for other materials can be found in the reference cited.
The drainage coefficients (m
i
) are calculated based upon the percent passing the
number 200 sieve (P
200
) of the material in question and the average annual rainfall in
inches (AAR) for the project location, as expressed by the following equations:
100/)(6.02.1 AARS
i
??= (2.11a)
100/)(6.02.1
200
PD
q
??= (2.11b)
qii
DSm ?= (2.11c)
Where S
i
is the level of saturation and D
q
is used to describe the drainage quality.
The design traffic (ESALs) is calculated for each project from the average
annual daily traffic and percent trucks for the design. To quantify the traffic, truck
volumes are calculated at various locations within the project length and an average is
computed. The truck volume from the location closest to, but just over, the average
value is used as the design value. This design traffic value is then multiplied by several
25
factors (365 days/year, Lane Distribution, Directional Distribution, Growth Factor,
EALF) to arrive at the design ESALs (Holman, 1990).
The ALDOT procedure (Holman, 1990) has a provision for estimating subgrade
soil modulus (M
R
) from California Bearing Ratio (CBR) testing according to the
following equation:
()971.2log851.0
10
+?
=
CBR
R
M (2.12)
ALDOT assumes this value to remain the same throughout the year unless there are data
to the contrary (Holman, 1990). The CBR value is found from the soil in the saturated
condition, and therefore is expected to be the worst case scenario for the soil subgrade.
In addition to using CBR data to estimate the resilient modulus, ALDOT has
been conducting extensive triaxial resilient modulus tests (AASHTO T307) of their
subgrade materials for the past seven years. Procedure 390 states that the design M
R
for
soils classified as A-1, A-3, A-2-4 and A-2-5 shall be the average M
R
values generated
by AASHTO T307 at a confining pressure of 4 psi and optimum moisture content. For
soil classes A-6 or A-7 (A-7-5 or A-7-6), 2 psi confining pressure is used, and samples
are compacted on the wet side of optimum moisture to generate more conservative
design soil moduli. For all other soil classes, the design M
R
used is the average M
R
value
generated at 2 psi confining pressure and optimum moisture content (ALDOT, 2004).
PAST CALIBRATION EFFORTS
Many studies have been conducted to determine layer coefficients for new
materials or for materials that were not used at the AASHO Road Test. However, little
change has occurred in the actual coefficients used for design due to the complex nature
26
of this parameter. As mentioned previously, the layer coefficient is dependent upon
several factors, including resilient modulus, layer thickness, underlying support, position
in the pavement structure, and stress state (AASHTO, 1993; Pologruto, 2001). Based
upon these facts, AASHTO urges agencies to determine their own layer coefficients if
data are available to do so.
Van Wyk, Yoder and Wood (1983) performed an investigation to determine the
layer coefficients of recycled asphalt pavement. Deflection basins from non-destructive
testing were compared to theoretical deflection basins using a layered elastic software
program called BISTRO. Once the deflections basins matched adequately based upon a
pavement cross section selected for use in BISTRO, distresses such as tensile strain at
the bottom of the asphalt, compressive subgrade strain and deformations were computed
for 25 test sections. These distresses were calculated so two similar pavement sections,
one with a recycled layer and one without, and with the same predicted time before
failure could be compared to determine the new layer coefficient for the recycled layer.
This accomplished using Equation 2.10 and setting the structural number of both
pavement sections equal to each other. The only parameter that could vary was the layer
coefficient of the recycled asphalt layer; the layer coefficient of the comparison layer on
the control pavement was held constant (0.44). The authors stated that the layer
coefficients should be determined using the distress criteria that constitutes the shortest
pavement life. The results of their study found that the layer coefficients increased
slightly over time after construction completion. They also concluded that the elastic
modulus was the single most important parameter for determining layer coefficients, and
that the layer coefficient changed slightly with changes in thickness. The authors noted
27
that their recommended procedure for determining the layer coefficients of recycled
materials was time consuming and required extensive testing to determine fatigue
characteristics. Based upon the wide range of layer coefficients found in their study
(0.11 to 0.39), they did not recommend any particular layer coefficient for recycled
asphalts, and stated that the selection of the coefficient was still the responsibility of the
pavement designer (Van Wyk et al., 1983).
In 1989, Corree and White determined layer coefficients for ten bituminous
mixes as single values and as distributions. These mixes were typically used by the
Indiana Department of Highways (IDOH). They used Odemark?s principle of
equivalent stiffness, which compares different material types using a ratio of strength
parameters. Applying this principle to find a new layer coefficient resulted in the
following equation (Corree and White, 1989):
3
1
?
?
?
?
?
?
=
AASHO
IDOH
AASHOIDOH
E
E
aa (2.13)
Where a
IDOH
is the desired layer coefficient for an IDOH mixture, a
AASHO
is the AASHO
Road Test layer coefficient, and E
IDOH
and E
AASHO
are the moduli of an IDOH asphalt
mixture and the AASHO Road Test asphalt mixture, respectively.
Equation 2.13 can be solved for a single value of the layer coefficient. To
determine the coefficient distributions, equations termed the Poel/Bonnaure et al.
relationships were utilized. A full description of these equations and concepts is beyond
the scope of this thesis, but can be found in the reference (Corree and White, 1989).
Distributions of parameters were created for the AASHO Road Test and the IDOH
mixtures. Three approaches were used to determine the layer coefficients, including a
28
deterministic method, a probabilistic method, and a method combining both
deterministic and probabilistic methods. The deterministic method used single values
for each parameter in Equation 2.13, while the probabilistic method used distributions
for all parameters in the same equation. The combination method used distributions for
the mixture stiffness variables only. Using the deterministic approach, the average
layer coefficient was 0.44. From the strictly probabilistic approach, the average
coefficient was 0.53 with an average standard deviation of 0.287. The combination
approach resulted in an average layer coefficient of 0.47 with an average standard
deviation of 0.101. The authors cautioned against using the results of the probabilistic
approach since the idea of a layer coefficient being represented by a distribution is not
widely accepted. They stated that the larger values for the layer coefficients of IDOH
mixtures compared to those of the AASHO Road Test could be attributed to the mixes
being stiffer; the penetration grade of the AASHO Road Test mixes was 85 ? 100, and
the IDOH mixes were classified as 60 ? 70. Finally, the authors think that the shift in
resulting layer coefficients from the three different approaches was due to the
distributions being asymmetrical.
To determine the layer coefficients for crumb-rubber modified (CRM) mixes for
the Kansas Department of Transportation (KDOT), Hossain et al. (1997) used falling
weight deflectometer (FWD) data collected from testing the in-place pavement structure.
Three backcalculation methods were used to convert the deflection data from 41
different test locations into moduli. Good agreement was found between the methods,
and the moduli were determined to be sound. To determine the layer coefficients from
29
the moduli, the structural number was found using the following equation recommended
by the AASHTO Design Guide (1993):
3
0045.0
peff
EDSN ??= (2.14)
Where D is the total thickness of the pavement cross section above the subgrade (in
inches), and E
p
is the effective modulus of the pavement cross section above the
subgrade (in psi). Using the backcalculated moduli and the layer thicknesses, the layer
coefficients were calculated for the CRM mixes.
Another method was used to calculate the layer coefficients for comparison to
the results of the AASHTO method. This method was termed the equal mechanistic
response (EMA) and used layer equivalency concepts (similar to the procedure of Van
Wyk et al., 1983) to find another set of layer coefficients. The average layer coefficient
for CRM mixes found using the AASHTO method was 0.28. The average layer
coefficient from the EMA method was 0.33. From this study, a particular layer
coefficient was not recommended for use in design. However, an equation was
developed to estimate the layer coefficient for CRM mixes, and is defined as follows
(after Hossain et al., 1997):
732.1)log(315.0 ?= Ea
CRM
(2.15)
Where E is the modulus of the CRM mix in MPa.
From the study, the authors concluded that using the AASHTO method to
estimate layer coefficients results in very high variabilities, and the equal mechanistic
approach was much less variable. They found a range of layer coefficients for CRM
asphalt mix overlays using the EMA ranging from 0.11 to 0.46, with most values falling
around 0.30. For newly constructed CRM pavements, they found a range of layer
30
coefficients of 0.25 to 0.50, with the average being approximately 0.35 (Hossain et al.,
1997). However, these values and the equation developed are only applicable to the
mixes tested.
In 1999, Romanoschi and Metcalf conducted research to analyze pavement
structural capacity on pavements at the Louisiana Transportation Research Center
Pavement Research Facility (PRF). FWD testing was performed on several sections at
the PRF, and backcalculation was performed to determine moduli values. The authors
chose to not use the AASHTO recommended method (Equation 2.14) because it was
cumbersome, difficult to solve in a database environment, and had no unique solution
(Romanoschi and Metcalf, 1999). They decided to use alternate equations developed by
other researchers to find the structural number. However, once the backcalculated
moduli were found, it was decided that the data were far too variable to use for the
determination of layer coefficients. Therefore, laboratory tests were performed to find
the resilient modulus for HMA cores taken from the sections at the PRF. The 1993
AASHTO Design Guide cautions against using laboratory moduli values for
determining layer coefficients, as these values are known to differ vastly from the in situ
moduli. While the authors recommended assigning layer coefficients based on
laboratory moduli values, no HMA layer coefficients were presented as the results of
their analysis.
Pologruto conducted a study in 2001 to determine the layer coefficients for
various paving materials in Vermont for the Vermont Transportation Agency (VTrans).
FWD data were gathered from the Strategic Highway Research Program (SHRP)
database. Seasonal data, collected over more than 5 years, were used for eight different
31
locations throughout the state of Vermont to determine the procedure for finding the
layer coefficients. The effective structural number (Equation 2.14) was calculated for
the backcalculated moduli and the results were plotted against the days of the year from
which they were calculated. The resulting graph illustrated that for Vermont, the SN
eff
remained fairly constant from May to October. High variations were found during the
spring-thaw period. Therefore, only the data from the stable months were used to find
the layer coefficients. A pilot project was created to determine the resulting layer
coefficients for one test section to verify the validity of the recommended procedure. To
find the layer coefficients for each respective layer in the pavement structure, the SN
eff
was calculated immediately above and below the layer in question. The difference
between these two values was found and then divided by the layer thickness. The SN
eff
at the top of the subgrade was defined as zero. The results of the pilot project found
layer coefficients within the AASHTO range for all materials except the HMA, which
was 0.639. This value, although approximately 50% higher than the recommended 0.44,
was not discounted from the results because the Marshall stability and resilient modulus
for the material were well beyond the AASHTO recommended upper limits for each
parameter. Since the results were encouraging, FWD testing was performed at three
other test sites to find layer coefficients. A total of 25 individual testing locations were
used in the author?s analysis. Elastic layer simulation (ELS) was used to verify the layer
coefficients found from the AASHTO procedure, and the two methods were compared.
From the AASHTO method, the average HMA layer coefficient was 0.60. The average
found using the ELS was 0.59. From these results, the author recommended using the
AASHTO method for determining new layer coefficients, and that further research
32
should be performed to see if similarly high HMA layer coefficients are found for other
HMA types and in other locations (Pologruto, 2001).
In 2005, Jess and Timm used the AASHTO procedure to find layer coefficients
from backcalculated moduli at the NCAT Test Track in Opelika, Alabama. The
AASHTO method was used (Equation 2.14) to find the effective structural numbers for
26 different test sections. A control test section with a HMA layer coefficient of 0.44
was used to determine the comparison layer coefficients for the other test sections.
From this study, the average layer coefficient found was 0.59 with a standard deviation
of 0.13. Additionally, the sections included in the study were unusually thick; on the
order of 24 inches of hot mix asphalt. Because of this, the sections did not experience
significant pavement distress and consequently the structural coefficients were merely
calibrated to surface deflection and not changes in serviceability. Therefore, it was
decided to recommend a conservative value based on the average minus one standard
deviation which resulted in 0.46 (Jess and Timm, 2005). Obviously, switching from
0.44 to 0.46 does not significantly alter pavement cross sections in design.
Harold Von Quintus conducted a study on layer coefficients for the Kansas
Department of Transportation in 2007. He concluded that the HMA layer coefficient for
the wearing surface and base mixtures should be increased. He stated that the
magnitude of the increase should be dependent upon a detailed analysis of material
properties, constructions records and pavement performance, and not solely on the HMA
modulus (Von Quintus, 2007).
33
SUMMARY
This literature review briefly discussed the AASHO Road Test and its
limitations, along with the findings from the road test. The origins of the layer
coefficient were explained, and the recommended value for the HMA layer coefficient
was discussed. The AASHTO traffic and flexible pavement design equations and their
respective inputs were presented and described. An explanation was provided for
ALDOT?s flexible pavement design procedure, and default values were given that are
commonly used by ALDOT for the AASHTO design equation. Finally, the procedures
and results from past layer coefficient calibration efforts were provided. As noted in this
chapter, there was a lack of information available on sensitivity of the AASHTO
equations to their inputs. Therefore, the following chapter presents a sensitivity analysis
as part of this investigation.
34
CHAPTER 3
SENSITIVITY ANALYSIS
INTRODUCTION
The 1993 AASHTO Design Guide flexible pavement design equation requires
several inputs to find a resulting HMA thickness. These inputs obviously all affect the
HMA thickness since they are included in the calculation to find it; however, obtaining
the relative influence of each would be a valuable tool for optimizing pavement designs.
A sensitivity analysis of all the inputs was performed to achieve that goal. The results
can provide a pavement designer with the knowledge of which inputs have the greatest
influence on the HMA thickness, and which have the least. Such information could be
used to determine further research needs for the more influential inputs, or the need to
better characterize those inputs for the greatest benefit to cost ratio.
METHODOLOGY
Fundamental Equations
A sensitivity analysis was conducted to determine which parameters in the
AASHTO Design Guide (1993) flexible pavement design equation are the most
influential on the thickness of the hot mix asphalt (HMA). Equation 3.1 shows the
parameters needed to arrive at the HMA thickness (D
1
), which comes from the structural
35
number (SN) shown in Equation 3.2. The other parameters include the number of
ESALs over the design period (W
18
), the design reliability (R), the amount of variability
(S
o
) in the design, the soil modulus (M
R
), and the expected loss of serviceability over the
lifetime of the pavement (?PSI).
07.8log32.2
)1(
1094
4.0
5.12.4
log
20.0)1log(36.9log
19.5
18
?+
+
+
?
?
?
?
?
?
?
?
+?++=
R
oR
M
SN
PSI
SNSZW
(3.1)
The structural number (SN) is used to define the structural capacity of a flexible
pavement structure, and is calculated using the layer coefficients of the asphalt, base and
subbase layers (a
1
, a
2
, and a
3
, respectively), the layer thicknesses (D
1
, D
2
and D
3
), and
the drainage coefficients (m
1
and m
2
) for the base and subbase layers as shown in
Equation 3.2.
33322211
mDamDaDaSN ++= (3.2)
Inputs
Before conducting the sensitivity analysis, a baseline pavement condition was
created to determine the relative influence of altering the inputs. A three-layer
pavement cross-section of HMA, granular base and subgrade soil was used. For the
base layer of granular material, a thickness (D
2
) of 6 inches was used with a layer
coefficient (a
2
) of 0.14. The layer coefficient is typical for crushed stone aggregate
bases. A value of 1.0 was used for the drainage coefficient (m
2
). This value was chosen
for simplicity, but is also frequently used for ALDOT pavement designs. It was
36
assumed that no subbase layer was used, so the final term in Equation 3.2 was zero. All
other parameters in the design equation were varied to determine their relative influence
on HMA thickness. Table 3.1 shows the values used for each input. These values were
chosen based upon typical values used for flexible pavement design, and extremes were
added to get a wide range of thicknesses and to characterize trends.
Table 3. 1 Values Used for Flexible Design Equation Inputs
Parameter Values
Layer coefficient (a
1
) 0.20, 0.30, 0.44, 0.60
Traffic level (W
18
) 1e6, 1e7, 1e8, 1e9 ESALs
Resilient modulus (M
R
) 3,000, 10,000, 20,000, 30,000 psi
Reliability (R) 50%, 80%, 90%, 99%
Change in serviceability (?PSI) 1, 1.5, 2.0, 2.5
Variability (S
o
) 0.20, 0.30, 0.40, 0.50, 0.60
To obtain the HMA layer thickness using the flexible design equation, first the
structural number was found using the bisection method. This method was needed since
equation 3.1 is difficult to solve explicitly. Once a structural number was computed,
Equation 3.2 was rearranged to solve for D
1
, which is the HMA layer thickness. Using
this concept and the varied parameters as shown in Table 3.1, the HMA thickness was
recalculated each time an input was changed. There were five inputs used for the
variability, and four inputs used for the other inputs (traffic, resilient modulus,
reliability, change in serviceability, and layer coefficient). Therefore, a total of 5 x 4
5
=
5,120 HMA thicknesses were calculated for this investigation.
37
RESULTS AND DISCUSSION
A Pearson?s correlation was performed on the entire data set (all of the 5,120
thickness calculations) to determine which of the parameters were the most influential
on the resulting HMA thickness. Table 3.2 shows the resulting sample Pearson
correlation coefficients (R), where the values range from -1 to 1. Values closer to those
range extremes are considered to be strongly correlated, and values close to zero are not
as closely correlated. They are shown in the table in order from the most influential (a
1
)
to the least (S
o
).
Clearly, the layer coefficient has the greatest influence on the HMA thickness.
The next two parameters in Table 3.2, traffic level and resilient modulus, though
influential cannot be changed from a design perspective; they are simply the conditions
of the design. Therefore, the layer coefficient is the most influential parameter as
measured by correlation coefficient with the other design parameters having much less
influence. To better illustrate the significance of the correlation results, the trends and
interdependency of each of these inputs is discussed below.
Table 3. 2 Correlation between HMA Thickness and Other Inputs
Parameter Correlation Coefficient
Layer coefficient (a
1
) -0.518
Traffic level (W
18
) 0.483
Resilient modulus (M
R
) -0.425
Reliability (R) 0.157
Change in serviceability (?PSI) -0.141
Variability (S
o
) 0.083
Input Trends
To determine the general trend of each input on the resulting HMA thickness, a
few points were selected of the 5,120 available for each input and were plotted to view
38
the relationship. These plots were not meant to exactly quantify the relationship of each
input with the HMA thickness, but rather to view the general trend and further illustrate
the relative influence of each input on the HMA thickness.
The thicknesses found from altering the layer coefficient for the HMA (a
1
)
generally follow a negative trend as shown in Figure 3.1. The graph shown is for a set
traffic level (1e8 ESALs), resilient modulus (20,000 psi), variability (0.40), reliability
(80%) and change in serviceability (2.0). To generate graphs for the other inputs, the
layer coefficient was set to 0.44. Figures 3.1 through 3.6 are ordered from the most
influential input to the least (as in Table 3.2), and observation of the graphs provides a
better understanding of the correlation results (i.e., that a
1
has the most influence and S
o
has the least). For example, the overall magnitude of difference in HMA thickness from
changing the layer coefficient is approximately 12 inches (Figure 3.1), while changing
the variability only creates an overall difference of 1 inch in HMA thickness (Figure
3.6).
39
0
2
4
6
8
10
12
14
16
18
0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6
a
1
HM
A Thick
nes
s
(in)
Figure 3. 1 General Trend of HMA Thickness with Layer Coefficient (a
1
).
0
2
4
6
8
10
12
14
16
18
1.E+06 1.E+07 1.E+08 1.E+09
ESALs
HMA Th
ickn
ess
(in)
Figure 3. 2 General Trend of HMA Thickness with Traffic (W
18
).
40
0
2
4
6
8
10
12
14
16
18
3000 8000 13000 18000 23000 28000
M
R
(psi)
HMA Th
ickn
ess
(in)
Figure 3. 3 General Trend of HMA Thickness with Resilient Modulus (M
R
).
0
2
4
6
8
10
12
14
16
18
50 60 70 80 90 100
Reliability (%)
HMA Th
ickn
ess
(in)
Figure 3. 4 General Trend of HMA Thickness with Reliability (R).
41
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
18.0
1.0 1.3 1.5 1.8 2.0 2.3 2.5
DPSI
HMA Th
ickn
ess
(in)
Figure 3. 5 General Trend of HMA Thickness with Serviceability (?PSI).
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
18.0
0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60
S
o
HM
A Thick
ness
(in)
Figure 3. 6 General Trend of HMA Thickness with Variability (S
o
).
42
Input Dependency
During the analysis, it became apparent that all of the inputs are dependent upon
the traffic level. For example, the layer coefficient value has more of an influence on
the resulting HMA thickness as the traffic level increases, as illustrated in Figure 3.7.
This chart shows how the HMA thicknesses change on average for the different traffic
levels specified when the layer coefficient is varied. This process was repeated for all
the inputs (Figures 3.8 through 3.11) except the traffic level because the relative
influence of each other input changed only as the traffic level changed.
0
5
10
15
20
25
30
35
40
1,000,000 10,000,000 100,000,000 1,000,000,000
ESALs
Av
er
a
g
e H
M
A
T
h
i
c
kne
s
s
(i
n)
0.2
0.3
0.44
0.6
Figure 3. 7 Resulting HMA Thickness from Changing Layer Coefficient (a
1
).
43
0
5
10
15
20
25
30
35
40
1,000,000 10,000,000 100,000,000 1,000,000,000
ESALs
A
v
e
r
age H
M
A
Thickness (in)
3000
10000
20000
30000
Figure 3. 8 Resulting HMA Thickness from Changing Resilient Modulus (M
R
).
0
5
10
15
20
25
30
35
40
1,000,000 10,000,000 100,000,000 1,000,000,000
ESALs
A
v
e
r
age H
M
A
Thickness (in)
50
80
90
99
Figure 3. 9 Resulting HMA Thickness from Changing Reliability (R).
44
0
5
10
15
20
25
30
35
40
1,000,000 10,000,000 100,000,000 1,000,000,000
ESALs
A
v
e
r
age H
M
A
Thickness (in)
1
1.5
2
2.5
Figure 3. 10 Resulting HMA Thickness from Changing Serviceability (?PSI).
0
5
10
15
20
25
30
35
40
1,000,000 10,000,000 100,000,000 1,000,000,000
ESALs
A
v
e
r
age H
M
A
Thickness (in)
0.2
0.3
0.4
0.5
0.6
Figure 3. 11 Resulting HMA Thickness from Changing Variability (S
o
).
45
It is important to note several trends from these data. First, the layer coefficient
(Figure 3.7) and resilient modulus (Figure 3.8) seem to follow similar trends; namely,
they have a greater affect on the HMA thickness as the traffic level increases. For
example, at the 1 million ESAL traffic level, going from a layer coefficient of 0.2 to 0.3
causes a thickness decrease of approximately 4 inches, whereas that same shift at the
100 million ESAL traffic level causes a decrease of approximately 9 inches (Figure 3.7).
This trend can also be seen in the reliability (Figure 3.9) and change in serviceability
(Figure 3.10) charts, though not to the same extent. It is also slightly apparent in the
variability chart (Figure 3.11), but it is even less obvious than the other charts. By
looking at these graphs, it is evident that the traffic level does have a significant impact
on the calculated HMA thickness, and that the other inputs are dependent upon it to
varying degrees. The layer coefficient and resilient modulus (along with the traffic
level) have the greatest influence on the resulting HMA thickness; the reliability,
variability and change in serviceability are not as significant. This is apparent in the
graphs, and further illustrates the correlation results found previously (Table 3.2), as
well as the general trends seen in Figures 3.1 through 3.6.
SUMMARY
A sensitivity analysis was performed on the variables of the 1993 AASHTO
Design Guide flexible pavement design equation to see which inputs had the greatest
influence on the resulting HMA thickness. A correlation between the inputs was
performed to analyze the significance of the Pearson sample R values. The correlation
46
results showed the layer coefficient was the most influential on the HMA thickness, and
the variability was the least influential. Between those inputs (in order from more
influential to least) were the traffic, resilient modulus, reliability and change in
serviceability. Plots were created for each input versus the resulting HMA thickness to
observe general trends. Input dependencies were found in the sensitivity analysis. The
relative influence of all inputs was dependent upon the traffic level.
The sensitivity analysis results proved the HMA layer coefficient to be the most
influential parameter on the resulting design HMA thickness. The two parameters with
similar magnitudes of influence, the traffic level and resilient modulus, are both
generally set parameters for a given pavement design. Therefore, this increases the
importance of being able to accurately characterize the HMA layer coefficient. This
input is the only one of the three most influential that can be changed; consequently,
better characterization of it would provide the greatest potential savings in HMA
thickness.
47
CHAPTER 4
RECALIBRATION OF LAYER COEFFICIENTS
INTRODUCTION
This investigation used pavement performance and detailed traffic data collected
from the National Center for Asphalt Technology (NCAT) Pavement Test Track from
the 2003 and 2006 test cycles to recalibrate the HMA layer coefficient (a
1
) used in the
1993 AASHTO Design Guide flexible pavement design equation as illustrated in the
flowchart in Figure 4.1.
As shown in Figure 4.1, there were two data sets needed for calibration: the
traffic and surface performance data. Both data sets were needed to calculate the ESALs
applied at the Test Track (an estimation of the actual ESALs), and only the performance
data set was needed to calculate the predicted ESALs. Before the performance data
could be used, it first had to be converted from IRI (in./mile) to serviceability (PSI).
This was achieved using the Al-Omari/Darter equation. Once converted, these data
were used to create plots for each test section that illustrated the change in PSI over
time. Points were selected from these charts to obtain terminal serviceability levels (p
t
)
for recalibration purposes. These p
t
values were used to find the calculated ESALs as
illustrated in the figure.
48
Figure 4. 1 Recalibration Procedure Illustration.
Traffic Data Set
(axle passes, weights, etc.)
Performance (IRI)
Data Set
p
t
?PSI
(Al-Omari/Darter equation)
Calculated ESALs
(W
tx
/W
t18
equation)
(AASHO Road Test traffic
equations: G
t
, ?
x
, EALF, ESAL)
SN
Predicted ESALs
(logW
18
equation)
(AASHTO
flexible pavement
design equation)
Calculated ESALs
Predic
ted E
S
ALs
*
*
*
a
1
*Minimize error between calculated and
predicted by changing only a
1
49
The PSI versus time charts were also used to find the change in serviceability
(?PSI) needed to calculate the predicted ESALs. This was achieved by taking the
terminal serviceability points (p
t
) just described, and subtracting them from the initial
serviceability level (p
o
) for each test section.
The other primary input, the structural number (SN) was necessary for the
calculation of both the calculated and predicted ESALs. This number was originally
calculated using thickness data from each test section as well as an assumed HMA layer
coefficient (a
1
) of 0.44. This layer coefficient comes from the AASHO Road Test and is
currently used by ALDOT for flexible pavement designs.
To find the calculated ESALs, the traffic data set, terminal serviceability, and
structural number were used as inputs for the traffic equations derived from the AASHO
Road Test as illustrated in Figure 4.1. The predicted ESALs were calculated using the
change in serviceability and structural number as inputs to the AASHTO flexible
pavement design equation. Once found, the calculated and predicted ESALs were
compared and a simple linear least squares regression was performed. The error was
minimized between the two data sets by changing only the HMA layer coefficient. This
process was repeated for each structural section of the 2003 and 2006 Test Track cycles,
resulting in a new regressed layer coefficient for each section. A more detailed
discussion of this process is provided later in this chapter.
50
TEST FACILITY
Overview
The recalibration of the layer coefficients was performed using data from
Auburn University?s NCAT Pavement Test Track located in Opelika, Alabama. The
Test Track is a 1.7 mile oval that is divided into 46 sponsored sections that are 200 ft
long as shown in Figure 4.2. The Test Track provides sponsors with a facility that
supports hot mix asphalt (HMA) research by applying live traffic in an accelerated
testing environment. The test sections consist of varying pavement cross sections and
materials based upon each sponsors? needs. Live traffic is applied 16 hours a day for 5
days a week, which adds up to approximately 10 million ESALs over a 3-year test cycle.
The data used in this investigation were from the 2003-2006 and 2006-2009 test cycles.
A full description of the 2003 and 2006 Test Track cycles are beyond the scope of this
report, but have been documented elsewhere (Timm et al., 2004; Timm, 2009).
Figure 4. 2 Layout of the NCAT Test Track.
N
North Tangent
South Tangent
Eas
t
Cu
rv
e
Wes
t
C
u
rv
e
S1 S2 S4 S5 S6 S8 S9 S10 S11 S12 S13 S7 S3
N13 N12 N10 N9 N8 N6 N5 N4 N3 N2 N1 N7 N11
Traffic
51
Structural Experiment
In the 2003 Test Track cycle, there were eight sections that comprised the
structural experiment. The structural experiment included sections with embedded
instrumentation to more accurately characterize pavement response under traffic
loadings. These sections were designed with varying thicknesses and materials as
shown in Figure 4.3. The thicknesses were varied to provide a wide array of distresses
to analyze at the end of the test cycle. As seen in the figure, each section shared the
same subgrade material that was already present at the Test Track. This soil, commonly
termed the ?Track soil?, can be classified as an AASHTO A-4(0) soil type (Timm,
2009). The test sections also shared the same 6 inch crushed aggregate base course.
Sections N1, N4 and N5 used modified PG 76-22 HMA layers of 5, 9 and 7 inches,
respectively. Sections N2, N3 and N6 were also 5, 9 and 7 inches thick; however, they
were unmodified PG 67-22 HMA layers. Section N7 consisted of 6 inches of
unmodified PG 67-22 HMA placed under a 1 inch thick layer of PG 76-22 stone matrix
asphalt (SMA). Finally, section N8 had a 2 inch thick rich bottom PG 67-22 layer with
an additional 0.5% binder, which was placed under 4 inches of unmodified PG 67-22,
and then topped with 1 inch of SMA (Timm et. al, 2004).
52
0
5
10
15
20
25
30
35
40
N1 N2 N3 N4 N5 N6 N7 N8
Test Section
De
pth, i
n
.
Modified HMA (PG 76-22)
Unmodified HMA (PG 67-22)
SMA (PG 76-22)
Unmodified HMA (PG 67-22), Opt +0.5%
Crushed Aggregate Base Course
Improved Roadbed (A-4(0)) Soil
Figure 4. 3 2003 Test Track Structural Sections (Timm et. al, 2004).
For the 2006 Test Track, five of the original eight structural sections (N3 through
N7) were left in place from the 2003 cycle; however N5 was milled and inlaid with a 2
inch asphalt layer to control top-down cracking that was present throughout the section.
Three of the sections were reconstructed (N1, N2 and N8), and three new sections were
added to the structural experiment (N9, N10 and S11). The cross sections of the 2006
Test Track structural sections are shown in Figure 4.4 along with their respective
sponsors. As seen in the figure, all sections other than N8 and N9 still utilized the Track
soil as subgrade material. The subgrade material used in sections N8 and N9 can be
classified as an AASHTO A-7-6 soil, and is known as Seale subgrade material since it
was imported from a borrow pit in Seale, Alabama (Taylor, 2008).
53
In sections N1 and N2, 10 inches of Florida limerock material was used as the
base layer. Both sections were topped with 7 inches of HMA: unmodified PG 67-22 for
all lifts of section N1, and a 3 inch lift of the same unmodified binder followed by two 2
inch lifts with modified PG 76-22 binder for section N2. For sections N3, N4, N5, N6,
N7 and S11, 6 inches of granite aggregate base material supplied from Vulcan materials
was used as the base layer. Sections N3 and N4 both consisted of 9 inches of HMA. N3
used unmodified PG 67-22 binder in all HMA lifts, and N4 used modified PG 76-22 in
all lifts. N5, N6 and N7 contained 7 inches of HMA in each section: section N5 had a
HMA layer created with unmodified PG 67-22 binder placed over modified PG 76-22
layers, section N6 was comprised of unmodified PG 67-22, and section N7 contained 6
inches of unmodified binder topped with a 1 inch lift of PG 76-22 SMA. Section N8
consisted of approximately 6 inches of Track soil as the base layer, followed by one
layer of HMA with PG 64-22 binder designed with 2% air voids, one layer of HMA
with PG 64-22 binder, one layer of HMA with PG 76-28 binder, and finally topped with
PG 76-28 binder SMA for a total HMA thickness of 10 inches. Section N9 used
approximately 9 inches of the Track soil as base material, followed by one layer with
PG 64-22 compacted to 2% air voids, two layers with PG 64-22, a layer with PG 76-28,
and finally topped with PG 76-28 SMA for a total HMA thickness of 14 inches. Section
N10 used 4 inches of a dolomitic limestone base material, termed Missouri Type 5 base.
Above the base was one HMA layer with PG 64-22 topped with two HMA layers with
PG 70-22 binder for a total of approximately 8 inches of HMA. Section S11 consisted 8
inches of HMA: two upper layers with modified PG 76-22 binder over two layers with
54
unmodified PG 64-22. These layers were placed atop the 6 inches of granite aggregate
base material utilized in sections N3 through N7.
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
18.0
20.0
22.0
24.0
N1 N2 N3 N4 N5 N6 N7 N8 N9 N10 S11
As
Built T
h
ic
knes
s
,
in.
PG 67-22 PG 76-22 PG 76-22 (SMA) PG 76-28 (SMA)
PG 76-28 PG 64-22 PG 64-22 (2% Air Voids) PG 70-22
Limerock Base Granite Base Type 5 Base Track Soil Seale Subgrade
Florida
(new)
Alabama & FHWA
(left in-place)
Oklahoma
(new)
FHWA
Missouri
(new)
Alabama
(new)
Figure 4. 4 2006 Test Track Structural Sections (Timm, 2009).
Performance Monitoring
During each Test Track cycle, the condition of each section is monitored to
determine the accumulation of distresses such as fatigue cracking and rutting over time.
These distresses contribute to an increase in roughness on the pavement surface, which
adversely affects ride quality. NCAT uses an Automatic Road Analyzer (ARAN)
Inertial Profiler (shown in Figure 4.5) at the Test Track to measure the small
wavelengths in the longitudinal profile in the pavement surface at high speeds for each
wheel path. It achieves this by using an accelerometer, lasers, a speedometer and a
computer. The accelerometer is used to measure the acceleration of the vehicle, which
55
is processed through data algorithms to establish an inertial reference. This reference is
used to determine the instantaneous height of the accelerometer in the vehicle. High
frequency lasers are used to determine the distance between the accelerometer and the
ground, and the speedometer is used to determine the distance between the
measurements taken by the laser (Sayers and Karamihas, 1998). These distance
measurements are continually stored in an on-board computer, and are later equated to a
standard measurement known as the international roughness index (IRI).
Figure 4. 5 ARAN Inertial Profiler at NCAT Test Track.
METHODOLOGY
IRI Data
The IRI data collected with the ARAN van over the course of each Test Track
cycle were used for the recalibration process. The IRI data (recorded in inches per mile)
were converted to units of present serviceability index (PSI), a term that is a direct input
into the AASHTO flexible pavement design equation. This conversion was made using
the following relationship (Al-Omari and Darter, 1994):
()IRI
ePSI
??
=
0038.0
5 (4.1)
56
Once the data were converted, plots were created for each section that showed the
decrease in PSI over time for the right (RPSI) and left wheel paths (LPSI), as well as the
average of the two (AvgPSI). From each of these plots, various points were selected for
calibration of the flexible pavement design equation. If considerable deterioration was
present over time, multiple points were used per section to provide a better fit. Figure
4.6 shows a plot of PSI over time for section N1 during the 2003 Test Track cycle. As
seen in the figure, there is more deterioration in the right wheel path than in the left
wheel path. This was not the case for all the sections; therefore the wheel path with the
most deterioration (the lower PSI values) was used in the recalibration procedure to be
conservative. Five points are shown in Figure 4.6 as circles on the right wheel path PSI
line. These five points were chosen to represent the trend of decreasing PSI over time.
It is important to note that there is a jump in the PSI level around January 2005, which is
when the section was milled and inlaid. When cases such as this occurred, points were
not selected beyond the jump in PSI.
57
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
28-Jun-03 14-Jan-04 01-Aug-04 17-Feb-05 05-Sep-05 24-Mar-06
Date
PSI
LPSI
RPSI
AvgPSI
Pt
Pt calibration points
Figure 4. 6 PSI Data Derived from IRI Data from Section N1 (2003 Test Track).
While the deterioration in Figure 4.6 is quite apparent, other sections did not
show similar trends. For example, Figure 4.7 shows section N3 during both the 2003
and 2006 Test Track cycles (as mentioned previously, this section was left in place after
the 2003 cycle). From the figure, it is seen that there is no major deterioration in this
section over the course of 6 years and 20 million ESALs of traffic; therefore, point
selection in this section was not possible. In sections such as this, an artificial terminal
PSI was assigned to the section to perform the recalibration. Each value assigned was
lower than the actual PSI of the section to be conservative. For this particular case, a
value of 3.5 was used, and the actual final PSI measurement was 4.3. This value was
chosen to be conservative, and because the regression procedure could not be performed
unless there was a substantial difference between the initial and final PSI values. The
58
other PSI versus time graphs for each section can be found in Appendix A. If point
selection was possible, the points were denoted on the figures in the Appendix as they
are in Figure 4.6.
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
28-Jun-03 09-Nov-04 24-Mar-06 06-Aug-07 18-Dec-08
Date
PSI
LPSI
RPSI
AvgPSI
Figure 4. 7 PSI Data from Section N3 (2003 and 2006 Test Track Cycles).
Predicted ESALs
The AASHTO Design Guide flexible pavement design equation was used to
predict the amount of applied ESALs, and is expressed as:
07.8log32.2
)1(
1094
4.0
5.12.4
log
20.0)1log(36.9log
19.5
18
?+
+
+
?
?
?
?
?
?
?
?
+?++=
R
oR
M
SN
PSI
SNSZW
(4.2)
59
Where Z
R
is the normal deviate for a given reliability, S
o
is the standard
deviation, ?PSI is the expected loss of serviceability over the lifetime of the pavement,
M
R
is the resilient modulus of the subgrade, and SN is the structural number, as defined
by the following equation:
33322211
mDamDaDaSN ++= (4.3)
Where a
1
, a
2
and a
3
are the layer coefficients for the hot mix asphalt, base and
subbase layers, respectively; D is the thickness of each respective layer in inches, and m
is the drainage coefficient for the base and subbase layers. For this analysis, there were
no subbase layers for the sections at the Track, so the final term was dropped from the
equation.
For Equation 4.2, the reliability was set at 50%. This value was chosen because
higher reliabilities are used to artificially increase the predicted traffic to account for
uncertainty in the design process. Since all the inputs necessary for use in the equation
were known, it was not necessary to provide this artificial traffic increase, and therefore
the reliability was set at 50%. This reliability resulted in a normal deviate (Z
R
) of zero;
therefore, the first term in the design equation was zero.
For the calculation of the structural number (SN), the thicknesses were obtained
from construction records for each section, the drainage coefficient for the base layer
(m
2
)
was assumed to be equal to one, and the layer coefficient for the base layer (a
2
) was
assumed to be 0.14. This layer coefficient is a recommended value for a crushed stone
base course (AASHTO, 1993). The layer coefficient for the HMA (a
1
) was set at a seed
value of 0.44, which is the current value recommended in the 1993 AASHTO Design
Guide and also commonly used by ALDOT. The thicknesses used for the analysis are
60
shown in Table 4.1. These thicknesses represent section-wide averages based on
surveyed depths.
Table 4. 1 Thickness Data for the Test Track Sections
Section Test Track Year D
1
(in) D
2
(in)
N1 2003 5.3 6.0
N1 2006 7.4 10.0
N2 2003 4.8 6.0
N2 2006 7.1 10.0
N3 2003-2006 9.2 6.0
N4 2003-2006 8.9 6.0
N5 2003-2006 6.9 6.0
N6 2003-2006 7.1 6.0
N7 2003-2006 7.1 6.0
N8 2003 7.0 6.0
N8 2006 9.9 6.4
N9 2006 14.4 8.4
N10 2006 7.7 5.0
S11 2006 7.6 6.1
To obtain the change in serviceability (?PSI) for each test section, the
serviceability data was utilized. The initial PSI (p
o
) value for each section was set to the
first PSI reading taken after the section?s construction. The final PSI value (p
t
) was
selected based upon the point selection procedure described previously. The difference
between these two values was the ?PSI used in the equation.
The resilient modulus (M
R
) was calculated for each section based on
backcalculated falling weight deflectometer (FWD) data collected over the course of
each Test Track cycle. An average was taken of the backcalculated data for each section
and then divided by three as recommended in the AASHTO Design Guide (1993). As
mentioned previously, this value is divided by three to account for differences in testing
procedures used to find the subgrade moduli. Table 4.2 shows the resulting M
R
values
used in Equation 4.2.
61
Table 4. 2 Resilient Modulus Data (after Taylor, 2008)
Section Test Track Year M
R
(psi)
N1 2003 8093
N1 2006 12279
N2 2003 8497
N2 2006 11749
N3 2003 10838
N4 2003 11296
N5 2006 10053
N6 2003 11427
N7 2003 11154
N8 2003 9800
N8 2006 10038
N9 2006 15630
N10 2006 14731
S11 2006 9593
After identifying all the inputs, the predicted traffic (logW
18
) was found for each
test section. The estimated ESALs were found by solving
18
log
10
W
. For example, for
section N1 of the 2003 Test Track, Table 4.3 shows the serviceability data that were
used in the predicted ESALs calculation (also shown graphically in Figure 4.6).
Table 4. 3 Serviceability Data for Section N1 (2003 Test Track)
Date Initial Serviceability (p
o
)
10/20/2003 4.14
Date Terminal Serviceability (p
t
)
5/24/2004 2.98
7/01/2004 2.48
8/17/2004 2.25
10/11/2004 1.67
12/13/2004 0.54
Using these data in conjunction with the resilient modulus and thickness data
mentioned previously, the predicted ESALs based upon this damage were calculated and
are shown in Table 4.4.
62
Table 4. 4 Predicted ESALs Applied for Section N1 (2003 Test Track)
Date Predicted ESALs
5/24/2004 802,367
7/01/2004 1,126,574
8/17/2004 1,270,712
10/11/2004 1,638,661
12/13/2004 2,340,290
Calculated ESALs
The AASHTO Design Guide quantifies pavement damage using Equivalent Axle
Load Factors (EALFs), which are used to find the number of ESALs. An EALF is used
to describe the damage done by an axle per pass relative to the damage done by a
standard axle (typically an 18-kip single axle) per pass. This equation comes from the
results of the AASHO Road Test, and is expressed as follows according to Huang
(2004):
tx
t
W
W
EALF
18
= (4.)
Where W
tx
is the number of x axle load applications at time t, and W
t18
is the
number of 18 kip axle load applications at time t.
The EALFs for each axle load group are used to find the total damage done
during the design period, which is defined in terms of passes of the standard axle load,
as shown in the following equation (Huang, 2004):
?
=
=
m
i
ii
nEALFESAL
1
(4.5)
Where m is the number of axle load groups, EALF
i
is the EALF for the ith axle
load group, and n
i
is the number of passes of the ith axle load group during the design
period.
63
These basic equations were used in conjunction with the following equations to
that were developed from the AASHO Road Test to characterize the traffic for the
recalibration process (Huang, 2004).
?
?
?
?
?
?
?
?
=
5.12.4
2.4
log
t
t
p
G (4.6a)
()
()
23.3
2
19.5
23.3
2
1
081.0
40.0
LSN
LL
x
x
?+
+?
+=? (4.6b)
()
18
22
18
log33.4log79.41252.6log
??
t
x
t
x
t
tx
GG
LLL
W
W
?+++?=
?
?
?
?
?
?
(4.6c)
Where G
t
is the logarithm of the ratio of loss of serviceability at some time t to
the potential loss of serviceability at terminal serviceability (p
t
) = 1.5, and the initial
serviceability is assumed to be 4.2; this value was typical for flexible pavements at the
AASHO Road Test, and is used as the initial value for ALDOT pavement designs as
well. ?
x
is a function of design and load variables, L
x
is the axle group load in kips, L
2
is
the axle code (1 for single, 2 for tandem and 3 for tridem), SN is the structural number,
W
tx
is the number of x axle load applications at time t, W
t18
is the number of 18 kip axle
load applications at time t, and ?
18
is the value of ?
x
when L
x
is equal to 18 and L
2
is
equal to one.
Most of the inputs needed for these equations were obtained from traffic data
collected during the 2003 and 2006 Test Track cycles. In the 2003 cycle, six different
trucks were used to apply traffic to the test sections. Five of the trucks (termed ?triple
trailers?) were comprised of one steer axle, a drive tandem axle, and five trailing single
axles as shown in Figure 4.8. The sixth truck (termed the ?box trailer?) consisted of a
64
steer axle and two tandem axles as shown in Figure 4.9. The weights of these axles
were recorded for each truck, and are shown in Table 4.5.
Figure 4. 8 Triple Trailer Truck at NCAT Test Track.
Figure 4. 9 Box Trailer Truck at NCAT Test Track.
Table 4. 5 Axle Weights for 2003 Test Track (after Priest and Timm, 2006)
Steer, lb Drive Tandem, lb Single Axle, lb
Truck ID 1 1 2 1 2 3 4 5
1-Triple 10150 19200 18550 21650 20300 21850 20100 19966
2-Triple 11000 20950 20400 20950 21200 21000 20900 20900
3-Triple 10550 20550 21050 21000 21150 21150 21350 20850
4-Triple 10500 21050 20700 21100 21050 21050 20900 21050
6-Triple 11200 19850 20750 20350 20100 21500 19500 20300
Steer, lb Drive Tandem, lb Rear Tandem, lb
5-Box 11550 16850 17000 16800 16100
For the 2006 Test Track cycle, only five triple trailer trucks were used to apply
traffic, and their axle weights are shown in Table 4.6.
65
Table 4. 6 Axle Weights for 2006 Test Track (Taylor, 2008)
Steer, lb Drive Tandem, lb Single Axle, lb
Truck ID 1 1 2 1 2 3 4 5
1-Triple 9400 20850 20200 20500 20850 20950 21000 20200
2-Triple 11200 20100 19700 20650 20800 20650 20750 21250
3-Triple 11300 20500 19900 20500 20500 21000 20650 21100
4-Triple 11550 21200 19300 21000 21050 21000 20750 20800
6-Triple 11450 20900 19400 20100 20450 21000 20050 20650
Using these axle weights, averages were computed for each axle type (steer,
single and tandem), for each truck type (triple and box), and for each Test Track cycle.
For the tandem axles, averages were computed for each tire set (1 and 2) and then
summed to obtain the total average tandem axle weight. For example, the 2003 weights
resulted in the averages shown in Table 4.7. The combined values are the result of the
average of steer axles, the sum of the average tandem axle weights, and the average of
the single axle average weights. Table 4.8 shows the average axle weights for the 2006
Test Track cycle.
Table 4. 7 Average Axle Weights for 2003 Test Track
Steer, lb Drive Tandem, lb Single Axle, lb
1 1 21234 5
Averages 10680 20320 20290 21010 20760 21310 20550 20613
Combined 10680 40610 20849
Table 4. 8 Average Axle Weights for 2006 Test Track
Steer, lb Drive Tandem, lb Single Axle, lb
1 1 21234 5
Averages 10980 20710 19700 20550 20730 20920 20640 20800
Combined 10980 40410 20728
These averages were used in Equation 4.6 (as the L
x
term) to compute the ?
x
and
W
tx
/W
t18
terms, which were then used to compute the amount of ESALs applied per axle.
The values chosen for p
t
and the calculations for SN were discussed in the previous
section. To provide an example of the calculations performed for the calculated ESALs,
66
the values shown in Table 4.9 were computed for section N1 of the 2003 Test Track
using the average axle weights shown in Table 4.7.
Table 4. 9 Section N1 (2003 Test Track) Traffic Calculation Results
?
x
Truck Steer Tandem Single
Triple 0.493 1.051 1.106
Box 0.518 0.757 --
log(W
tx
/W
t18
)
Truck Steer Tandem Single
Triple 0.719 -0.299 -0.197
Box 0.603 -0.039 --
ESALs/Axle
Truck Steer Tandem Single
Triple 0.19 1.99 1.57
Box 0.25 1.09 --
Detailed data were collected for the amount of traffic applied at the test track.
For each day that trucks were driving during the test cycle, the total amount of steer,
single and tandem axle passes were recorded for both the triple and box trailers, and a
sample of those data are shown in Figure 4.10. To calculate the ESALs applied by each
axle, these axle passes were multiplied by their respective ESALs/Axle factors shown in
Table 4.9 to obtain the total ESALs per day for each axle type. The ESALs were
summed across all axle types to obtain the total amount of ESALs applied per day, and
these were summed cumulatively to get the total ESALs applied up to a certain day in
the test cycle, as shown the ?Cumulative Sum? column in Figure 4.10.
67
Figure 4. 10 Sample of Detailed Axle Data.
Using these axle data, the total amount of applied ESALs could easily be
obtained for various dates. Using section N1 from the 2003 Test Track as an example,
the calculated ESALs shown in Table 4.10 were recorded for the same dates that the
ESALs were predicted for in Table 4.4. It is important to note that the calculated
ESALs shown in Table 4.10 are the result of not only the number of axle passes applied
up to that date in the cycle, but also from a unique set of ESAL/axle factors for each
date. This is because each date represents a different p
t
value and, consequently, a
different set of ESAL factors for each axle type.
Table 4. 10 Calculated ESALs for Section N1 (2003 Test Track)
Date Calculated ESALs
5/24/2004 2,267,922
7/01/2004 2,837,091
8/17/2004 2,963,064
10/11/2004 3,212,141
12/13/2004 4,321,771
68
Regression
When comparing the predicted and calculated ESALs for section N1 of the 2003
Test Track, it is apparent that there are some substantial differences when using 0.44 for
the HMA layer coefficient. Table 4.11 shows the calculated and predicted ESALs for
section N1 of the 2003 Test Track, as well as the difference between the two. In
general, the current structural coefficient (0.44) results in gross underpredictions of the
ESAL-capacity of the pavement structure. This is likely due to the newer and more
advanced HMA materials that are used at the track, which implies that the layer
coefficient should be higher. The large error percentages show a need to bring these
values closer together for a more realistic ESAL prediction, and a least squares
regression was performed to accomplish that task.
Table 4. 11 ESAL Differences Assuming a
1
= 0.44 for Section N1 (2003 Test Track)
Predicted ESALs Calculated ESALs Difference % Error
802,367 2,267,922 1,465,555 -65%
1,126,574 2,837,091 1,710,517 -60%
1,270,712 2,963,064 1,692,352 -57%
1,638,661 3,212,141 1,573,480 -49%
2,340,290 4,321,771 1,981,481 -46%
To perform the regression, first the differences between calculated and predicted
were squared. These values were summed to obtain the error sum of squares (SSE),
which is defined by the following equation:
()
?
?=
i
ii
yySSE
2
? (4.7)
The mean was obtained for the calculated ESALs, and the difference between
that mean and each predicted ESAL level was taken and then squared. These values
were summed to obtain the total sum of squares (SST), as seen in the following equation:
69
()
?
?=
i
i
yySST
2
(4.8)
The Pearson?s coefficient of determination (R
2
) was calculated from these values
to determine the goodness of fit using the following formula:
SST
SSE
R ?=1
2
(4.9)
To perform the regression, Microsoft Excel Solver was utilized. The solver was
set to minimize the SSE term while only changing the HMA layer coefficient (a
1
). This
process is inherently iterative in nature: every time the layer coefficient changes (i.e.
from 0.44 to a new regressed value), both the calculated and predicted ESALs change.
This is because both of these values are calculated using the structural number (SN), and
that is calculated using the layer coefficient (a
1
).
RESULTS AND DISCUSSION
Regressed Layer Coefficients
The regression procedure was performed for each test section to determine the
new HMA layer coefficients. Table 4.12 shows the regression statistics for section N1
of the 2003 Test Track. This regression resulted in a HMA layer coefficient of 0.50.
There is a noticeable improvement in the calculated and predicted ESAL differences
after the regression procedure. Regression statistics for all other sections (other than
those that did not display a change in serviceability) can be found in Appendix B.
Although relatively large percent errors are observed between the calculated and
predicted ESALs, especially at the lowest ESAL level, this is not a significant cause of
concern. In fact, it is expected that there could be considerable differences due to the
70
log effect of ESALs within the AASHTO design system. As discussed in Chapter 2,
taking the log of 5 million and 6 million results in very similar values (6.70 and 6.78,
respectively). Therefore, it is not surprising that some relatively large percent errors
were found in the regression procedure. The main purpose in the regression was to
minimize the errors, but it was not expected to eliminate them. Additionally, comparing
the results from Table 4.12 (recalibrated) to Table 4.11 (assumed a
1
= 0.44) shows
considerable improvement in the ESAL predictions.
Table 4. 12 Regression Statistics for Section N1 (2003 Test Track)
Predicted ESALs Calculated ESALs Difference % Error Diff
2
STDiff
2
1,314,680 2,224,691 910,012 41% 8.28E+11 3.21E+12
2,007,491 2,806,554 799,065 28% 6.39E+11 1.21E+12
2,332,763 2,939,906 607,145 21% 3.69E+11 5.98E+11
3,203,489 3,207,147 3,661 0% 1.34E+07 9.44E+09
4,996,650 4,353,456 643,194 15% 4.14E+11 3.57E+12
Average 3,106,351 Sum 2.25E+12 8.60E+12
R
2
0.738
For sections that did not exhibit considerable damage at the end of the Test
Track cycle, an artificial terminal serviceability was selected for use in the regression
procedure. These values were always equal to or lower than the actual serviceability
level of the test section, and therefore provide conservative estimates of the layer
coefficient. For example, in section N3 of the 2003 and 2006 Test Track cycles (refer to
Figure 4.7), the final serviceability value measured was 4.27. The initial reading was
4.36, resulting in a ?PSI value of only 0.09. In cases such as this, the solver function
was used to create a difference in calculated and predicted ESALs of zero by only
changing the layer coefficient. For each section where artificial terminal serviceabilities
were used, the first p
t
used was the actual terminal level found in the section. If the
71
solver could not converge on a solution for the layer coefficient, then the p
t
was
decreased by one tenth and then the process was repeated until the solver converged on
an answer. In the case of N3, an artificial terminal level of 3.9 was assigned to create a
large enough ?PSI for convergence to a solution for the layer coefficient, which resulted
in a layer coefficient of 0.62. Figure 4.11 shows the calculated versus predicted ESALs
for each test section after the regression was performed. The data in Figure 4.11
illustrate section-specific regression results.
0.0E+00
5.0E+06
1.0E+07
1.5E+07
2.0E+07
0.0E+00 5.0E+06 1.0E+07 1.5E+07 2.0E+07
Calculated ESALs
Predict
e
d ESALs
N1 2003
N1 2006
N2 2003
N2 2006
N3 2003-2006
N4 2003-2006
N5 2006
N6 2003-2006
N7 2003-2006
N8 2003
N8 2006
N9 2006
N10 2006
S11 2006
Figure 4. 11 Calculated vs. Predicted ESALs.
Table 4.13 provides a summary of the structural coefficients found for each
section, as well as the R
2
values. If there is no associated R
2
, then those sections were
assigned artificial terminal serviceability levels as discussed previously.
72
Although it is apparent that the models do not describe 100% of the data used in
this study, the coefficient of determination (R
2
) values are still reasonably high
considering the highly variable nature of research involving pavements and live traffic.
Even the AASHO Road Test results had R
2
values that were not optimum; the overall
average R
2
was approximately 0.85. Additionally, for those analyses, many more test
sections (284) were used to arrive at a layer coefficient.
Table 4. 13 Regressed HMA Layer Coefficients
Section Cycle Year a
1
R
2
N1 2003 0.50 0.73
N1 2006 0.59 0.90
N2 2003 0.56 0.70
N2 2006 0.63 NA
N3 2003-2006 0.62 NA
N4 2003-2006 0.58 NA
N5 2006 0.48 0.95
N6 2003-2006 0.59 0.71
N7 2003-2006 0.58 0.61
N8 2003 0.43 0.68
N8 2006 0.48 0.64
N9 2006 0.44 NA
N10 2006 0.41 0.96
S11 2006 0.68 NA
Average 0.54 0.76
Std Dev 0.08 0.14
Figure 4.12 shows the individual section layer coefficients and the average layer
coefficient graphically. As seen in Table 4.13 and Figure 4.12, most of the values found
were higher than the current recommended value of 0.44. It is important to note that
although the sections assigned artificial terminal serviceability levels do provide
conservative estimates of the HMA layer coefficient, the pavements did not actually
reach that level of serviceability in most cases. There were five sections that were
assigned a terminal level of serviceability, and if these sections are not included in the
73
analysis, the resulting average HMA layer coefficient is 0.51; slightly lower than the
overall average value shown in Table 4.13.
0.50
0.59
0.56
0.63
0.62
0.58
0.48
0.59
0.58
0.43
0.48
0.44
0.41
0.68
0.54
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
N1
20
03
N1
20
06
N2
20
03
N2
20
06
N3 200
3-20
06
N4 200
3-20
06
N5
20
06
N6 200
3-20
06
N7 200
3-20
06
N8
20
03
N8
20
06
N9
20
06
N10
20
06
S11
20
06
Average
L
a
ye
r Co
e
f
f
i
cie
n
t
Figure 4. 12 Regressed Layer Coefficients.
There were two sections that resulted in coefficients lower than 0.44: N8 of the
2003 Track, and N10 of the 2006 Track. After the end of the 2003 Test Track cycle,
section N8 showed considerable signs of fatigue cracking damage which was not
expected given the pavement cross section and materials used. A forensic investigation
of the section indicated that debonding had occurred between the HMA lifts, making the
pavement much more prone to damage. A full report of the investigation of debonding
in section N8 has been documented elsewhere (Willis and Timm, 2006). Section N10 of
the 2006 Test Track also displayed more damage than expected at the end of the test
cycle. Considerable surface distortion was present throughout the section, which
74
warranted another forensic investigation. Trenches were cut in the section to view the
damage throughout the cross section, and the individual HMA lifts were easily
delaminated from one another using a backhoe. This phenomenon was not observed in
any other sections that had trenches cut on the same day (January 29, 2009). While no
reports have been officially published on this topic yet, the following pictures (Figures
4.13 and 4.14) illustrate the likelihood that debonding was occurring. Based on the
published report for section N8 and the forensic photos of section N10, it is possible that
the HMA layer coefficients found for these sections were lower than the recommended
value of 0.44 due to their probable debonding issues.
Figure 4. 13 Trench Showing Signs of Debonding in Section N10.
75
Figure 4. 14 Trench Showing Delamination of HMA Lifts in Section N10.
After the regression was performed, the average value for the layer coefficient
(0.54) was used to create a graph of calculated versus predicted ESALs with all test
sections, and is shown in Figure 4.15. As seen in the figure, the data are fairly evenly
distributed around the line of equality. A similar graph was also created using the
recommended value of 0.44, and is shown in Figure 4.16. From this figure it is apparent
that using the recommended layer coefficient results in an under-prediction of calculated
ESALs using the flexible pavement design equation for 89% of the sections at the Test
Track, which would result in overly conservative designs.
76
0.0E+00
5.0E+06
1.0E+07
1.5E+07
2.0E+07
0.0E+00 5.0E+06 1.0E+07 1.5E+07 2.0E+07
Calculated ESALs
Predicted ESALs
N1 2003
N1 2006
N2 2003
N2 2006
N3 2003-2006
N4 2003-2006
N5 2006
N6 2003-2006
N7 2003-2006
N8 2003
N8 2006
N9 2006
N10 2006
S11 2006
Figure 4. 15 Calculated vs. Predicted ESALs Using a
1
= 0.54.
0.0E+00
5.0E+06
1.0E+07
1.5E+07
2.0E+07
0.0E+00 5.0E+06 1.0E+07 1.5E+07 2.0E+07
Calculated ESALs
Predicted ESALs
N1 2003
N1 2006
N2 2003
N2 2006
N3 2003-2006
N4 2003-2006
N5 2006
N6 2003-2006
N7 2003-2006
N8 2003
N8 2006
N9 2006
N10 2006
S11 2006
Figure 4. 16 Calculated vs. Predicted ESALs Using a
1
= 0.44.
77
Trends
No trends were apparent in the regression analysis. Pavement cross section,
HMA thickness, and binder type all had no obvious effect on the resulting layer
coefficient. For example, sections N1 and N2 from the 2003 Test Track both had very
similar cross sections of 5 inches HMA over a 6 inch granular base. The resulting layer
coefficients were 0.50 and 0.56, respectively. In the 2006 Test Track, the same sections
were rebuilt with similar cross sections of 7 inches HMA over a 10 inch granular base,
and the layer coefficients were 0.59 and 0.63, respectively. Other sections with similar
cross sections and HMA layer thicknesses were compared, and no trend was found.
Sections N3 and N4 of the 2006 Test Track both consisted of 9 inches of HMA, N3
being unmodified PG 67-22, and N4 being modified PG 76-22. The resulting layer
coefficients were opposite of what was expected: 0.62 and 0.58, respectively. The
highest layer coefficient was found for section S11, which consisted 8 inches of HMA:
two upper layers of modified PG 76-22 binder over two layers of unmodified PG 64-22.
There are several sections with thicker cross sections than S11, as well as higher PG
grades. From these data and other similar comparisons, it was concluded that there were
no trends found relative to overall cross section, HMA thickness, or binder type. This
could be due to other factors that can affect the layer coefficient within the pavement
structure. Debonding between HMA lifts likely caused lower layer coefficient values in
sections N8 and N10 as discussed previously. Other factors such as compaction, binder
content, air voids or pavement age might also have significant (and perhaps
confounding) impacts on the differences in layer coefficients, which may be why no
trends are apparent in the data. Conversely, it could be that a
1
is generally insensitive to
78
these factors. This is evidenced by many states, ALDOT included, by using a single a
1
value in structural design for a wide variety of asphalt mixtures.
Impact of Changing Layer Coefficient
Changing the HMA layer coefficient from 0.44 to the average value of 0.54
found at the NCAT Test Track for flexible pavement designs would have a significant
impact on the resulting HMA layer thickness. Figure 4.17 shows how this thickness
would change over varying traffic levels for a given design (R of 50%, S
o
of
0.40, M
R
of
10,000 psi, ?PSI of 2, D
2
of 6 inches, and a
2
of 0.14). At 1 million ESALs, the savings
in thickness is approximately 0.7 inches; at 100 million ESALs, it is 1.7 inches. These
values are only applicable to the design given. For example, a lower M
R
value would
result in a greater difference between using the two layer coefficients, and vice versa.
Regardless of the other input values, changing to a layer coefficient of 0.54 from 0.44
would always result in a thinner pavement, and in an approximate savings of 18% in
HMA thickness.
Minimum Thickness
It is important to note that the regressed layer coefficient of 0.54 was calibrated
to sections with HMA thicknesses no less than 5 inches. Therefore, this coefficient
should not be used for designs that result in pavements with a HMA thickness of less
than 5 inches. It is recommended that for designs resulting in thicknesses of less than 5
inches, the AASHTO recommended coefficient of 0.44 be used, or the minimum
thickness be set to 5 inches.
79
0
2
4
6
8
10
12
14
1,000,000 10,000,000 100,000,000 1,000,000,000
ESALs
HM
A Depth (in)
a1 = 0.44
a1 = 0.54
Figure 4. 17 Change in Resulting HMA Thickness from a
1
= 0.44 to a
1
= 0.54.
SUMMARY
Pavement performance and traffic data were collected over the course of the
2003 and 2006 Test Track cycles. These data were used to perform a recalibration of
the HMA layer coefficient (a
1
) that is used in the current ALDOT flexible pavement
design methodology. The recalibration was achieved by calculating the predicted
ESALs using the 1993 AASHTO Design Guide flexible pavement design equation, and
also calculating the ESALs applied at the Test Track during the two test cycles. The
pavement performance data (IRI measurements) were used to find a change in
serviceability (?PSI) or a terminal serviceability level (p
t
) for use in the design
equations. Some sections did not exhibit an increase in roughness over the course of the
Test Track cycle(s), and therefore were assigned artificial terminal serviceability levels
80
to provide a ?PSI term large enough for convergence to a layer coefficient. The values
chosen were always less than or equal to the actual final serviceability level at the end of
the cycle, and therefore are conservative. The predicted and calculated ESALs were
compared, and a least squares regression was performed to minimize the difference
between the two values while only changing the HMA layer coefficient. This resulted in
an average layer coefficient of 0.54 with a standard deviation of 0.08 for all the test
sections analyzed. If the sections assigned a terminal serviceability level were not
included in the analysis, the average layer coefficient was 0.51. These values can be
compared to the current value used for the HMA layer coefficient of 0.44, which comes
from the AASHO Road Test. There were no trends in the data regarding the pavement
cross section, HMA thickness or binder type. The impact of changing the layer
coefficient to the average value found in this analysis would result in a reduced HMA
thickness, regardless of design. The amount of reduced thickness is dependent upon
other design inputs such as resilient modulus, traffic, etc.
81
CHAPTER 5
CONCLUSIONS AND RECOMMENDATIONS
SUMMARY
This investigation was performed to determine the relative sensitivity of HMA
thickness to the inputs of the AASHTO Design Guide flexible pavement design
equation, and to recalibrate the HMA layer coefficient used for flexible pavement
designs. For the recalibration procedure, traffic and performance data from the 2003
and 2006 NCAT Test Track cycles were used in conjunction with flexible pavement
design and traffic equations developed from the AASHO Road Test. Calculated and
predicted ESALs were computed and compared, and a least squares regression was
performed to determine new layer coefficients for each test section.
CONCLUSIONS
From the literature review, it was apparent that research was needed to determine
the relative sensitivity of the inputs to the AASHTO flexible pavement design equation
since no literature could be found on this topic. It was also concluded that based upon
the limited parameters of the AASHO Road Test, the recommended default HMA layer
coefficient of 0.44 should be reanalyzed to ensure accuracy for current materials. While
82
several studies have been conducted to determine the layer coefficients of new materials,
there is no recommended tried-and-true procedure that all researchers can agree upon.
In addition, the results found from many layer coefficient studies tended to be highly
variable, and a specific layer coefficient was typically not recommended for a particular
material.
The input sensitivity analysis showed that the layer coefficient, resilient modulus
and traffic are by far the most influential parameters on the resulting HMA thickness.
Since the resilient modulus and traffic are typically given parameters for a particular
pavement design, it was concluded that an accurate characterization of the layer
coefficient is extremely important. Input dependencies were found in the sensitivity
analysis; all inputs had an increasing influence on the resulting HMA thickness as the
traffic level increased.
The recalibration procedure resulted in an average HMA layer coefficient of 0.54
with a standard deviation of 0.08 from the 14 pavement sections studied. Five sections
that did not exhibit considerable deterioration were assigned artificially low, yet
conservative, terminal serviceability levels to obtain a ?PSI term large enough for
convergence to a layer coefficient. If these sections are not included in the calculations,
the result is an average layer coefficient of 0.51. The only two test sections that resulted
in regressed layer coefficients lower than the AASHTO recommended value of 0.44 had
probable slippage failures, as found in forensic investigations. No trends were observed
in the resulting layer coefficients when comparing binder type, HMA layer thickness or
overall pavement cross section. The impact of changing the layer coefficient to the
83
average value found in this analysis would result in a reduced design HMA thickness,
regardless of the values of other inputs to the design.
RECOMMENDATIONS
Based upon the results of this investigation, it is recommended that ALDOT use
a layer coefficient of 0.54 for flexible pavement designs using the AASHTO design
methodology. This coefficient is larger than the recommended value of 0.44; however,
it was expected to increase due to the numerous advancements in HMA materials and
construction since the AASHO Road Test was completed in 1961. Using a layer
coefficient of 0.54 would result in a HMA thickness savings of approximately 18%.
Care should be taken when applying this coefficient to other states. The regressed layer
coefficient is the result of the environmental conditions and materials used in this study.
84
REFERENCES
AASHTO. AASHTO Guide for Design of Pavement Structures. American Association of
State Highway and Transportation Officials, Washington, D.C., 1993.
ALDOT. ALDOT Procedure 390: Procedure for Conducting Soil Surveys and
Preparing Materials Reports. ALDOT Bureau of Materials and Tests, 2004.
Al-Omari, B. and M.I. Darter, Relationships between International Roughness Index and
Present Serviceability Rating. Transportation Research Record 1435, Transportation
Research Board, Washington, D.C. 1994.
Corree, B.J. and T.D. White, The Synthesis of Mixture Strength Parameters Applied to
the Determination of AASHTO Layer Coefficient Distributions. Asphalt Paving
Technology, vol. 58. 1989.
Gulen, S., R. Woods, J. Weaver, and V.L. Anderson, Correlation of Present
Serviceability Ratings with International Roughness Index. Transportation Research
Record 1435, Transportation Research Board, Washington, D.C. 1994.
85
Hall, K.T., and C.E.C. Munoz, Estimation of Present Serviceability Index from
International Roughness Index. Transportation Research Record 1655, Transportation
Research Board, Washington, D.C. 1999.
Holman F., Drainage of Water from Pavement Structures. Alabama Department of
Transportation. Research Project No. 930-275. 1996.
Holman, F., Guidelines for Flexible Pavement Design in Alabama. Alabama Department
of Transportation, 1990.
Hossain, M., A. Habib and T.M. LaTorella. Structural Layer Coefficients of Crumb-
Rubber Modified Asphalt Concrete Mixtures. Transportation Research Record 1583,
Transportation Research Board, Washington, D.C. 1997.
HRB. The AASHO Road Test. Special Reports 61A, 61C, 61E. Highway Research
Board, 1962.
Huang, Y.H., Pavement Analysis and Design. 2
nd
ed. New Jersey: Prentice Hall, 2004.
Jess, J.C. and D.H. Timm, Structural Coefficients for New Asphalt Mixtures, ALDOT
Project No. 930-559, National Center for Asphalt Technology, Auburn University, 2005.
86
Pologruto, M., Procedure for Use of Falling Weight Deflectometer to
Determine AASHTO Layer Coefficients. Transportation Research Record 1764,
Transportation Research Board, Washington, D.C. 2001.
Priest, A.L. and D.H. Timm, Methodology and Calibration of Fatigue Transfer
Functions for Mechanistic-Empirical Flexible Pavement Design, Report No. 06-03,
National Center for Asphalt Technology, Auburn University, 2006.
Romanoschi, S. and J.B. Metcalf, Simple Approach to Estimation of
Pavement Structural Capacity. Transportation Research Record 1652,
Transportation Research Board, Washington, D.C., 1999.
Sayers, M.W and S.M. Karamihas, The Little Book of Profilijng: Basic Information
about Measuring and Interpreting Road Profiles. University of Michigan, 1998.
Smith, K.D., K.A. Zimmerman and F.N. Finn, The AASHO Road Test: The Living
Legacy for Highway Pavements. TR News No. 232, Transportation Research Board,
2004.
Taylor, A. J., Mechanistic Characterization of Resilient Moduli for Unbound Pavement
Layer Materials. M.S. Thesis, Auburn University, 2008.
87
Timm, D.H., A.L. Priest and T.V. McEwen, Design and Instrumentation of the
Structural Pavement Experiment at the NCAT Test Track, Report No. 04-01, National
Center for Asphalt Technology, Auburn University, 2004.
Timm, D.H., Design, Construction, and Instrumentation of the 2006 Test Track
Structural Study, Report No. 09-01, National Center for Asphalt Technology, Auburn
University, 2009.
Van Wyk, A., E.J. Yoder and L.E. Wood, Determination of Structural Equivalency
Factors of Recycled Layers by Using Field Data. Transportation Research Record 898,
Transportation Research Board, Washington, D.C., 1983.
Von Quintus, H.L., Evaluation of Procedure to Assign Structural Layer Coefficients for
Use in Flexible Pavement Design. Kansas Department of Transportation Report No. KS-
07-9. 2007.
Willis, J.R. and D.H. Timm, Forensic Investigation of a Rich Bottom Pavement, Report
No. 06-04, National Center for Asphalt Technology, Auburn University, 2006.
88
APPENDIX A
PSI VERSUS TIME GRAPHS FOR EACH TEST SECTION
89
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
10-Oct-06 18-Jan-07 28-Apr-07 06-Aug-07 14-Nov-07 22-Feb-08 01-Jun-08 09-Sep-08
Date
PSI
LPSI
RPSI
AvgPSI
Pt
Figure A1: PSI Data from Section N1 of the 2006 Test Track.
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
28-Jun-03 14-Jan-04 01-Aug-04 17-Feb-05 05-Sep-05 24-Mar-06
Date
PSI
LPSI
RPSI
AvgPSI
Pt
Figure A2: PSI Data from Section N2 of the 2003 Test Track.
90
0
0.5
1
1.5
2
2.5
3
3.5
4
10-Oct-06 18-Jan-07 28-Apr-07 06-Aug-07 14-Nov-07 22-Feb-08 01-Jun-08 09-Sep-08
Date
PS
I
LPSI
RPSI
AvgPSI
Figure A3: PSI Data from Section N2 of the 2006 Test Track.
?
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
20-Mar-03 01-Aug-04 14-Dec-05 28-Apr-07 09-Sep-08
Date
PSI
LPSI
RPSI
AvgPSI
Figure A4: PSI Data from Section N4 of the 2003 and 2006 Test Track Cycles.
?
91
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
20-Mar-03 01-Aug-04 14-Dec-05 28-Apr-07 09-Sep-08
Date
PSI
LPSI
RPSI
AvgPSI
Pt
Figure A5: PSI Data from Section N5 of the 2006 Test Track.
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
20-Mar-03 01-Aug-04 14-Dec-05 28-Apr-07 09-Sep-08
Date
PSI
LPSI
RPSI
AvgPSI
Pt
Figure A6: PSI Data from Section N6 of the 2003 and 2006 Test Track Cycles.
92
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
01-Sep-02 14-Jan-04 28-May-05 10-Oct-06 22-Feb-08 06-Jul-09
Date
PSI
LPSI
RPSI
AvgPSI
Pt
Figure A7: PSI Data from Section N7 of the 2003 and 2006 Test Track Cycles.
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
28-Jun-03 14-Jan-04 01-Aug-04 17-Feb-05 05-Sep-05 24-Mar-06
Date
PSI
LPSI
RPSI
AvgPSI
Pt
Figure A8: PSI Data from Section N8 of the 2003 Test Track.
93
0
0.5
1
1.5
2
2.5
3
3.5
4
10-Oct-06 18-Jan-07 28-Apr-07 06-Aug-07 14-Nov-07 22-Feb-08 01-Jun-08 09-Sep-08
Date
PSI
LPSI
RPSI
AvgPSI
Pt
Figure A9: PSI Data from Section N8 of the 2006 Test Track.
0
0.5
1
1.5
2
2.5
3
3.5
4
10-Oct-06 18-Jan-07 28-Apr-07 06-Aug-07 14-Nov-07 22-Feb-08 01-Jun-08 09-Sep-08
Date
PSI
LPSI
RPSI
AvgPSI
Figure A10: PSI Data from Section N9 of the 2006 Test Track.
?
94
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
10-Oct-06 18-Jan-07 28-Apr-07 06-Aug-07 14-Nov-07 22-Feb-08 01-Jun-08 09-Sep-08
Date
PS
I
LPSI
RPSI
AvgPSI
Pt
Figure A11: PSI Data from Section N10 of the 2006 Test Track.
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
10-Oct-06 18-Jan-07 28-Apr-07 06-Aug-07 14-Nov-07 22-Feb-08 01-Jun-08 09-Sep-08
Date
PSI
LPSI
RPSI
AvgPSI
Figure A12: PSI Data from Section S11 of the 2006 Test Track.
?
?
Point selection not possible. No substantial decrease in serviceability.
95
APPENDIX B
REGRESSION STATISTICS FOR EACH TEST SECTION
96
Table B1 Regression Statistics for Section N1 of the 2006 Test Track
Predicted ESALs Calculated ESALs Difference % Error Diff
2
STDiff
2
1,814,085 1,676,044 138042 8% 1.91E+10 2.89E+12
3,653,019 3,021,544 631475 17% 3.99E+11 1.25E+11
4,658,149 5,051,502 393354 8% 1.55E+11 2.81E+12
Average 3,375,084 Sum 5.73E+11 5.82E+12
R
2
0.902
Table B2 Regression Statistics for Section N2 of the 2003 Test Track
Predicted ESALs Calculated ESALs Difference % Error Diff
2
STDiff
2
2,653,268 1,452,211 1201058 45% 1.44E+12 3.96E+12
2,767,858 1,730,741 1037117 37% 1.08E+12 2.93E+12
4,014,443 3,985,550 28893 1% 8.35E+08 2.96E+11
4,329,912 4,874,551 544639 13% 2.97E+11 2.05E+12
Average 3,441,370 Sum 2.82E+12 9.23E+12
R
2
0.700
Table B3 Regression Statistics for Section N5 of the 2006 Test Track
Predicted ESALs Calculated ESALs Difference % Error Diff
2
STDiff
2
2,498,192 2,598,918 100726 4% 1.01E+10 4.95E+12
3,992,174 3,267,565 724610 18% 5.25E+11 2.42E+12
5,742,145 5,662,943 79202 1% 6.27E+09 7.03E+11
7,066,598 7,348,984 282386 4% 7.97E+10 6.37E+12
Average 4,824,777 Sum 6.21E+11 1.45E+13
R
2
0.957
Table B4 Regression Statistics for Section N6 of the 2003 and 2006 Test Tracks
Predicted ESALs Calculated ESALs Difference % Error Diff
2
STDiff
2
5,880,826 176,433 5704393 97% 3.25E+13 9.72E+13
14,187,307 13,768,047 419260 3% 1.76E+11 1.39E+13
Average 10,034,067 Sum 3.27E+13 1.11E+14
R
2
0.706
Table B5 Regression Statistics for Section N7 of the 2003 and 2006 Test Tracks
Predicted ESALs Calculated ESALs Difference % Error Diff
2
STDiff
2
6,004,943 1,044,458 4960485 83% 2.46E+13 7.08E+13
9,317,670 5,160,057 4157613 45% 1.73E+13 1.85E+13
13,051,495 14,008,131 956635 7% 9.15E+11 2.07E+13
Average 9,458,036 Sum 4.28E+13 1.10E+14
R
2
0.611
Table B6 Regression Statistics for Section N8 of the 2003 Test Track
Predicted ESALs Calculated ESALs Difference % Error Diff
2
STDiff
2
3,072,062 2,084,428 987634 32% 9.75E+11 9.08E+12
4,625,663 3,934,268 691395 15% 4.78E+11 1.35E+12
4,519,510 6,243,857 1724347 38% 2.97E+12 1.31E+12
8,174,480 7,249,997 924482 11% 8.55E+11 4.63E+12
Average 5,097,929 Sum 5.28E+12 1.64E+13
R
2
0.678
97
Table B7 Regression Statistics for Section N8 of the 2006 Test Track
Predicted ESALs Calculated ESALs Difference % Error Diff
2
STDiff
2
3,097,060 747,606 2349454 76% 5.52E+12 1.33E+13
4,427,676 3,972,332 455344 10% 2.07E+11 1.78E+11
5,657,763 6,096,567 438804 8% 1.93E+11 2.90E+12
Average 4,394,166 Sum 5.92E+12 1.64E+13
R
2
0.638
Table B8 Regression Statistics for Section N10 of the 2006 Test Track
Predicted ESALs Calculated ESALs Difference % Error Diff
2
STDiff
2
1,853,463 1,261,542 591921 32% 3.50E+11 6.77E+12
3,553,293 3,793,560 240266 7% 5.77E+10 4.75E+09
6,180,789 6,099,393 81396 1% 6.63E+09 5.00E+12
Average 3,862,515 Sum 4.15E+11 1.18E+13
R
2
0.965