DYNAMIC WHEEL LOADS FROM HEAVY VEHICLES

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8 Δεκ 2013 (πριν από 3 χρόνια και 8 μήνες)

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DYNAMIC WHEEL LOADS FROM HEAVY VEHICLES
Dr Lloyd Davis
PhD, Grad Dip(Control), BEng(Elec),
Cert(QMgt), CEng, RPEQ, FIET
Abstract
Research was undertaken to determine the forces
exerted on pavements from an instrumented tri-
axle group of a semi-trailer. A combination of
accelerometers and strain gauges was used to
determine both static and dynamic wheel forces. A
novel roughness value of the roads during testing was
derived. Dynamic pavement forces are presented
according to the range of novel roughness of
pavement surfacings encountered during testing. Left/
right imbalances of wheel forces are presented for
varying speeds. A conclusion drawn from research
indicates that pavement models need to be revised as
instantaneous dynamic wheel forces are not generally
considered in contemporary pavement designs. The
mean and standard deviation of heavy vehicle wheel
forces do not correlate with pavement roughness
however peak wheel forces do.
Introduction
This article is a combination of earlier work presented
at the Transport and Main Roads Technology Forum
2009 combined with subsequent results from a recent
research project, Heavy Vehicle Suspensions –Testing
and Analysis.
Pavement design life calculations are based on
repetitive loadings arising from repeated passes of a
theoretical heavy vehicle (HV) axle. Conceptually,
this pavement life design parameter is based on the
number of passes of a standard axle over a pavement.
This measure is, in turn, based on tests conducted after
the World War II by the US military where trucks
were driven repetitively over a pavement until the
pavement became unserviceable (6). The number
of passes that the trucks made (i.e. the number of
axle repetitions including some dynamic forces)
determined the design parameter for pavement
life. The terms “equivalent standard axle” (ESA)
and “standard axle repetition” (SAR) came into
use to allow pavement life to be correlated to axle
repetitions or passes at different axle masses. The
physical size of vehicles, number of axles and
axle loads has increased historically as a result of
technology and the push for more freight effi cient
vehicles.
As the need for a vehicle driver is a given, costs are
reduced in these freight effi cient vehicles by utilising
more axles, more mass per axle and more trailers.
Increased wheel loads have added additional stress to
the road surfacings. Continued pressure is maintained
on road authorities for increases in HV mass limits
and other HV changes. Nonetheless, the basic theory
for determining pavement life as a value of vehicle
passes has not altered signifi cantly since the US
military experiments last century (1,22).
Australia’s accelerated loading facility (ALF) and
New Zealand’s Canterbury accelerated pavement
testing indoor facility (CAPTIF) have been used
to determine pavement life in a similar manner to
the original US testing, that is; repeated passes of
a test wheel at a particular increased load over a
pavement (22,23). Much work has been done using
the CAPTIF to correlate dynamic wheel forces with
axle passes (13,14,15). Further, a considerable body
of work has been undertaken in the UK (3,4,5,6) on
dynamic wheel loadings from HVs. Results of that
work have not yet been incorporated into general
pavement design, particularly in Australia (22,23).
Unoffi cial estimates put the number of road friendly
suspensions (RFS) sold in Australia per year at 90%
to 95% (28) of the total HV fl eet
1
. RFS in Australia
generally incorporate air springs, although there are
some steel-sprung RFS emerging onto the market. A
body of work has already been performed some time
ago on dynamic HV wheel forces. However this
previous research focused mainly on the suspension
types of the day such as Hendrickson and simple leaf
spring suspensions with inter-leaf friction dampening.

1 Actual numbers are not readily available as commercial sensitivity and competitive forces between manufacturers limit reporting more accurately.
Because of the current predominance of air spring
suspensions in HVs, there exists a need to understand
the fundamental characteristics of air spring
suspensions and determine the corresponding dynamic
interaction between the vehicle tyres and the road
pavement. A semi-trailer with air springs was chosen
for the testing and the axles instrumented to measure
dynamic wheel forces. Although other HVs were
tested as part of the project (7,10,11,12), the semi-
trailer test is the subject of this article. The semi-
trailer tri-axle group spacing was 1.4m. The wheel
forces were measured on typical pavements at various
roughness levels and at different road speeds.
The instrumentation installed on the semi-trailer
allowed a novel roughness measure to be derived
together with the mean, dynamic range and peak
dynamic pavement forces. This article presents
heavy vehicle dynamic wheel-forces at the pavement
according to the range of novel roughness of pavement
surfacings encountered during testing.
Determining dynamic wheel forces
Measuring dynamic wheels forces directly at the
wheel is not an easy task. In this project the wheel
forces were calculated by the use of a combination of
accelerometers and strain gauges mounted onto the
axle. The strain gauges were mounted on the sides
Figure 1. Instrumented HV axle used to derive tyre forces (8)
of the axle as close as possible to the wheel hub.
These gauges were calibrated to measure the vertical
shear force, F
shear
. The strain gauges in this position
could not detect the inertial component of wheel
forces further outboard from the point where they
were mounted. These inertial forces were measured
by mounting an accelerometer outboard of the strain
gauges and as close as possible to the hub of interest.
Dynamic wheel forces were determined by combining
the accelerometer and strain gauge signals as indicated
in equation (1).

This is sometimes termed the “balance of forces”
technique (6,8,13,21,29,30) and is illustrated
diagrammatically in Figure 1 where:

Strain gauges
Wheel force - F
wheel
Accelerometer
Axle
Shear forces - F
shear
≧≘≕≕≜
≣≘≕≑≢








≝≑
(1)
a
= acceleration experienced by the mass
outboard of the strain gauge
m
= mass outboard of the strain gauge
s
hear
F
= shear force on the axle at the strain gauge

Bins loaded with scrap steel were used to load the
semi-trailer (Figure 2) to the maximum allowable mass
for a tri-axle group — 3.3t per set of duals or 1.65t per
tyre.
HV air spring suspensions have very little internal
damping. Hence dampers (shock absorbers) play a
very important role in an air suspension’s performance
characteristics. All suspension dampers were renewed
for the testing. New tyres were fi tted and infl ated
to the manufacturer’s specifi cation. Auxiliary
roll stiffness and Coulomb friction within the HV
suspension were in accordance with the manufacturer’s
specifi cation and remained consistent during the tests.
Tests were performed in the Brisbane area on both
highway and suburban roads and at different speeds.
The roads chosen had a mix of speed, roughness and
surface textures and were representative of what may
be expected during typical low, medium and high-
speed HV operation.
Figure 2. Test weights on semi-trailer vehicle
The dynamic signals from the on-board
instrumentation were recorded over a 10s sample time
at a 1kHz sample rate resulting in 10,000 data points
per test. Detailed testing procedures are documented
elsewhere (7,9,10,12).
Novel roughness
Road roughness is usually designated by a standard
measure - the international roughness index (IRI).
This measure is the sum of vertical oscillation
movement distance of a calibrated vehicle relative to
the horizontal distance travelled along the road during
the test run.
The units of this roughness measure are mm/m or
m/km. This measure is now standardised for use
around the world (25,26). Early Australian efforts
need to be recognised (18) - Figure 3 shows a device
for measuring roughness developed in Australia
in the early 1970s by NAASRA
2
. Roughness
was derived from the positive-going movements
between the chassis and rear axle of a calibrated
vehicle (usually a Ford Falcon station sedan). Each
count was proportional to approximately 15mm of
movement. Modern techniques measure roughness
by a combination of height measuring lasers and
accelerometers.

2 NAASRA was the National Association of Australian State Road Authorities. Its name changed and later became Austroads.
Figure 3. Diagram of the NAASRA novel rough-
ness meter
Differential
2 1
7
4
Revolution counter
Sprocket with
one-way clutch
Spring
Each semi-trailer hub had acceleration data recorded
during the on-road testing. Net vertical acceleration
measured at the hub was used after compensation for
the constant gravity component. A double integration
was performed on the vertical acceleration data. This
yielded a novel roughness value of positive vertical
movement of the axle for a given horizontal distance
travelled at a constant speed. The horizontal distance
travelled during each 10s sample period is dependent
on vehicle speed; hence the HV speed during each
test was recorded and included in the derivation of the
roughness results.
Equation 2 provides a mathematical derivation of the
novel roughness value used.
Note: Only the positive values of acceleration are
integrated, in line with the philosophy of the IRI
measure.
This novel roughness value should not be equated to
the IRI value as the novel roughness is determined
for a very short length of road while IRI tends to
be calculated over longer distances. It was derived
to provide an indicative measure of roughness as
experienced by representative hub accelerometers. It
arose from the unsprung mass dynamics combined
with road surface irregularities, wheel load and
speed. In this way, it was similar to the methodology
for determining IRI; that methodology does not
distinguish between contributory forces from the
axle-to-body dynamics of the test vehicle compared
with those from the surface irregularities of the
pavement (25,26). Even so, the novel roughness value
provided an independent variable against which to

plot
wheel force as the dependent variable.
Wheel forces vs. novel roughness
The data plotted from Figures 4 to 6 shows the peaks,
standard deviations and means of the wheel forces vs.
novel roughness values for the front axle of the tri-axle
group of the semi-trailer. The front axle plots were
very similar to those of the other two axles.
The linear regression correlation coeffi cients for
the relationship between semi-trailer wheel force
parameters and novel roughness (Figures 4 to 6) were
derived and are summarised in Figure 7.
In general, the semi-trailer’s increasing peak wheel
forces, exemplifi ed in Figure 4, corresponded to
increasing “novel roughness” values with linear
regression correlation coeffi cients well above 0.707.
Neither the standard deviation, nor the mean of the
wheel forces, correlated to increasing novel roughness,
even though Figure 6 may have indicated this on visual
inspection.
Figure 4. Semi-trailer axle peak wheel forces vs. novel
0 XXX 0000
Peak wheel forces vs. Novel roughness - front semi-trailer axle
3000
4000
5000
6000
7000
8000
9000
2.03
2.31
2.46
2.53
2.55
2.62
3.51
3.8
4.3
5.22
5.89
Novel roughness (mm/m)
Wheel force (kg)
LHS wheel force - semi-trailer axle
RHS wheel force - semi-trailer axle

novel roughness =
n a
a
a
v


 
 
 
 
0 0
x 1000
mm/m (2)
where:
a = net upward hub acceleration during the
recording period in ms
-2

v = velocity in ms
-1
per 10s sample period
n = the number of data points recorded per 10s
sample period
Figure 5. Semi-trailer axle mean wheel forces vs. novel roughness
Figure 6. Semi-trailer axle std. dev. of wheel forces vs. novel roughness
0 XXX 0000
Document7
Std. dev. of wheel force vs. Novel roughness - front semi-trailer axle
0
100
200
300
400
500
600
700
800
900
1000
2.03
2.31
2.46
2.53
2.55
2.62
3.51
3.8
4.3
5.22
5.89
Novel roughness (mm/m)
Wheel force (kg)
LHS wheel force - semi-trailer axle
RHS wheel force - semi-trailer axle
Std. dev. of wheel force vs. Novel roughness - front semi-trailer axle
0
100
200
300
400
500
600
700
800
900
1000
2.03
2.31
2.46
2.53
2.55
2.62
3.51
3.8
4.3
5.22
5.89
Novel roughness (mm/m)
Wheel force (kg)
LHS wheel force - semi-trailer axle
RHS wheel force - semi-trailer axle



















Std. dev. of wheel force vs. Novel roughness - front semi-trailer axle
0
100
200
300
400
500
600
700
800
900
1000
2.03
2.31
2.46
2.53
2.55
2.62
3.51
3.8
4.3
5.22
5.89
Novel roughness (mm/m)
Wheel force (kg)
LHS wheel force - semi-trailer axle
RHS wheel force - semi-trailer axle



















Figure 7. Correlation coeffi cients for wheel forces vs. novel roughness
The linear regression values for the three derived
parameters on the left side did not vary from those
on the right. Accordingly, whole-of-axle results are
shown in Figure 7.
A t-test is one test for confi rming, or otherwise, a
hypothesis where the test results follow a Student’s t
distribution if the null hypothesis is supported (20).
Figure 8. t-test results for left/right wheel force variation over “novel roughness” range.
A t-test (Figure 8) was performed for variations of
the left and right hand sides of the axle with respect
to standard deviation, mean and peak wheel forces
against increasing novel roughness values.
The shaded areas of Figure 8 indicate that the only
forces that varied per side were the mean wheel
forces with a 90% confi dence value.
Figure 9. t-test summary table for left/right variation axle forces vs. speed
Left/right wheel force t-test table for range of novel roughness – semi trailer axle group
Std. dev. per axle Mean per axle Peak per axle
Rear
Mid Front Rear Mid Front Rear Mid Front
0.923
0.852 0.840
0.0406
1 x 10
-4

1 x 10
-4
0.527 0.194 0.537

Speed
(km/h)
Left/right wheel force t-test table – semi trailer axle group
Std. dev. per axle Mean per axle Peak per axle
Rear Mid Front Rear Mid Front Rear Mid Front
40 0.576 0.883 0.768 0.633
0.016
0.018 0.801 0.434 0.344
60 0.978 0.867 0.887 0.591
0.001
0.003 0.801 0.544 0.943
80 0.851 0.809 0.767 0.290
0.028
0.036 0.624 0.631 0.831
90 0.881 0.909 0.885
0.063
0.010
0.019 0.795 0.684 0.804

Correlation coefficient, R, of wheel force parameters
over novel roughness range – semi trailer axle group

Std. dev. per axle Mean per axle Peak per axle
Rear Mid Front Rear Mid Front Rear Mid Front
<0.707 <0.707 <0.707 <0.707 <0.707 <0.707
>0.707
>0.707
>0.707

Wheel forces left/right variation vs. speed
Semi-trailer wheel forces were subjected to a t-test for
left/right position correlation vs. speed; the results are
shown in Figure 9. The t-tests indicated that the mean
wheel forces on the front and middle axles of the
semi-trailer varied per side for all speeds and
with a 90% confi dence value (shaded). This was
predominantly on the left but was biased toward the
right for one-way right lane test sections.
It is likely that these variations resulted from the
centre-of-gravity (CoG) of the semi-trailer shifting
to the left or the right, depending on cross fall. This
result was not too dissimilar from that for the mean
forces being dependent on side as in Figure 5. The
semi-trailer’s front and middle axles were particularly
affected by left/right variation but the rear axle was
only affected at the highest test speed. This would
seem to indicate that the front two axles on the semi-
trailer had left/right imbalances where the CoG was
thrown to one side or the other by the
cross-fall of the road for suburban up to intermediate
speeds. The rear axle was not so affected until
highway speeds were reached.
Road damage wavelength
Government Acts and Regulations, pavement design
manuals, etc tend to refer to vehicle static axle loads.
Indeed, when HVs are weighed for regulatory purposes
they are weighed statically not dynamically. When
Transport and Main Roads installs in-road dynamic
weight systems for survey information, particular care
is exercised to ensure the road prior to the weighing
device is smooth and fl at. Similarly, lay-bys for
enforcement weighing and the decks and approaches of
static weighbridges are smooth and level. Measuring
dynamic wheel forces directly is complex, as shown
above. Dynamic forces are considered, to some extent,
Figure 10. Predominant suspension frequencies and wavelength distances

3 lower bound for semi-trailer axle-hop.
4 upper bound for semi-trailer axle-hop.
by the adoption of road friendly suspensions but the
effi cacy of these in reducing wheel forces is still open
to debate, especially when these are not maintained (5,
8, 27).
When a vehicle’s tyres hit imperfections in the road
surface, dynamic wheel forces result. These dynamic
wheel forces have various frequencies of vibration.
There are two predominant types of vibrations -
axle-hop and body bounce. Body bounce has the
lower vibration frequency of the two.
As semi-trailer axle-hop and body-bounce frequencies
are the inverse of a signal’s period, this may be
translated back into a value of wavelength as measured
on the road. The result of these cyclic variations in
axle loads may be seen as road damage at regularly
spaced intervals. This cyclic length is dependant
on vehicle speed and may be derived from the
fundamental relationship between speed and distance
as follows:

Applying equation 5 to the test data, the HV’s
suspension wavelengths were derived after examining
the dominant axle-hop and body-bounce frequencies
at the corresponding test speeds (12). For brevity only
wavelengths for highway speeds are shown in
Figure 10.
Vehicle/axle
group
Speed
(km/h)
Body-
bounce
frequency
(Hz)
Axle-hop
frequency
(Hz)
Suspension wavelength
distance corresponding
to the body-bounce
frequency (m)
Suspension
wavelength distance
corresponding to the
axle-hop frequency (m)
80 1.7 10.0
3
13.1 2.2
90 1.7 10.0 14.7 2.5
80 1.7 12.0
4
13.1 1.9
Semi-trailer
tri-axle group
90 1.7 12.0 14.7 2.1
Distance travelled = velocity x time for one cycle (3)

Time for one cycle
f
requency

1

(4)

Combining equations 3 and 4 gives:

velocity
Distancetravelled
f
requency

(5)
The value of N is dependent on the type of materials
used in the pavement construction.
The current pavement models that use a number
of quasi-static passes of a HV axle at a theoretical
loading to determine pavement life do not always
consider peak dynamic forces; usually they consider
some nominal static force with an allowance for
standard deviation of the dynamic forces. On-board
mass research has found that mean wheel forces of
HVs in travel mode are not equal to static wheel
forces (19). The quasi-static application of pavement
loads from HV wheel forces in these models for
pavement design should be reviewed in light of the
dynamic data from the research presented here and
by others (3,4,5,6). More realistic dynamic pavement
loads from HVs need to be considered.
The semi-trailer wheel force standard deviations and
mean wheel forces did not correlate with increasing
novel roughness values. However, peak wheel forces
from the semi-trailer did correlate to increasing
values in novel roughness. Indicatively, the semi-
trailer exhibited variation per side in mean wheel
forces. These results obtained in this project make
a case for micro-profi ling or pavement overlays
on roads which have gone beyond some threshold
roughness value. Perhaps beyond some threshold
roughness, additional accelerated deterioration occurs
beyond normal predicted values due to the increased
dynamic wheel forces. Roughness increases dynamic
wheel forces which in turn cause accelerated road
damage (roughness) and so on — a vicious circle.
Pavement life calculations are based on standard axle
loads with equal wheel loads. However, in practice,
equal wheel loads from one side of a vehicle to the
other are rarely achieved. As an indicative exercise, a
3% cross-fall with a conservative CoG height of 1.5m
causes a variation in wheel loads of approximately 4.5
% when compared to the theoretical value for a fl at
surface (Figure 11). This 4.5% variation correlates
conservatively with the results as indicated in Figure 5.

Wheels on the left of the vehicle will add additionally
to pavement distress in two ways.
Moisture related pavement distress is caused
1.
by water infi ltration from road shoulders and
embankment edges. Hence moisture content is
typically higher in the LHS or outer wheel path.
Higher pavement moisture content accompanies
reduction in pavement strength. Seasonal rainfall
has thus more effect on the outer wheel path than
the inner wheel path. One consequence of these
effects is increased wheel rutting in the outer
wheel path which further leads to water ponding
in ruts and depressions with increased moisture
penetration and accelerated pavement degradation.
For a standard road formation with a cross-fall
2.
toward the LHS, a vehicle’s centre-of-gravity will
be closer to the LHS wheel than the RHS wheel
(Figure 11). The amount of weight increase on
the LHS will be matched by a decrease in weight
on the RHS wheel. The increase on the LHS
wheel load will be correspondingly accompanied
by an increased probability of greater dynamic
wheel forces. Accordingly, further unpredicted
accelerated deterioration will occur when more
heavily-loaded LHS wheels combine with higher
moisture content pavements.
Discussion
The measures of standard deviation, mean and peak
dynamic wheel forces all combine to show a picture
of pavement forces in the real world. Instantaneous
values of these forces can be up to double those of
the static force for which the pavement was designed.
Pavement damage models use a “power law” damage
exponent to account for the variation in empirical
pavement life correlated to axle load (Equation 6).

(6)
Pavement damage
N
Load ontest axle
Standard axleload
 

 
 

As indicated in equation 7 below, a 4.5% increase in
wheel load over a standard ESA wheel load will result
in a 20% increase in road damage. This increase is
very conservative as a damage factor of 4 is used
with no other allowance for dynamic effects. Even
using existing, conservative models, an indicative
20% increase in damage on the LHS of the lane would
indicate the need for a different design standard on
that part of the running lane. The model in Figure
11 does not take into account dynamic vehicle roll or
the additional load transfer as a result of fi fth wheel
interaction, tyre defl ections, chassis and suspension
interaction. Geotechnical domain experts should
consider the above factors in combination with a
higher damage power value.

(7)
A solution to this issue that was proposed some years
ago was to replace the uniform thickness base layer
with a tapered base layer. The base would be thinnest
at the crown and thickest at the shoulders. This
solution was not put into practice.
The contribution that body-bounce force makes to
pavement force is approximately equal to that of axle-
hop force (12). Accordingly, two sets of suspension
wavelengths need to be examined as they both
5 27.7m for 10Hz @ 100km/h
contribute to peak pavement forces from HV wheels.
Wheel forces from body bounce at highway speeds
will be repeated at approximately 15 - 28 m spacings
5
.
Axle-hop repetitive forces will occur at approximately
2 - 2.5 m intervals, depending on speed of travel.
This is termed “spatial repetition” and has been well
documented (17). Should a particular suspension have
its axle hop frequency
(i.e. axle hop force repetition) as a multiple of its
body-bounce frequency, a doubling of the
instantaneous pavement force will occur where the two
coincide at a common wavelength node.
Conclusion
The results of the testing indicate that augmentation
of existing pavement models should be examined.
Some pavement damage models that use static load
values have been mentioned above. Further, neither
roughness values nor peak wheel forces are included
in Australian pavement design models (2,22,23). The
results here indicate that the correlation of wheel
forces to roughness needs to be explored further, as
noted in other research (24). Further, the adherence
to HV suspension dynamic metrics containing only
standard deviations (16,27) needs to be re-examined
since the peak wheel forces of one of the workhorses
of the Australian HV fl eet, the semi-trailer, varied
proportional to novel roughness in a statistically
signifi cant manner whereas neither the wheel force
Figure 11. Effect of crossfall on wheel loads

948mm
1038mm
1
5
0
0
mm
3
%
c
r
o
s
s
f
a
l
l
R
av
+ 4.5%
R
av
- 4.5%
.%
4
1.045
12 20
1.0
Pavement damage or increase
 
 
 
 

standard deviations nor the mean wheel forces so
varied.
Augmentation of pavement models should account for:
actual dynamic wheel loading effects

a more complex set of considerations than simply

the static loads
the issue that neither standard deviation nor mean

wheel forces are dependant on roughness
changes of wheel loads due to pavement cross fall

and vehicle dynamics.
In particular, the left/right variation apparent in mean
wheel forces and the highly-dependent relationship
between novel roughness values and peak wheel
forces needs to be investigated further by pavement
technologists, geotechnical engineers and other domain
experts. Particular attention needs to be made to the
indication that the pavement under the outer wheel
path may need a different design standard from that of
the inner wheel path pavement.
The cause and effect relationship between roughness,
dynamic wheel loads and accelerated pavement
deterioration are other areas worthy of further research.
Acknowledgements
I would like to acknowledge the contribution and
advice from various offi cers of the Department of
Transport and Main Roads, Dr. Jon Bunker, Dr.
John Fenwick, Greg Hollingworth, Dr. Hans Prem,
Tramanco, Volvo Australia, RTA, Mylon Motorways
and Haire Truck & Bus.
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Davis L.
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Davis L, Bunker J.
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