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 triaxle 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 efficient
vehicles.
As the need for a vehicle driver is a given, costs are
reduced in these freight efficient 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 significantly 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).
Unofficial estimates put the number of road friendly
suspensions (RFS) sold in Australia per year at 90%
to 95% (28) of the total HV fleet1. 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 semitrailer test is the subject of this article. The semitrailer 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.
of the axle as close as possible to the wheel hub.
These gauges were calibrated to measure the vertical
shear force, Fshear. 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).
(1)
This is sometimes termed the “balance of forces”
technique (6,8,13,21,29,30) and is illustrated
diagrammatically in Figure 1 where:
a
=
acceleration experienced by the mass
outboard of the strain gauge
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
m
=
Fshear =
mass outboard of the strain gauge
shear force on the axle at the strain gauge
Axle
Shear forces - Fshear
Strain gauges
Wheel force - Fwheel
Figure 1. Instrumented HV axle used to derive tyre forces (8)
Accelerometer
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 fitted and inflated
to the manufacturer’s specification. Auxiliary
roll stiffness and Coulomb friction within the HV
suspension were in accordance with the manufacturer’s
specification 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 highspeed HV operation.
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.
Sprocket with
one-way clutch
2174
Spring
Revolution counter
Differential
Figure 3. Diagram of the NAASRA novel roughness meter
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).
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.
2 NAASRA was the National Association of Australian State Road Authorities. Its name changed and later became Austroads.
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.
Equation 2 provides a mathematical derivation of the
novel roughness value used.
novel roughness =
ªn a f º
«³ ³ a»
¬ 0 a 0 ¼ x 1000
mm/m
v
(2)
where:
Wheel forces vs. novel roughness
= net upward hub acceleration during the
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.
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
The linear regression correlation coefficients for
the relationship between semi-trailer wheel force
parameters and novel roughness (Figures 4 to 6) were
derived and are summarised in Figure 7.
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
In general, the semi-trailer’s increasing peak wheel
forces, exemplified in Figure 4, corresponded to
increasing “novel roughness” values with linear
regression correlation coefficients 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.
Peak wheel forces vs. Novel roughness - front semi-trailer axle
9000
LHS wheel force - semi-trailer axle
RHS wheel force - semi-trailer axle
7000
6000
5000
4000
Novel roughness (mm/m)
0 XXX 0000
Figure 4. Semi-trailer axle peak wheel forces vs. novel
5.89
5.22
4.3
3.8
3.51
2.55
2.53
2.46
2.31
3000
2.03
Wheel force (kg)
8000
2.62
a
Std. dev. of wheel force vs. Novel roughness - front semi-trailer axle
1000
900
700
600
500
400
300
200
5.89
5.22
4.3
3.51
2.55
2.53
2.46
2.31
2.03
0
3.8
LHS wheel force - semi-trailer axle
RHS wheel force - semi-trailer axle
100
2.62
Wheel force (kg)
800
Novel roughness (mm/m)
Figure 5. Semi-trailer axle mean wheel forces vs. novel roughness
Std. dev. of wheel force vs. Novel roughness - front semi-trailer axle
Std. dev. of wheel force vs. Novel roughness - front semi-trailer axle
1000
1000
600
500
400
300
200
5.89
5.22
4.3
3.8
3.51
2.55
2.53
2.46
600
2.31
0
2.62
LHS wheel force - semi-trailer axle
RHS wheel force - semi-trailer axle
100
2.03
700
700
Novel roughness (mm/m)
500
400
300
200
0 XXX 0000
Novel roughness (mm/m)
5.89
5.22
4.3
3.8
3.51
2.55
2.53
2.46
2.31
0
2.62
LHS wheel force - semi-trailer axle
RHS wheel force - semi-trailer axle
100
2.03
Wheel force (kg)
800
800
Wheel force (kg)
900
900
Document7
Figure 6. Semi-trailer axle std. dev. of 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 (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.
A t-test is one test for confirming, or otherwise, a
hypothesis where the test results follow a Student’s t
distribution if the null hypothesis is supported (20).
The shaded areas of Figure 8 indicate that the only
forces that varied per side were the mean wheel
forces with a 90% confidence value.
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
Figure 7. Correlation coefficients for wheel forces vs. novel roughness
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
Figure 8. t-test results for left/right wheel force variation over “novel roughness” range.
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
Figure 9. t-test summary table for left/right variation axle forces vs. speed
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% confidence 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 semitrailer 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.
by the adoption of road friendly suspensions but the
efficacy 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:
Distance travelled = velocity x time for one cycle (3)
Time for one cycle
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 flat. 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,
Vehicle/axle
group
Semi-trailer
tri-axle group
1
frequency
Combining equations 3 and 4 gives:
Distance travelled
velocity
frequency
(5)
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.
Speed
(km/h)
Bodybounce
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
90
80
90
1.7
1.7
1.7
1.7
10.03
10.0
12.04
12.0
13.1
14.7
13.1
14.7
2.2
2.5
1.9
2.1
Figure 10. Predominant suspension frequencies and wavelength distances
3 lower bound for semi-trailer axle-hop.
4 upper bound for semi-trailer axle-hop.
(4)
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).
§ Load on test axle ·
Pavement damage ¨
¸
© Standard axle load ¹
N
(6)
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 flat
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.
1. Moisture related pavement distress is caused
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 semitrailer exhibited variation per side in mean wheel
forces. These results obtained in this project make
a case for micro-profiling 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.
by water infiltration 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.
2. For a standard road formation with a cross-fall
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.
1500mm
3% crossfall
Rav + 4.5%
948mm
Rav - 4.5%
1038mm
Figure 11. Effect of crossfall on wheel loads
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 fifth wheel
interaction, tyre deflections, chassis and suspension
interaction. Geotechnical domain experts should
consider the above factors in combination with a
higher damage power value.
4
ª1.045 º
Pavement damage v «
» | 1.2 or 20% increase
¬ 1.0 ¼
(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 axlehop 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 spacings5.
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 fleet, the semi-trailer, varied
proportional to novel roughness in a statistically
significant manner whereas neither the wheel force
standard deviations nor the mean wheel forces so
varied.
Augmentation of pavement models should account for:
4. Cebon D. Interaction between heavy vehicles
•
actual dynamic wheel loading effects
5. Cebon D. Tyres, Suspensions and Road Damage.
•
a more complex set of considerations than simply
the static loads
and roads. Paper presented at the 39th L Ray
Buckendale lecture. 1993
5th Brazilian Congress on Roads and Concessions.
2007
6. Cebon D. Handbook of vehicle-road interaction.
•
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.
Lisse, South Holland, Netherlands: Swets &
Zeitlinger. (Ed.) 1999
7. Davis L. Further developments in dynamic testing
of heavy vehicle suspensions. Paper presented at
the 30 th Australasian Transport Research Forum
(ATRF). 2007
8. Davis L, Bunker J. Heavy Vehicle Suspensions
– Testing and Analysis. A literature review.
Brisbane, Queensland: Queensland Department
of Main Roads; Queensland University of
Technology. 2007
9. Davis L, Bunker J. Heavy vehicle suspensions testing and analysis: Phase 3 - eigenfrequency
peak loads. Test plan. Brisbane, Queensland:
Queensland University of Technology. 2008
10. Davis L, Bunker J. Larger air lines in heavy
Acknowledgements
I would like to acknowledge the contribution and
advice from various officers 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.
References
1. Alabaster D, Arnold G, Steven B. The equivalent
standard axle approach and flexible thin surfaced
pavements. Christchurch New Zealand: Transit
New Zealand, Pavespec Limited, University of
Canterbury. 2004
2. Austroads Pavement design: A guide to the
structural design of road pavements. Sydney,
NSW, Australia: Austroads. 1992
3. Cebon D. Assessment of the dynamic wheel forces
generated by heavy road vehicles. Paper presented
at the Symposium on Heavy Vehicle Suspension
Characteristics, Canberra, Australia. 1987
vehicle suspensions – differences in wheel and
air spring forces. Paper presented at the 31st
Australasian Transport Research Forum (ATRF).
2008
11. Davis L, Bunker J. Suspension testing of 3 heavy
vehicles – methodology and preliminary frequency
analysis. Brisbane, Queensland: Queensland
Department of Main Roads; Queensland
University of Technology. 2008
12. Davis L, Bunker J. Suspension testing of 3 heavy
vehicles – dynamic wheel force analysis. Brisbane,
Queensland, Australia: Queensland Department
of Main Roads & Queensland University of
Technology. 2009
13. de Pont J J. Assessing heavy vehicle suspensions
for road wear Research report No. 95. Wellington,
New Zealand: Transfund New Zealand. 1997
14. de Pont J J, Pidwerbesky B. Vehicle dynamics and
pavement performance models. Paper presented
at the 17th Australian Road Research Board Ltd
(ARRB) Conference, Gold Coast, Queensland,
Australia. 1994.
15. de Pont J J, Steven B. Suspension dynamics
and pavement wear. Paper presented at the
Conference on Vehicle-Infrastructure Interaction
VI, Zakopane, Poland. 1999
16. Eisenmann J. Dynamic wheel load fluctuations road stress. Strasse und Autobahn, 4, 2. 1975
17. Jacob B. Spatial repeatability Summary of the
final report DIVINE Element No. 5, Paris: OECD.
1996
18. Kaesehagen R L, Wilson O A, Scala A J, Leask
A. The development of the NAASRA roughness
meter. Paper presented at the 6th Australian Road
Research Board (ARRB) Conference, Canberra,
Australia. 1972
19. Karl C, Davis L, Cai D, Blanksby C, Germanchev
A, Eady P et al. On-board mass monitoring test
report (final). Melbourne, Victoria, Australia:
Transport Certification Australia Ltd. 2009
20. Kleyner A V. Determining optimal reliability
targets through analysis of product validation cost
and field warranty data. University of Maryland,
College Park, Maryland, USA. 2005
21. LeBlanc P A, Woodroofe J H F, Papagiannakis A
T. A comparison of the accuracy of two types of
instrumentation for measuring vertical wheel load.
In D. Cebon & C. G. B. Mitchell (Eds.), Heavy
vehicles and roads: technology, safety and policy
(pp. 86-94). London: Thomas Telford. 1992.
22. Main Roads Western Australia. Engineering
Road Note 9. 2005 Retrieved from http://standards.
mainroads.wa.gov.au/NR/rdonlyres/8A3AFFDB-068D-41DFABF6-ED290B98E525/0/E6907_20080314160946492.PDF.
23. Moffatt M A. The accelerated loading facility
as an accelerated learning tool. Edition No 6
Queensland Roads, Main Roads Queensland.
2008
24. OECD. Dynamic interaction between vehicles
and infrastructure experiment (DIVINE).
Technical report no. DSTI/DOT/RTR/IR6(98)1/
FINAL. Paris, France: Organisation for Economic
Co-operation and Development (OECD). 1998
25. Sayers M W, Gillespie T D, Paterson W D O.
Guidelines for conducting and calibrating road
roughness measurements. World Bank technical
paper no. 46. Washington DC, USA: World Bank.
1986
26. Sayers M W, Gillespie T D, Hagan M.
Methodology for road roughness profiling and rut
depth measurement. Washington, DC, USA; Ann
Arbor, Michigan, USA: United States Federal
Highway Administration; University of Michigan.
1987
27. Sweatman P F. A study of dynamic wheel forces in
axle group suspensions of heavy vehicles. Special
report no 27. Vermont South, Victoria, Australia:
Australian Road Research Board (ARRB). 1983
28. Sweatman P F, McFarlane S. Investigation into
the Specification of Heavy Trucks and Consequent
Effects on Truck Dynamics and Drivers: Final
Report. DoTaRS. 2000
29. Whittemore A P. Measurement and prediction of
dynamic pavement loading by heavy highway
vehicles. SAE technical paper, No: 690524,
15. 1969
30. Woodroofe J H F, LeBlanc P A, LePiane K R.
Vehicle weights and dimensions study; volume
11 - effects of suspension variations on the
dynamic wheel loads of a heavy articulated
highway vehicle (Technical report). Ottawa,
Ontario, Canada: Canroad Transportation;
Roads and Transportation Association of
Canada (RTAC). 1986