Research Paper
it’s must follow the requirements and format with professional writing supported by evidence, table , graphs and calculations. Also, use other references along with the given ones.
Note: must meet the deadline.
General
Every graduate student will complete an individual study project related to pavement design. This project should include
more than one of the items listed and other items as desired: review of literature, numerical analysis, assessment of
the current state of practice, design methods, suggestions for improvement supported by appropriate analysis, and/or
case studies as closely related as possible. The project deliverable is a paper written in the Transportation Research
Board (TRB) format, which is provided at the link below. Follow formatting for the TRB annual meeting, not the
Transportation Research Record (TRR). The only exception to the formatting requirements is to add a Table of
Contents after the title page. The formatting guidelines take some time to digest, which is part of this year’s exercise.
A key element is the paper written cannot exceed the maximum length requirements. Note these papers are not going
to be submitted to TRB, or anywhere else, this is only for learning purposes.
http://onlinepubs.trb.org/onlinepubs/am/infoforauthors
Topic
This semester there are two topic options. There is some independent thought required for either, and there are also
some specific requirements.
Option 1: AASHTO 1986 or 1993 Empirically Based Investigation
The primary objective is to document how layer coefficients (i.e. ai terms such as a1, a2, a3…have been developed).
These terms are the most important inputs to determining a pavement’s available structural capacity based on the
materials used. Three documents must be referenced as described below, alongside additional sources as needed
(only referencing these three documents won’t result in a good grade, they are just to get the process started).
• NCAT Report 14-08
• Florida Study BDV31-977-27
• A study where the Falling Weight Deflectometer (FWD) was used to determine in-situ ai terms
The project is due by (02/12/2020)
AStudy of In Situ Pavement Material Properties
Determined from
FWD
Testing
December 2004
RSCH008-936
Vermont Agency of Transportation
Pavement Design Committee
“The information contained in this report was compiled for the use of the Vermont Agency of
Transportation. Conclusions and recommendations contained herein are based upon the research data
obtained and the expertise of the researchers, and are not necessarily to be construed as Agency policy.
This report does not constitute a standard, specification, or regulation. The Vermont Agency of
Transportation assumes no liability for its contents or the use thereof.”
1. Report No. 2. Government Accession No. 3. Recipient’s Catalog No.
2004-6
4. Title and Subtitle 5. Report Date
December 2004
6. Performing Organization Code
A Study of In Situ Pavement
Material
Properties Determined from FWD Testing
7. Author(s) 8. Performing Organization Report No.
Michael Pologruto, P.E.
9. Performing Organization Name and Address 10. Work Unit No.
11. Contract or Grant No.
Vermont Agency of Transportation
Materials and Research Section
National Life Building
Montpelier, VT 05633-5001
12. Sponsoring Agency Name and Address 13. Type of Report and Period Covered
14. Sponsoring Agency Code
Federal Highway Administration
Division Office
Federal Building
Montpelier, VT 05602
15. Supplementary Notes
16. Abstract
The Vermont Agency of Transportation (Agency) developed pavement design procedures
patterned after the American Association of State Highway and Transportation
Officials (AASHTO) pavement design model described in the AASHTO 1993 Pavement
Design Guide (Guide). While the Guide provides one of the most widely used
empirical design models for flexible pavement design, a factor complicating its
utility is the use of an abstract quality, the structural number (SN), to quantify
the strength of the total pavement structure. A consequence of the SN is the need
for structural layer coefficients (ai) to characterize the component materials of
the pavement structure. The Agency found it difficult to quantify these design
parameters because they are difficult to assess directly and consequently found it
equally difficult to calibrate the AASHTO model to Vermont conditions.
However, the Agency has developed and tested a method for determining layer
coefficients using a falling weight deflectometer (FWD), and the resulting layer
coefficients are representative of the in situ behavior of the pavement materials.
This method is based on a model provided in the Guide for assessing the effective
SN of a pavement structure. The Agency found layer coefficients determined for
unbound subbases to be reasonable, while layer coefficients estimated for ACC
materials were generally 25-35% higher than AASHTO’s implied maximum of 0.44.
17. Key Words 18. Distribution Statement
Pavement Design, Layer
Coefficient, Falling Weight
Deflectometer, subbase
19. Security Classif. (of this
report)
20. Security Classif. (of this page) 21. No.
Pages
22. Price
17
1
Table of Contents
Executive Summary ………………………………………………………………………………………………………………………… 3
Objective ……………………………………………………………………………………………………………………………………….. 4
Background ……………………………………………………………………………………………………………………………………. 4
AASHTO Method …………………………………………………………………………………………………………………………… 5
Development of Experimental Model ………………………………………………………………………………………………… 5
Pilot Project to Test Experimental Model …………………………………………………………………………………………. 10
Data Analysis ……………………………………………………………………………………………………………………………….. 11
Fwd Results ……………………………………………………………………………………………………………………………… 11
Layer Coefficients …………………………………………………………………………………………………………………….. 11
Final Structure Simulation ………………………………………………………………………………………………………….. 12
Comparative Analysis of Layer Coefficients …………………………………………………………………………………. 13
Discussion of Results …………………………………………………………………………………………………………………….. 14
Conclusions ………………………………………………………………………………………………………………………………….. 17
Recommendations …………………………………………………………………………………………………………………………. 18
References ……………………………………………………………………………………………………………………………………. 20
2
Table of Figures
Figure 1 Seasonal Variation in SN ………………………………………………………………………………………………….. 6
Figure 2 Granular Subbase Behavior ………………………………………………………………………………………………. 8
Figure 3 Subbase Simulation of Layer Coefficient…………………………………………………………………………….. 9
Figure 4 FWD Testing Progression ……………………………………………………………………………………………….. 11
Figure 5 Determination of Layer Coefficients from FWD Testing …………………………………………………….. 12
Figure 6 ACC Layer Coefficient vs. Depth to Subgrade …………………………………………………………………… 16
List of Tables
Table 1 p-values from Paired t-Testing of FWD Computed and Simul 14
Table 2 14
Table 3 17
Table 4 Recommended Material Properties for Design Using the AASH 19
3
EXECUTIVE SUMMARY
The Vermont Agency of Transportation (Agency) developed pavement design procedures patterned after the
American Association of State Highway and Transportation Officials (AASHTO) pavement design model
described in the AASHTO 1993 Pavement Design Guide (Guide). While the Guide provides one of the most
widely used empirical design models for flexible pavement design, a factor complicating its utility is the use
of an abstract quality, the structural number (SN), to quantify the strength of the total pavement structure. A
consequence of the SN is the need for structural layer coefficients (ai) to characterize the component
materials of the pavement structure. The Agency found it difficult to quantify these design parameters
because they are difficult to assess directly, and consequently found it equally difficult to calibrate the
AASHTO model to Vermont conditions.
However, the Agency has developed and tested a method for determining layer coefficients using a
falling weight deflectometer (FWD), and the resulting layer coefficients are representative of the in situ
behavior of the pavement materials. This method is based on a model provided in the Guide for assessing
the effective SN of a pavement structure. The Agency found layer coefficients determined for unbound
subbases to be reasonable, while layer coefficients estimated for ACC materials were generally 25-35%
support for the predictive qualities of FWD derived layer coefficients to approximate layer coefficients
simulated from the in situ conditions expected to prevail in the final pavement structure.
4
OBJECTIVE
Ever since the Vermont Agency of Transportation (Agency) adopted the American Association of State
Highway and Transportation Officials (AASHTO) pavement design method in 1993, one of the most vexing
problems facing Agency pavement designers has been the calibration of the AASHTO pavement design
procedure for Vermont conditions. Key to this calibration is the determination of the layer coefficients
necessary for characterizing Vermont pavement materials. It has been well established by others that there is
no direct method for quantifying the layer coefficient for a particular material. The AASHTO Pavement
Design Guide (Guide) does provide relationships for determining layer coefficients for several pavement
materials (1), however, these relationships were unique to the materials used to build the AASHO Road Test
in the 1950s. The Guide cautions against using the relationships provided to characterize local materials.
The Guide also suggests that each design organization determine relationships unique to the materials they
use to build pavement structures (1). Unfortunately, the Guide stops short of recommending any procedure
that may be used to determine layer coefficients, or how to develop models for predicting layer coefficients
tee (Committee) undertook a
serious investigation into determining layer coefficients for Vermont pavement materials. The Committee
evaluated as much research as was available on the topic before proposing the multi-year investigation
summarized in this report.
BACKGROUND
There have been several investigations reported using a falling weight deflectometer (FWD) to characterize
the structural properties of pavement materials. Zhou, et al. (2), Hossain, et al. (3), and Janoo (4) all used an
FWD in one way or another to determine material properties for the constituent pavement materials, some
conducting FWD testing on top of each material as the structure was being constructed. However, the
Committee did not consider the methods described for determining layer coefficients, utilizing the AASHTO
modulus/coefficient relationships provided in the Guide, desirable.
While the layer coefficient relationships provided in the Guide are convenient and tempting to use
once a resilient modulus has been established, their use is not necessarily appropriate. The Guide gives no
specific direction, but it does emphasize the importance for designers to calibrate various components of the
design model to local conditions and experience before implementing the AASHTO procedure. Layer
coefficients are certainly no exception to this caveat. Layer coefficients themselves are believed to be a
function of material thickness, underlying material support, and stress state. Further, the modulus/coefficient
relationships provided in the AASHTO Guide were developed for AASHO Road Test materials as they were
constructed at the Road Test site in 1958. The usage of these relationships for materials considerably
different from those used at the Road Test is unsubstantiated and can be misleading. Ideally, AASHTO
should have provided a procedure for designers to develop their own layer coefficient relationships for the
5
materials with which they commonly build pavement structures.
The AASHTO approach to flexible pavement performance quantifies the pavement structure as a
structural number (SN) and further divides the pavement structure into three constituent parts: surface, base,
and subbase. Although it is not very clear what conditions or stress states constitute or distinguish the
surface, base, or subbase from each other, the interplay among the three pavement components and how they
work in concert as a single structure is illustrated by Equation 1,
33221
1
DaDaDaSN (1)
where ai represents the layer coefficient and Di is the thickness of the material.
Accordingly, layer coefficients for a particular material can be thought to represent the SN
–
contribution per unit thickness of that material to the total SN of the pavement structure.
Ideally, what is needed is a way to measure the SN provided by a particular material as a component
of a final pavement structure. This method should be relatively easy to perform so that a variety of
conditions may be surveyed.
AASHTO METHOD
It was not until the publication of the 1993 edition of the AASHTO Guide that a procedure was provided by
AASHTO for determining the in-place SN of a pavement structure using FWD deflection data. This
procedure is described in Appendix L of the 1993 Guide and provides a method for determining the
eff. However, Ioannides expressed concern about the
development of this method, particularly the introduction of mechanistic properties into the
statistical/empirical AASHTO model (5). Regardless, the Committee considered the possibility of deriving
layer coefficients from SNeff
efforts with this model have given this method tacit legitimacy. Specifically, if FWD testing were performed
on the top surface of each component material in a manner similar to that described by Zhou, et al., and
Janoo, the SNeff may be characterized for individual components of a pavement structure. It would follow
that layer coefficients should result from dividing the SNeff-contribution for each material by the thickness of
that material. The veracity of these resulting layer coefficients should then be supported by a comparison
with the layer coefficients that would be expected for the final pavement structure under in situ conditions.
DEVELOPMENT OF EXPERIMENTAL MODEL
The Committee decided to evaluate the SNeff method described in the Guide on several years of seasonal
FWD data initially collected to support the Strategic Highway Research Program (SHRP). Ultimately, over
five years of data, collected at eight different locations throughout the state and representing close to 30,000
deflection basins, provided a comprehensive assessment of the variation in SN for Vermont pavement
structures due to annual seasonal variability. It was observed after spring thaw, a somewhat elusive
6
phenomenon to capture, the SNeff remained fairly stable between days 100 and 300 and exhibited a
coefficient of variation under 10%. This stable time period corresponds very well with the typical April 15
to November 1 construction timeframe established for Agency construction projects. A summary of these
findings for five of the eight sites is illustrated in Figure 1, with SNeff values plotted against the Julian day of
the year (1-365).
SN Seasonal Variation
0
5
10
15
20
25
0 50 100 150 200 250 300 350
Day of year
S
N
Berlin – Site 1 Berlin – Site 2 Charlotte New Haven South Hero
Figure 1 Seasonal Variation in SN
The foregoing findings led the Committee to form several assumptions:
if FWD testing were restricted to the May through October timeframe, fairly stable, essentially
unchanging, effective SNs may be expected at a given location,
barring any extreme fluctuations in temperature or moisture conditions, the SN contribution of any
component material, hence the layer coefficient, should also remain fairly stable during the May
through October timeframe, and
the SN contribution of any pavement structure component is independent of the stress states
produced from the range of loads (6,000 to 16,000 pounds) applied to the surface.
The first two assumptions seemed rather obvious from observation of the data presented in Figure 1.
The third assumption was a result of evaluating the daily results and recognizing that all seasonal locations
were tested using the SHRP FWD protocol, which targets four different loads: 6,000, 9,000, 12,000, and
16,000 pounds. Upon a detailed observation, the effective SNs derived from the SHRP protocol loading
range were surprisingly consistent for a given testing day and the coefficient of variation on the range of
7
effective SNs characteristic for any given day was typically about 1%. Put another way, 95% of the effective
SNs for a particular location and developed during a given day of testing were within less than 1% of the
average SN for that day.
The consistency in the SN was unexpected and truly remarkable. Considering the impulse load
more than doubles during the FWD test, the stress-dependency of the modulus for the unbound materials,
and the visco-elasticity of the asphalt stabilized materials, it seemed highly unlikely that the interplay among
the various material stiffnesses would exactly compensate to provide a constant SN to such a precise degree.
It seemed more plausible that each constituent SN associated with the surface, base, and subbase, should
remain relatively constant on its own.
If the foregoing is true, this last assumption supports the notion that the SNeff established for a
particular material may remain reasonably stable from its placement to its service in the final structure if:
1. All construction and FWD testing activities take place during May through October,
2. No extreme temperature or moisture fluctuations occur prior to FWD testing, and
3. FWD target loads for the base and subbase materials are within the magnitude of stresses likely for
the final structure under normal loadings and do not induce shear failure in the unbound materials.
While strongly implied from the analysis of the seasonal data, the Committee nonetheless attempted
to analytically corroborate the second assumption of a stable SN contribution from any component material.
Unfortunately, this analysis of the SNeff method described in the Guide proved beyond a simple algebraic
manipulation of the SNeff model. A more practicable solution considered was to perform a simulation of the
expected behavior of typical Vermont subbase materials using an elastic layer simulation (ELS).
Two conditions were simulated with the ELS to evaluate the behavior of a pavement structure
subjected to an FWD test. Of particular interest in this simulation is the behavior of the granular subbase
material. Two different stages of the pavement construction were examined. The first condition simulated
the FWD test on the stress-dependent granular subbase resting on a stress-dependent fine-grained subgrade.
The second condition simulated the FWD test of a constant-modulus surface material on stress-dependent
granular base, subbase, and fine-grained subgrade materials. The material properties and performance of the
subbase were compared as illustrated in Figure 2.
8
Figure 2 Granular Subbase Behavior
Resilient moduli for these stress-dependent materials in both simulations were determined using a
simple K-theta model as illustrated in Equation 2,
2
1
k
R
kM (2)
where: MR is the resilient modulus,
k1 and k2 are material-specific regression constants, and
Under the initial conditions, FWD tests were simulated on the surface of each component material.
This was a straightforward analysis from which deflections, loading plate pressures, and subgrade properties
were readily available. However, when simulating the final condition, the loading plate pressures for the
soils engineers may agree on a Boussinesq stress-distribution for a point load, a typical pavement structure
does not behave the same as an equivalent, relatively homogeneous, soil mass. A different approach is
necessary to model the stress-distribution occurring beneath a circular load on a relatively stiff upper layer
into a less stiff (by an order of magnitude) unbound aggregate. Noureldin and Al Dhalaan (6) proposed a
stress-
the loading plate to a circular area with a radius corresponding to the depth from the surface within a depth
BaseYields an SNeff, but does this equal
the SNeff contributed by the subbase
in the final structure?
Subgrade
Subbase
Surface
FWD
FWD
9
ral numbers for base and subbase materials in the
final structure simulation.
Subbase layer coefficients determined from the simulation results of the initial condition described
above were generally within 5% of the layer coefficients determined for the subbase performing in the final
condition and are illustrated in Figure 3. The Committee interpreted the results of this pavement simulation
to validate the assumption that the SN for any component of a pavement structure may remain stable enough
for the design of flexible pavement structures. Without finding any research to contradict the findings of the
simulation, the Committee decided to sponsor a pilot study to determine real world layer coefficients from
FWD testing.
0.950
1.000
1.050
1.100
1.150
14,000 16,000 18,000 20,000 22,000 24,000 26,000 28,000 30,000 32,000
Subbase Modulus – K1 (psi)
Subbase Simulation of Layer Coefficient
Initial to Final Condition
R
a
ti
o
o
f
a
3
K
2
=
0.6
K
2
=
0.4
K
2
= 0.5
Figure 3 Subbase Simulation of Layer Coefficient
In summary, the layer coefficient determination model consisted of the following steps:
1) Assume the SN for any material is a fixed property and remains constant throughout the
construction operation, after it has reached its design condition,
2) Collect FWD deflection data on the top surface of each pavement material, during the
construction season of April 15 through November 1,
3) Use backcalculation software to determine the subgrade MR at the centerline of the load for each
10
FWD test,
4) Correct any deflections taken directly on the pavement, or asphalt cement concrete (ACC), to 68°
F,
5) Determine the SNeff appropriate for each successive build-up of pavement material, and
6) Determine each layer coefficient for each material by taking the difference in the SNeff
determined directly on top and directly below the material layer, and dividing by the material thickness.
Note: The SNeff on top of the subgrade is defined as zero.
PILOT PROJECT TO TEST EXPERIMENTAL MODEL
The next step was to identify a pilot project and collect real data representative of materials used for the
construction of pavement structures in Vermont.
Since analysis of the seasonal data would seem to indicate the drop weight used has little effect on
the SNeff finally determined for any given pavement structure, this study focused on the deflection basins
generated by a single target weight for each material. The target drop weights applied on the surface of each
material were consistent with the effects that would be expected from a 100-psi tire pressure applied at the
plate pressures below 10 psi difficult. This only presented a concern with the sand subbase, which should
have been tested using a pressure in the range of two to three psi. But, testing the sand subbase at 10 psi
yielded no evidence of shear failure due to overstressing and backcalculation results exhibited root-mean-
square (RMS) variations from the FWD-measured deflection basins of less than 25%. The Committee
considered this compromise to be satisfactory for a sand subbase.
The layer coefficients for the pilot project were 0.074, 0.163, and 0.639 for the sand borrow
subbase, dense-graded crushed stone (DGCS), and ACC, respectively. These findings were encouraging
since the layer coefficients established for the unbound materials were within the ranges established by
AASHTO for these materials.
The layer coefficient for the ACC was not discounted outright. Although 0.639 is almost 50%
higher than the 0.44 upper limit established by AASHTO for ACC surface course, two other indicators of
layer coefficients for ACC, a Marshall stability of 2,730 lbf. and a resilient modulus of 580,000 psi, were
also beyond the upper AASHTO limits of 2,100 lbf. and 450,000 psi respectively.
The findings from the data analysis of the pilot project were encouraging. Consequently, the
Committee considered the experimental model developed thus far to be a success. The Committee endorsed
further collection of FWD data, using the experimental model developed with the pilot project, at several
more projects to determine if the method developed was capable of providing satisfactory estimates of
material properties and that these properties are representative of in-service performance. In all, nearly 50
test sites were evaluated for this next phase of the research.
11
DATA ANALYSIS
FWD Results
Backcalculations were performed on all deflection basins to determine the resilient modulus of the subgrade,
a necessary input for the SNeff calculations. Two independent applications were used: ELMOD 4.0 and
EVERCALC 5.0. These two applications perform similar functions, using different algorithms. Both
attempt to achieve convergence between the FWD measured deflection basin and a calculated deflection
basin based on the backcalculated layer moduli.
lent thickness
developed by Odemark and described by Ullidtz (7), was used to spot check a random sample of ELMOD
and EVERCALC output, to ensure reliability of the backcalculation results.
In order to control the quality of the backcalculation findings, goodness-of-fit thresholds were
established for deflection basins taken on the sand, DGCS, and ACC surfaces of 25, 10, and 2% RMS,
respectively. That is, if a backcalculation for a sand deflection basin could not produce a solution with an
RMS less than 25%, that site was removed from further consideration in this study. Similarly, if either the
DGCS or ACC backcalculation failed to meet the appropriate RMS threshold, the entire site was considered
compromised and removed from the study. Figure 4 illustrates how the SNeff progresses as FWD testing is
conducted on each successive pavement material.
Figure 4 FWD Testing Progression
Layer Coefficients
The estimation of layer coefficients (ai) uses the SNeff contributed by each pavement material. Figure 5
Subgrade
S
and
DGCS
ACC
SNeff=10.71
FWD
FWD
FWD
SNeff=5.37
SNeff=1.52
12
illustrates as the SNeff is established for each material interface, the change in SNeff for any two adjacent
material interfaces represents the SN contribution for the material bounded by these adjacent interfaces. The
resulting layer coefficient is the SN contribution for any particular material divided by the thickness of that
material layer. But, if the thickness has not been accurately assessed, this will have a corresponding adverse
effect on the layer coefficient.
Subgrade
Sand
DGCS
ACC
SNeff=10.71
SNeff=5.37
SNeff= 0
t = 7.54 in.
t = 24.36 in.
t = 19.80 in.
SNeff=1.52
SNACC = 10.71-5.37 = 5.34
and
aACC = 5.34÷7.54 = 0.708
SNDGCS = 5.37-1.52 = 3.85
and
aDGCS = 3.85÷24.36 = 0.158
SNSand = 1.52, and
aSand = 1.52÷19.80 = 0.077
Figure 5 Determination of Layer Coefficients from FWD Testing
The development of layer coefficients using the procedure just outlined is relatively easy and
applicable to the materials in question. The issue of whether layer coefficients developed in this manner are
characteristic of material performance of the final (in-place) structure and appropriate for design must be
supported.
Final Structure Simulation
When evaluating the suitability of layer coefficients for use as design parameters, the only pertinent standard
should be their prediction of layer coefficient behavior in the final structure. Ideally, a fully instrumented
pavement structure, with a full array of stress and strain sensors to monitor the behavior of each material
interface, would provide the necessary data to make this comparison. However, based on past experience,
the Committee considered subsurface instrumentation too unreliable.
Instead, an ELS was conducted to simulate the response of the final structure. The simulation was
carried out on a model of the final structure using the actual layer thickness and backcalculated resilient
modulus for each material.
13
calculated below the
surface as proposed by Noureldin and Al Dhalaan, to simulate the behavior of the final structure under an
FWD load and to estimate the SNeff at each material interface. Once the SNeff was determined at the surface
of each material, the layer coefficients were calculated as illustrated previously in Figure 5.
Comparative Analysis of Layer coefficients
In all, six experimental projects amounting to almost 50 test sites were evaluated to establish the significance
between calculating layer coefficients from FWD testing and how well they represent the in situ conditions
estimated by simulation of the final structure. Although cursory observation revealed satisfactory agreement
between centerline deflections measured with the FWD and deflections predicted by the ELS, a more
detailed statistical analysis of the layer coefficients developed from FWD test data and the ELS was done
to
provide a more objective means of establishing that no significant difference existed between the results of
the two methods. If no statistically significant difference is found, then any distinction observed may be
attributable to normal variation in the material properties i.e., the materials do not exhibit linear elastic,
isotropic, and homogeneous properties and normal error in data acquisition. Also, if both methods yield
similar results, it would further substantiate the assumption that the SN contributed by a pavement material is
a fixed property and, more importantly, layer coefficients determined via FWD tests are suitable for design
of the final structure.
The statistical analysis was carried out using a paired t Test, which assumes the difference between
pairs of data to average zero. Ordinarily, a low p-value (a statistical metric that quantifies the rarity of an
occurrence) resulting from a paired t Test indicates little relationship between the two data sets being
compared. For this research, a high p-value (>0.05) suggests a statistically significant correlation exists
between the paired data sets. Thus, the p-values determined by this analysis indicate the layer coefficients
determined via FWD tests are suitable for design of the final structure as indicated in Table 1.
-value (that is, for those results determined at each project
-value (representing the results of an analysis carried out as the
results of each successive project are added to the cumulative database). These results indicate a significant
level of agreement, or correlation between, the two data sets suggesting no statistically significant difference
exists between the two methods: FWD- and ELS-derived layer coefficient determinations. Thus, it may be
concluded, with a high degree of certainty, that FWD-derived layer coefficients are sufficiently accurate to
predict in situ behavior to be useful pavement design parameters.
14
Table 1 p-values from Paired t-Testing of FWD Computed and Simulated Layer Coefficients
p-value (at 95% level of confidence)
Project specific Research cumulative
Vergennes-Ferrisburgh 0.29 0.29
Montpelier State Highway 0.48 0.34
Bolton-South Burlington 0.10 0.28
Burlington 0.09 0.13
Colchester 0.09 0.33
Addison 0.09 0.32
DISCUSSION OF RESULTS
As the results of the statistical analysis supported
determined from FWD testing are sufficiently representative of in situ conditions (exhibited via simulation of
the final structure) an evaluation of the results determined up to this point was warranted.
A summary of the findings for the first six projects studied in this investigation are presented in
Table 2, listing the layer coefficients and resilient moduli so far determined and the number of test locations
for which all quality control criteria were met.
Table 2 Summary of Material Properties for First Six Projects
Sand DGCS ACC I ACC II ACC III ACC IS ACC IIS ACC IIIS
ai 0.073 0.152 0.386 0.687 0.855 0.839 0.588 0.495
Mr (psi) 18,900 41,900 397,000 343,000 360,000 321,000 153,000 346,000
N 47 47 30 30 30 15 17 17
Of particular interest are the layer coefficients determined for the unbound materials. The sand
the fact that this material is much deeper than the unbound subbase materials were at the Road Test. Since
the sand is placed so deeply in Vermont pavement structures, where it would experience lower stress states
than Road Test unbound subbases, it may be performing like a fine-grained material and may explain why
the resilient modulus of 18,900 psi falls on the high side of the AASHTO scale, in relation to the layer
coefficient. The value of 0.152 for the DGCS falls on the higher end of the range established by AASHTO
for an unbound base material. This higher layer coefficient is consistent with the higher resilient modulus of
41,900 psi determined for DGCS and also conforms to the behavior one would expect of a stress-stiffening
coarse-graded granular material. By comparison, laboratory testing of these materials has established
15
estimates of the resilient modulus to be 25-35% of the backcalculated resilient modulus for sand (8) and 30-
45% of the backcalculated resilient modulus for DGCS (9).
Probably the most conspicuous eccentricity with the results established thus far in this effort is the
unusually high layer coefficients established for the ACC materials. Although there appears to be nothing
fundamentally wrong with the layer coefficients determined for the ACC materials i.e., the same procedure
was used to derive reasonable unbound layer coefficients and the elastic layer simulation would seem to
indicate an accurate prediction of in-place behavior their use with the AASHTO design model presented
some concerns. Most obviously, any layer coefficients over 0.50 represent a range of conditions as of yet
unsubstantiated for the empirically derived AASTHO model. Also, the ACC layer coefficients developed
under this investigation were established for materials that were designed using much lower layer coefficients
(0.32-0.39) with the AASHTO model. And finally, if the layer coefficients presented here (>0.50) are used
for an AASHTO design under typical Vermont traffic loading, almost no base material (DGCS) is called for
because all of the strength (SN) is provided by a few inches of ACC. The Committee considered several
mechanisms likely to generate layer coefficients outside the traditional range established by AASHTO.
First, environmental conditions in Vermont necessitate thick pavement structures to mitigate the
effects of frost penetration. These substantial structures are likely far beyond anything studied at the Road
Test.
ikely to be different from,
if not an improvement upon, those materials from which the AASHTO relationships have been derived.
Vermont is fortunate to have readily available, high-quality, and affordable aggregates. The Agency has also
traditionally used stiff asphalt cements and high compactive efforts in an attempt to minimize distresses
Third, the ELSs were conducted using the elastic moduli determined from backcalculations of the
FWD deflection basins taken on the surface of the finished pavement structure. Even though many of the
ACC moduli were consistently in excess of the 450,000-psi upper limit published by AASHTO, the layer
coefficients determined via ELS still corroborated the layer coefficients determined from the FWD deflection
data.
And finally, the FWD measures in situ behavior. It is not unreasonable to contend that laboratory-
supported AASHTO modulus/coefficient relationships may not accurately predict in situ behavior for any
material, whether unbound or asphalt stabilized. Indeed, Figure 6 illustrates how the ACC layer coefficients
Interestingly enough, when analyzed using the top of the unbound portion of the structure as the subgrade,
the ACC layer coefficients thus determined cluster within the more traditional range of 0.20-0.44 established
for ACC materials used in the AASHTO model. This interplay between ACC layer coefficients and its
support structure may be analogous to the synergism of a concrete bridge deck supported by steel girders.
Neither is adequate to the task in isolation, but when acting in unison, they achieve an effect of which each is
16
individually incapable.
ACC Layer Coefficients vs. Depth to Subgrade
0
0.2
0.4
0.6
0.8
1
1.2
0 10 20 30 40 50 60 70
De pth to Subgrade (in)
A
C
C
L
a
y
e
r
C
o
e
ff
ic
ie
n
t
assumed
on top of
stone
assumed
on top of
sand
ordinarily
defined
Figure 6 ACC Layer Coefficient vs. Depth to Subgrade
Valid resilient moduli for the various types of ACC (I, II, III, etc.) materials used by Agency
designers may have to be determined indirectly, since backcalculation limitations cannot distinguish such
subtleties within the FWD loading plate radius of the testing surface. Marshall stabilities were considered
useful for estimating the resilient moduli of the ACC materials, assuming there exists a correlation between
Marshall stabilities and resilient moduli (a notion implied by AASHTO). The Marshall stabilities may give
an indication of the relative proportions of the individual resilient moduli compared to the resilient modulus
backcalculated for the total ACC thickness. Another possibility may be an indirect tension test (like ASTM
D4123), which establishes the resilient modulus for ACC samples. For this investigation, Marshall stabilities
were used, when available, as a proxy to isolate the resilient moduli for different ACC types.
At this time, it is uncertain why there exist such marked disparities between the layer coefficients
determined for Marshall and Superpave materials. The Committee debated this issue extensively and finally
conceded that Marshall and Superpave mixes are two different materials and layer coefficients may simply
be one more manifestation of these differences. The Committee endorsed further study to bolster or refute
some of these concerns with the ACC properties.
Ten additional projects were identified for further study to allow for additional data collection and
to improve the predictive capabilities of the subsequent estimates. Another benefit to further study was the
potential for investigation into additional materials. Two of the additional projects used gravel for subbase
17
instead of the DGCS usually required on the State system. One Interstate project provided for an
rvice for nearly
40 years. Also novel to the Interstate project was an experimental material to provide for better drainage: an
asphalt-treated permeable base (ATPB).
Table 3 summarizes the properties established from all 16 projects investigated.
Table 3 Summary of Material Properties
Material
Layer Coefficient Resilient Modulus (psi)
N
Standard
deviation
Average 95% Pre. N
Standard
deviation
Average. 95% Pre.
Sand 139 0.013 0.078 2.9% 139 10,200 19,100 9.0%
Gravel 21 0.033 0.134 11.1% 21 12,500 29,600 19.2%
Old stone 21 0.021 0.102 9.2% 19 12,100 26,200 22.2%
DGCS 164 0.032 0.137 3.6% 164 16,800 29,700 8.7%
ATPB 21 0.067 0.398 7.7% 21 64,700 110,500 26.6%
ACC I 75 0.190 0.483 9.1% 76 169,800 357,600 10.8%
ACC II 62 0.284 0.630 11.5% 62 188,600 347,500 13.8%
ACC III 76 0.517 0.844 14.0% 76 200,500 304,500 15.0%
ACC IS 83 0.256 0.536 10.4% 21 85,300 191,200 20.2%
ACC IIS 102 0.184 0.504 7.2% 40 44,100 140,600 10.0%
ACC IIIS 93 0.170 0.533 6.6% 65 213,100 322,500 16.4%
ACC IVS 35 0.223 0.570 13.4% 35 49,700 92,400 18.5%
In addition to the number of data points (N), the standard deviation, and the average, Table 3
includes the level of precision on the average at the 95% level of confidence. Put another way, the level of
precision ensures that if one were to use the average value for design, it would be reasonable to assume that
the value provided under conditions of actual performance would be within the precision indicated 95% of
the time.
CONCLUSIONS
The AASHTO guide describes a procedure for determining the effective SN provided by a pavement
structure from FWD deflection data. While Ioannides presented compelling justification for questioning the
theoretical purity of this concept, the success of its practical application as investigated by this research is
difficult to ignore.
When FWD testing is conducted during the April 15 through November 1 construction season, and
no drastic temperature and moisture fluctuations occur, the SNeff and resulting layer coefficient associated
with a particular component of a pavement structure appear to remain reasonably stable, even after additional
material is placed.
The stress distribution described by Noureldin and Al Dhalaan appears to provide a reasonably
accurate portrayal of the effective plate radius that develops below the surface of a pavement structure for an
applied circular load, without which the simulated layer coefficients would have been difficult to determine.
18
It is paramount to accurately and precisely determine the thickness of each material being evaluated.
Depending upon the material, any error in the thickness assessment can have a corresponding error in the
layer coefficient determination, e.g., a 25% thickness error may lead to a 25% error in the layer coefficient
determination. While this magnitude of error is not desirable in any of the materials, it can certainly have
alarming consequences with the stiffer and thinner ACC materials.
The layer coefficients determined for the unbound materials appear reasonable, while the ACC layer
coefficients are outside the range typical for the AASHTO procedure. However, there does appear to be
substantiation for these higher ACC layer coefficients from other material properties, namely the Marshall
stabilities and backcalculated resilient moduli. Further, all the layer coefficients determined by the method
developed under this investigation are reasonably accurate estimates of the in situ behavior simulated by
elastic layer theory. Indeed, such high correlation between these two different procedures would be highly
unlikely, considering the variables that lead to their development.
Whether by serendipity or by design, the development of the AASHTO effective SN procedure
provides designers with a very powerful tool for the determination of layer coefficients.
RECOMMENDATIONS
Considering the emphasis that will be placed upon mechanistic design in the next version of the AASHTO
to
calibrate the AASHTO pavement design model to Vermont materials and the conclusion to that effort as
conjunction with the current AASHTO pavement design model. The Committee considered the 85
th
–
percentile for ACC layer coefficients to ensure reasonableness of designs provided by the model.
Any follow up research should focus on supplementing the database for the mechanistic properties
thus far established. Work should continue on the resilient modulus for all unbound materials and the
pavement design guide for ACC materials.
19
Table 4 Recommended Material Properties for Design Using the AASHTO Model
Material
Layer Coefficient Resilient Modulus (psi)
N
Standard
deviation
Average Rec. N
Standard
deviation
Average Rec.
Sand 139 0.013 0.078 0.078 139 10,200 19,100 19,100
Gravel 21 0.033 0.134 0.134 21 12,500 29,600 29,600
Old stone 21 0.021 0.102 0.102 19 12,100 26,200 26,200
DGCS 164 0.032 0.137 0.137 164 16,800 29,700 29,700
ATPB 21 0.067 0.398 0.331 21 64,700 110,500 110,500
ACC I 75 0.190 0.483 0.293* 76 169,800 357,600 357,600
ACC II 62 0.284 0.630 0.346 62 188,600 347,500 347,500
ACC III 76 0.517 0.844 0.327 76 200,500 304,500 304,500
ACC IS 83 0.256 0.536 0.280* 21 85,300 191,200 191,200
ACC IIS 102 0.184 0.504 0.320 40 44,100 140,600 140,600
ACC IIIS 93 0.170 0.533 0.363 65 213,100 322,500 322,500
ACC IVS 35 0.223 0.570 0.347 35 49,700 92,400 **
* If an ATPB is used, the layer coefficient for the base course (either ACC I or ACC IS) should be
increased to at least the 0.331 used for the ATPB.
** At this time, there is no recommendation for the ACC IVS resilient modulus.
ACKNOWLEDGEMENTS
This research would not have been possible without the persistent hard work of Duane Stevens and Jim
Pavement Design Committee, particularly Chris Benda, Jim Bush, Mike Hedges, Alec Portalupi, and Roger
Lyon-Surrey, for advice and review of the findings.
20
REFERENCES
(1) AASHTO Guide for Design of Pavement Structures. American Association of State Highway and
Transportation Officials, Washington, D.C., 1993.
(2) Zhou, H., G.R. Rada, and G.E. Elkins. Investigation of Backcalculated Moduli Using Deflections
Obtained at Various Locations in a Pavement Structure. In Transportation Research Record 1570, TRB,
National Research Council, Washington, D.C., 1997, pp. 96-107.
(3) Hossain, M., A. Habib, and T.M. LaTorella. Structural Layer Coefficients of Crumb Rubber-Modified
Asphalt Concrete Mixtures. In Transportation Research Record 1583, TRB, National Research Council,
Washington, D.C., 1997, pp. 62-70.
(4) Janoo, V.C. Layer Coefficients for NH DOT Pavement Materials. Special Report 94-30, U.S. Army
Corps of Engineers, Cold Regions Research & Engineering Laboratory, September, 1994.
(5) Ioannides, Anastasios M. Theoretical Implications of the AASHTO 1986 Nondestructive Testing
Method 2 for Pavement Evaluation. In Transportation Research Record 1307, TRB, National Research
Council, Washington, D.C., 1991, pp. 211-220.
(6) Noureldin, A.S. and M.A. Al Dhalaan. Establishment of Some Structural Parameters to Pavement
Evaluation Using the Falling Weight Deflectometer. A presentation given at the 70
th
TRB Annual Meeting,
Washington, D.C., January 1991.
(7) Ullidtz, P. Modeling Flexible Pavement Response and Performance. Polyteknisk Forlag, Denmark,
1998.
(8) Chitty, Daniel E., Blouin, Scott E., Quenneville, Steven R., and Beckwith, Daniel B. Laboratory Tests
and Analysis: Resilient Modulus and Low Strain Rate Modulus Testing of Sands. ARA Report Number
4835-2, Applied Research Associates, Inc., South Royalton, Vermont, June, 2001.
(9) Janoo, Vincent C. and Bayer II, John J. The Effect of Aggregate Angularity on Base Course
Performance. Technical Report ERDC/CRREL TR-01-14, U.S. Army Corps of Engineers, Cold Regions
Research & Engineering Laboratory, September, 2001.
SYNTHESIS/LITERATURE REVIEW FOR DETERMINING STRUCTURAL
LAYER COEFFICIENTS (SLC) OF BASES
FINAL REPORT
Sponsored by the Florida Department of Transportation Research Center
Contract Number
BDV31-977-2
7
Dr. Dennis R. Hiltunen, P.E.
Principal Investigator
DEPARTMENT OF CIVIL & COASTAL ENGINEERING
UNIVERSITY OF FLORIDA
December 201
4
2
DISCLAIMER
The opinions, findings, and conclusions
expressed inthis publication are those of the
authors and not necessarily those of the State
of Florida Department of Transportation or the
U.S. Department of Transportation.
Prepared in cooperation with the State of
Florida Department of Transportation and the
U.S. Department of Transportation.
3
METRIC CONVERSION TABLE
4
METRIC CONVERSION TABLE
5
1. Report No.
2. Government Accession No.
3. Recipient’s Catalog No.
4. Title and Subtitle
Synthesis/Literature Review for Determining Structural Layer
Coefficients (SLC) of Bases
5. Report Date
December 20
14
6. Performing Organization Code
7. Author(s)
Dennis R. Hiltunen
8. Performing Organization Report No.
9. Performing Organization Name and Address
Department of Civil and Coastal Engineering
University of Florida
365 Weil Hall, P.O. Box 116580
Gainesville, FL 32611-6580
10. Work Unit No. (TRAIS)
11. Contract or Grant No.
BDV31-977-
27
12. Sponsoring Agency Name and Address
Florida Department of Transportation
605 Suwannee Street, MS
30
Tallahassee, FL 3239
9
13. Type of Report and Period Covered
Final Report
June 2014-December 2014
14. Sponsoring Agency Code
15. Supplementary Notes
16. Abstract
FDOT’s current method of determining a base material structural layer coefficient (SLC) is detailed in the
Materials Manual, Chapter 2.1, Structural Layer Coefficients for Flexible Pavement Base Materials.
Currently, any new base material not approved under FDOT specifications must undergo (1) laboratory
testing, (2) test pit investigation, and (3) a project test section for constructability and roadway performance
evaluation to determine a SLC for design purposes. The test section evaluation phase can take up to five
years to compare the pavement performance of the new base material with a limerock base control section.
In this project, a thorough review of literature has been conducted of current and past practices for the
determination of structural layer coefficients (SLC) of pavement base materials. The review organizes the
methodologies into
three broad categories: (1) methods that determine SLCs via relationships with other
material parameters; (2) methods that determine SLCs via estimates of the structural number (SN) of
existing and available pavement sections; and (3) methods that establish SLCs via equivalencies with a
reference material. Several of the strategies reviewed provide opportunities for estimating SLCs of both
traditional and new base course materials in a more accelerated fashion and in considerably less time than
the five years often required at present.
17. Key Word
AASHTO pavement design, base materials,
structural layer coefficient, structural number
18. Distribution Statement
No Restrictions
19. Security Classif. (of this report)
Unclassified
20. Security Classif. (of this page)
Unclassified
21. No. of Pages
33 Pages
22. Price
6
EXECUTIVE SUMMARY
FDOT’s current method of determining a base material structural layer coefficient
(SLC) is detailed in the Materials Manual, Chapter 2.1, Structural Layer Coefficients for
Flexible Pavement Base Materials. Currently, any new base material not approved
under FDOT specifications must undergo (1) laboratory testing, (2) test pit investigation,
and (3) a
project test section for constructability and roadway performance evaluation to
determine a SLC for design purposes. The test section evaluation phase can take up to
five years to compare the pavement performance of the new base material with a
limerock base control section. In this project, a thorough review of literature has been
conducted of current and past practices for the determination of structural layer
coefficients (SLC) of pavement base materials. The review organizes the methodologies
into three broad categories: (1) methods that determine SLCs via relationships with
other material parameters; (2) methods that determine SLCs via estimates of the
structural number (SN) of existing and available pavement sections; and (3) methods
that establish SLCs via equivalencies with a reference material. Several of the
strategies reviewed provide opportunities for estimating SLCs of both traditional and
new base course materials in a more accelerated fashion and in considerably less time
than the five years often required at present.
7
TABLE OF CONTENTS
page
DISCLAIMER…………………………………………………………………………………… 2
METRIC CONVERSION TABLE……………………………………………………………… 3
TECHNICAL REPORT DOCUMENTATION PAGE…………………………………………5
EXECUTIVE SUMMARY………………………………………………………………………. 6
CHAPTER 1 – INTRODUCTION …………………………………………………………………………. 9
CHAPTER 2 – MATERIAL PARAMETER RELATIONSHIPS …………………………………. 11
CHAPTER 3 – STRUCTURAL NUMBER (SN) OF PAVEMENT SECTIONS ……………. 15
3.1 Introduction …………………………………………………………………………………………. 15
3.2 SN from Performance Relationship …………………………………………………………. 15
3.3 SN from FWD Deflections ……………………………………………………………………… 18
CHAPTER 4 – EQUIVALENCY WITH REFERENCE MATERIAL …………………………… 22
4.1 Introduction …………………………………………………………………………………………. 22
4.2 Material Property Criterion …………………………………………………………………….. 22
4.3 Pavement Response Criterion ……………………………………………………………….. 24
4.4 Pavement Performance Criterion ……………………………………………………………. 26
CHAPTER 5 – CONCLUSIONS …………………………………………………………………………. 29
LIST OF REFERENCES ………………………………………………………………………………….. 30
8
LIST OF FIGURES
Figure page
1 Variation in Granular Base Layer Coefficient (a2) with Various
11
Material Parameters (from AASHTO 1993)
9
CHAPTER 1
INTRODUCTION
The Florida Department of Transportation’s (FDOT) Flexible Pavement Design
Manual, March 2008, provides procedures for determining the design thickness of base
course materials. In these procedures, layer coefficients have been developed that
represent the relative strength of different pavement materials in Florida. Standard
Index 514 identifies the structural layer coefficient (SLC) for combinations of base types
and thicknesses for general and limited use optional bases. Contractors can select from
the base materials shown on the Typical Section Sheet or from Standard Index 514.
Except as limited by Standard Index 514 or as may be justified by special project
conditions, the options for base material are not restricted. Allowing a contractor the full
range of base materials will permit the contractor to select the least costly material,
resulting in the lowest bid price.
FDOT’s current method of determining a base material SLC are detailed in the
Materials Manual, Chapter 2.1, Structural Layer Coefficients for Flexible Pavement
Base Materials. Currently, any new base material not approved under FDOT
specifications must undergo (1) laboratory testing, (2) test pit investigation, and (3) a
project test section for constructability and roadway performance evaluation to
determine a SLC for design purposes. The test section evaluation phase can take up to
five years to compare the pavement performance of the new base material with a
limerock base control section. Materials that perform equivalently to a limerock control
section may obtain a recommendation of a SLC of 0.18 in/in.
The objective of this project was to produce a synthesis of current and past
practices for the determination of structural layer coefficients (SLC) of pavement base
10
materials. A thorough review of literature has been conducted and is presented in the
following sections. The synthesis does not rank or evaluate the differences or
advantages of various methods. In general, the review organizes the methodologies into
three broad categories: (1) methods that determine SLCs via relationships with other
material parameters, (2) methods that determine SLCs via estimates of the structural
number (SN) of existing and available pavement sections, and (3) methods that
establish SLCs via equivalencies with a reference material. The three categories are
discussed sequentially in the following sections.
11
CHAPTER 2
MATERIAL PARAMETER RELATIONSHIPS
The AASHTO Guide for Design of Pavement Structures (AASHTO 1993)
provides a chart (Figure 1) for determining the structural layer coefficient of granular
base materials using various known material parameters, such as California Bearing
Ratio (CBR) and elastic (resilient) modulus. Alternatively, the following equation may be
used to estimate the SLC for a granular base material, a2, from its elastic modulus, EBS
(AASHTO 1993):
a2 = 0.249(log10EBS) – 0.977 (1)
Figure 1. Variation in Granular Base Layer Coefficient (a2) with Various Material
Parameters (from AASHTO 1993)
A number of researchers have utilized these relationships to determine SLCs for both
traditional and new base course material applications.
12
Bahia et al. (2000) determined the SLC of reprocessed asphaltic mixtures used
in Wisconsin as base materials via the AASHTO correlation with elastic (resilient)
modulus. The resilient modulus of the materials was measured with standard
laboratory techniques. Trends observed in resilient modulus compared with
measured rutting performance of the materials did not match, and the
researchers suggest that SLC determination should combine both elastic and
damage behavior of pavement materials.
Baus and Li (2006) determined the SLC of various graded aggregate bases used
in South Carolina via the AASHTO correlation with elastic (resilient) modulus.
The resilient modulus of the materials was measured with a plate load method in
test pit experiments. The researchers were concerned to report SLC values
ranging from 0.05 to 0.24 for the various graded aggregates investigated, despite
the fact that South Carolina uses a constant value of 0.18 for all graded
aggregate bases.
Butalia et al. (2011) determined the SLC of full-depth reclaimed asphalt
pavements mixed with coal ash, lime, and lime kiln dust used as a base material
in Ohio via the AASHTO correlation with elastic (resilient) modulus. Full-depth
reclamation (FDR) is a recycling technique where the existing asphalt pavement
and a predetermined portion of the underlying granular material are blended to
produce an improved base course. The resilient modulus of the materials was
determined via backcalculation from measured falling weight deflectometer
(FWD) deflections on the actual reclaimed pavement sections. For one test
pavement, the SLCs estimated from resilient modulus ranged from 0.27 to 0.54
13
(with an average of about 0.35), following reclamation with fly ash and lime, while
the SLCs for the control section (no admixture, just mill and overlay) were much
lower (average of about 0.1). For a second test pavement, the researchers report
SLCs from resilient modulus as follows: (1) 0.35 to 0.45 with an average of about
0.37 for a section reclaimed with fly ash and lime kiln dust; (2) 0.25 to 0.5 with an
average of about 0.4 for a section reclaimed with fly ash and lime; (3) 0.4 to 0.5
with an average of about 0.46 for a section reclaimed with cement; and (4) much
lower values for the control section (no admixture, just mill and overlay).
Janoo (1994) determined the SLC of various base materials used in New
Hampshire via the AASHTO correlations with both elastic (resilient) modulus and
CBR. The base materials investigated included crushed gravel, reclaimed
asphalt and gravel base stabilized with asphalt, asphalt concrete base, and
pavement millings. The resilient modulus of the materials was determined via
backcalculation from measured FWD deflections on 10 experimental pavement
test sections. The CBR values were determined via correlation with measured
results from Clegg hammer and dynamic cone penetrometer (DCP) tests on the
10 experimental pavement test sections. Further comments on the Janoo (1994)
results are found in Section 3.3 below.
Rada and Witczak (1983) determined the SLC of various graded aggregate base
and subbase materials used in Maryland via the AASHTO correlation with elastic
(resilient) modulus. The resilient modulus of the materials was measured with
standard laboratory techniques. The wide range of materials and conditions
14
investigated in this study subsequently provided significant basis for AASHTO to
recommend SLC design ranges for unbound base and subbase materials.
Richardson (1996) determined the SLC of cement-stabilized soil bases used in
Missouri via the AASHTO correlation with elastic (resilient) modulus. The moduli
of the materials were determined from standard static compression tests on
laboratory cylinders. The SLCs ranged from 0.09 to 0.27, depending on soil type
and cement content. The researcher indicates that these values match well with
values from 10 state departments of transportation reported in the literature.
15
CHAPTER 3
STRUCTURAL NUMBER (SN) OF PAVEMENT SECTIONS
3.1 Introduction
A formulation of the AASHTO equation for the structural number (SN) of a
flexible pavement section with two layers above the subgrade is as follows:
SN = a1D1 + a2D2 (2)
where the ai and Di represent the structural layer coefficients and the thicknesses,
respectively, of the asphalt surface and base layers in the pavement. A simple algebraic
solution for an unknown SLC, a2, for example, can be made if the layer thicknesses,
remaining SLCs, and the structural number (SN) of the pavement section are all known:
SN – a1D1
a2 = ————— (3)
D2
Two approaches have typically been applied for determination of the structural number
(SN) of the pavement section,
and each are described in the following sections.
3.2 SN from Performance Relationship
The structural number (SN) of an existing pavement section can be determined
from the original AASHTO performance equation or from a similar AASHTO-like
performance relationship if the performance of the pavement section has been
observed under known loading conditions. For example, the SN can be determined from
the original AASHTO performance equation if the subgrade resilient modulus is known,
and the change in serviceability index (from initial design to terminal) is observed for a
known application of 18,000-lb equivalent single axle loads. This process is well
described by Timm et al. 2014. A number of researchers have utilized observed
16
pavement section performance and performance relationships to determine SLCs for
both traditional and new base course material
applications.
Peter-Davis and Timm (2009) determined the SLC of asphalt surface layers used
in Alabama via observed performance (rut depth, surface cracking, and surface
roughness) and traffic data from experimental test sections. The researchers
determined the unknown layer coefficient by adjusting its value until load
repetitions to failure computed from the original AASHTO performance equation
matched the load repetitions to failure observed in the field test sections. This
approach yielded an average layer coefficient of 0.51, versus a value of 0.44
used for design in Alabama.
Hicks et al. (1979) and Hicks et al. (1983) backcalculated the SLC of open-
graded asphalt emulsion surface layers used on in-service U.S. Forest Service
roads in Oregon and Washington via observed performance (rut depth, surface
cracking, and surface roughness), estimates of other input parameters, and the
original AASHTO performance equation. The researchers indicate that this
method is particularly useful for the estimation of conservative, minimum values
of layer coefficients.
Little and Epps (1980) backcalculated the SLCs of recycled asphalt concrete
pavement layers from 26 field projects in 11 states using the AASHTO
performance equation and the known thicknesses and SLCs of the other
pavement layers. Because these were all recently-constructed pavements and
performance and traffic loading information of the pavement sections was not
available for the AASHTO performance equation, the researchers developed and
17
utilized an empirical relationship between load repetitions and the computed
elastic deflection of the subgrade to estimate the anticipated performance of the
pavement sections. The empirical relationship was developed from the known
performance results of the original AASHO Road Test pavement sections, and
the subgrade deflections were computed via an elastic layer analysis of the
pavement sections. The SLCs of recycled asphalt pavement used as a surface
layer were found to typically exceed the value of 0.44 established for an AASHO
Road Test conventional asphalt surface layer. The SLCs of recycled asphalt
pavement used as a base layer were found similar to bituminous stabilized and
cement and lime stabilized bases at the AASHO Road Test.
Wang and Larson (1977, 1979) determined the SLCs of asphaltic concrete base,
cement-stabilized limestone aggregate base, and limestone aggregate subbase
materials used in Pennsylvania via observed performance (rut depth, surface
cracking, and surface roughness) and traffic data from experimental test sections
at the Pennsylvania State Test Track. The SLCs were backcalculated from an
AASHTO-type relationship developed at the Test Track between observed
performance and load repetitions and the known thicknesses and SLCs of the
other pavement layers.
Wu et al. (2012) determined the SLCs of base course materials constructed from
blended calcium sulfate (BCS) stabilized with slag and fly ash in Louisiana via
observed performance and traffic data from experimental test sections. The test
sections were constructed and loaded at the Accelerated Loading Facility (ALF)
at the Louisiana Transportation Research Center (LTRC), and the experiment
18
data was used to construct a performance relationship between the number of
load repetitions to failure and structural number. The unknown base SLC was
backcalculated from the performance equation and using the known SLCs and
thicknesses of the remaining pavement layers. A value of 0.34 was reported for
the BCS/slag and 0.29 for the BCS/fly ash.
3.3 SN from FWD Deflections
The structural number (SN) of an existing pavement section can be determined
from deflections measured with a falling weight deflectometer (FWD). Several methods
are available, including AASHTO (1993), Rohde (1994), Crovetti (1998), Romanoschi
and Metcalf (1999), and Kim et al. (2013). All of the methods utilize fundamental
equations of pavement mechanics and empirical relationships from pavement studies to
estimate the structural number of a pavement section from measured FWD deflections.
A number of researchers have utilized such measurements on available pavement
sections to determine SLCs for both traditional and new base course material
applications. The AASHTO (1993) procedure is most widely used and is well described
by Timm et al. (2014).
In addition to the resilient-modulus-based results reported above, Baus and Li
(2006) determined the SLC of a graded aggregate base used in South Carolina
via the AASHTO FWD procedure. Two test sections were investigated that
incorporated three base thicknesses and with and without a cement stabilized
subgrade. The researchers were concerned to report inconsistent SLC values
ranging from 0.13 to 0.36 for the same graded aggregate investigated, and
despite the fact that South Carolina uses a constant value of 0.18 for all graded
19
aggregate bases. This range of values is also notably higher than the range
reported above based upon resilient modulus measurements.
Gautreau et al. (2008) determined the SLC of clayey subgrade soil treated with
cement, lime, and lime-fly ash used as a subbase layer in Louisiana via the
AASHTO FWD procedure. Test sections were constructed and loaded at the
Accelerated Loading Facility (ALF) at the Louisiana Transportation Research
Center (LTRC). Based upon FWD deflections, the researchers found that layer
coefficients for the cement-stabilized soil may be assigned a value of 0.06, while
for lime-treated soil, no structural contribution should be allowed. Unfortunately,
the researchers did not determine an SLC for the materials using performance
data from the loaded test sections.
Hossain et al. (1997) determined the SLCs of crumb-rubber-modified (CRM)
asphalt mixtures used in Kansas for both surface and base layers via the
AASHTO FWD procedure. Several test sections of recently constructed
pavements along three routes in Kansas were used for the study. The
researchers found average values for the layer coefficients typical of practice, but
also reported very high variability in the results across the multiple test sections
investigated. Further comments on the Hossain et al. (1997) results are found in
Section 4.3, below.
In addition to the material-parameter-based results reported above, Janoo (1994)
determined the SLC of various base materials used in New Hampshire via the
Rohde (1994) FWD procedure on 10 experimental pavement test sections. The
researcher notes that the SLC for asphalt concrete base from the Rohde
20
procedure was similar to that used by the New Hampshire DOT (NHDOT), which
gave the researcher confidence in using this procedure for the other base
materials. Further, the layer coefficients from the Clegg hammer and DCP were
all close to those obtained from Rohde, which provided further confidence in the
suggested SLC values. On the other hand, the researcher found that the values
determined from backcalculated elastic moduli results were typically higher than
those from the Rohde, Clegg, and DCP methods, noting that the discrepancies
could be due to difficulty in obtaining a good fit to the measured FWD deflection
measurements during the backcalculation process.
Marquis et al. (2003) determined the SLC of a recycled asphalt concrete base
with foamed asphalt additive in Maine via the AASHTO FWD procedure.
Sections of four pavement projects were investigated, and the layer coefficients
were found to be 0.22, 0.23, 0.22, and 0.35.
Pologruto (2001) utilized the AASHTO FWD procedure to determine the SLCs of
all pavement layers on a pilot project using representative materials for the
construction of pavements in Vermont. Three different test locations were
specified and constructed with the same type of materials: three different types of
asphalt concrete for surface, binder, and base, a densely-graded crushed stone
base/subbase, and a sand subbase. At each of the three test site locations, three
structural configurations of the materials were implemented. The FWD testing
was conducted on the surface of each successive layer during construction as
means for determining each SLC. The average SLC values were found to be
0.60 for all asphalt layers, 0.14 for crushed stone base/subbase, and 0.07 for
21
sand subbase. The researcher notes that: (1) the value of 0.14 for crushed stone
falls within the range established by AASHTO for an unbound base material, (2)
the value of 0.07 for sand is on low side of AASHTO range for subbase, and (3)
the value of 0.60 for asphalt concrete is considerably higher than the AASHTO
value of 0.44. The researcher does note that the average value of 0.60 is partially
substantiated by other properties measured on these materials, including
Marshall stability and moduli backcalculated from FWD deflections.
Romanoschi et al. (2003a, 2003b, 2004) determined the SLC of base layers from
full-depth reclamation of an asphalt-bound pavement constructed in Kansas and
stabilized with foamed asphalt via the AASHTO FWD procedure. Four
experimental test pavements were constructed at research facilities at Kansas
State University, and the average SLC found for the materials was 0.18.
Wen et al. (2004) determined the SLC of of a base layer constructed from full-
depth reclamation (FDR) of an asphalt-bound pavement stabilized with fly ash
and constructed in Wisconsin via the Crovetti (1998) FWD procedure. An initial
SLC of 0.16 was determined following construction of the pavement section, and
a value of 0.23 was calculated the following year, indicating that improvement of
the material occurred with time. The improvement was attributed to pozzolanic
reaction in the mixture due to the fly ash stabilizer.
22
CHAPTER 4
EQUIVALENCY WITH REFERENCE MATERIAL
4.1 Introduction
The equivalency methods are based upon a fundamental premise of the
AASHTO pavement design methodology that two differing materials will provide the
same structural capacity (or number) in a pavement if the product of their layer
coefficient and thickness are equal:
auDu = arDr (4)
where au = structural layer coefficient of unknown material, Du = thickness of unknown
material, ar = structural layer coefficient of known reference material, and Dr = thickness
of known reference material. Using this equivalency premise, the structural layer
coefficient of a previously unknown material can be determined as follows:
1. Choose a reference material with a known SLC, ar, and a relevant pavement
cross section.
2. Determine the thickness required for the known reference material, Dr, that
provides an acceptable pavement section according to a chosen design criterion.
3. Determine the thickness required for the unknown material, Du, that provides an
acceptable pavement section according to the same chosen design criterion.
4. Solve for the unknown structural layer coefficient, au, using the above equation.
Three types of design criteria have typically been utilized to establish the equivalency,
and each are described in the following sections.
4.2 Material Property Criterion
A simple equivalency between an unknown material and a known reference
material can be based upon a relevant material property, with the elastic modulus being
23
the typical property of choice. Several researchers have utilized material property
equivalencies to determine SLCs for both traditional and new base course material
applications.
Coree and White (1989) determined the SLCs of 10 asphaltic concrete mixtures
used in Indiana via comparison of stiffnesses measured in the laboratory with the
stiffness and layer coefficient of an asphalt mixture used in the AASHO Road
Test. Using Odemark’s equivalent stiffness principle, they developed the
following equivalency relationship:
au = ar (Er/Eu)
1/3 (5)
where au = structural layer coefficient of unknown material, Eu = modulus of
unknown material, ar = structural layer coefficient of known reference material,
and Er = modulus of known reference material. They also utilized a probabilistic
approach in which a distribution for the layer coefficient is determined based
upon estimates of the uncertainties in the measured moduli and the layer
coefficient of the known AASHO reference material.
Rada et al. (1989) documented two procedures for estimating the structural
number (SN) of pavement sections via FWD measurements. In one method, the
FWD deflections are used to determine elastic moduli via backcalculation, and
then the SLCs of each layer are determined using the moduli and an equivalency
technique based upon Odemark as shown by Coree and White (1989) discussed
above. With the layer coefficients available, the SN is calculated directly using
layer thicknesses and the standard AASHTO equation for SN.
24
Tang et al. (2012) determined the granular equivalencies of base layers
constructed from full-depth reclamation of asphalt-bound pavements constructed
in Minnesota. In some cases, a stabilizer such as fly ash or asphalt emulsion was
added to the mixture. Similar to a SLC, granular equivalency (GE) indicates the
contribution of a given layer of pavement material relative to the performance of
the entire pavement section. It is dependent upon the properties of that layer in
relation to the properties of the other layers. The relative thickness between the
layers is known as the granular equivalency factor. The layer equivalency can be
determined by laboratory and field tests. In this study, the GE of stabilized FDR
was determined from several field test sections via a method established in
Minnesota using FWD deflections. The equivalency with a standard granular
base material (GE=1.0) was found to be about 1.5.
4.3 Pavement Response Criterion
An equivalency between an unknown material and a known reference material
can be based upon a relevant response parameter of the chosen pavement section,
such as surface deflection, the tensile strain at the bottom of the asphalt surface layer,
or the compressive strain at the top of the subgrade. A number of researchers have
utilized equivalencies based upon pavement response model criteria to determine SLCs
for both traditional and new base course material applications. In all cases the
pavement response models will require the determination of relevant input parameters
to characterize the pavement sections and materials, including layer thicknesses and
elastic moduli.
25
In addition to the FWD-based results reported above, Hossain et al. (1997)
determined the SLCs of crumb-rubber-modified (CRM) asphalt mixtures used in
Kansas for both surface and base layers using an equivalency based upon
pavement response modeling. Here, the unknown SLC was computed as shown
above using a design thickness for the unknown material and the SLC and
design thickness of a reference material. The design thicknesses were
determined via an elastic layered analysis of the pavement sections and an
equivalency based upon the vertical compressive strain in the subgrade. For
CRM asphalt overlays, an average value of 0.30 was reported, which they note is
slightly lower than for conventional asphalt concrete. For newly constructed CRM
asphalt pavements, an average value of 0.35 was reported, which they note is
similar to an AASHTO-recommended value for conventional asphalt concrete. In
comparison with the FWD-based results presented above, the researchers note
that the average values were similar, but the FWD-based results displayed
considerably higher variability across the various test sections.
Mallick et al. (2002) determined the SLCs of base layers constructed in Maine
from full-depth reclamation of an asphalt-bound pavement with additives,
including emulsion, lime, and cement, and using an equivalency based upon
pavement response modeling. As with Hossain et al. (1997) above, the unknown
SLC was computed using a design thickness for the unknown material, and the
SLC
and design thickness of a reference material. The design thicknesses were
determined via an elastic layered analysis of the pavement sections, and an
equivalency based upon the surface deflection of the pavement. The SLCs were
26
found to be 0.24 for emulsion additive, 0.28 for cement additive, and 0.37 for
emulsion plus lime additive.
4.4 Pavement Performance Criterion
An equivalency between an unknown material and a known reference material
can be based upon a pavement performance criterion for the chosen pavement section,
such as fatigue cracking or rutting. Several researchers have utilized equivalencies
based upon pavement performance model criteria to determine SLCs for both traditional
and new base course material applications. In all cases the pavement performance
models will require the determination of relevant input parameters to characterize the
pavement sections and materials, including layer thicknesses, elastic moduli, and other
material properties that govern performance or damage.
George (1984) determined the SLCs of asphalt mixtures used as both surface
and base layers, soil-cement base, and soil-lime subbase using an equivalency
based upon pavement performance. Here, the unknown SLC was computed as
shown above using a design thickness for the unknown material, and the SLC
and design thickness of a reference material. The design thicknesses were
determined via a fatigue cracking performance model presented by George
(1984). The author reports SLCs of 0.44, 0.38, 0.24, and 0.20 for asphalt surface,
asphalt base, soil-cement base, and soil-lime subbase, respectively, and
demonstrates these values to be in good accord with those of AASHTO.
In addition to the observed performance-based results reported above, Hicks et
al. (1979) determined the SLC of open-graded asphalt emulsion surface layers
used on in-service U.S. Forest Service roads in Oregon and Washington via
27
equivalency based upon pavement performance modeling. As with George
(1984) above, the unknown SLC was computed using a design thickness for the
unknown material, and the SLC and design thickness of a reference material.
Here, the design thicknesses were determined via an elastic layered analysis of
the pavement sections, and a fatigue relationship between tensile strain in the
surface layer and number of load repetitions. The researchers note that the
computed values were in good agreement with those backcalculated from in-
service roads.
Li et al. (2011) revised the SLC of asphalt surface layers in the state of
Washington from 0.44 to 0.50 via equivalency based upon pavement
performance modeling. Here, the pavement performance modeling was
conducted with the Mechanistic Empirical Pavement Design Guide (MEPDG)
calibrated locally using pavement performance data observed in Washington.
Van Wijk et al. (1983) determined the SLC of cold recycled asphalt pavement
mixed with emulsion and foamed asphalt and used as a base layer for
pavements in Indiana. As with George (1984) above, the unknown SLC was
computed using a design thickness for the unknown material, and the SLC and
design thickness of a reference material. Here, the design thicknesses were
determined via an elastic layered analysis of the pavement sections, and several
response and performance criteria were evaluated, including: (1) tensile strain at
the bottom of recycled layer, (2) tensile strain at the bottom of remaining initial
pavement layer, (3) compressive subgrade strain, (4) subgrade deformation, and
(5) surface deformation. Each criteria was evaluated for the test sections
28
investigated, and the SLC was based on the criterion that produced the shortest
service life. For these recycled pavements, the controlling criterion was found to
be either the subgrade deformation or the tensile strain at the bottom of the
recycled layer. The researchers note that this approach yielded layer coefficients
with considerable variability among the pavement sections investigated, and
suggested that a single SLC cannot be determined without reliable fatigue
performance characteristics for all the pavement layers.
29
CHAPTER 5
CONCLUSIONS
FDOT’s current method of determining a base material structural layer coefficient
(SLC) is detailed in the Materials Manual, Chapter 2.1, Structural Layer Coefficients for
Flexible Pavement Base Materials. Currently, any new base material not approved
under FDOT specifications must undergo (1) laboratory testing, (2) test pit investigation,
and (3) a project test section for constructability and roadway performance evaluation to
determine a SLC for design purposes. The test section evaluation phase can take up to
five years to compare the pavement performance of the new base material with a
limerock base control section. In this project, a thorough review of literature has been
conducted of current and past practices for the determination of structural layer
coefficients (SLC) of pavement base materials. The review organizes the methodologies
into three broad categories: (1) methods that determine SLCs via relationships with
other material parameters; (2) methods that determine SLCs via estimates of the
structural number (SN) of existing and available pavement sections; and (3) methods
that establish SLCs via equivalencies with a reference material. Several of the
strategies reviewed provide opportunities for estimating SLCs of both traditional and
new base course materials in a more accelerated fashion and in considerably less time
than the five years often required at present.
30
LIST OF REFERENCES
AASHTO (1993), AASHTO Guide for Design of Pavement Structures, American
Association of State Highway and Transportation Officials, Washington, D.C.
Bahia, H.U., Bosscher, P.J., Christensen, J., and Hu, Y. (2000), Layer Coefficients for
New and Reprocessed Asphaltic Mixes, Report No. WI/SPR-04-00, Wisconsin
Department of Transportation, January, 129 pp.
Baus, R.I. and Li, T. (2006), Investigation of Graded Aggregate Base (GAB) Courses,
Report No. FHWA-SC-06-03, South Carolina Department of Transportation,
February, 95 pp.
Butalia, T., Wolfe, W., and Kirch, J. (2011), Structural Monitoring of Full-Scale Asphalt
Pavements Reclaimed Using Class F Fly Ash, World of Coal Ash (WOCA)
Conference, Denver, May 9-12.
Coree, B.J. and White, T.D. (1989), The Synthesis of Mixture Strength Parameters
Applied to the Determination of AASHTO Layer Coefficient Distributions,
Association of Asphalt Paving Technologists, Vol. 58, pp. 109-141.
Crovetti, J. (1998), Design, Construction, and Performance of Fly Ash–Stabilized CIR
Asphalt Pavements in Wisconsin. Wisconsin Electric–Wisconsin Gas, Milwaukee.
Gautreau, G., Zhang, Z., and Wu, Z. (2008), Accelerated Loading Evaluation of
Subbase Layers in Pavement Performance, Report No. FHWA/LA.09/468,
Louisiana Department of Transportation and Development, 160 pp.
George, K.P. (1984), Structural Layer Coefficient for Flexible Pavement, Journal of
Transportation Engineering, ASCE, Vol. 110, No. 3, pp. 251-267.
Hicks, R.G., Hatch, D.R., Williamson, R., and Steward, J. (1979), Open-Graded
Emulsion Mixes for Use as Road Surfaces, Transportation Research Record
702, Transportation Research Board, Washington, D.C., pp. 64-72.
Hicks, R.G., Santucci, L.E., Fink, D.G., and Williamson, R. (1983), Performance
Evaluation of Open-Graded Emulsified Asphalt Pavement, Proceedings of
Association of Asphalt Paving Technologists, Vol. 52, pp. 441-473.
Hossain, M., Habib, A., and LaTorella, T.M. (1997), Structural Layer Coefficients of
Crumb-Rubber Modified Asphalt Concrete Mixtures, Transportation Research
Record 1583, Transportation Research Board, Washington, D.C., pp. 62-70.
Janoo, V.C. (1994), Layer Coefficients for NHDOT Pavement Materials, Special Report
94-30, New Hampshire Department of Transportation, September.
31
Kim, M.Y., Kim, D.Y., and Murphy, M.R. (2013), Improved Method for Evaluating the
Pavement Structural Number with Falling Weight Deflectometer Deflections,
Transportation Research Record: Journal of the Transportation Research Board,
No. 2366, pp. 120-126.
Li, J., Uhlmeyer, J.S., Mahoney, J.P., and Muench, S.T. (2011), Use of the 1993
AASHTO Guide, MEPDG and Historical Performance to Update the WSDOT
Pavement Design Catalog, WA‐RD 779.1, Washington State Department of
Transportation.
Little, D. N. and Epps, J.A. (1980), Evaluation of Certain Structural Characteristics of
Recycled Pavement Materials, Proceedings of the Association of Asphalt Paving
Technologists, Vol. 49, pp. 219-251.
Mallick, R.B., Bonner, D.S., Bradbury, R.L., Andrews, J.O., Kandhal, P. S., and
Kearney, E.J. (2002), Evaluation of Performance of Full-Depth Reclamation
Mixes, Transportation Research Record: Journal of the Transportation Research
Board, No. 1809, TRB, Washington, D.C., pp. 199–208.
Marquis, B., Peabody, D., Mallick, R., and Soucie, T. (2003), Determination of Structural
Layer Coefficient for Roadway Recycling Using Foamed Asphalt, Final Report,
Maine Department of Transportation, 31 pp.
Peter-Davis, K.P. and Timm, D.H. (2009), Recalibration of the Asphalt Layer Coefficient,
Final Report 09-03, National Center for Asphalt Technology, August, 75 pp.
Pologruto, M. (2001), Procedure for Use of Falling Weight Deflectometer to Determine
AASHTO Layer Coefficients, Transportation Research Record 1764,
Transportation Research Board, Washington, D.C., pp. 11-19.
Rada, G. and Witczak, M.W. (1983), Material Layer Coefficients of Unbound Granular
Materials from Resilient Modulus, Transportation Research Record 852,
Transportation Research Board, Washington, D.C., pp. 15-21.
Rada, G., Witczak, M.W., and Rabinow, S.D. (1989), Comparison of AASHTO
Structural Evaluation Techniques Using Nondestructive Deflection Testing,
Transportation Research Record 1207, Transportation Research Board,
Washington, D.C., pp. 134-144.
Richardson, D. N. (1996), AASHTO Layer Coefficients for Cement-Stabilized Soil
Bases, Journal of Materials in Civil Engineering, ASCE, Vol. 8, No. 2, May, pp.
83-87
Rohde, G.T. (1994), Determining Pavement Structural Number from FWD Testing,
Transportation Research Record 1448, Transportation Research Board,
Washington D.C., pp. 61-68.
32
Romanoschi, S.A., Hossain, M., Heitzman, M., and Gisi, A., (2003a), Foamed Asphalt
Stabilized Reclaimed Asphalt Pavement: A Promising Technology for Mid-
Western Roads, Proceedings of the 2003 Mid-Continent Transportation
Research Symposium, Ames, Iowa, August, pp. 6-11.
Romanoschi, S.A., Hossain, M., Gisi, A., and Heitzman, M. (2004), Accelerated
Pavement Testing Evaluation of the Structural Contribution of Full-Depth
Reclamation Material Stabilized with Foamed Asphalt, Transportation Research
Record: Journal of the Transportation Research Board, No. 1896, pp. 199-207.
Romanoschi S.A., Hossain, M., Lewis, P., and Dumitru, O. (2003b), Performance of
Foamed Asphalt Stabilized Base in Full-Depth Reclaimed Asphalt Pavement,
Final Report, Kansas Department of Transportation, July.
Romanoschi, S.A. and Metcalf, J.B. (1999), Simple Approach to Estimation of
Pavement Structural Capacity, Transportation Research Record 1652,
Transportation Research Board, Washington, D.C., pp. 198-205.
Tang, S., Cao, Y., and Labuz, J.F. (2012), Structural Evaluation of Asphalt Pavements
with Full-Depth Reclaimed Base, Report No. MN/RC 2012-36, Minnesota
Department of Transportation, December, 53 pp.
Timm, D.H., Robbins, M.M., Tran, N., and Rodezno, C. (2014), Recalibration
Procedures for the Structural Asphalt Layer Coefficient in the 1993 AASHTO
Pavement Design Guide, NCAT Report 14-08, National Center for Asphalt
Technology, Auburn University, November, 35 pp.
Van Wijk, A., Yoder, E.J., and Wood, L.E. (1983), Determination of Structural
Equivalency Factors of Recycled Layers by Using Field Data, Transportation
Research Record No. 898, Transportation Research Board, Washington, D.C.,
pp. 122-132.
Wang, M.C. and Larson, T.D. (1977), Performance Evaluation for Bituminous-Concrete
Pavements at the Pennsylvania State Test Track, Transportation Research
Record No. 632, Transportation Research Board, Washington, D.C., pp. 21-27.
Wang, M.C. and Larson, T.D. (1979), Evaluation of Structural Coefficients of Stabilized
Base-Course Materials, Transportation Research Record No. 725,
Transportation Research Board, Washington, D.C., pp. 58-67.
Wen, H., Tharaniyil, M.P., Ramme, B., and Krebs, S. (2004), Field Performance
Evaluation of Class C Fly Ash in Full-Depth Reclamation, Transportation
Research Record: Journal of the Transportation Research Board, No. 1869, pp.
41-46.
33
Wu, Z., Zhang, Z., and King, W.M. (2012), Accelerated Loading Evaluation of Stabilized
BCS Layers in Pavement Performance, Report No. FHWA/LA.08/474, Louisiana
Transportation Research Center, March, 101 pp.
NCAT Report 14‐0
8
RECALIBRATION PROCEDURES FOR THE
STRUCTURAL ASPHALT LAYER COEFFICIENT IN
THE 1993 AASHTO PAVEMENT DESIGN GUIDE
By
Dr. David H. Timm, P.E
.
Dr. Mary M. Robbins
Dr. Nam Tran, P.E.
Dr. Carolina Rodezno
November 2014
Timm, Robbins,
Tran & Rodezno
i
RECALIBRATION PROCEDURES FOR THE STRUCTURAL ASPHALT LAYER COEFFICIENT
IN THE 1993 AASHTO PAVEMENT DESIGN GUIDE
NCAT Report 14‐08
Dr. David H. Timm, P.E.
Brasfield and Gorrie Professor of Civil Engineering
Principal Investigator
Dr. Mary M. Robbins
Assistant Research Professor
National Center for Asphalt Technology
Dr. Nam Tran, P.E.
Associate Research Professor
National Center for Asphalt Technology
Dr. Carolina Rodezno
Assistant Research Professor
National Center for Asphalt Technology
November 2014
Timm, Robbins,
Tran & Rodezno
ii
ACKNOWLEDGEMENTS
The authors wish to thank the National Asphalt Pavement Association for sponsoring this
research as part of the Optimizing Flexible Pavement Design and Material Selection research
project and for providing technical review of this document.
DISCLAIMER
The contents of this report reflect the views of the authors who are responsible for the facts
and accuracy of the data presented herein. The contents do not necessarily reflect the official
views or policies of the National Center for Asphalt Technology or Auburn University. This
report does not constitute a standard, specification, or regulation. Comments contained in this
paper related to specific testing equipment and materials should not be considered an
endorsement of any commercial product or service; no such endorsement is intended or
implied.
Timm, Robbins,
Tran & Rodezno
iii
TABLE OF CONTENTS
1. Introduction ……………………………………………………………………………………………………………… 1
2. Overview of the AASHTO Empirical Design Procedure ……………………………………………………. 2
2.1. AASHTO Empirical Design Inputs ……………………………………………………………………………… 3
2.2. AASHTO Empirical Design Procedure ……………………………………………………………………….. 6
2.3. AASHTO Empirical Design Limitations ………………………………………………………………………. 8
2.4. Structural Coefficients ……………………………………………………………………………………………. 9
3. Recalibration Procedures ………………………………………………………………………………………….. 12
3.1. Deflection‐Based Procedures ………………………………………………………………………………… 12
3.1.1. Identify and Characterize Pavement Sections to be Evaluated ………………………. 13
3.1.2. Perform Deflection Testing on Pavement Sections ………………………………………. 13
3.1.3. Backcalculate Pavement Layer Properties …………………………………………………… 1
5
3.1.4. Compute New Structural Coefficients ………………………………………………………… 17
3.2. Performance‐Based Procedure ………………………………………………………………………………. 21
3.2.1. Performance (IRI) Data …………………………………………………………………………….. 23
3.2.2. Traffic Data and Actual ESALs ……………………………………………………………………. 24
3.2.3. Predicted ESALs ……………………………………………………………………………………….. 25
3.2.4. Determination of â1 …………………………………………………………………………………. 26
3.3. Mechanistic‐Empirical Procedures …………………………………………………………………………. 29
3.3.1. MEPDG Local Calibration ………………………………………………………………………….. 29
3.3.2. Use MEPDG to Generate Pavement Thicknesses …………………………………………. 3
0
3.3.3. Recalibrate a1 to Match MEPDG Thicknesses ………………………………………………. 31
4. Conclusions and Recommendations …………………………………………………………………………… 31
5. References ……………………………………………………………………………………………………………… 35
Timm, Robbins,
Tran & Rodezno
iv
LIST OF TABLES
Table 2.1 HMA Layer Coefficients from AASHO Road Test (data from 1) …………………………….. 10
Table 2.2 Correlation between HMA Thickness and Input Parameters (8) …………………………… 11
Table 3.1 Asphalt Concrete Structural Coefficient Equations …………………………………………….. 20
Table 3.2 Example ESAL Differences Assuming a1 = 0.44 (8) ………………………………………………. 26
Table 3.3 WSDOT MEPDG Calibration Results (data from 11) ……………………………………………. 30
Table 3.4 WSDOT Design Comparisons (data from 11) ……………………………………………………… 31
Table 4.1 Summary of Methods ……………………………………………………………………………………… 3
3
LIST OF FIGURES
Figure 1.1 MEPDG and Design Software Implementation (data from 5) ……………………………….. 2
Figure 2.1 ESALs versus Axle Weight (3) ……………………………………………………………………………. 4
Figure 2.2 AASHO Road Test Present Serviceability Rating Form (1) …………………………………….. 5
Figure 2.3 Pavement Performance History Quantified by PSI (3)………………………………………….. 5
Figure 2.4 Structural Number Concept (3) …………………………………………………………………………. 6
Figure 2.5 AASHTO Flexible Pavement Design Nomograph (2) …………………………………………….. 7
Figure 2.6 Pavement Design with Empirical AASHTO Design Equation (3) …………………………….. 8
Figure 2.7 Flexible Pavement Design Curves (1) …………………………………………………………………. 9
Figure 2.8 Determining a1 based on HMA Modulus (data from 2) ………………………………………. 10
Figure 2.9 Asphalt Structural Coefficients (data from 10) ………………………………………………….. 12
Figure 3.1 Deflection versus Load Example (14) ……………………………………………………………….. 14
Figure 3.2 Deflection vs. Temperature Example (14) …………………………………………………………
15
Figure 3.3
SNeff
Schematic ……………………………………………………………………………………………… 18
Figure 3.4 Paired Test Sections (14) ………………………………………………………………………………… 18
Figure 3.5 Computed SNeff and Computed OGFC Structural Coefficient (14) ……………………….. 20
Figure 3.6 Performance‐Based Recalibration Procedure (8) ………………………………………………. 22
Figure 3.7 PSI Data Obtained from IRI Data (8) ………………………………………………………………… 23
Figure 3.8 Actual vs. Predicted ESALs Before and After Calibration …………………………………….. 28
Figure 3.9 NCAT Test Track Asphalt Layer Coefficients (8) …………………………………………………. 29
Timm, Robbins,
Tran & Rodezno
1
1. INTRODUCTION
Pavement thickness design in the U.S. has been predominantly empirically‐based since the
1960’s. The American Association of State Highway and Transportation Officials (AASHTO)
pavement design guides published from 1962 through 1993 (1,2) were based primarily on
the AASHO Road Test (1) conducted in Ottawa, Illinois from 1958 until 1960. A more recent
edition of the AASHTO Guide was published in 1998 but focused primarily on improving
rigid pavement design and is outside the scope of this document. Though updated and
improved over time, the design guides still rely heavily upon observed pavement
performance during the road test. The performance resulted from the cross‐sections,
climate, materials, construction practices and traffic applications representing late 1950’s
conditions and technology at this one test location. For example, the thickest asphalt
section placed at the AASHO Road Test was 6 inches. Furthermore, the advances in
pavement engineering, design, materials and construction fields over the past 52 years has
made the AASHTO Design Guide (2) more outdated with every passing year, forcing
designers to extrapolate well beyond the original conditions of the road test. These
advances include the development of the Superpave asphalt mix design procedures, the
development of the performance graded (PG) asphalt binder specification, the use of
polymers and other modifiers in asphalt, improved asphalt plant production controls,
improved construction techniques and quality control procedures, to name just a few.
As documented previously (3), the National Cooperative Highway Research Program
(NCHRP) recognized the need for an improved and updated pavement design system and
began Project 1‐37A in 1998 entitled, “Development of the 2002 Guide for the Design of
New and Rehabilitated Pavement Structures: Phase I.” The project ran through 2004 and
resulted in the Mechanistic Empirical Pavement Design Guide (MEPDG). In 2008, the
MEPDG was transitioned to the AASHTOWare series of programs and was renamed
DARWin‐ME as the program developers continued to improve the program’s capabilities.
In 2013, the software became commercially available under the name AASHTOWar
e
T
M
Pavement ME Design. The software and accompanying documentation (4), represents a
tremendous leap forward from the 1993 Design Guide (2) and software, DARW
in.
Though the MEPDG is recognized as a technological advance in pavement design, there are
costs associated with implementing the new procedure. The costs include software
licensing and training, development of numerous data sets through laboratory and field
testing required to run the software and validation/calibration studies that must be
conducted before fully implementing the new procedure. These activities can also take
significant amounts of time to accomplish. Currently, the older empirically‐based design
procedure is the most popular approach in the U.S. with 78% of states using some edition
(i.e., 1972, 1986 or 1993 Design Guide) of the older empirical AASHTO procedure (3,5). A
recent survey of state agencies, as summarized in Figure 1.1, indicated that many states
plan to adopt the MEPDG, but only three have currently done so and fourteen expect to
implement within the next two years (5). The other states are at least two years from
implementing the MEPDG while six do not currently plan to implement (5). For states that
have already begun working toward implementing the MEPDG, there are many data sets
Timm, Robbins,
Tran & Rodezno
2
(i.e., traffic, material properties, performance records) that are common between the
empirical and mechanistic‐empirical approaches, so it would make sense to update the old
method while implementing the new approach. Finally, given the complexities of the
MEPDG and design software, there may be many design scenarios (e.g., facilities such as
city streets, county roads, lower volume state routes) that simply do not warrant such a
detailed analysis.
Figure 1.1 MEPDG and Design Software Implementation (data from 5).
Clearly, there is a gap between the outdated empirically‐based procedure and the MEPDG
that should be filled to achieve optimal pavement structural designs. The purpose of this
document is to provide recommended procedures for updating the empirically‐based
design method to reflect modern pavement performance. As explained below, focus is
placed on recalibrating the asphalt structural coefficient as it has the strongest correlation
amongst all the design variables to pavement thickness. Further rationale for recalibrating
the asphalt coefficient is that it was AASHTO’s original intent that states develop agency‐
specific structural coefficients. As stated by George (6), “Because of wide variations in
environment, traffic and construction practices, it is suggested that each design agency
establish layer coefficients based on its own experience and applicable to its own practice.”
2. OVERVIEW OF THE AASHTO EMPIRICAL DESIGN PROCEDURE
Before discussing methods for updating the AASHTO empirical design procedure, it is
important to establish a firm understanding of the design process and how it was
developed. Subsections 2.1 through 2.3 explain the process and its limitations and were
excerpted from a previous report (3), while section 2.4 further explains the importance of
the structural coefficient.
Timm, Robbins,
Tran & Rodezno
3
2.1 AASHTO Empirical Design Inputs
Observations from the AASHO Road Test established correlations between the following
four main factors for flexible pavements:
Soil condition as quantified by the subgrade resilient modulus (Mr)
Traffic as quantified by equivalent single axle loads (ESALs)
Change in pavement condition as quantified by the change in pavement serviceability
index (PSI)
Pavement structure as quantified by a structural number (SN)
The soil resilient modulus describes the inherent ability of the soil to carry load and can be
measured in the laboratory through triaxial resilient modulus testing or in the field through
falling weight deflectometer (FWD) testing. Generally, lower Mr values will require more
pavement thickness to carry the given traffic. The soil modulus during the AASHO road test
was approximately 3,000 psi, and care should be taken when using the AASHTO empirical
method to be sure Mr values obtained through modern means are adjusted to reflect test
conditions (1,2). For example, AASHTO recommends dividing the soil modulus obtained
through FWD testing by three before using in the empirical design equation (2). It is also
important to emphasize that there was only one soil type used during the AASHO Road Test
(1). Though there were seasonal fluctuations in the soil modulus from which empirical
correlations between soil modulus and pavement condition were developed, they are
strictly limited to that soil type.
The AASHO Road Test featured various test loops that were constructed of asphalt concrete
thicknesses ranging from 1 to 6 inches and trafficked with different axle types and load
levels (1). The researchers noted an approximate fourth‐power relationship between the
amount of pavement damage and the load level applied to the pavement section. This
relationship was the central idea in the equivalent single axle load (ESAL), which was
selected to be an 18,000‐lb single axle with dual tires. AASHTO developed empirical
equations to relate the number of applications of all other axle types (single, tandem and
tridem) and load magnitudes to that of the ESAL. Figure 2.1 illustrates ESAL values for single
and tandem axles over a range of axle weights. The single and tandem curves clearly show
the fourth‐order nature of ESALs versus axle weight. The benefit of spreading the load over
more axles is evident in Figure 2.1 by the dramatic reduction in ESALs for the tandem axle
group at any given axle weight, relative to the single axles. Finally, the ESAL standard is
shown in the plot at 18 kip with an ESAL value of one. Within the AASHTO empirical design
system, total traffic must be decomposed into vehicle types with known axle weight
distributions. The axle weight distributions are then used with the ESAL equations to
determine ESALs per vehicle from which a total design ESAL over the pavement life is
computed. It should also be noted that the ESAL assumes a tire inflation pressure of 70 psi
and a tire with a bias‐ply design. Today, tire pressures in excess of 100 psi are common with
a radial design. These factors are not accounted for in the ESAL equations.
Timm, Robbins,
Tran & Rodezno
4
Figure 2.1 ESALs versus Axle Weight (3).
During the AASHO Road Test, routine inspections of each section were made by a panel of
raters. Figure 2.2 shows the rating form and the zero to five scale used by the raters to
quantify current pavement condition. Though actual pavement distress measurements
were made during the road test, this rating scale was the only performance parameter used
in the thickness design procedure. The researchers compiled the average ratings and
plotted them against the amount of applied traffic in each section to develop performance
history curves as shown schematically in Figure 2.3. The AASHTO design procedure relies
upon characterizing the change in serviceability (PSI) from the start (po) to the end (pt) of
the design life as a function of applied ESALs. Typical PSI design values range from 2 to 3
as a function of roadway classification (2). For example, a high volume interstate would be
designed with a smaller PSI compared to a low volume county road.
Timm, Robbins,
Tran & Rodezno
5
Figure 2.2 AASHO Road Test Present Serviceability Rating Form (1).
Figure 2.3 Pavement Performance History Quantified by PSI (3).
Since flexible pavements are typically comprised of diverse layers with varying engineering
properties, it was necessary for AASHTO to introduce the pavement structural number (SN)
concept. SN represents the cumulative pavement structure above subgrade expressed as a
product of individual layer thicknesses (Di), their respective structural coefficients (ai) and
drainage coefficients (mi) as illustrated in Figure 2.4. The layer thicknesses are output from
the AASHTO design process as will be described below. The structural coefficients are
empirical values meant to relate the relative load‐carrying capacity of different materials.
For example, many state agencies use 0.44 for asphalt and 0.14 for granular base as
originally recommended by AASHO (1). These particular structural coefficients mean that
one inch of asphalt is roughly equivalent to 3.1 inches (0.44÷0.14) of aggregate base. The
drainage coefficients are meant to empirically adjust the design according to site‐specific
po
pt
Present Serviceability Index
0
5
Traffic, ESALs
PSI = p0‐pt
Timm, Robbins,
Tran & Rodezno
6
rainfall expectations and quality of drainage provided by the material itself (1). Drainage
coefficients range from 0.4 to 1.4 with the original AASHO Road Test condition represented
as 1.0.
Figure 2.4 Structural Number Concept (3).
2.2 AASHTO Empirical Design Procedure
As described above, the AASHO Road Test (1) established a correlation between soil
condition, traffic, change in pavement condition and pavement structure. This relationship
is shown in Equation 1 (2). The Mr, PSI and SN terms are as defined above. ESALs are
represented by the W18 term. The ZR and S0 terms are reliability and variability factors not
originally part of the AASHTO design procedure but added later to incorporate a safety
factor into the design. They are not present in the 1972 edition of the Design Guide (7)
which some states still use (3). The other quantities in the equation are regression
coefficients that provided the best match between the independent variables (SN, PSI, Mr)
and the performance of the pavement section as quantified by ESALs.
07.8log32.
2
1
109
4
4.
0
5.12.4
log
20.01log36.9log
19.
5
018
RR M
SN
PS
I
SNSZW (Equation 1)
While the purpose of Equation 1 is to determine the required structural number of a
proposed pavement section, it is written to compute ESALs (W18) and solving algebraically
for SN is a daunting task. To alleviate this problem, AASHTO published a design nomograph
(Figure 2.5) that solves for SN given the other inputs. Notice that W18 (ESALs) is treated as
another input with the nomograph solving toward SN. Alternatively, the DARWin software
developed for AASHTO, or solver subroutines in spreadsheets, are used to solve the
equation for SN. It is important to note that Equation 1 uses ZR to represent reliability while
in the nomograph, reliability is used directly as a percentage. More precisely, ZR represents
the z‐statistic corresponding to the chosen level of reliability. When using the equation, ZR
must be entered. When using the nomograph, the reliability percentage must be entered.
AASHTO has recommended levels of reliability (2), based upon highway functional
classification, and the value should be carefully selected as pavement thickness is correlated
Asphalt Concrete (a1)
Granular Base (a2, m2)
Granular Subbase (a3, m3)
Subgrade (Mr)
D1
D2
D3
a1*D1
+a2*m2*D2
+a3*m3*D3
SN =
Timm, Robbins,
Tran & Rodezno
7
to the reliability level and choosing values outside of the recommended ranges can greatly
increase pavement thickness.
Figure 2.5 AASHTO Flexible Pavement Design Nomograph (2).
The AASHTO design equation (Equation 1 or Figure 2.5) is meant to be used for each layer in
a multilayer pavement structure to determine the required pavement thicknesses. As
described by AASHTO (2), this is done in a top‐down fashion as depicted in Figure 2.6. The
design begins by finding the required structural number above the granular base (SN1) using
the granular base modulus and other input parameters in the design equation or
nomograph. By definition, this structural number is the product of the structural coefficient
and thickness of layer one, so it can be used to solve for the thickness of the first layer.
Next, the required structural number above the granular subbase (SN2) is found by using the
subbase modulus and other input parameters in the design equation or nomograph. As
shown in Figure 2.6, SN2 is the sum of the layer one contribution (a1*D1) and the layer two
contribution (a2*m2*D2). Since D1 was already found in the previous step, the SN2 equation
can be solved for D2. This procedure is followed again for the subgrade (or next sublayer, if
present), as shown in Figure 2.6, to arrive at a unique set of pavement layer thicknesses.
Timm, Robbins,
Tran & Rodezno
8
SN1 = a1*D1
D1
SN
SN2 = a1*D1+a2*m2*D2
D2
SN a ∗
D
a ∗ m
SN3 = a1*D1+a2*m2*D2+a3*m3*D3
D
3
SN a ∗ D a ∗ m ∗ D
a ∗ m
Figure 2.6 Pavement Design with Empirical AASHTO Design Equation (3).
2.3 AASHTO Empirical Design Limitations
Though the empirical AASHTO design procedure has been used since the 1960’s, there are
many factors that limit its continued use and provide motivation for developing and
implementing more modern methods. Most notably among these factors is the very nature
of the method itself: empirical. This means that the design equations described above are
strictly limited to the conditions of the original road test. This includes all the coefficients in
Equation 1, the structural coefficients (ai), drainage coefficients (mi), ESAL equations and so
forth. Any deviation from these conditions results in an unknown extrapolation.
The limitations of the AASHO Road Test are numerous. The experiment had one soil type,
one climate, one type of asphalt mix (pre‐Marshall mix design), limited pavement cross‐
sections, limited load applications and tires inflated to 70 psi (1). Any deviation from these
factors in modern design means extrapolation, which can lead to under or over‐design.
Most designs conducted today are extrapolations beyond the original experimental
conditions. Consider, for example, the thickness design curves published in 1962 as part of
the AASHO Road Test report shown in Figure 2.7. The shaded gray area above 1.1 million
axle loads is entirely extrapolated. Also, the dashed portions of the curves are
Asphalt Concrete (a1)
Granular Base (a2, m2)
Granular Subbase (a3, m3)
Subgrade (Mr)
D1
D2
D3
SN3 SN2 SN1
Modulus of granular base,
and other inputs
(W18, ZR, S0, PSI)
used to find SN1
Modulus of granular subbase,
and other inputs
(W18, ZR, S0, PSI)
used to find SN2
Modulus of subgrade,
and other inputs
(W18, ZR, S0, PSI)
used to find SN3
Timm, Robbins,
Tran & Rodezno
9
extrapolations. As evidenced by Figure 2.7, there was very little, even in 1962, that was not
an extrapolation.
Figure 2.7 Flexible Pavement Design Curves (1).
2.4 Structural Coefficients
The structural coefficients are of great importance in the AASHTO procedure. These
empirical terms are meant to reflect the relative structural contributions of each pavement
layer and have a direct impact on the derived layer thicknesses as demonstrated in Figure
2.6. Though AASHO recommended 0.44 for the asphalt layer in 1962, a range of values
were actually reported. Table 2.1 lists the reported values by test loop ranging from 0.33 to
0.83. Loop 1 is not included in the table because it was never trafficked; it was used to
evaluate environmental impacts on pavements. The authors of the 1962 report (1) stated
that a weighted average was used to determine 0.44 as the recommended value, but
inspection of the data does not clearly indicate how the values were weighted to achieve
0.44.
As described by Peters‐Davis and Timm (8), a relationship was created in 1972 that linked
the layer coefficient to the elastic modulus (E) of the HMA at 70°F, and is shown in Figure
2.8. Strictly speaking, 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 (2). In 2006, Priest and Timm (9) found a relationship relating
temperature and stiffness for all the structural sections in the 2003 research cycle of the
Timm, Robbins,
Tran & Rodezno
10
National Center for Asphalt Technology’s Pavement (NCAT) Test Track. Using their
relationship, the average HMA modulus was calculated as 811,115 psi. If the curve in Figure
2.3 was extrapolated out to this modulus value, the resulting layer coefficient would be
equal to 0.54.
Table 2.1 HMA Layer Coefficients from AASHO Road Test (data from 1)
Loop Layer Coefficient (a1) 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
Figure 2.8 Determining a1 based on HMA Modulus (data from 2).
The structural coefficients not only appear in the structural design equations (Equation 1,
Figures 2.5 and 2.6) but they are also present in the ESAL computations. The 4
th
order
relationship between axle weight and pavement damage was mentioned in Section 2.1.
More specifically, at the AASHO Road Test, replicate cross sections were constructed in
different test loops to apply repeated axle loads at various load levels on the same
pavement structure. This allowed the researchers to measure the damage caused by axles
at various weights and create mathematical relationships based upon that damage, which
included a factor accounting for the pavement structure. This factor was the structural
number, as is used in the design equations shown above (Equation 1, Figures 2.5 and 2.6),
0
0.1
0.2
0.3
0.4
0.5
0 1 2 3 4 5
HMA Elastic Modulus at 70
o
F (
10
5
psi)
S
tr
u
c
tu
r
a
l
C
o
e
ff
ic
ie
n
t
(a
1
)
Timm, Robbins,
Tran & Rodezno
11
and is a product of the layer thicknesses, drainage coefficients and structural coefficients.
Since ESALs are needed in the structural design equation to determine the required SN from
which thicknesses are computed, and an SN is required to determine ESALs, the design
process follows circular reasoning. To overcome this problem, many designers simply
assume an SN equal to 5 to compute ESALs as the starting point, from which the actual
design SN may be determined from the structural design equation.
When considering updating the empirically‐based procedure, one may consider adjusting
values other than the asphalt layer coefficient. A previous investigation (8) conducted a
sensitivity analysis to determine which parameters had the greatest impact on asphalt
concrete (AC) thickness. The analysis considered a wide range of layer coefficients (a1),
traffic levels (ESALs), soil moduli (Mr), reliability (R), change in serviceability (PSI) and
design variability (S0). Table 2.2 summarizes the Pearson correlation coefficients for the
5,120 design thicknesses determined in the sensitivity analysis with the parameters ranked
from most to least influential (8). Clearly, the asphalt layer coefficient is the most
influential. The next two parameters, though also strongly correlated, may be considered
simply part of the design scenario or site‐specific conditions. The remaining parameters are
much less correlated and do not affect pavement thickness as significantly as the first three.
Therefore, it makes sense to focus recalibration efforts on the asphalt layer coefficient to
better align observed performance with performance predicted by the design procedure.
Table 2.2 Correlation between HMA Thickness and Input Parameters (8)
Parameter Correlation Coefficient
Layer coefficient (a1) ‐0.518
Traffic level (ESALs) 0.483
Resilient modulus (MR) ‐0.425
Reliability (R) 0.157
Change in serviceability (ΔPSI) ‐0.141
Variability (So) 0.083
The asphalt structural coefficient plays a vital role in pavement design and should reflect
performance characteristics of modern materials. However, a recent survey of state
agencies (10), summarized in Figure 2.9, shows the distribution of asphalt structural
coefficients across the U.S., where 45% of states currently use 0.44 for at least one paving
layer, though some states specify according to the lift or mix design using a number of
design gyrations (Ndes). Many states (28%) use less than the originally recommended
AASHO value of 0.44 (3). Two states, Alabama (8) and Washington (11), recently revised
their structural coefficients to 0.54 and 0.50, respectively. These increases reflect modern
advances in the materials and construction practices and are more consistent with field
performance of flexible pavements in these states. The changes result in optimum asphalt
pavement thickness design that can potentially provide significant savings to the state
agencies. A change from 0.33 to 0.44 would result in 25% thinner sections. An increase
from 0.44 to 0.54, as done in Alabama, reduces the pavement thickness by 18.5%. As stated
Timm, Robbins,
Tran & Rodezno
12
by Larry Lockett (12), the ALDOT State Materials and Tests Engineer at the time the change
was implemented, “This means that our resurfacing budget will go 18% farther than it has in
the past. We will be able to pave more roads, more lanes, more miles, because of this 18%
savings.” Any change considered by a state agency should be carefully evaluated and
supported by actual pavement performance data.
Figure 2.9 Asphalt Structural Coefficients (data from 10).
3. RECALIBRATION PROCEDURES
The outcome of any pavement design procedure is a set of layer thicknesses that will be
sufficient to carry the expected traffic, in the given environment, with a specified level of
performance over a fixed period of time. The success of the design procedure hinges on the
ability of the procedure to make accurate predictions of pavement performance given a set
of input parameters. Safety factors may be added to the predictions to account for
uncertainty in the process as is done in the AASHTO method (2) through the reliability (R or
ZR) and variability (S0) terms. Three general classes of recalibration methods are discussed
in the following subsections, each of which should be judged against the ability to make
accurate predictions of pavement performance over time.
3.1 Deflection‐Based Procedures
Deflection‐based procedures rely on field testing of existing pavements to determine in‐
place modulus. The in‐place modulus is then correlated to a structural coefficient through
existing empirical equations. The main advantage of this approach is that it requires
relatively little data generation through deflection testing. The main disadvantage is that
the approach relies upon existing empirical equations that are based on past performance
Timm, Robbins,
Tran & Rodezno
13
and may not accurately reflect the performance of the pavement materials under
evaluation. The general procedure includes the following steps discussed in the subsections
below:
1. Identify and characterize pavement sections to be evaluated.
2. Perform deflection testing on pavement sections.
3. Backcalculate pavement layer properties.
4. Compute new structural coefficients.
3.1.1 Identify and Characterize Pavement Sections to be Evaluated
The first step is to identify and select candidate pavement sections to include in the
analysis. Recently constructed, undamaged pavement sections should be characterized
since the structural coefficient is meant to represent “new” conditions. Information
regarding the pavement cross section that includes material type and as‐built layer
thicknesses at the test location is critical.
3.1.2 Perform Deflection Testing on Pavement Sections
Deflection testing, using a falling weight deflectometer (FWD), should be conducted on the
selected pavement sections. For details regarding FWD best practices, consult the FHWA
manual on field guidelines for FWD testing (13).
Depending on the backcalculation scheme to be used, as discussed in the next subsection,
the FWD should be configured to measure deflections at critical offsets. At a minimum, the
center and outer (60 or 72 inches from load center) deflections should be measured.
Typically, deflections may be measured with 6 to 9 sensors, which include the center and
outermost deflection measurements.
Many FWD’s are configured to test at multiple load levels. To determine the structural
coefficient, it is important to have test results at 9,000 lb, which is the AASHTO standard
load level. This may be achieved either by setting the drop height to achieve 9,000 lb or by
interpolating results from multiple load levels. For example, Figure 3.1 shows the
interpolation process from data collected at the NCAT Test Track (14). In the figure, the
center (D1) and outermost (D9) deflections were plotted against load level. Regression
equations were determined for each set of deflections from which deflection at the target
load level was determined.
Timm, Robbins,
Tran & Rodezno
14
Figure 3.1 Deflection versus Load Example (14).
It is also important to measure and account for the temperature at the time of testing. The
AASHTO system is currently based on a 68F (20C) pavement reference temperature.
Therefore, any deflection data must be adjusted to this reference temperature. AASHTO (2)
has published temperature correction charts that may be used to correct the center
deflection for backcalculation. Alternatively, tests could be conducted over a range of
temperatures and deflections interpolated at the reference temperature as shown by the
example in Figure 3.2. The center deflection (D1) shows a strong dependence on
temperature characterized by the corresponding regression equation. The equation was
used to establish the best estimate of deflection at 68F, and the deflections at other
temperatures were corrected to 68F represented by the D1 at 68F data series in Figure 3.2.
The outermost deflection (D9) shows very little correlation with temperature, as expected,
since it represents the behavior of the subgrade soil, and no temperature correction is
needed. This approach, though effective, would require accessing the pavement at multiple
times to gather the required data and may not be practical in all situations. In any case, it is
important to have deflections representing the AASHTO reference temperature.
Deflection = 0.0024*Load + 3.1322
R
2
= 0.9
9
Deflection9000 = 0.0024*9000+3.1322
= 24.732 milli-in
Deflection = 0.0002*Load – 0.319
6
R
2
= 0.99
Deflection9000 = 0.0002*9000-0.3196
= 1.480 milli-in
0
5
10
15
20
25
30
35
40
45
0
1
0
0
0
2
0
0
0
3
0
0
0
4
0
0
0
5
0
0
0
6
0
0
0
7
0
0
0
8
0
0
0
9
0
0
0
1
0
0
0
0
1
1
0
0
0
1
2
0
0
0
1
3
0
0
0
1
4
0
0
0
1
5
0
0
0
1
6
0
0
0
Load, lb
D
e
fl
e
c
ti
o
n
,
m
il
li
-i
n
.
D1
D9
AASHTO Reference Load = 9,000 lb
S9 – Location 1
July 26, 2010
Timm, Robbins,
Tran & Rodezno
15
Figure 3.2 Deflection vs. Temperature Example (14).
3.1.3 Backcalculate Pavement Layer Properties
There are several approaches to backcalculating in‐place pavement layer properties from
measured deflections. They range from relatively simple equations solved by hand or in a
spreadsheet to very complex computational algorithms executed in self‐contained
computer programs. Regardless of the approach, the objective of any backcalculation
scheme is to determine the layer properties under the given applied load and
environmental conditions that produced the measured deflections. While only the
relatively simple AASHTO two‐layer backcalculation procedure (2) is discussed here, there
are many more sophisticated multi‐layer backcalculation programs available that include
EVERCALC, MODCOMP and MICHBACK, to name a few.
The AASHTO two‐layer backcalculation approach (2) is based on fundamental pavement
mechanics and determines the in‐place subgrade soil modulus (Mr) and the composite
modulus of all pavement layers (Ep) above the subgrade soil. The approach was originally
intended to provide estimates of in‐place effective structural number (SNeff) as part of the
AASHTO overlay design procedure (2). However, it can also be used to provide the
information necessary to find structural coefficients as will be demonstrated in the next
subsection.
y = 3.5594e
0.0173
x
R
2
= 0.9304
y = 0.0043x + 0.9504
R
2
= 0.3555
0
5
10
15
20
25
30
35
0 20 40 60 80 100 120 140
Mid-Depth Temperature, F
D
e
fl
e
c
ti
o
n
a
t
9
,0
0
0
l
b
,
m
il
li
-i
n
D1
D9
D1 at 68F
AASHTO Reference Temp = 68F
S9-1 – All Dates
Timm, Robbins,
Tran & Rodezno
16
The first step in the AASHTO backcalculation approach is to determine the soil modulus
according to (2):
r
P
M
r
R
*
*24.0
(Equation 2)
where:
MR = subgrade modulus, psi
P = load magnitude, lb (9,000 lb recommended by AASHTO)
r = measured deflection at offset, r, in.
r = radial offset, in.
AASHTO (2) recommends a radial offset that exceeds 70% of the effective radius (ae) of the
stress bulb at the subgrade/pavement interface. This is to insure that the sensor chosen
provides only a measure of subgrade deflection while providing sufficiently high deflections
to minimize the impact of measurement error. The effective radius may be calculated by
(2):
2
32
R
p
e
M
E
Daa (Equation 3)
where:
ae = effective radius of stress bulb at subgrade/pavement interface, in.
a = FWD load plate radius, in.
D = total pavement depth above subgrade, in.
Mr = subgrade modulus computed from Equation 2, psi
Ep = composite pavement modulus computed from Equation 4, psi
Note that a specific sensor offset must be chosen to compute the subgrade modulus
according to Equation 2, but whether it satisfies the 70% of ae criteria cannot be checked
until further computations are made since Equation 3 also requires the composite
pavement modulus (Ep). After the subgrade modulus has been determined, assuming a
sensor offset, Ep is backcalculated from the center deflection using the following equation
(2):
(Equation 4)
p
R
p
R
E
a
D
M
E
a
D
M
ap
2
2
3
1
1
1
1
1
1
**5.1
Timm, Robbins,
Tran & Rodezno
17
where:
1 = center deflection, in. (called D1 above)
p = contact pressure, psi (computed from load, P, and circular contact radius, a)
a = FWD load plate radius, in.
D = total pavement depth above subgrade, in.
Mr = subgrade modulus computed from Equation 2, psi
Ep = composite pavement modulus, psi
Equation 4 is easily solved for Ep in a spreadsheet using some kind of iterative solution like
the built‐in Solver function in Excel
®
or using a bisection method to determine the correct Ep
that will produce the measured center deflection. After computing Ep, it should be used in
Equation 3 with the other variables to check that the selected sensor met the radial offset
requirement.
3.1.4 Compute New Structural Coefficients
There are two approaches to finding the AC structural coefficient both of which use the
composite pavement modulus (Ep). The first may be used with individual pavement
sections if the underlying (non‐AC) structural and drainage coefficients are known or
assumed. The second may be used if there are paired sections where the only difference
between sections is one particular AC layer. Both approaches rely on computing the
effective structural number from the composite pavement modulus. The effective structural
number represents the structural integrity of the pavement as an empirical function of the
thickness of the pavement and the composite pavement modulus. The equation was based
on performance at the AASHO Road Test (1,2) and is expressed as:
3**0045.0 peff EDSN (Equation 5)
where:
SNeff = effective structural number of in‐place pavement
D = total pavement depth above subgrade, in.
Ep = composite pavement modulus, psi
The first approach, depicted in Figure 3.3, assumes that the structural and drainage
coefficients of the layers beneath the AC are known. If that is the case, then SNeff may be
computed according to Equation 5 and equated to the other parameters by:
SNeff = a1*D1 + a2*m2*D2+a3*m3*D3 (Equation 6)
Since every parameter in Equation 6 is known except for a1, the AC structural coefficient
may be simply calculated as:
a1 = [SNeff – a2*m2*D2 – a3*m3*D3] / D1 (Equation 7)
Timm, Robbins,
Tran & Rodezno
18
Figure 3.3 SNeff Schematic.
This approach was used in a Kansas study (15) to determine the structural coefficient of
crumb rubber modified asphalt mixtures. In that study, the underlying base and subgrade
layer moduli were determined through backcalculation and correlated to structural
coefficients through existing equations published by Ullidtz (16).
The second approach that uses the SNeff computation relies on having two nearly identical
pavements where only one layer differs between the two sections and the structural
coefficient of one of the two different materials is known or assumed. Figure 3.4 shows an
example from the NCAT Test Track where two sections differed only in their surfacing layers
while the underlying materials were nearly identical with only slight differences due to
inevitable construction variation (14). In this particular case, the objective was to establish
a structural coefficient of the open graded friction course in Section S8 (14).
Figure 3.4 Paired Test Sections (14).
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
S8-OGFC S9-Control
D
e
p
th
B
e
lo
w
S
u
rf
a
c
e
,
in
.
12.5 mm NMAS OGFC PG 76-22
(5.1% AC, 25% Air Voids)
19 mm NMAS
PG 76-22
19 mm NMAS
PG 67-22
9.5 mm NMAS PG 76-22
(6.1% AC, 6.9% Air)
Crushed Aggregate Base
(4.6% AC, 6.3% Air Voids) (4.4% AC, 7.2% Air Voids)
(4.9% AC, 8.3% Air Voids) (4.7% AC, 7.4% Air Voids)
Asphalt Concrete (a1 unknown)
Granular Base (a2 & m2 known)
Granular Subbase (a3, m3 known)
Subgrade (Mr)
D1
D2
D3
SNeff
Timm, Robbins,
Tran & Rodezno
19
The procedure involves computing Ep for each section from which SNeff is determined. Since
the sections are nearly identical except for one lift of AC, any difference in SNeff may be
attributed to the difference in that one lift. From a general perspective, the SNeff of two
pavements (A and B) may be computed as:
SNeffA = a1A*D1A + a2*m2*D2+a3*m3*D3 (Equation 8)
SNeffB = a1B*D1B + a2*m2*D2+a3*m3*D3 (Equation 9)
Taking the difference between Equations 8 and 9, assuming everything below the first layer
is equivalent, yields:
SNeffA – SNeffB = SN = a1A*D1A – a1B*D1B (Equation 10)
Assuming that pavement A has a known structural coefficient (a1A), and having measured
the SN and thickness of both pavement layers, then the structural coefficient of the
unknown layer may be computed by solving Equation 10 for a1B:
a1B = [a1A*D1A – SN] / D1B (Equation 11)
This procedure was followed for the sections in Figure 3.4, and the data are summarized in
Figure 3.5. The computed difference (SN) between the two sections, which was shown to
be statistically significant (14), was 0.45. The equations shown in Figure 3.5 follow the form
of Equation 11, which produced an OGFC structural coefficient equal to 0.15 (14).
Timm, Robbins,
Tran & Rodezno
20
Figure 3.5 Computed SNeff and Computed OGFC Structural Coefficient (14).
Aside from the two methods described above, there are a variety of existing equations to
estimate structural coefficient from the backcalculated in‐place AC modulus, which is
different than composite pavement modulus (Ep) determined from the AASHTO two‐layer
backcalculation. A backcalculated AC modulus is determined through a multilayer
backcalculation program and should be used in conjunction with the structural coefficient
equations listed in Table 3.1. Since the equations are empirical, the original references
should be consulted to determine if the test conditions are applicable to the pavements
currently under evaluation.
Table 3.1 Asphalt Concrete Structural Coefficient Equations
Material Type Equation Reference
Asphalt Concrete
a1 = 0.171*ln(EAC) – 1.784
where EAC = AC modulus, psi
2
Asphalt Concrete
a1 = 0.4*log(EAC/3000) + 0.44
where EAC = AC modulus, MPa
16
Crumb Rubber
Asphalt Concrete
a1 = 0.315*log(EAC) – 1.732
where EAC = AC modulus, MPa
15
As noted above, it must be re‐emphasized that these deflection‐based methodologies rely
on past‐performance characterization and may not accurately reflect performance of new
or site‐specific materials. They should only be used if performance data are not available,
3.11
2.66
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
S8 S9
A
ve
ra
g
e
S
N
e
ff
SN = 0.45
15.0
35.1
45.022.1*54.0
OGFC
OGFC
surfacecontrolcontrol
OGFC
a
D
SNDa
a
Timm, Robbins,
Tran & Rodezno
21
or more preferably, in conjunction with performance data as explained in the subsequent
sections.
3.2 Performance‐Based Procedure
Recalibration of the asphalt layer coefficient based on observed pavement performance
most closely matches how the coefficients were originally calibrated (1). This approach
should be considered an improvement over deflection‐based procedures because it
considers the actual performance of the material under investigation rather than relying on
previously developed correlations. The main disadvantage of this approach is that detailed
traffic and pavement performance records over time are needed, thus pavements selected
for evaluation must be done so carefully. Also, this approach is not generally capable of
discerning individual lifts of asphalt.
Figure 3.6 summarizes the performance‐based recalibration procedure as previously
documented by Peters‐Davis and Timm (8). The procedure relies on two primary data sets.
The first is historical traffic data in terms of axle weights, axle configuration and volume,
which are needed to compute ESALs over time. The second is performance data expressed
as International Roughness Index (IRI), which can be converted to pavement serviceability
(PSI) over time. As shown in Figure 3.6 and explained further below, these two primary
data sets are used in several equations to generate the actual ESALs applied to the
pavement and the predicted ESALs that the pavement is expected to withstand. Since the
asphalt structural coefficient (a1) is used to determine the structural number (SN), which
appears in both the actual and predicted ESAL equations, â1 may be iteratively adjusted to
minimize the error between actual and predicted ESALs. The â1 symbol is used to indicate
that it is a value that will be determined through a best‐fit iterative procedure. This is the
essence of how the original calibration was done for the AASHO Road Test results (1,8). The
following subsections detail the procedural elements of Figure 3.6.
Timm, Robbins,
Tran & Rodezno
22
Figure 3.6 Performance‐Based Recalibration Procedure (8).
Traffic Data Set
(axle passes, weights, etc.)
Performance (IRI)
Data Set
pt ΔPSI
(Al‐Omari/Darter equation)
Actual ESALs
(Wtx/Wt18 equation)
(AASHO Road Test traffic equations:
Gt, βx, EALF, ESAL)
SN
Predicted ESALs
(logW18 equation)
(AASHTO
flexible pavement
design equation)
Actual ESALs
P
re
d
ic
te
d
E
S
A
Ls
*
*
*
â 1
*Minimize error between actual and predicted by
changing only a1
Timm, Robbins,
Tran & Rodezno
23
3.2.1 Performance (IRI) Data
The AASHTO procedure requires pavement performance expressed in terms of present
serviceability index (PSI). However, many agencies do not collect PSI values as part of
pavement management activities, but rather IRI. Therefore, there is typically a need to
convert IRI to PSI so the data may be used within the AASHTO system. While there are a
number of equations available in the literature (e.g., 17‐19), one recommended for use by
the National Highway Institute and used in a previous investigation (8) was developed by Al‐
Omari and Darter (20) and recommended for use in this document. It was based on
studying pavements from 5 different states and yielded an R
2
of 0.81 (20):
IRIePSI 0038.05 (Equation 12)
where:
PSI = present serviceability index (0‐5 scale)
IRI = International Roughness Index, in./mile
Once IRI data versus time for a pavement section have been obtained, it is straightforward
to convert from IRI to PSI using Equation 12 and develop performance curves, such as those
shown in Figure 3.7. Note in the figure that the data are separated by wheelpath
representing the left (LPSI), right (RPSI) and average (AvgPSI) serviceability ratings. If
datasets from both wheelpaths are available, it is recommended to use the data set
representing the worst performance in the recalibration process to be conservative. At this
stage, it is important to establish the initial serviceability (po) and terminal (pt) calibration
points. These will be used to establish PSI values and points in time corresponding to
cumulative ESAL applications at those times.
Figure 3.7 PSI Data Obtained from IRI Data (8).
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
P
S
I
L
PSI
RPSI
AvgPSI
P
t
Pt calibration points
Po
Timm, Robbins,
Tran & Rodezno
24
3.2.2 Traffic Data and Actual ESALs
It is imperative that reasonably accurate historical traffic records are obtained for this
recalibration procedure. Information regarding axle types (single, tandem, tridem), axle
weights and volume of axles is critical in computing the actual ESALs applied. This
information may come from weigh‐in‐motion or static scale sites. After assembling the
necessary information, the total actual ESALs must be computed as detailed below.
As described by Peters‐Davis and Timm (8), the AASHTO Design Guide (2) quantifies
pavement damage using Equivalent Axle Load Factors (EALFs), which are used to find the
number of ESALs. An EALF quantifies the damage done per pass of any axle relative to the
damage done per pass by a standard axle (typically an 18‐kip single axle). This equation
comes from the results of the AASHO Road Test (1), and is expressed as follows according to
Huang (21):
tx
t
W
W
EALF 18 (Equation 13)
where:
Wtx = number of x axle load applications at time t
Wt18 = number of 18 kip axle load applications at time t
Equations 14b and 14c are used within 14a to generate the Wtx/Wt18 value from which the
EALF value may be determined from Equation 13 for any axle type relative to the standard
(21). Equation 14a represents the fourth‐power relationship presented in Figure 2.1,
though it is impossible to clearly see the fourth‐power trend in the equation due to its
complexity.
18
22
18
log33.4log79.41252.6log
t
x
t
x
t
tx GGLLL
W
W
(Equation 14a)
5.12.4
2.4
log tt
p
G (Equation 14b)
23.32
19.5
23.3
2
1
081.0
40.0
LSN
LLx
x
(Equation 14c)
where:
Lx = axle group load in kips
L2 = axle code (1 for single, 2 for tandem and 3 for tridem)
SN = structural number
Wtx = number of x axle load applications at time t
Wt18 = number of 18 kip axle load applications at time t
x = a function of design and load variables
Timm, Robbins,
Tran & Rodezno
25
18 = value of βx when Lx is equal to 18 and L2 is equal to one
pt = terminal serviceability determined from IRI data converted to PSI
Gt = a function of serviceability levels
The EALFs for each axle load group, determined by equations 13 and 14 above, are used to
find the total damage done during the design period, which is defined in terms of passes of
the standard axle load (ESALs), as shown in the following equation (21):
m
i
ii nEALFESAL
1
(Equation 15)
where:
ESAL = actual ESALs
m = number of axle load groups
EALFi = EALF for the ith axle load group
ni = number of passes of the ith axle load group during the design period
It is important to note that Equation 14b requires a terminal serviceability value, pt. This
comes directly from the discussion above in subsection 3.2.1. Also, Equation 14c requires
an SN value, which may be computed for the pavement as previously defined:
SN = â1*D1 + a2*m2*D2+a3*m3*D3 (Equation 16)
It is assumed for the purposes of this recalibration procedure that the thicknesses are
known and the non‐AC structural and drainage coefficients are known. Therefore, â1 is the
only unknown and is the value that will be adjusted, as noted in Figure 3.6, to arrive at the
best match between actual and predicted ESALs.
3.2.3 Predicted ESALs
The predicted ESAL computation is made directly by the AASHTO pavement design equation
presented earlier (Equation 1) and repeated here as Equation 17. A primary input to the
equation is the pavement performance characterized by PSI obtained through the IRI data
set.
07.8log32.2
1
1094
4.0
5.12.4
log
20.01log36.9log
19.5
018
RR M
SN
PSI
SNSZW (Equation 17)
where:
logW18 = predicted ESALs
ZR = standard normal deviate for a given reliability
S0 = standard deviation
ΔPSI = difference between initial and terminal serviceability at time t
MR = resilient modulus of the subgrade, psi
Timm, Robbins,
Tran & Rodezno
26
SN = structural number (Equation 16)
Equation 17 is normally used for design, where ESALs (W18) are input, SN is computed and a
reliability in excess of 50% is used to act as a safety factor when determining the required
structural number. However, in the case of recalibration, the objective is to closely match
predicted and actual ESALs applied without this design safety factor applied. Therefore,
reliability should be set at 50% (average), which yields a standard normal deviate equal to 0
and the ZRS0 term drops out of Equation 17.
The PSI term should be obtained as described in Section 3.2.1, and the SN term is as
defined in Equation 16 based on the iterative â1 term. The soil resilient modulus (MR)
should be calculated from falling weight deflectometer (FWD) testing of the section at a
9,000 lb load level. Refer to Section 3.1.1 and Equation 2 for the AASHTO recommendations
regarding determination of subgrade soil modulus. AASHTO further recommends, when
using Equation 17, that the MR value determined through backcalculation be divided by
three to account for differences in how testing was conducted during the AASHO Road Test
versus modern FWD testing (2). This AASHTO (2) recommendation is only for fine‐grained
cohesive soils and no recommendation is made for granular, coarse‐grained soils. Finally, if
the soil modulus changes appreciably with the seasons, it is recommended that the AASHTO
procedure for adjusting soil modulus to reflect these seasonal changes be followed (2). This
requires testing at multiple times during the course of a year to establish the seasonal
trends and using another AASHTO empirical equation that relates pavement damage to soil
modulus to compute a weighted average soil modulus based on seasonal duration and
damage potential (2).
3.2.4 Determination of â1
For a given pavement section, the outcome of subsections 3.2.1 through 3.2.3 is a simple
table listing the predicted and actual ESALs at specific points in time for a particular â1
value. For example, Table 3.2 shows the actual and predicted ESALs for an NCAT Test Track
section assuming 0.44 as the asphalt structural coefficient. Notice that the predicted ESALs
far underestimate the actual ESALs applied by 46% to 65%. The objective is now to improve
the prediction by adjusting â1 such that the error is minimized. It is recommended to follow
a least‐squares regression procedure to minimize the error.
Table 3.2 Example ESAL Differences Assuming a1 = 0.44 (8)
Predicted ESALs Actual 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%
Timm, Robbins,
Tran & Rodezno
27
Following standard statistical regression procedures (22), the differences between actual
and predicted ESALs must be squared and summed to obtain the error sum of squares (SSE),
which is defined as:
i
ii ActualESALSALPredictedESSE
2
(Equation 18)
Next, the mean should be obtained for the actual ESALs (ActualESAL) and the difference
between that mean and each predicted ESAL level must be squared. The sum of these
values represent the total sum of squares (SST):
i
i ActualESALSALPredictedE
SST
2
(Equation 19)
The Pearson’s coefficient of determination (R
2
) may be calculated from the SSE and SST as a
measure of how well the predicted and actual ESALs match (22):
SST
SSE
R 12 (Equation 20)
To perform the regression, it is recommended to use the Solver add‐in within Excel. Solver
may be set to minimize the SSE term while only changing the AC layer coefficient (â1). 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 actual and predicted ESALs change. This is because
both of these values are calculated using the structural number (SN), which is calculated
using the layer coefficient (â1). However, Excel should automatically converge to a final
least‐squares solution.
Figure 3.8 summarizes the before and after calibration results for the example shown in
Table 3.2. This regression resulted in a HMA layer coefficient of 0.50 and an R
2
equal to
0.74. There is a noticeable improvement in the actual vs. predicted ESAL differences after
the regression was completed. It is also important to note that the errors were not
completely eliminated. The objective of the regression procedure is to minimize error and
bias, not to eliminate these factors.
Timm, Robbins,
Tran & Rodezno
28
Figure 3.8 Actual vs. Predicted ESALs Before and After Calibration.
The procedure described above formed the basis of the ALDOT newly‐recommended
asphalt structural coefficient equal to 0.54 (8). Figure 3.9 shows the range of values
obtained in that investigation, which found all the values were within the range originally
calculated at the AASHO Road Test (1) that varied from 0.33 to 0.83. When conducting
recalibration, it is important to check the final results for reasonableness against the original
values. It is also important to select a range of pavement sections that exhibited a range of
performance to avoid biasing the recalibrated coefficient toward conservative or liberal
designs. In the case of the Test Track sections depicted in Figure 3.9, they represented a
range of cross‐sections that included a variety of thicknesses (5 inches to 14 inches of AC),
two subgrade types (AASHTO A‐4 and A‐7‐6) and different types of aggregate base. They
also included a range of AC materials that included unmodified and SBS‐modified asphalt
binder, SMA, and mixtures designed as a rich‐bottom (2% air voids). This variety of cross‐
sections resulted in a wide range of performance histories that included bottom‐up fatigue
cracking, surface rutting, substructure rutting, top‐down cracking and, in some cases, no
measurable distress (8).
Timm, Robbins,
Tran & Rodezno
29
Figure 3.9 NCAT Test Track Asphalt Layer Coefficients (8).
3.3 Mechanistic‐Empirical Procedures
The last procedure to consider relies upon using the MEPDG, locally calibrated with
performance data, to establish pavement layer thicknesses from which the structural
coefficients may be determined. This comprehensive approach, developed and used in
Washington (11), is conceptually straightforward but very time and data intensive.
Agencies should consider this approach if efforts are already in progress toward calibrating
the MEPDG or if local calibration has been completed. The general steps are as follows and
discussed in the following subsections:
1. Locally calibrate the MEPDG.
2. Use the locally calibrated MEPDG to generate pavement thickness designs.
3. Recalibrate a1 to match AASHTO empirical designs to MEPDG designs.
3.3.1 MEPDG Local Calibration
Local calibration of the MEPDG is no easy task and full discussion of this topic is outside the
scope of this document. However, detailed procedures were published in 2010 by AASHTO
(23) that should be followed to execute local calibration of the MEPDG. As a brief summary,
the MEPDG local calibration procedure involves identifying candidate pavement sections
that have:
as‐built material property characterization
performance data in terms of cracking, rutting and ride quality
traffic history data characterized as load spectra
detailed climate records
Once each of these data sets has been developed, pavement sections are simulated in the
MEPDG software with trial calibration coefficients, which predict performance over time.
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
N
1
2
0
0
3
N
1
2
0
0
6
N
2
2
0
0
3
N
2
2
0
0
6
N
3
2
0
0
3
-2
0
0
6
N
4
2
0
0
3
-2
0
0
6
N
5
2
0
0
6
N
6
2
0
0
3
-2
0
0
6
N
7
2
0
0
3
-2
0
0
6
N
8
2
0
0
3
N
8
2
0
0
6
N
9
2
0
0
6
N
1
0
2
0
0
6
S
1
1
2
0
0
6
A
ve
ra
g
e
L
a
y
e
r
C
o
e
ff
ic
ie
n
t
Timm, Robbins,
Tran & Rodezno
30
Comparisons between the MEPDG predictions and actual performance are made, from
which the calibration coefficients may be adjusted to reduce the bias and error so that the
MEPDG makes realistic predictions of measured pavement performance. The outcome of
the MEPDG calibration procedure is a new set of calibration coefficients specific to a state
or region for various distress predictions. For example, Table 3.3 lists the calibration
coefficients obtained by the WSDOT study (11). It is important to emphasize that these
coefficients are specific to WSDOT as they were calibrated to performance data in the
Washington State Pavement Management System (WSPMS).
Table 3.3 WSDOT MEPDG Calibration Results (data from 11)
Distress Coefficient
Original (National
Calibration) Value
Local Calibration
Value
AC Fatigue
f1 1 0.96
f2 1 0.945
f3 1 1.055
Longitudinal Cracking
C1 7 6.42
C2 3.5 3.8
C3 0 0
C4 1,000 1,000
Alligator Cracking
C1 1 1
C2 1 1
C3 6,000 6,000
AC Rutting
r1 1 1.05
r2 1 1
r3 1 1.06
Subgrade Rutting s1 1 0
3.3.2 Use MEPDG to Generate Pavement Thicknesses
Once the MEPDG has been well calibrated, it is possible to execute pavement designs under
a variety of conditions to determine the required asphalt concrete thickness. In the WSDOT
study, for example, Li et al. (11) developed pavement thicknesses under a range of traffic
levels and corresponding reliabilities as part of updating the WSDOT pavement design
catalog. They fixed the aggregate base thickness according to WSDOT construction practice
and experience and determined the required AC thickness using the local‐calibration
coefficients listed above in the MEPDG (11). Table 3.4 summarizes the required AC
thickness for the six traffic and reliability levels in the WSDOT design catalog.
Timm, Robbins,
Tran & Rodezno
31
Table 3.4 WSDOT Design Comparisons (data from 11)
50‐Year
ESALs,
Millions
Reliability
Base Thickness,
in.
AC Thickness by Method
MEPDG
AASHTO 1993
a1=0.44 a1=0.50
5 85% 6 6 7.5 6.5
10 85% 6 7.4 8.5 7.5
25 95% 6 9.0 11.2 9.9
50 95% 7 11.2 12.3 10.8
100 95% 8 12.1 13.3 11.8
200 95% 9 13.2 14.5 12.8
3.3.3 Recalibrate a1 to Match MEPDG Thicknesses
After establishing AC thicknesses for a range of pavement conditions with the MEPDG, the
AASHTO empirical procedure is used to determine corresponding AC thicknesses. Table 3.4
shows thicknesses resulting from the 1993 AASHTO Guide (2) assuming 0.44 as the default
structural coefficient. On average, using 0.44 results in pavements overdesigned by 1.4
inches. Li et al. (11) recalibrated a1 to 0.50 resulting in an average difference of 0.07 inches,
which was considered negligible. In other words, 0.50 better reflects the performance of
asphalt materials in Washington as characterized by actual pavement performance data and
modeling within the MEPDG.
The mechanistic‐empirical approach to recalibration using the MEPDG is the most data
intensive procedure. However, for states in the process of calibrating and implementing the
MEPDG, it may be a viable option. It also serves the dual purpose of providing similar
pavement design results with both the older empirical and newer M‐E procedures. This is
desirable since even when the new system is adopted, there may be many scenarios that do
not warrant its use and the empirical design system will be employed. It is important that
the empirical design system accurately reflect modern pavement performance.
4. CONCLUSIONS AND RECOMMENDATIONS
Though mechanistic‐empirical pavement design may gain widespread use across the U.S. in
the coming years, there is a need to update the AASHTO empirical pavement design system
to account for advances in pavement materials, construction and performance. Updating
the structural coefficient can help optimize asphalt pavement cross sections leading to
better use of financial and natural resources. This recalibration document described three
general approaches to recalibrating the asphalt structural coefficient, which are
summarized in Table 4.1. Based on the information provided in this document, the
following conclusions and recommendations are made:
1. The asphalt layer coefficient originally recommended by AASHO in 1962 (1) is not
necessarily applicable in all situations. Studies in Alabama (8) and Washington (11)
found a higher value better reflected actual performance. The values in each state
(Alabama = 0.54; Washington = 0.50) were remarkably similar despite geographical
Timm, Robbins,
Tran & Rodezno
32
distance and different approaches taken in the recalibration process. State agencies
might consider evaluating their value with respect to actual pavement performance.
2. Deflection‐based approaches can provide structural coefficients in a relatively short
time with relatively little data required. However, regression equations were developed
from past pavement performance observations that may not accurately reflect the
material under investigation. In the absence of historical performance records,
deflection‐based approaches may be considered to provide provisional structural
coefficients until the new coefficient is validated with material‐specific performance
data.
3. The performance‐based method used by Alabama (8) most closely replicates the
process used to develop the original AASHO structural coefficient. Though historical
traffic and performance records (i.e., IRI) are needed, the data are often readily
available and collected as part of routine pavement management activities in many
states.
4. The MEPDG approach is the most time and data‐intensive procedure to follow. It
should only be undertaken if MEPDG calibration activities are already in process or
completed. One could view this approach as an additional useful output of the MEPDG‐
calibration process, as it allows states to continue using the AASHTO empirical
procedure and produce pavement designs consistent between the MEPDG and
empirical approach.
5. The results of any recalibration investigation should be checked against the range of
original AASHO values and other investigations. The fact that the Alabama and
Washington coefficients after recalibration were so similar, despite very different
conditions and recalibration procedures, lends confidence to using the new values.
6. Local agencies or municipalities that may not have all the information required for
recalibration could still perform recalibration by utilizing existing information available
through state or other local agencies for similar roadways in their geographic regions.
Timm, Robbins,
Tran & Rodezno
33
Table 4.1 Summary of Methods
Procedure Type General Process Advantages Disadvantages
Deflection‐
Based
Conduct deflection testing on
existing pavement section.
Use deflection data to
backcalculate pavement
properties. Correlate
backcalculated properties to
structural coefficients using
pre‐existing equations.
Relatively rapid
procedure.
Requires only short‐
term data sets.
Relatively little
deflection testing
needed.
Does not
correlate to
section‐specific
performance.
Relies primarily
on past
correlation
studies.
Performance‐
Based
Pavement ride quality data
are used to quantify changes
in pavement serviceability
over time. These changes
are correlated to measured
traffic levels (Actual ESALs)
and the structural number
equation is used to provide
predicted traffic levels
(Predicted ESALs). The
structural coefficient is used
as a calibration coefficient to
minimize the error between
actual and predicted ESALs.
Most closely
replicates how the
original AASHO layer
coefficients were
determined.
Calibrates to actual
pavement
performance.
Relatively simple
method, once traffic
and performance
records have been
compiled.
Historical
performance data
needed.
Historical traffic
data (ESALs)
needed.
Mechanistic‐
Empirical
The MEPDG is locally
calibrated and used to
generate pavement thickness
designs. The asphalt layer
coefficient is then
recalibrated to provide
thicknesses that match the
MEPDG thicknesses.
Calibrates both
empirical and M‐E
approaches.
Calibrates to actual
pavement
performance.
Provides continuity
between design
systems.
Most intensive
procedure in
terms of required
data.
Requires
calibration of the
MEPDG, which is
a costly and time‐
consuming
process.
Timm, Robbins,
Tran & Rodezno
34
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1. Highway Research Board, “The AASHO Road Test”, Report 5, Pavement Research Special
Report 61E, National Academy of Sciences – National Research Council, Washington, DC,
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Association of State and Highway Transportation Officials, 1993.
3. Timm, D.H., M.M. Robbins, N. Tran and C. Rodezno, “Flexible Pavement Design – State
of the Practice,” National Asphalt Pavement Association, 2014.
4. AASHTO, Mechanistic‐Empirical Pavement Design Guide, A Manual of Practice, Interim
Edition, July 2008.
5. Pierce, L.M. and G. McGovern, “Implementation of the AASHTO Mechanistic‐Empirical
Pavement Design Guide (MEPDG) and Software,” Third Draft, NCHRP Project 20‐05,
Topic 44‐06, October, 2013.
6. George, K.P., “Structural Layer Coefficient for Flexible Pavement,” ASCE Journal of
Transportation Engineering, Vol. 110, No. 2, 1984, pp. 251‐267.
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D.C., 1972.
8. Peters‐Davis, K. and D.H. Timm, “Recalibration of the Asphalt Layer Coefficient,” Report
No. 09‐03, National Center for Asphalt Technology, Auburn University, 2009.
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Study,” Report No. 06‐01, National Center for Asphalt Technology, Auburn University,
2006.
10. Davis, K. and D. Timm, “Structural Coefficients and Life Cycle Cost,” Proceedings, T&DI
Congress 2011: Integrated Transportation and Development for a Better Tomorrow,
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MEPDG and Historical Performance to Update the WSDOT Pavement Design Catalog,”
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Rubber‐Modified Asphalt Concrete Mixtures,” Transportation Research Record No.
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Timm, Robbins,
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18. Holman, F., Guidelines for Flexible Pavement Design in Alabama. Alabama Department
of Transportation, 1990.
19. Hall, K.T., and C.E.C. Munoz, Estimation of Present Serviceability Index from
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Research Board, Washington, D.C. 1999.
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Research Board, Washington, D.C. 1994.
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Company, New York, New York, 1994.
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Guide,” American Association of State Highway and Transportation Officials,
Washington, D.C., 2010.