Reference Manual
Module 2-3. Nondestructive Testing and Data Analysis
MODULE 2-3. NONDESTRUCTIVE TESTING AND DATA
ANALYSIS
1. INSTRUCTIONAL OBJECTIVES
This module presents the concepts and procedures for conducting nondestructive testing (NDT) on an
existing HMA pavement using deflection testing equipment. Also described are the procedures for
processing and interpreting the deflection testing data, including the use of backcalculation techniques.
The participant should be able to accomplish the following upon completion of this module:
1. Describe how an HMA pavement responds to load.
2. List some of the available pavement deflection measuring devices and their operating
characteristics.
3. List the major factors that influence HMA pavement deflections.
4. Describe procedures for conducting NDT on a typical highway project.
5. Describe the uses of NDT data.
6. Describe the basic principles and procedures for backcalculation.
2. INTRODUCTION
NDT refers to a wide variety of in situ tests that can be conducted on any structure without involving
physical testing of samples obtained from the structure or destructive testing of the samples that are
representative of the in-place material. The focus of this module is a specific class of NDT devices that
can be used to quantify a pavement’s ability to support traffic loads, namely deflection testing. In the
context of NDT, deflection refers to the vertical displacement of the pavement surface in response to
simulated wheel loads.
Deflection testing is an extremely valuable engineering tool for assessing the uniformity and structural
adequacy of existing pavements (Tabrizi, Ganji, and Sauber 2000; Garg and Thompson 1999; Alvarez
and Thompson 1998; Zhou, Rada, and Elkins 1997). Numerous types of equipment are available for
pavement deflection testing that are robust and capable of producing repeatable results. Many of the
equipment also have a high production rate. For example, the production rate for a falling weight
deflectometer (FWD) is up to 400 measurements per day. The high productivity of NDT makes it
feasible to collect an extensive amount of data along the length of the project, which is important for
assessing variability in condition along the project.
NDT data can be analyzed to determine various characteristics of the pavement structure that are
extremely valuable in rehabilitation design, including the following:

Pavement layer and subgrade moduli values.

Variability in the pavement structure and subgrade stiffness along the project.

Seasonal variation in base and subgrade soil stiffness and pavement response.
Many states operate NDT equipment as part of their network- and project-level evaluation needs. The
emphasis of this module is on project-level applications.
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3. HMA PAVEMENT RESPONSE
Pavement deflections represent an overall “system response” of the pavement structure and subgrade soil
to an applied load. When a load is applied at the surface, all layers deflect, creating stresses and strains in
each layer, as illustrated in figure 2-3.1. For HMA pavements, the critical pavement responses under a
wheel load are the following:

Maximum deflections immediately beneath the wheel load.

Tensile strain at the bottom of the HMA surface and asphalt-treated base layers.

Vertical strain in the base/subbase layers.

Vertical strain at the top of subgrade soil.
Axle
Load
 Surface
HMA Surface
Base/Subbase
Subgrade Soil
Surface = Surface deflection
HMA = Tensile strain at the bottom
of HMA surface layer
 HMA
 Base
Base
 Subgrade
Subgrade = Vertical strain at the
top of subgrade soil
= Vertical strain in the base/
subbase layer
Figure 2-3.1. Illustration of HMA pavement responses to a wheel load.
Figure 2-3.2 illustrates the effects of the “strength” of a pavement structure on deflection profile. As
shown in this figure, the deflection profile reflects the structural capacity of the pavement. A “stronger”
pavement exhibits a flatter deflection profile, because it is able to spread the load to a larger area. The
deflection profile also reflects the stiffness of the pavement structure relative to subgrade soil stiffness.
These relationships can be used to determine (backcalculate) the moduli values of pavement layers and
subgrade soil.
NDT Load
“Strong”
Pavement
“Weak”
Pavement

Figure 2-3.2. Illustration of the effects of pavement structure on deflection profile.
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4. TYPES OF NDT EQUIPMENT
The four general classes of NDT deflection equipment currently available are: static load deflection
equipment, steady-state vibratory load deflection equipment, impulse load deflection equipment, and
surface wave propagation equipment (Hudson et al. 1987). The key factors that must be considered in the
selection of an NDT device for pavement evaluation include the following (Lytton et al. 1990):




Operational characteristics

Data collection and recording ability.

Traffic delay.

Calibration requirements.

Transportability.

Training requirements.
Data quality

Data format.

Repeatability.

Accuracy.
Versatility

Number of sensors.

Sensor configuration.

Range of load levels.
Cost

Capital cost.

Operating cost.
Static Load Deflection Equipment
Static load deflection equipment measures the maximum deflection response of a pavement to static or
slowly applied loads. The most commonly used static deflection device is the Benkelman Beam. Figure
2-3.3 shows a sketch of the basic components of the Benkelman Beam. The deflection measurements are
made using the standard procedures presented by either AASHTO (1990) or the Asphalt Institute (1987).
Other static deflection devices used include the Plate Bearing Test Equipment and the Curvature Meter,
which are described in Asphalt Institute (1988) and CALTRANS (1978). In some cases, the static load
deflection equipment are automated, providing a slowly moving load. Examples of automated static
deflection equipment are the La Croix Deflectograph and the California Traveling Deflectometer (Lytton,
Moore, and Mahoney 1975; CALTRANS 1978).
Advantages of the Benkelman Beam include ease of use, low equipment cost, and the existence of a large
database from its use over many years. The major technical problems associated with the Benkelman
Beam include the following:

The difficulty of ensuring that the front supports are not in the deflection basin.

The difficulty or inability to determine the shape and size of the deflection basin.
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Figure 2-3.3. Basic components of the Benkelman Beam.

Poor repeatability of measurements obtained by the device.

The labor intensive and cumbersome nature of the device.
In addition to the problems noted above, a major technical problem associated with the static load
deflection devices is the method of load application. The static or quasi-static loading employed does not
accurately represent the effects of a moving wheel load.
Steady-State Dynamic Load Deflection Equipment
Steady-state dynamic load deflection devices apply a static preload and a sinusoidal vibration to the
pavement with a dynamic force generator (figure 2-3.4). A series of sensors is located at fixed intervals
to measure the resulting deflection. To ensure that the device does not bounce off the pavement surface,
the magnitude of the peak-to-peak dynamic force (high to low) must be less than twice the static preload.
Consequently, the static preload must be increased as the dynamic load is increased. The most common
devices in this category are the Dynaflect and Road Rater.
Load
Static
load
0
Dynamic force
(peak-to-peak)
Time
Figure 2-3.4. Typical output of vibrating steady-state force generator.
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Module 2-3. Nondestructive Testing and Data Analysis
The normal sequence of operation is to move the device to the test point and hydraulically lower the
loading wheels and transducers to the pavement surface. A test is run, the data recorded, and the device
moved to the next site. In general, these devices are rapid, repeatable, and robust. In addition, they
record the entire deflection basin, which is needed for backcalculation.
While steady-state vibratory load equipment is an improvement over static load deflection equipment (in
that a reference point is not needed), the static preload still presents a technical problem. The static
preload in most cases is relatively large in comparison to the maximum peak-to-peak loading. Since most
paving materials are stress-sensitive (fine-grained soils exhibit stress softening and coarse-grained
materials exhibit stress hardening), their stress states and stiffness may be modified by the static preload.
In addition, the frequency of loading affects the resultant deflection, and it is difficult to establish a load
frequency that matches that of moving vehicles.
Impulse Load Deflection Equipment
Impulse load deflection equipment delivers a transient impulse force to the pavement. A weight is lifted
to a given height on a guide system and then dropped onto a buffering plate on the pavement. A transient
impulse force, which can be changed by varying the magnitude of the falling weight or by varying the
drop height, is generated in the pavement by the impact of the falling weight. This is illustrated in figure
2-3.5. A series of sensors is located at various distances from the load plate to measure pavement
deflections. Commercial impulse load deflection devices include the Dynatest, KUAB, JILS, and Phonix
FWDs.
Force exerted
on pavement
C
A
B
Time
A - Time at which load is released
B - Load makes first contact with the load plate
C - Peak load reached
Figure 2-3.5. Typical load pulse produced by falling weight deflectometer.
In the normal sequence of operation, the device is moved to a test point and the loading plate and
transducers are hydraulically lowered to the pavement. A test sequence is then completed with generally
a seating drop followed by three drops at different load levels (typically 40, 53, and 71 kN [9,000, 12,000,
and 16,000 lb] for highway testing). The pavement deflection under each drop is recorded automatically.
The loading plate and sensors are then hydraulically lifted and the device is moved to the next test site.
Devices capable of conducting the tests while moving (rolling deflectometer) are currently under
development.
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A major advantage of the impulse loading devices is their ability to more accurately model a moving
wheel load in both magnitude and duration, thus producing a deflection that simulates the pavement
deflection caused by a moving vehicle. In addition, as illustrated in figure 2-3.5, a relatively small
preload is applied in comparison to the impulse load generated. This preload varies with the equipment
used, but is usually in the range of 8 percent to 18 percent of the maximum impulse load, prior to the
release of the weights. During the period when the weights are dropping, this preload normally falls to
the range of 5 percent to 14 percent of the maximum impulse load.
Numerous factors make FWD the equipment of choice for pavement deflection testing, including the
following:

The ability to better simulate a moving wheel load.

The ability to measure deflections at varying loads over time.

The ability to record a deflection basin.

The speed, repeatability, and robustness of the equipment.
Surface Wave Propagation
An alternate means of nondestructive testing is through the spectral-analysis-of-surface-waves (SASW)
method. If a pavement structure is subjected to a vertical impact, surface waves propagate downward and
laterally away from the location of the vertical impact. The surface waves are recorded by vertical
receivers placed at predetermined distances (based on the wavelength of the test) from the point of
impact. Since the velocity of the propagation is a direct indicator of the stiffness of the material, the shear
and elastic modulus of the paving layers can be backcalculated by using relationships based on seismic
analysis and elastic layer theory.
While SASW methods are not new (procedures for conducting the analysis were introduced in the 1950s),
their use in pavement applications had been somewhat limited. Several field demonstrations of SASW
equipment have been conducted and procedures for analyzing highway pavements with SASW are
reported in Gucunski and Krstic (1996); Sanchez-Salinero et al. (1987); Sheu, Stokoe, and Roesset
(1988); Nazarian et al. (1988); and Rix, Bay, and Stokoe (1990). An automated device known as the
seismic pavement analyzer (SPA) has been developed and is being tested in Texas (Nazarian, Baker, and
Crain 1993; Nazarian, Yuan, and Baker 1995).
5. FACTORS THAT INFLUENCE MEASURED DEFLECTIONS
Numerous factors can influence the magnitude of measured pavement deflections, which makes the
interpretation of deflection results difficult. Proper consideration of the factors that affect pavement
deflections is important, because they can affect the backcalculation results. In this section, three primary
factors that influence pavement deflection are discussed: load, pavement, and climate.
Load Factors
The type and magnitude of the applied load influences the deflection response of the pavement. As the
load increases, the pavement deflection will also increase. However, the relationship may not be linear,
since most subgrade soil and granular materials are stress dependent. The non-linearity of the loaddeflection relationship is illustrated in figure 2-3.6. In figure 2-3.6, the extrapolated deflection at 40 kN
(9,000 lb) based on a 4.4-kN (1,000-lb) load is significantly less than that obtained using an actual 40-kN
(9,000-lb) load. Because of the potential for significant error, deflection testing should be conducted
using equipment that is capable of producing a load in the range of the actual traffic load. Traffic loads
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Module 2-3. Nondestructive Testing and Data Analysis
0.40
Measured 40-kN deflection
0.35
Measured deflection:
40-kN = 0.35 mm
Deflection (mm)
0.30
Projected 40-kN deflection
0.25
Projected deflection:
40-kN = 0.25 mm
0.20
0.10
25.4 mm =1 in
1 kN = 224.8 lb
0.028
0
10
20
30
Load (kN)
40
50
Figure 2-3.6. Pavement deflection as a function of dynamic load.
are most closely simulated by an FWD. The use of this type of equipment eliminates the problems
encountered in extrapolating heavy load responses based on pavement response to light loads.
Several agencies have developed correlations between light and a heavy load deflection devices (figure
2-3.7). These are used to convert deflections measured with a light load device into equivalent
deflections for heavier, design loads. However, such correlations must be used with great caution because
of the following:

The data from which these relationships are developed typically contain a large amount of scatter.
Thus, the correlation could lead to a large error.

The correlations made for one type of pavement/subgrade soil structure may not be applicable to
a different structure.
Even when the magnitude of the load applied by different types of devices is the same, the deflection
response may differ. This is because different types of load tend to produce different pavement
responses. One main factor that distinguishes the type of loading is load duration. The duration of
loading associated with an NDT device causes the deflections to vary. Faster moving vehicles produce
shorter load pulses and lower deflections. For example, static load devices tend to produce deflections
significantly larger than those produced by moving wheel loads.
The response of steady-state dynamic deflection devices vary with the load frequency. This is illustrated
in figure 2-3.8. Impulse load deflection devices produce surface deflections that most closely simulate
the deflections produced by a moving wheel load. Lytton, Moore, and Mahoney (1975) provides further
discussion of the effects of the equipment factors on measured pavement response.
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Traveling deflectometer (0.001 in)
100
80
60
40
20
0
0.0
1.0
2.0
3.0
4.0
Dynaflect deflection (0.001 in)
Figure 2-3.7. Correlation between light load (Dynaflect) and heavy load (Traveling Deflectometer) NDT
equipment (Lytton, Moore, and Mahoney 1975).
Figure 2-3.8. Variation of deflection with frequency of loading (Moore et al. 1978).
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Module 2-3. Nondestructive Testing and Data Analysis
Pavement Factors
Numerous pavement factors can cause variations in pavement deflections, including the following:

HMA pavement deflections in or near distressed areas (e.g., alligator cracking, linear cracks) are
typically much higher than those in nondistressed areas, as illustrated in figure 2-3.9.

Deflections in wheelpaths are typically higher than that between wheelpaths in HMA pavements.

Variations in subsurface conditions can cause significant variations in deflections. The effects of
subgrade soil type on seasonal variations in pavement deflections are illustrated in figure 2-3.10.
The presence of underlying hard layers (bedrock or high water table) also affects pavement
deflections.

Cut sections, sections at grade, and fill sections may exhibit significantly different deflections
(Khogali and Anderson 1996).

Random variations in factors such as layer thickness, compaction, and material properties
(including water content) can cause a high variation in deflections along a typical project, even at
close intervals (e.g., 3 m [10 ft]).

The condition of the interface between the surface and treated base layers can significantly affect
pavement deflection. If the interface is effectively bonded (no slip at the interface), the pavement
deflection will be significantly less than if the interface is unbonded.
2.5
Deflection (mm)
2.0
1.5
1.0
0.5
0
Alligator Cracking
2
4
6
8
Station
10
12
14
16
1 in =25.4 mm
Figure 2-3.9. Effect of alligator cracking on deflections in a HMA pavement (40kN load).
The coefficient of variation for deflection measurements along a project is typically 20 to 30 percent. To
ensure that obvious pavement factors such as presence of cracks, visible material deterioration, or visible
structures do not falsely indicate variability in pavement deflections, care must be taken during deflection
testing to avoid testing over such features. (Alternatively, the presence of such features should be noted
in the testing log). It is important to note that accurate layer thicknesses are needed to properly interpret
the deflection test data. Pavement deflection is sensitive to layer thicknesses, especially the thickness of
the surface layer. If not available from original plans or specifications, layer thicknesses may be obtained
from cores or borehole logs.
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3.0
1 in =25.4 mm
Deflection (mm)
2.5
Clay
2.0
Silty Clay
1.5
Poorly Drained Silty Clay
1.0
Well Drained Sand
0.5
0
MAR
JUNE
SEPT
DEC
Time of Year
Figure 2-3.10. Influence of subgrade type on seasonal pavement deflection variations.
Climatic Factors
Climatic factors affect pavement deflections on a daily and seasonal basis. The effects of both
temperature and moisture can be significant. As the mean HMA layer temperature increases, the
pavement deflection increases, as illustrated in figure 2-3.11. This is a result of asphalt softening at high
temperatures. The effects of seasonal conditions on pavement deflections are illustrated in figure 2-3.12.
There are four distinct seasons in cold climatic areas (Scrivner et al. 1969):

A period of deep frost when the pavement is the strongest and the measured deflection the lowest.

A thaw period during which the frost begins to disappear from the pavement/subgrade soil system
and the deflection increases greatly.

A period during which the excess free water from the melting frost leaves the pavement/subgrade
soil structure, the soil begins to recover, and the deflection decreases.

A period during which the deflection levels off as water content slowly decreases.
Normal Procedure Deflection (mm)
Loop 3 sections
1.0
3” surfacing
2” surfacing
4” surfacing
0.5
1 in =25.4 mm
ºF = ºC * 9 / 5 + 32
0
10
20
30
o
Surfacing Temperature, C
Figure 2-3.11. Influence of temperature on flexible pavement deflection
(Bushey, Baumeister, and Mathews 1976).
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Module 2-3. Nondestructive Testing and Data Analysis
Period of
Strength Loss
Period of Rapid
Strength Recovery
Period of
Deep Frost
DEFLECTION
Period of Slow
Strength Recovery
DEC JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV
TIME
Figure 2-3.12. Influence of season on pavement deflection (Lytton, Moore, and Mahoney 1975).
For pavements in areas that do not experience freeze-thaw, deflections follow a flatter "sine wave," with
the peak deflection occurring in the wet season where significant free moisture exists. In relatively dry
areas, the period of maximum deflection on flexible pavements may occur in the hot summer when the
asphalt surface softens due to high temperatures (Poehl 1971).
The effects of moisture and temperature conditions on pavement deflections are also reflected in seasonal
deflections of HMA pavements constructed on different types of bases. Figure 2-3.13 shows seasonal
variations in deflection of AASHO Road Test sections with different types of base (HRB 1962). The
aggregate base section exhibited the highest deflection during spring thaw when the pavement was
exposed to excess free water. This indicates that, for the aggregate base section, the effects of excess
CS = CRUSHED STONE
AC = ASPHALT BASE
CT = CEMENT BASE
3.0
CS
100 mm HMA
2.5
Deflection (mm)
225 mm Base
100 mm Subbase
2.0
CS
1.5
CT
AC
CT
CS
1.0
CS
CT
AC
0.5
AC CT
FALL
AC
SPRING SUMMER
SEASON
FALL
Figure 2-3.13. Pavement deflection as a function of base type and season (HRB 1962).
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moisture far outweigh the effects of HMA softening during the summer months. The treated base
sections, which are less sensitive to moisture effects than aggregate base sections, exhibited the highest
deflection during the summer months. This is an indication that, for the treated base sections, the effects
of HMA softening during hot summer months are more significant than the effects of excess moisture.
It is important to consider the time of day and the season when scheduling an NDT program and when
interpreting NDT results. Deflection measurements should be corrected to a standard temperature
(typically 21 ºC [70 ºF]) and critical season equivalent deflections based on locally developed procedures.
6. CONDUCTING NDT FIELD SURVEYS
The NDT deflection testing (ASTM D 4695; AASHTO T256) must be conducted in conjunction with
information from the distress survey. NDT should be completed prior to any destructive testing to assist
in locating areas where sampling and testing will be conducted. When NDT data are used in a deflectionbased overlay design procedure, obtaining a series of deflection measurements throughout the year is
desirable to characterize the seasonal variations in pavement/soil structure strength. The AASHTO Guide
for Design of Pavement Structures makes provision for determining an effective year-round subgrade soil
modulus value based on estimates of soil strength for each season (AASHTO 1993).
The current FHWA Long-Term Pavement Performance program has an on-going study to evaluate
seasonal variations as part of its Seasonal Monitoring Program. When these data become available, they
should help highway agencies better address the effects of seasonal variations. For the time being
(because it is impractical to measure deflections throughout the year), the next best practice is to measure
pavement deflections at a time that best represents the effective year-round condition.
In climates where frost penetrates into the subgrade soil during winter, the best time for NDT testing may
be shortly after the spring thaw, after the soil has regained some of its strength. Testing during the spring
thaw is not recommended because it is likely to produce overly conservative results. The deflection
survey should never be conducted when the pavement or subgrade soil is frozen, because misleading
information will be obtained (Hall, Darter, and Kuo 1995).
Temperature Measurements
The pavement temperature must be measured periodically throughout the duration of testing when
conducting an NDT deflection survey so that the deflections or backcalculated moduli can be corrected to
a standard temperature. A relationship can be developed by locating a few points on the pavement and
repeatedly measuring deflections at those points throughout the day, typically from very early morning to
late afternoon. Air and pavement temperatures and deflections should be measured every hour and the
results plotted to determine the temperature-deflection relationships. The locations selected should be
representative of those at which the deflection measurements will be taken over the entire project (i.e.,
wheelpaths). Using this data, a temperature correction curve can be developed for the project so that the
deflections can be adjusted to a standard temperature (such as 21ºC [70 ºF]) if required by overlay design
procedures or for comparing deflections along the project (Asphalt Institute 1987).
As a minimum, the air and pavement surface temperatures should be recorded at each test location
(ASTM D 4695). The measurement of the mid-depth temperature of the HMA surface layer is also
recommended. The mid-depth temperature of HMA surface can be obtained by drilling a hole in the
pavement at appropriate depth. If drilling is not possible, then pavement surface temperatures should be
obtained along with a 5-day average of air-temperatures to estimate the layer temperatures (Lukanen,
Stubstad, and Briggs 2000; Roberts, Mann, and Curtis 1977). Many deflection-testing devices
automatically record the air and pavement surface temperatures during testing.
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Module 2-3. Nondestructive Testing and Data Analysis
Testing Locations and Frequency
HMA pavement deflections should be measured in the outer wheelpath in each lane at 30- to 150-m (100to 500-ft) intervals. On multiple-lane facilities, it is normally sufficient to take measurements only in the
outer or truck lane. However, it may be desirable to take measurements in one or more additional lanes if
the extent of load-associated distress varies greatly across lanes. On two-lane highways, the profiles in
each direction should be staggered. The suggested testing pattern is shown in figure 2-3.14 for divided
highways and figure 2-3.15 for two-way traffic.
Inner lane
Traffic
Outer lane
Traffic
Outer wheel path
30- to 150-m intervals
Figure 2-3.14. Recommended NDT deflection testing pattern for divided highways.
30- to 150-m intervals
Outer wheel path
Traffic
Traffic
Outer wheel path
30- to 150-m intervals
Figure 2-3.15. Recommended NDT deflection testing pattern for two-way traffic.
Intensive Deflection Testing
If further information is needed to ascertain either the cause or extent of certain distress types (e.g., soft
areas, delamination, HMA stripping), an intensive deflection test program may be required. Specific
areas of intensive testing along the project can be selected so that deflection measurements may be taken
at close intervals. These tests should be closely coordinated with any coring tests that may be conducted
at the same time.
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7. INTERPRETATION OF NONDESTRUCTIVE TEST DATA
The NDT deflection data should be used in conjunction with the distress, drainage, materials, and
subgrade soil test results to determine the pavement structural condition. Several ways that deflection
data are interpreted are discussed in this section.
Uniformity of Project
Normalized maximum deflection, mm
The deflection data can be normalized to a standard load (e.g., 40-kN [9,000-lb]) and plotted as shown in
figures 2-3.16 to graphically evaluate the variation along the project. The deflections should be
referenced directly to stationing so that they can be related to the distress, drainage, materials, and
subgrade soil surveys. The deflection profile along the project may be examined to determine if
significant variability exists in the pavement’s structural response along the length of the project. The
deflection profile should be compared with the results from the distress, drainage, materials, and subgrade
soil surveys to identify the possible causes for areas of high or low deflections. Plotting and comparing
deflection profile, distress, and subgrade soil properties/types on strip maps can accomplish this. It may
be advantageous to conduct the NDT evaluation after the distress survey, but before subgrade soil and
materials testing, to assist in locating areas where the more intensive tests will be required. Based on all
of this information, the project may be divided into two or more “design sections.” Each design
section may be treated separately for rehabilitation design purposes. For example, the overlay design or
subdrainage design may be different for each of the distinct design sections.
0.75
25.4 mm = 1 in
1 m = 3.28 ft
0.50
0.25
0
0
1000
2000
3000
Distance Along Roadway (m)
Figure 2-3.16. Illustration of deflection variation along a project.
Backcalculation
“Backcalculation” is the accepted term used to identify a process whereby the fundamental engineering
properties of the pavement structure (layer moduli values) and underlying subgrade soil (subgrade
resilient modulus) are estimated based on measured surface deflections. The process can be illustrated
using the case of a simply supported beam (figure 2-3.17). Given the dimensions of the beam (length,
height, and width), the load magnitude and position and the measured deflection at midspan, it is possible
to “backcalculate” the elastic modulus (E) of the beam.
2-3.14
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Module 2-3. Nondestructive Testing and Data Analysis
P
h
D
b
L/ 2
L
P = load
b = width
L = length h = height
Figure 2-3.17. Illustration of simply supported beam with a concentrated load at midspan.
From fundamental engineering mechanics, the equation for calculating the midspan deflection is:
PL3
D
48EI
where:

(2-3.1)
D = Measured midspan deflection, mm (in).
P = Applied load, N (lbf).
L = Length of the beam, mm (in).
I = Moment of inertia for a rectangular beam (I = bh3/12), mm4 (in4).
E = Elastic modulus of the beam, MPa (lbf/in2).
By substituting the known values of D, P, L, b, and h, the elastic modulus of the beam (E) can be
backcalculated.
While similar in concept, the process is more complicated for pavements because pavement deflection is
affected by subgrade resilient modulus as well as the moduli of the pavement layers (all unknown values).
In the beam example, the elastic modulus of the beam was the only unknown. Another complicating
factor is that the equations for HMA pavement surface deflection (or any other pavement response) are
not closed form.
Figure 2-3.18 illustrates the traditional model of an HMA pavement under an NDT load (AASHTO
1993). The pavement is viewed as a multi-layered elastic system, and deflections are measured at radial
offset, from the center of the load plate to define the deflection basin. The typical approach to
backcalculation for HMA pavements involves an iterative process in which an elastic layer program is
used to determine theoretical deflections. In the first iteration, assumed layer moduli (a.k.a., "seed"
moduli) are used to determine a theoretical deflection basin, which is then compared with the measured
deflection basin. The moduli are then adjusted and the deflections recalculated until the calculated
deflections match the measured values. An example of this iterative procedure is illustrated in table
2-3.1.
HMA Pavement Evaluation and Rehabilitation
2-3.15
Module 2-3. Nondestructive Testing and Data Analysis
Reference Manual
Figure 2-3.18. Schematic of stress zone under the FWD load (AASHTO 1993).
Table 2-3.1. Example of an iterative backcalculation solution for a three-layer HMA pavement.
Trial Moduli , MPa
E2
E3
E4
1
2
Predicted Deflections, mm
3
4
5
6
7
Average
Difference*
Iter.
E1
1
1,724
276
138
690
0.276 0.201 0.166 0.132 0.108 0.075 0.040
20.5%
2
1,724
276
207
345
0.238 0.167 0.136 0.105 0.083 0.055 0.031
36.4%
3
1,724
207
103
276
0.335 0.257 0.218 0.177 0.147 0.104 0.058
5.9%
4
1,793
224
107
297
0.320 0.245 0.208 0.169 0.141 0.100 0.056
1.3%
5
1,862
224
107
297
0.316 0.243 0.207 0.169 0.141 0.100 0.056
0.9%
Measured Deflections, mm:
0.309 0.243 0.208 0.171 0.140 0.099 0.054
*Calculated average difference between measured and predicted deflections for all sensors.
1 Mpa = 145 lbf/in2
0.0254 mm = 0.001 in
The underlying assumption in the backcalculation process is that a set of layer moduli exists that yields
calculated deflection values that match the measured deflections. It is important to note, however, that
the solution may not be unique. More than one set of moduli values can yield the same deflection profile.
To obtain good results, engineering judgment must be used to ensure that the modulus value selected for
each layer is within a reasonable range for the material type. Backcalculation results can be highly
variable due to variability in pavement condition, subsurface condition, material properties, and pavement
structure along the project.
2-3.16
HMA Pavement Evaluation and Rehabilitation
Reference Manual
Module 2-3. Nondestructive Testing and Data Analysis
Typical modulus values for paving materials are given in table 2-3.2. For the backcalculation process to
work, it requires the thickness and Poisson’s ratio must be supplied for each layer. Accurate layer
thickness information is important to obtain accurate backcalculation results. The layer thicknesses can
be determined based on cores or design thicknesses. Analysis of ground penetrating radar (GPR) may
also be used to estimate layer thicknesses. For Poisson’s ratio, the common practice is to use typical
value based on the type of material. The typical values for various materials are given in table 2-3.3.
Table 2-3.2. Typical moduli values for common paving materials.
Material
General range (MPa)
Typical value (MPa)
1,500 - 3,500
3,000
20,000 - 55,000
30,000
Asphalt-Treated Base*
700 - 6,000
1,500
Cement-Treated Base
3,500 - 7,000
5,000
Lean Concrete
7,000 - 20,000
10,000
Granular Base
100 - 350
200
Granular Subgrade Soil
50 - 150
100
Fine-Grained Subgrade Soil
20 - 50
30
Hot-Mix Asphalt*
Portland Cement Concrete
*Highly temperature dependent. The modulus values are based on pavement temperatures in the range
20 ºC to 30 ºC (68 ºF to 86 ºF).
1 Mpa = 145 lbf/in2
Table 2-3.3. Typical Poisson ratio values (AASHTO 1993).
Material
General range
HMA/Asphalt
Treated Base
0.15 - 0.45
Portland cement
Concrete
0.10 - 0.20
Cement stabilized
Base
0.15 - 0.30
Granular
base /subbase
0.30 - 0.40
Subgrade soils
0.30 - 0.50
Remarks
Highly dependent on temperature; use low
value (0.15) for cold temperatures (less than
30 ºC [86 ºF]) and high value (0.45) for
warm pavement 50 ºC (122 ºF).
No remarks.
Degree of cracking in stabilized layer tends
to increase value towards 0.30 From sound
(crack free) value of 0.15.
Use lower value for crushed material and
high value for unprocessed rounded
gravels/sands.
Value dependent on type of subgrade soil.
For cohesionless soils, use value near 0.30.
A value of 0.50 is approached for very
plastic clays (cohesive soils).
Typical
value
0.35
0.15
0.20
0.35
0.40
It is important to note that the backcalculated material properties correspond to the site conditions during
deflection testing. Various adjustments may be required before the backcalculation results can be
evaluated or used in a design procedure. For example, the backcalculated HMA modulus needs to be
adjusted for temperature. Some design procedures (e.g., AASHTO) include a provision for seasonal
adjustment to the subgrade soil resilient modulus.
HMA Pavement Evaluation and Rehabilitation
2-3.17
Module 2-3. Nondestructive Testing and Data Analysis
Reference Manual
The backcalculated HMA modulus relates to the structural capacity (or remaining life) of the existing
pavement. The AASHTO overlay design procedure (AASHTO 1993) makes provision for determining
the structural capacity of the existing HMA pavement based on backcalculation results. In this procedure,
the effective modulus of all pavement layers combined and the subgrade soil modulus are used to
calculate the effective structural capacity of the existing pavement structure.
Some of the latest information on backcalculation technology was presented in a symposium sponsored
by the American Society for Testing and Materials (ASTM 1999).
Backcalculation Programs
Numerous programs are available that automate the backcalculation of HMA layer moduli from NDT
deflection data. Deflections measured using all types of NDT equipment (steady-state, vibratory and
impulse) may be used to backcalculate pavement layer moduli. However, FWD is the most widely used
device, and most backcalculation programs are designed to work with FWD data. Most backcalculation
programs for HMA pavements utilize an elastic layer program to determine the theoretical deflections.
Therefore, linear elastic material behavior is assumed, but some programs incorporate stress-dependent
material properties for unbound granular materials and subgrade (e.g. EVERCALC, MODCOMP,
ELMOD).
The most common approach to backcalculation for HMA pavements is the iterative solution method,
which is illustrated in table 2-3.1. In this method, the solution is obtained as follows:

Assume a set of moduli values for all layers, including subgrade.

Calculated deflections based on the assumed moduli values using an elastic layer program.

Compare the calculated and measured deflections.

Determine error.

Adjust layer moduli values and repeat the process until the error is within acceptable level.
Examples of programs employing the iterative method include BISDEF, ELSDEF, and CHEVDEF, based
on the elastic layered programs BISAR, ELSYM5, and CHEVRON, respectively (Bush 1985; Lytton et
al. 1990; Moore et al. 1978; Peutz, Van Kempen, and Jones 1968; Ahlborn 1972; Warren and Diekmann
1963). Although these programs can be used to evaluate both HMA and PCC pavements, they are
particularly suitable for HMA pavements.
A list of backcalculation programs currently available for HMA pavements is given in table 2-3.4, but this
list is by no means exhaustive. The programs BOUSDEF and ELMOD utilize Boussinesq theory, a
closed form solution for a single layer problem (Zhou, Hicks, and Bell 1990). Backcalculation of multilayer systems is accomplished by converting the pavement layers into an equivalent thickness of material
with the same modulus as the subgrade soil. This method is very fast, but there are a number of
limitations on its use, including:

The layer moduli should increase with depth, preferably by a factor of at least two between
consecutive layers.

The equivalent thickness of a layer should be larger than the radius of the loaded area.
In a variation of the traditional backcalculation programs, there are programs in which the measured
deflections are directly compared to sets of deflection basins stored in a database. Typically, elastic layer
programs are used to generate a set of deflection basins based on pavement system parameters, including
layer thicknesses, layer combinations, and acceptable ranges of moduli values. The deflection basins
2-3.18
HMA Pavement Evaluation and Rehabilitation
Reference Manual
Module 2-3. Nondestructive Testing and Data Analysis
Table 2-3.4. HMA pavement backcalculation programs.
Backcalculation
program
Basis
Method
Max. number
of layers
BISDEF
BISAR
Iterative
4
Bush 1985; Peutz, Van Kempen,
and Jones 1968
ELSDEF
ELSYM5
Iterative
4
Lytton et al. 1990; Ahlborn, 1972
CHEVDEF
CHEVRON
Iterative
4
Moore et al. 1978; Warren and
Diekmann 1963
MODULUS
WESLEA
4
Uzan et al. 1988
COMDEF1
CHEVRON
3
Anderson 1989
8
Irwin 1983
Iterative
4
Zhou, Hicks, and Bell 1990
Iterative
4
Ullidtz 1977
MODCOMP22
BOUSDEF
ELMOD2
ELSYM5
Equivalent
Thickness
Equivalent
Thickness
Basin
matching
Basin
matching
Iterative
Reference
EVERCALC2
WESLEA
Iterative
5
UW 1987; NHI 1994
WESDEF
WESLEA
Iterative
5
Van Cauwelaert et al. 1989
1
For composite pavements (HMA overlay over PCC).
2
Incorporates stress-dependent material properties.
collected by the NDT device are then compared to the basins in the database. Examples of programs that
use this approach are MODULUS and COMDEF, both of which utilize databases generated using
CHEVRON (Uzan et al. 1988; Anderson 1989; Warren and Diekmann 1963). MODULUS, which uses
the WESLEA program to generate its database of deflection basins, is applicable to HMA pavements
while COMDEF was developed specifically for composite pavements consisting of an HMA overlay over
a PCC layer.
Following are some general “rules of thumb” that have evolved over the years based on experience with
HMA pavement backcalculation:

Deflections greater than about 1 m (3 ft) from the center of the load are almost completely
dependent on the modulus of the subgrade soil. If there is one layer for which a closed-form
solution (between deflection and modulus) might exist, it is the subgrade soil. Theoretically,
thicknesses and modulus values of the pavement layers do not significantly influence deflections
away from the load.

Underlying rigid layers (ranging from bedrock to high water tables) affect pavement deflections;
therefore, they should be considered in the backcalculation process. Ignoring the rigid layers
when they are present will frequently result in a poor “match” and an unconservative, high
subgrade soil modulus.

Deflections from pavements with multiple-bound surface layers tend to have multiple solutions.
For example, increasing the modulus of the surface HMA layer while simultaneously reducing
the modulus of an asphalt stabilized base layer can produce similar theoretical deflections. In
these cases, it is useful to have information from laboratory testing (on one of the layers) to help
eliminate the duplicity.
HMA Pavement Evaluation and Rehabilitation
2-3.19
Module 2-3. Nondestructive Testing and Data Analysis

Reference Manual
The modulus of a thin (less than 75 mm [3 in]) layer is difficult to backcalculate, especially if the
layer is close to surface. Variations in the moduli of thin layers, theoretically, do not produce
significant variations in surface deflection (at least by measurement standards).
8. SUMMARY
This module describes the application, collection, processing, and interpretation of NDT (deflection
testing) data for project level pavement evaluation. Deflection testing serves as one of the basic tool for
assessing the structural adequacy of an existing pavement. Various types of equipment are available for
deflection testing, but FWD is by far the most common type in use.
The NDT data can be analyzed to determine various characteristics of the pavement structure that are
extremely valuable in rehabilitation design including the following:

Moduli values of the pavement layers and subgrade soil.

Variability in pavement and subgrade stiffness along a project.

Areas of significant weakness.

The structural capacity of a pavement (remaining life).

Seasonal variation in base and subgrade stiffness and pavement response.
Pavement deflections represent an overall “system response” of the pavement structure and subgrade soil
to an applied load. The major factors that influence the measured pavement deflections include the
following:

Type of loading (static, vibratory, impulse), loading frequency, and magnitude of the load.

Pavement structure, subgrade soil, existing distress, and random variations in material properties.

Temperature and moisture conditions.
These factors must be considered carefully in selecting equipment for deflection testing and in developing
testing plan. Because load factors can significantly affect pavement deflections, the equipment that most
closely simulates the actual traffic loads should be used for deflection testing. The recommendations for
HMA pavement deflection testing program are summarized in the following:

The suggested deflection measurement locations for HMA pavements are shown in figure 2-3.14
for divided highways and figure 2-3.15 for two-way traffic. Theses figures show the following:

Test in the outer wheelpath at 30- to 150-m (100- to 500-ft) intervals.

On two-lane highways (two-way traffic), the testing points in each direction should be
staggered.

It may be desirable to test one or more additional lanes if the extent of load-associated distress
varies greatly across lanes.

NDT surveys should be conducted during the period that best represents the effective year-round
condition.

For climates with frost penetration, this should be shortly after the spring thaw.

NDT should not be run during periods of deep frost or during the spring thaw.
2-3.20
HMA Pavement Evaluation and Rehabilitation
Reference Manual
Module 2-3. Nondestructive Testing and Data Analysis
Numerous programs are available for backcalculation of HMA pavements. A list of available programs is
provided in table 2-3.4. There are two basic approaches to backcalculation for HMA pavements:

Iterative solution—in this approach, the layer moduli values are determined iteratively, by
comparing theoretical deflections based on assumed moduli values and measured deflections.
The theoretical deflections are calculated using an elastic layer program. The moduli values are
adjusted and the deflections recalculated until the calculated deflections closely match the
measured values.

Basin matching—in this approach, an elastic layer program is used to generate a comprehensive
database of deflection basins for a wide range of pavement parameters (different thickness, layer
combinations, and moduli values) and incorporated in the backcalculation program. The
backcalculation involves searching through the database to find the basin that best matches the
measured deflection basin.
Most backcalculation programs for HMA pavements utilize an elastic layer program to determine
theoretical deflections. Therefore, linear elastic material behavior is assumed in backcalculation, but
stress-dependent material properties are modeled in some programs (e.g., EVERCALC, ELMOD, and
MODCOMP). The backcalculated HMA modulus relates to the structural capacity of the existing
pavement structure.
9. REFERENCES
Ahlborn, G. 1972. ELSYM5 Computer Program for Determining Stresses and Deformation in Five
Layer Elastic System. University of California.
Alvarez, C. and M. Thompson. 1998. Mechanistic-Empirical Evaluation of the Mn/Road Mainline
Flexible Pavement Sections. Report No. FHWA-IL-UI-263. Federal Highway Administration,
Washington DC.
American Association of State Highway and Transportation Officials (AASHTO). 1990. “Standard
Recommended Practice for Pavement Deflection Measurements.” Standard Specifications for
Transportation Materials and Methods of Sampling and Testing, Part II. T 256-77. American
Association of State Highway and Transportation Officials, Washington, DC.
American Association of State Highway and Transportation Officials (AASHTO). 1993. AASHTO
Guide for Design of Pavement Structures. American Association of State Highway and Transportation
Officials, Washington, DC.
American Society for Testing and Materials (ASTM). 1999. Nondestructive Testing of Pavements and
Backcalculation of Moduli, STP 1375. American Society for Testing and Materials, West Conshohocken,
PA.
Anderson, M. 1989. “A Database Method for Backcalculation of Composite Pavement Layer Moduli,”
Nondestructive Testing of Pavements and Backcalculation of Moduli. ASTM STP 1026. A. J. Busch III
and G. Y. Baladi, Eds. American Society for Testing and Materials, Philadelphia, PA.
Asphalt Institute (AI). 1987. Asphalt Overlays for Highway and Street Rehabilitation. The Asphalt
Institute Manual Series No. 17 (MS-17). The Asphalt Institute, Lexington, KY.
Asphalt Institute (AI). 1988. Soils Manual for the Design of Asphalt Pavement Structures. The Asphalt
Institute Manual Series No. 10 (MS-10). The Asphalt Institute, Lexington, KY.
HMA Pavement Evaluation and Rehabilitation
2-3.21
Module 2-3. Nondestructive Testing and Data Analysis
Reference Manual
Bushey, R. W., L. K. Baumeister, and J. A. Matthews. 1976. “Structural Overlays for Pavement
Rehabilitation.” Transportation Research Record 572. Transportation Research Board, Washington, DC.
Bush, A. J. 1985. Computer Program BISDEF. United States Army, Corps of Engineers, Waterways
Experiment Station, Vicksburg, MS.
California Department of Transportation (CALTRANS). 1978. Methods of Test to Determine Overlay
Requirements by Pavement Deflection Measurements. California Test 356. California Department of
Transportation, Sacramento, CA.
Garg, N. and M. R. Thompson. 1999. “Structural Response of LVR Flexible Pavements at Mn/Road
Project.” Journal of Transportation Engineering. Volume 125, Issue 3. American Society of Civil
Engineers, Reston, VA.
Gucunski, N. and V. Krstic. 1996. “Backcalculation of Pavement Profiles from Spectral-Analysis-ofSurface-Waves Test by Neural Networks Using Individual Receiver Spacing Approach.” Transportation
Research Record 1540. Transportation Research Board, Washington. DC.
Hall, K. T., M. I. Darter, and C. Kuo. 1995. “Improved Methods for Selection of k Value for Concrete
Pavement Design.” Transportation Research Record 1505. Transportation Research Board, Washington,
DC.
Highway Research Board (HRB). 1962. The AASHO Road Test, Report 5—Pavement Research. Special
Report 61E. Highway Research Board, Washington, DC.
Hudson, W. R., G. E. Elkins, W. Uddin, and K. T. Reilley. 1987. Evaluation of Pavement Deflection
Measuring Equipment. Report No. FHWA-TS-87-208. Federal Highway Administration, Washington,
DC.
Irwin, L. H. 1983. Users Guide to MODCOMP2. Report No. 83-8. Cornell University, Ithaca, NY.
Khogali, W. and K. O. Anderson. 1996. “Evaluation of Seasonal Variability in Cohesive Subgrades
Using Backcalculation.” Transportation Research Record 1546. Transportation Research Board,
Washington. DC.
Lukanen, E. O., R. Stubstad, and R. Briggs. 2000. Temperature Predictions and Adjustment Factors for
Asphalt Pavement. Report No. 06-04-2000. Federal Highway Administration, Washington, DC.
Lytton, R. L., F. P. Germann, Y. J. Chou, and S. M. Stoffels. 1990. Determining Asphaltic Concrete
Pavement Structural Properties by Nondestructive Testing. NCHRP Report 327. Transportation
Research Board, Washington, DC.
Lytton, R. L., W. M. Moore, and J. P. Mahoney. 1975. Pavement Evaluation Equipment. Report No.
FHWA-RD-75-78. Federal Highway Administration, Washington, DC.
Moore, M. R., C. R. Haile, D. I. Hanson, and J. W. Hall. 1978. “An Introduction to Nondestructive
Structural Evaluation of Pavements.” Transportation Research Circular 189. Transportation Research
Board, Washington, DC.
National Highway Institute (NHI). 1994. Pavement Deflection Analysis. NHI Course No. 13127.
Report No. FHWA-HI-94-021. Federal Highway Administration, Washington, DC.
2-3.22
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Module 2-3. Nondestructive Testing and Data Analysis
Nazarian S., Baker M. and Crain K. 1993. Developing and Testing of a Seismic Pavement Analyzer.
Report SHRP-H-375. Strategic Highway Research Program, Washington, DC.
Nazarian, S., K. H. Stokoe II, R. C. Briggs, and R. Rogers. 1988. “Determination of Pavement Layer
Thicknesses and Moduli by SASW Method.” Transportation Research Record 1196. Transportation
Research Board, Washington, DC.
Nazarian S., Yuan D. and Baker M. R. 1995. Rapid Determination of Pavement Moduli with SpectralAnalysis-of-Surface-Waves Method. Research Report 1243-1F. Center for Geotechnical and Highway
Materials Research. University of Texas at El Paso, TX.
Peutz, M. G. F., H. P. Van Kempen, and A. Jones. 1968. “Layered Systems under Normal Surface
Loads.” Highway Research Record 228. Highway Research Board, Washington, DC.
Poehl, R. 1971. Seasonal Variations of Pavement Deflections in Texas. Research Report 136-1. Texas
Transportation Institute, College Station, TX.
Rix, G. J., J. A. Bay, and K. H. Stokoe II. 1990. “Assessing In Situ Stiffness of Curing Portland Cement
Concrete with Seismic Tests.” Transportation Research Record 1284. Transportation Research Board,
Washinton, DC.
Roberts, D. V., G. W. Mann, and C. A. Curtis. 1977. Evaluation of the Cox Deflection Devices. Report
number FHWA-CA-TL-3150-77-14. California Department of Transportation, Sacramento, CA.
Sanchez-Salinero, I., J. M. Roesset, K. Y. Shao, K. H. Stokoe II, and G. J. Rix. 1987. “Analytical
Evaluation of Variables Affecting Surface Wave Testing of Pavements.” Transportation Research
Record 1136. Transportation Research Board, Washington, DC.
Scrivner, F. H., R. Poehl, W. M. Moore, and M. B. Phillips. 1969. Detecting Seasonal Changes in LoadCarrying Capabilities of Flexible Pavements. NCHRP Report 76. Highway Research Board,
Washington, DC.
Sheu, J. C., K. H. Stokoe II, and J. M. Roesset. 1988. “Effect of Reflected Waves in SASW Testing of
Pavements.” Transportation Research Record 1196. Transportation Research Board, Washington, DC.
Tabrizi, K, V. Ganji, and R. Sauber. 2000. “Project Level Application of Falling Weight Deflectometer.”
Proceedings, Structural Materials Technology IV—An NDT Conference. ISBN 1566769493. Technomic
Publishing Company, Inc., Lancaster, PA.
Ullidtz, P. 1977. “Overlay and Stage by Stage Design.” Proceedings, Fourth International Conference
on the Structural Design of Asphalt Pavements, Volume I. University of Michigan, Ann Arbor, MI.
University of Washington (UW). 1987. EVERCALC User’s Guide. Washington State Transportation
Center, University of Washington, Seattle, WA.
Uzan J., T. Scullion, C. H. Michalek, M. Paredes, and R. L. Lytton, 1988. A Microcomputer-Based
Procedure for Backcalculating Layer Moduli From FWD Data. Research Report 1123-1. Texas
Transportation Institute, College Station, TX.
Van Cauwelaert, F. J., D. R. Alexander, T. D. White, and W. R. Barker. 1989. “Multilayer Elastic
Program for Backcalculating Layer Moduli in Pavement Evaluation.” Nondestructive Testing of
Pavements and Backcalculation of Moduli. ASTM STP 1026. A. J. Busch III and G. Y. Baladi, Eds.
American Society for Testing and Materials, Philadelphia, PA.
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Reference Manual
Warren, T. and W. L. Diekmann. 1963. Numerical Computation of Stresses and Strains in MultipleLayer Asphalt Pavement System. Internal Report. Chevron Research and Technology Company,
Richmond, CA.
Zhou, H. G., R. G. Hicks, and C. A. Bell. 1990. “BOUSDEF: A Backcalculation Program for
Determining Moduli of a Pavement Structure.” Transportation Research Record 1260. Transportation
Research Board, Washington. DC.
Zhou, H. G., R. Rada, and G. E. Elkins. 1997. “Investigation of Backcalculated Moduli Using
Deflections Obtained at Various Locations in a Pavement Structure.” Transportation Research Record
1570. Transportation Research Board, Washington. DC.
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HMA Pavement Evaluation and Rehabilitation