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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

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

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

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.

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

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

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

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 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

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.

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,

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

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

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

FWD test,

4) Correct any deflections taken directly on the pavement, or asphalt cement concrete (ACC), to 68°

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.

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

and

DGCS

ACC

SNeff=10.71

FWD
FWD
FWD

SNeff=5.37

SNeff=1.52

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.

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

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.

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

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

individually incapable.

ACC Layer Coefficients vs. Depth to Subgrade

0.2

0.4
0.6

0.8

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

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)

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.

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

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.

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.

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

Dr. Dennis R. Hiltunen, P.E.
Principal Investigator

DEPARTMENT OF CIVIL & COASTAL ENGINEERING

UNIVERSITY OF FLORIDA

December 201

DISCLAIMER

The opinions, findings, and conclusions

expressed inthis 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.

METRIC CONVERSION TABLE

4
METRIC CONVERSION TABLE

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

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-

12. Sponsoring Agency Name and Address

Florida Department of Transportation
605 Suwannee Street, MS

Tallahassee, FL 3239

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

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.

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

LIST OF FIGURES

Figure page

1 Variation in Granular Base Layer Coefficient (a2) with Various

Material Parameters (from AASHTO 1993)

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

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.

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.

 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

(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

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.

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

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

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

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

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

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

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.

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

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.

 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.

 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

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

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

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.

CHAPTER 5
CONCLUSIONS

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.

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.

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.

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.

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

RECALIBRATION PROCEDURES FOR THE

STRUCTURAL ASPHALT LAYER COEFFICIENT IN

THE 1993 AASHTO PAVEMENT DESIGN GUIDE

Dr. David H. Timm, P.E

Dr. Mary M. Robbins

Dr. Nam Tran, P.E.
Dr. Carolina Rodezno

November 2014

Timm, Robbins,
Tran & Rodezno

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

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

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

3.3.3. Recalibrate a1 to Match MEPDG Thicknesses ………………………………………………. 31

4. Conclusions and Recommendations …………………………………………………………………………… 31
5. References ……………………………………………………………………………………………………………… 35

Timm, Robbins,
Tran & Rodezno

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

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) …………………………………………………………

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. 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

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

(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

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

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

Present Serviceability Index

0
5

Traffic, ESALs

PSI = p0‐pt

Timm, Robbins,
Tran & Rodezno

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.

109

5.12.4
log

20.01log36.9log

19.

018 



















 RR M

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)

a1*D1

+a2*m2*D2

+a3*m3*D3

SN =

Timm, Robbins,
Tran & Rodezno

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

SN1 = a1*D1

SN2 = a1*D1+a2*m2*D2

D2
SN a ∗

a ∗ m

SN3 = a1*D1+a2*m2*D2+a3*m3*D3

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

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

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

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),

0.1

0.2

0.3

0.4

0.5

0 1 2 3 4 5

HMA Elastic Modulus at 70
o
F (

5
psi)

S
tr

u
c

tu
r

l
C

o
e

ie
n

t
(a

1
)

Timm, Robbins,
Tran & Rodezno

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

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

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

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

Deflection9000 = 0.0024*9000+3.1322
= 24.732 milli-in

Deflection = 0.0002*Load – 0.319

R
2
= 0.99

Deflection9000 = 0.0002*9000-0.3196
= 1.480 milli-in

0
5
10

1
0

0
0

0
0
0

3
0
0
0

4
0
0
0

5
0
0
0

6
0
0
0

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

e
c

ti
o

,
m

il
li

-i

n
.

AASHTO Reference Load = 9,000 lb

S9 – Location 1
July 26, 2010

Timm, Robbins,
Tran & Rodezno

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

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

The first step in the AASHTO backcalculation approach is to determine the soil modulus
according to (2):

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):

















p
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

p
R

a
D

M
E
a
D
M

2
2
3
1
1
1
1
1

1
**5.1

Timm, Robbins,
Tran & Rodezno

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

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

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

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

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

Crumb Rubber
Asphalt Concrete

a1 = 0.315*log(EAC) – 1.732
where EAC = AC modulus, MPa

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

2.5

3.5

4.5

S8 S9

A
ve

ra
g

e
S

N
e

SN = 0.45

15.0
35.1

45.022.1*54.0








OGFC

surfacecontrolcontrol
OGFC

a
D

SNDa
a

Timm, Robbins,
Tran & Rodezno

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

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)

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

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

PSI

RPSI
AvgPSI
P

Pt calibration points

Timm, Robbins,
Tran & Rodezno

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):

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

tx GGLLL
W

W









(Equation 14a)













5.12.4

2.4
log tt

p
G (Equation 14b)

 
  23.32

19.5

23.3
2

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

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

(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

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

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

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

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

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

0
0
3

1
2

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

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

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

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

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

5. REFERENCES
1. Highway Research Board, “The AASHO Road Test”, Report 5, Pavement Research Special

Report 61E, National Academy of Sciences – National Research Council, Washington, DC,
1962.

2. AASHTO Guide for Design of Pavement Structures. Washington D.C.: American
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.

7. AASHO, “AASHO Interim Guide for Design of Pavement Structures‐1972,” Washington,
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.

9. Timm, D.H. and A.L. Priest, “Material Properties of the 2003 NCAT Test Track Structural
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,
Proceedings of the First T&DI Congress 2011, American Society of Civil Engineers,
Chicago, IL, 2011, pp. 646‐655.

11. Li, J., J.S. Uhlmeyer, J.P. Mahoney and S.T. Muench, “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, 2011.

12. Kuennen, T., “How Alabama Gets More Bang for Its Asphalt Buck,” Volume 15, No. 1,
Hot Mix Asphalt Technology, January/February 2010, 30‐35.

13. FHWA, “LTPP Manual for Falling Weight Deflectometer Measurements Operational Field
Guidelines,” Version 3.1, August 2000.

14. Timm, D.H., A. Vargas‐Nordcbeck, “Structural Coefficient of Open Graded Friction
Course,” Transportation Research Record 2305, Transportation Research Board, 2012,
pp. 102‐110.

15. Hossain, M., A. Habib and T.M. LaTorella, “Structural Layer Coefficients of Crumb
Rubber‐Modified Asphalt Concrete Mixtures,” Transportation Research Record No.
1583, Transportation Research Board, 1997, pp. 62‐70.

16. Ullidtz, P., “Pavement Analysis,” Elsevier, N.Y., 1987, pp. 221‐223.
17. Gulen, S., R. Woods, J. Weaver, and V.L. Anderson, Correlation of Present Serviceability

Ratings with International Roughness Index. Transportation Research Record 1435,
Transportation Research Board, Washington, D.C. 1994.

Timm, Robbins,
Tran & Rodezno

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
International Roughness Index. Transportation Research Record 1655, Transportation
Research Board, Washington, D.C. 1999.

20. Al‐Omari, B. and M.I. Darter, Relationships between International Roughness Index and
Present Serviceability Rating. Transportation Research Record 1435, Transportation
Research Board, Washington, D.C. 1994.

21. Huang, Y.H., Pavement Analysis and Design. 2nd ed. New Jersey: Prentice Hall, 2004.
22. McClave, J.T. and F.H. Dietrich II, Statistics, Sixth Edition, MacMillan College Publishing

Company, New York, New York, 1994.
23. AASHTO, “Guide for the Local Calibration of the Mechanistic‐Empirical Pavement Design

Guide,” American Association of State Highway and Transportation Officials,
Washington, D.C., 2010.

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