Effect of Different Axle Configurations

on Fatigue Life of Asphalt Concrete Mixture

Karim Chatti and Chadi S. El Mohtar
period. The fatigue lives, corresponding to various axle configurations
and truck types, determined by using the dissipated energy-based
fatigue curve, were then compared.

The fatigue life of an asphalt mixture under different truck axle configurations was determined directly from the indirect tensile cyclic load
test by using load pulses that were equivalent to the passage of an entire
axle group or truck. The dissipated energy approach was adopted in
analyzing the results and determining the number of repetitions to failure for each case; a unique fatigue curve that can be used for multiaxle
configurations was developed. Trucks consisting of up to 11 axles and
axle groups of up to 8 axles were studied. The results indicated that the
normalized damage per load carried decreased with an increasing number of axles within an axle group. Additionally, the fatigue lives predicted by using single load pulses were compared with the measured
ones from the different axle groups and trucks.

RESEARCH OBJECTIVE
The objective of the research described here was to investigate the
effect of different axle configurations and truck types on the fatigue
response of an asphalt mixture by laboratory testing and the dissipated
energy approach.
INDIRECT TENSILE CYCLIC LOAD TEST

Most fatigue tests on asphalt-based mixes are performed under

single pulse loads or continuous sinusoidal loading. However, in the
field, the pavement is subjected to different axle configurations,
causing multiple pulse loading within a passage of a single axle
group, with the shape of the pulse being a function of axle spacing,
pavement structure, vehicle speed, and so forth. To determine the
fatigue life under multiple axles, Miners hypothesis is commonly
applied to accumulate the damage resulting from the different axles
within an axle group. This relation is given by Equation 1.
n1
n
n
n
+ 2 + 3 +...+ i +... 1
N1 f
N2 f
N3 f
Nif

The indirect tensile test is conducted by applying a vertical compressive strip load on a cylindrical specimen. The load is distributed
over the thickness of the specimen through two loading strips at the
top and bottom, as indicated in Figure 1a. The strips are curved and
have a radius equal to that of the specimen to ensure full contact over
the entire seating area. All specimens tested were 4 in. in diameter
and 2.5 in. thick, with a 0.5-in.-wide loading strip. This combination
of specimen geometry and boundary conditions induces tensile and
compressive stresses along both the vertical and the horizontal
diameters, as indicated in Figure 1b. The tensile stresses, developed
perpendicular to the direction of the load, have a relatively constant
value over a large portion of the vertical diameter. This would result
in failure of the specimen by splitting along the vertical diameter, as
indicated in Figure 1a. Under high vertical loads, local shear failure
may occur near the loading strips. In this research, care was taken to
prevent this mode of failure and to ensure that the specimen failed
in fatigue with cracking initiating at the center.
Five linear variable differential transformers (LVDTs) were used
to measure the response of the specimen: four in the horizontal
direction (two along the thickness of the specimen and two along the
diameter of the specimen) and one used to monitor the vertical
deformation, as indicated in Figure 2. The analytical formulations
to calculate the stresses and strains at the center of the specimen are
well known and can be found elsewhere (46 ). The strains at the
center of the specimen can be calculated directly as a function of the
measured deformations.

(1)

where
i = ith level of applied strainstress at point under consideration,
ni = actual number of applications at strain level i that is
anticipated, and
Ni f = number of applications at strain level i expected to cause
fatigue failure if applied separately.
Typically, the damage is calculated by using either the peak strains
from all pulses or the peak of the first pulse and the intermediate
strains (difference between peaks and valleys) within a multiple strain
pulse (13).
In this paper, the fatigue response of an asphalt mixture was studied by using multiple pulse loadings within a cycle, simulating different axle configurations. The dissipated energy approach was used
to analyze the test results, and a unique fatigue curve was established.
This curve was shown to describe the fatigue response due to any axle
configuration regardless of axle spacing, interaction level, and rest

DISSIPATED ENERGY DENSITY

AND FATIGUE FAILURE CRITERION
Dissipated Energy Density

Department of Civil and Environmental Engineering, Michigan State University,

3546 Engineering Building, East Lansing, MI 48824.

Several researchers have proposed using dissipated energy to predict the fatigue life of asphalt mixtures (2, 710). Dissipated energy
density is defined as the area within a stressstrain hysteresis loop

Transportation Research Record: Journal of the Transportation Research Board,

No. 1891, TRB, National Research Council, Washington, D.C., 2004, pp. 121130.

121

122

Transportation Research Record 1891

Vertical LVDT

Loading Strip

Failure Plane

Horizontal
LVDT

Vertical Load

FIGURE 2 LVDT configurations for indirect

tensile cyclic load.

(a)

yc : Compressive
Vertical Stresses
along Y- axis
yc

yt : Tensile
Horizontal Stresses
along Y-axis

xt

xc
yt

Longitudinal LVDT

xc : Compressive
Horizontal Stresses
along X-axis
xt : Tensile
Vertical Stresses
along X-axis

y
(b)
FIGURE 1 Indirect tensile test: (a) indirect tensile loading and
(b) stresses in the indirect tensile test specimen.

under cyclic loading and represents the energy lost at a specific point
due to a load application. In this paper, the tensile stresses and strains
at the center of an indirect tensile specimen are used to calculate the
dissipated energy density.

Fatigue Failure Criterion

It is well known that for portland cement concrete mixes, fatigue
curves are defined in terms of the stress ratio, /MR, where is the
applied cyclic bending stress and MR is the modulus of rupture
determined from a flexural strength test. The main advantage of this
concept is that it links fatigue testing to a simple strength test.
For flexible pavement design, the strain level and the asphalt mix
stiffness are used instead in the fatigue relationship. The concept
of relating fatigue test results to a simple strength test is appealing
because of the simplicity of such a test and because it characterizes
the mixture. Because the strain level is important in fatigue testing of
asphalt mixtures, a good way to relate fatigue testing to a strength test
would be with energy. The energy density is defined as the product
of stress and strain, so that

1. Under cyclic loading, a given strain level, 0, corresponds to a

dissipated energy density, w0 (equal to the area within the stressstrain
hysteresis loop) (Figure 3a) and
2. Under a strength test, the stored energy until cracking (SEC)
is equal to the area under the stressstrain curve up to its peak stress
(Figure 3b).
To determine the fatigue life of asphalt mix specimens from laboratory testing, it is necessary to decide on a fatigue failure criterion.
Different failure criteria result in different numbers of load repetitions until failure. The most common failure criterion is the 50%
reduction in the modulus, where failure is defined as the cycle at
which the modulus value is half the initial value. An alternative
approach is to use the energy concept to link fatigue and strength
testing and to define fatigue failure.
Such a fatigue failure criterion can be defined by equating the
cumulative dissipated energy density under cyclic loading to the SEC
value obtained from a strength test. This criterion can be applied to
any test type (e.g., flexural, tension, indirect tension tests) provided
the fatigue and strength tests are conducted with the same test setup.
For example, if one were to extend this criterion to flexural beam testing, then the SEC value would be the flexural strength obtained by
loading a beam to failure under a constant rate of deformation.
Typically, the dissipated energy density remains constant and
then starts increasing until the point of failure. The point at which
the dissipated energy density starts increasing can be interpreted as
the initiation of failure, and the corresponding cycle number could
be the number of load repetitions to crack initiation.
Figure 4a shows the Nf value using the dissipated energy density
per cycle plot. The shaded area bounded by Nf corresponds to SEC.
Figure 4b presents the SEC value plotted on the cumulative dissipated energy density curve. The intersection of the SEC line with the
cumulative dissipated energy density curve is the fatigue life (Nf ).
The validity of the failure criterion is shown by using the fatigue test
results described in the following section.

LABORATORY FATIGUE TESTING

The asphalt mix used in this study was a 4E3 Superpave mix with
a top aggregate size of 12 in. and a target asphalt content of 5.9%.
The mix was obtained from an actual batch that was produced in a

Chatti and El Mohtar

123

180
160

Tensile Strain (psi)

140
120
100
80

Stored Energy
Density Until
Cracking

60
40
20
0

001

002

003

004

005

Tensile Strain
(b)

(a)

FIGURE 3 Stressstrain relationships under cyclic load and strength testing: (a) dissipated energy density under
cyclic load testing and (b) stored energy density until failure under strength testing.
30

Cumulative DE (psi)

25
20
Nf

15
10
5

SEC

0
1

10

100

1,000

10,000

100,000

N
(a)
0.0035
0.003
Nf

DE (psi)

0.0025
0.002
0.0015
0.001

SEC

0.0005
0
11

100

1,000

10,000

100,000

N
(b)
FIGURE 4 Fatigue failure criteria: (a) determining N f from cumulative dissipated
energy (DE) density and SEC and (b) determining N f from dissipated energy density per
cycle and SEC.

006

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Transportation Research Record 1891

TABLE 1

Volumetric Properties of Mix

Property
Value

Gmm
2.487

Gmb
2.388

Gse
2.731

Gsb
2.661

VMA
15.6%

VFA
74.4%

Gb
1.026

NOTE: Gmm = maximum theoretical specific gravity of the mix, Gmb = bulk specific gravity of the
mix, Gse = effective specific gravity of the aggregate, Gsb = bulk specific gravity of the aggregate,
VMA = voids in mineral aggregate, VFA = voids filled with asphalt, Gb = specific gravity of the
binder (asphalt).

by the SAPSI-M computer program (11), with the tensile strain at

the center of the 4-in. specimen in the laboratory. The low and high
stress levels (4.375 and 17.5 psi) were equal to half and double the
medium stress level, respectively. The shape of the load pulse also
was obtained by matching the tensile strain time histories at the bottom of the AC layer as predicted by SAPSI-M. Figure 5a presents
an example of the strain time histories for a tridem axle, and Figure
5b presents a typical stressstrain hysteresis loop under a tridem
load pulse. The ratio of loadingunloading duration to rest period
was held constant at 1:4. For single axles, the loadingunloading
duration was found to be 0.1 s by using the response calculated from
SAPSI-M due to a load moving at 40 mph; therefore, a rest period
of 0.4 s was used. For multiple axle configurations and trucks, the
loading time was taken as the time from the beginning of the response due to the first axle until the time when the response of the
axle dies, as calculated by SAPSI-M. Figure 6 presents examples of
loading cycles used for fatigue testing. Three interaction levels were
used for multiple axle groups: high, medium, and low. The interaction level is defined as the peakvalley stress ratio and represents
different AC layer thicknesses (the thicker the AC, the higher the
interaction level).

mixing plant and used by the Michigan Department of Transportation on a project in the summer of 2002. The volumetric properties
of the mix are presented in Table 1.
Fifty-seven samples (4 in. in diameter) were compacted in the laboratory with the gyratory compactor. The average air voids content
was 3.9% and the standard deviation was 0.2%. Because specimens
with high or low air voids were not tested, the total number of specimens used in the experiment equaled 47. Thirty-five specimens
were tested for fatigue; three samples were tested under the indirect
tensile strength test to determine the indirect tensile strength, and
three more samples were tested under the indirect tensile strength test
with horizontal deformation measurements to determine SEC. Three
samples were tested for resilient modulus; three were tested under
cyclic loading to determine the initial dissipated energy under various axle configurations. All testing was done at room temperature,
with the average temperature recorded at about 70F.
The average tensile strength was 171 psi, with the lowest and highest values being 168 and 174 psi, respectively. The average stored
energy density until failure was 1.556 psi with the lowest and highest
values being 1.547 and 1.568 psi, respectively. The average resilient
modulus was 252,575 psi, and the standard deviation was 18,706 psi.
Thirty-one samples were tested for fatigue according to the test
matrix presented in Table 2. Specimens were tested under different
load pulses corresponding to five axle configurationssingle, tandem, tridem, four axles, and eight axleswith each individual axle
carrying a nominal load of 13 kips and with spacing between axles
at 3.5 ft. In addition, two specimens were tested under continuous
pulse loading (i.e., with no rest period), and two others were tested
under a full truck with an 11-axle configuration(one single axle,
two tandem axles, and two tridem axles). The total number of fatigue
tests equaled 35.
Three tensile stress levels were used: low, medium, and high. The
medium stress level (8.75 psi) was determined by equating the horizontal (transverse) tensile strain at the bottom of a 6-in. asphalt concrete (AC) layer subjected to a 13-kip single axle load, as predicted

TABLE 2
Stress
Level
Low

Medium

High

EXPERIMENTAL RESULTS
To verify the new failure criterion discussed previously, the number
of cycles to failure, Nf, was determined with the new criterion as
well as from visual inspection of the curve relating the dissipated
energy per cycle to the number of load repetitions (for an example,
see Figure 4). Figure 7a presents the relationship between Nf obtained by using SEC and that from visual inspection by using the
dissipated energy density per cycle. The figure indicates that they
are correlated, although there is large scatter. This is due to experimental error that makes it difficult to determine visually the number
of cycles at which the dissipated energy density value starts to

Experimental Fatigue Test Matrix

Axle no.
1
Interaction
Low (25%)
Medium (50%)
High (75%)
Low (25%)
Medium (50%)
High (75%)
Low (25%)
Medium (50%)
High (75%)

8
xx

xx
xx
xxx
xxx

xx
xx

No. of xs represents the number of samples tested.

xxx

xxx

xxx
xx

xx
xx

125

Response (10-6 in./in.)

Chatti and El Mohtar

160
140
120

SAPSI-M

100

ITCLT

80
60
40
20
0
0

0.1

0.2

0.3
Time (sec)

0.4

0.5

8.E-05

1.E-04

0.6

(a)

10
9
8
Stress (psi)

7
6
5
4
3
2
1
0
0.E+00

2.E-05

4.E-05

6.E-05
Strain
(b)

1.E-04

FIGURE 5 Example strain and stressstrain response curves from cyclic load
testing: (a) typical strain pulses from SAPSI-M and indirect tensile cyclic load
test (ITCLT) results and (b) typical stressstrain hysteresis loop for tridem axle.

increase. This is confirmed by comparing the corresponding fatigue

curves. Figure 7b presents the fatigue curve that is based on visual
inspection; it shows a high degree of scatter. In contrast, Figure 8a
presents the dissipated energybased fatigue curve by using the new
SEC criterion; the correlation has an R2 value of 0.99. Clearly, this
curve is unique and represents different axle configurations with different interaction and stress levels. Thus, using this fatigue curve
would allow for determining the number of repetitions until failure
for any axle configuration in one step without the need to build up
an axle group from its components.
The fatigue model obtained is as follows:
N f = 2.12 W0-0.955

(2)

where W0 is initial dissipated energy density (psi).

Two samples were tested under a continuous (i.e., without rest
period) haversine load at a medium stress level. Two more samples
were tested under a load pulse simulating a whole truck. The truck
used was an 11-axle Michigan truck (Truck 13 in Table 3). The
whole truck was treated as one load cycle, and the dissipated energy
density was calculated for passage of the whole truck. The rest
period was determined on the basis of the same ratio used for the axle

groups (1 loading to 4 rest periods). The loading duration was taken

from the point when the influence of the steering axle starts until the
response due to the final axle dies. The results from continuous single pulse loading and truck loading were plotted on the same graph
with the dissipated energy fatigue curve and are presented in Figure 8b. The points lie on top of the master dissipated energybased
fatigue curve and thus confirm its uniqueness. Therefore, no further
fatigue testing was performed for other trucks or axle groups because
the dissipated energy fatigue curve was found to be unique regardless of the load pulse. The procedure used to determine the damage
factors for axle groups and trucks is presented next.

FATIGUE DAMAGE FACTORS FOR DIFFERENT

AXLE GROUPS AND TRUCKS
In this section, the values of load equivalency factors (LEFs), truck
factors (TFs), and axle factors (AFs) were determined by using the
fatigue curve described previously. For a given axle group or truck
configuration, LEF, TF, or AF was calculated from the fatigue curve
by using the initial value of dissipated energy density corresponding to the passage of the entire axle group or truck. Some of the
terms used in this analysis are defined next. LEF and TF are defined

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Transportation Research Record 1891

Load

4t

4t

4t
Time (sec)

(a)

Load

4t

4t

4t

Time (sec)

(b)

Load

4t

Time (sec)

(c)
FIGURE 6 Examples of load cycles used in fatigue testing: (a) single axle,
(b) tandem axle, and (c) Truck 10 (t is the duration of loading pulse and 4t is
the rest period).

as the relative damage of an axle group or a truck to that of a standard axle, where damage is the inverse of the number of repetitions
until failure.
LEF or TF =
=

damage (axle configuration)

damage (18-kip standard axle)
N f (18-kip standard axle)
N f (axle configuration)

(3)

AF is defined here as the relative damage of an axle group to that

of a single axle carrying the same load as any of the axle group components. For example, the AF of a 39-kip tridem is determined as
follows:
AF =

N f (13-kip single)
damage (39-kip tridem )
=
damage (13-kip single)
N f (39-kip tridem )

( 4)

LEF, AF, and TF per tonnage can be determined by dividing their

respective values with the total load carried by the axle configura-

tion. Using the per tonnage values allows for determining the most
efficient axle configuration to carry a given payload.
The same specimen was used to determine the initial dissipated
energy density for all axle groups and trucks studied, by using a limited number of load cycles and thus eliminating the variability of air
voids content and the AC internal structure. Additionally, performing all the tests while the specimen was still in the same position in
the loading frame decreased any errors due to specimen misalignment with the loading strips. Because the specimen was at the initial stage of the test, there was a negligible accumulated strain from
subsequent load cycles. To verify this, the first axle configuration
tested for initial dissipated energy on the specimen was again tested
at the end of the test, and the corresponding dissipated energy was
calculated to make sure it matched with the first value calculated at
the beginning of the test. Trucks consisting of up to 11 axles and
axle groups of up to 8 axles were studied. Ten trucks were selected
for laboratory testing. The trucks were chosen to cover all axle configurations used in Michigan. Table 3 presents the truck configurations used. Three triplicates were used, and each load combination
was applied for 15 cycles to determine the initial dissipated energy
density. The results are presented in the following paragraphs.

Chatti and El Mohtar

127

1.0E+05

Nf Visual

1.0E+04

1.0E+03

1.0E+02
1.0E+02

1.0E+03

1.0E+04

1.0E+05

Nf SEC
(a)
1.00E-02

Initial DE, psi

Nf =105.9 Wo-0.4517
2
R =0.209
1.00E-03

1.00E-04

1.00E-05

100

1,000

10,000

100,000

Nf
(b)
FIGURE 7 Comparisons of visual and SEC failure criteria: (a) N f based on
visual criteria and SEC and (b) fatigue curve based on visual criteria
(DE  dissipated energy).

Axle Fatigue Damage Factors

Table 4 presents the LEF and LEF per tonnage values for all axle
groups studied, while Figure 9 presents the AF values per tonnage.
The results confirm that using multiaxles to carry the same payload
increases the fatigue life of an asphalt mix. The increase in fatigue life
is much more significant when one goes from a single to tandem and
tridem axles; the damage values per tonnage start to even out as the
number of axles exceeds five. This implies that from a fatigue damage perspective, using an eight-axle configuration to carry 104 kips is
much more beneficial than using eight separate axles carrying 13 kips
each. The results also show that the effect of interaction level on the
equivalent damage factors is not significant.

Truck Fatigue Damage Factors

The fatigue life corresponding to each truck was determined by
using the dissipated energy fatigue curve, and the corresponding TF
and TF per tonnage were calculated. Figure 10 presents the TFs per
tonnage. The results show that Truck 1 is the most damaging per
tonnage. Truck 1 is a two-axle single-body truck that consists of a
15.4-kip front steering axle and a single 18-kip standard axle in the

rear. Trucks 13, 14, 17, 19, and 20 have the lowest TFs per tonnage
because their payload is distributed over larger axle groups. The
decrease in TF per tonnage from Truck 1 to Truck 4 emphasizes the
same finding mentioned previously that multiaxle groups are less
damaging than individual axles when one considers the load they
carry. Truck 20, which has the most axles and least axle groups, is
the most efficient of all trucks investigated.

CONCLUSION
On the basis of experimental results from fatigue testing of an AC
mix under multiple axle configurations with the indirect tensile cyclic
load test, the following conclusions are drawn:
1. The SEC failure criterion, developed in this study, was found
to be a good failure criterion for fatigue life of AC mixes when the
dissipated energy approach is used. This failure criterion indicates
crack initiation in the specimen.
2. A unique energy-based fatigue curve developed for different
axle and truck configurations is useful for predicting the fatigue life
of an axle group or a truck at once without the need for summing up
the damage from individual axles.

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Transportation Research Record 1891

1E-02

Nf = 2.12 Wo-0.955
R2 = 0.9926

Initial DE

1E-03

1E-04

1E-05
100

1,000

10,000

100,000

Nf
Low Stress

Medium Stress

High Stress

(a)
1.00E-02

DE Initial

1.00E-03

1.00E-04

1.00E-05
100

1,000

10,000

100,000

Nf
Continuous Pulse

Truck 13
(b)

FIGURE 8 Dissipated energy (DE)based fatigue curve: (a) fatigue curve using various
axle configurations and (b) fatigue responses under pulse load and truck.

Chatti and El Mohtar

TABLE 3

129

Truck Axle Configurations

Truck No. No. of Axle

Groups

No. of
Axles

Truck 0

Truck 1

Truck 2

Truck 3

Truck 4

Truck 10

Truck 13

11

Truck 14

11

Truck 17

10

Truck 19

10

Truck 20

11

TABLE 4 Summary of Results in Terms of Axle Load

Equivalency Factors

Truck Configuration

Nf

Nf

LEF

LEF/Tonnage

1 axle 18-kip
1 axle 13-kip
2 axles
3 axles
4 axles
25%
Interaction 5 axles
7 axles
8 axles
2 axles
3 axles
50%
4 axles
Interaction 5 axles
7 axles
8 axles
2 axles
3 axles
75%
4 axles
Interaction 5 axles
7 axles
8 axles

5,388
7,750
4,889
3,876
2,889
2,377
1,893
1,707
5,987
4,592
3,577
2,992
2,477
2,289
5,644
4,155
3,431
3,058
2,549
2,439

1.00
0.70
1.10
1.39
1.87
2.27
2.85
3.16
0.90
1.17
1.51
1.80
2.18
2.35
0.95
1.30
1.57
1.76
2.11
2.21

1.00
0.96
0.76
0.64
0.65
0.63
0.56
0.55
0.62
0.54
0.52
0.50
0.43
0.41
0.66
0.60
0.54
0.49
0.42
0.38

1.20
1.00

-0.3363

y = 1.0043x
2

AF/Tonnage

R = 0.89
0.80
0.60
0.40
0.20
0.00
0

Axle No.
25% Interaction
FIGURE 9

50% Interaction

75% Interaction

Axle factors per tonnage for different interaction levels.

130

Transportation Research Record 1891

2.0
1.8
Truck Factor/Tonnage

1.6

Sample 135

1.4

Sample 125

1.2
1.0
0.8
0.6
0.4
0.2

FIGURE 10

Truck 20

Truck 19

Truck 17

Truck 14

Truck 13

Truck 10

Truck 4

Truck 3

Truck 2

Truck 1

Truck 0

Std Axle

0.0

Truck factors per tonnage (Std  standard).

3. Multiple-axle groups were found to be less damaging per tonnage than single axles. Increasing the number of axles carrying the
same load resulted in less damage. This decrease in damage was
found to be more significant for single, tandem, and tridem axles,
while it started to level off at higher axle numbers. Similar results
were obtained for trucks, where trucks with more axles and axle
groups had lower TFs per tonnage than those with single axles.

6.

7.
8.

ACKNOWLEDGMENT
9.

The research in this study was funded by the Michigan Department

of Transportation. The project manager was Thomas E. Hynes.
10.

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The Michigan Department of Transportation assumes no liability for the contents

and use of this paper. The contents of this paper reflect the views and opinions
of the authors, who are responsible for the accuracy of the information presented
here. The contents do not necessarily reflect the views of the Michigan Department of Transportation and do not constitute a department standard, specification,
or regulation.
Publication of this paper sponsored by Characteristics of Bituminous Paving
Mixtures to Meet Structural Requirements Committee.