Author
Dipl.-Ing. Roland Spielhofer
Institution
arsenal research – Österreichisches Forschungs- und Prüfzentrum
Arsenal Ges.m.b.H.
Business Field Transport Routes Engineering
1210 Vienna, Giefinggasse 2
T: +43 (0) 50 550-6284, F: +43 (0) 50 550-6599
E: [email protected]
Title
Describing longitudinal evenness
Keywords and Topics
Longitudinal evenness, roughness, road engineering, high speed profilometer
Abstract
Longitudinal evenness is an important influencing factor as well on road safety (ruts,
aquaplaning) and ride comfort as on the durability of roads (increased dynamic axle loads of
trucks). The wavelengths covered by longitudinal evenness range from 0.5 to 50 m.
Different approaches have been made over the years to describe and judge the different forms
of (un-)evenness, mainly periodic and irregular discontinuities and singular events. Each of
these descriptive parameters has another weakness, most of them not covering periodic
discontinuities. In Austria, the International Roughness Index (IRI) is in use for pavement
management systems at present, the 4 m-straight edge is used for acceptance tests. Both
methods have their own problems: The IRI is not capable to detect periodic discontinuities
and is – overall – a rather inaccurate parameter, while the 4 m-straight edge is unable to cover
longer wavelengths. To overcome these shortcomings, a research project was started to
develop a better parameter as well for pavement management as for acceptance tests.
After a comprehensive literature review thirty test sections containing all different aspects of
longitudinal evenness problems were picked out. The focus was set on a good representation
of the different road designs used in Austria (asphalt, asphalt concrete, concrete), different age
of the pavements and different types of roads (motorways, city streets, …) These sections
were measured with a high speed laser profilometer (RoadSTAR) and true profiles where
calculated.
Then, the true profiles were examined and a characterization of the profiles was done.
Knowing the “real” unevenness of the sections, different parameters (PSD, IRI, AUN, LWI,
…) from the literature review were applied on the profiles to see how good these parameters
judge the evenness problems. The weighted longitudinal profile showed good results and is
able to judge all relevant phenomena of longitudinal evenness. The used weighting function
allows the user to adjust for his own highway level characteristics. A detailed investigation
with this parameter on network level has still to be done.
DI Roland Spielhofer
Vienna, 2004-04-24
1. Introduction
Longitudinal evenness is an important influencing factor on road safety (ruts, aquaplaning)
and ride comfort and on the durability of roads (increased dynamic axle loads of trucks) as
well. Axle loads increased during the past twenty years, a further increase of allowed axle
loads is in discussion at the moment. As the axle load is generally considered with its fourth
power in road deterioration, just a small increase in axle load has an effect on road
deterioration.
Concerning the longitudinal eveneness (or roughness) of roads, three phenomena are
generally distinguished:
•
general unevenness
•
periodical unevenness
•
singular obstacles
To characterize road roughness the road profile is considered a stochastic signal. Wavelengths
ranging from 0.5 to 50 m are defined as unevenness, wavelengths below belong to
megatexture (0.05 to 0.5 m) and wavelengths above belong to road alignment [1].
2. Motivation – situation in Austria
In Austria, longitudinal evenness is described with two different parameters: The IRI
(International Roughness Index) is used for pavement management purposes, and the 4 m
straight edge is used for acceptance tests. This regime shows several weaknesses: The IRI is
not able to differentiate between general and periodical unevenness. Singular obstacles are not
DI Roland Spielhofer
Vienna, 2004-04-24
judged properly. The 4 m-straight edge is a time consuming procedure and does not cover the
longer wavelengths. It is not possible to use the 4 m-straight edge on network level.
In comparison, here the situation in other countries: In Germany, the 4 m-straight edge is used
for acceptance tests as well, for pavement management purposes, the effective longitudinal
evenness index (LWI) is used, as well as a new parameter named “Bewertetes Längsprofil”
(weighted longitudinal profile).
In Switzerland, the goniometry method is used for acceptance tests, but in discussion with the
Suisse colleagues we discovered that they were not satisfied with their parameter and are
looking for a new method to describe the longitudinal evenness as well.
In several other countries, the IRI is used for pavement management purposes.
This led to a research project funded by the Austrian ministry of transport, infrastructure and
technology. Partners in this project – that will last until end of 2007 – are arsenal research as
project leader, the institute for road construction and road maintenance of Vienna’s technical
university and Magna Steyr Fahrzeugtechnik.
3. Research projects
3.1
Literature review
At first a comprehensive literature survey was done. Special focus was set on the following
topics:
•
Measurement of longitudinal evenness. Different measurement techniques were
described, ranging from rather simple devices as straight edge or bump integrator over
the advanced contactless devices using laser measurements up to full 3D photographic
measurements 3D laser scans.
•
Description of longitudinal evenness. The standards in different countries (Austria,
Germany, Switzerland, France, USA) were compared and the different indices for
describing longitudinal evenness itself or the effects of longitudinal evenness on the
road and on the road user (vehicles as well as humans) were reviewed.
3.2
Definition of test sections
A pool of thirty test sections was defined for measurements. The thirty test sections were
chosen to represent different aspects of longitudinal evenness. The following criteria were
used:
•
different materials: asphalt, asphalt concrete, concrete, cobblestones
•
different age of the pavements
DI Roland Spielhofer
Vienna, 2004-04-24
•
different street categories: motorways, expressways, federal roads, urban roads
•
sections with a subjective impression of a bad driving comfort
•
sections with very low as well as sections with very high IRI
•
sections with all over bad road conditions
The lengths of the sections varied from one to fifteen kilometres which led to a total length of
115 km.
A map of Austria showing the distribution of the test sections is shown in Figure 1 below.
Figure 1: The thirty test sections (marked black)
3.3
Measurement of true profile
All test sections were measured with the Austrian high performance measurement vehicle
“RoadSTAR”. Profile measurements are done with a device consisting of four laser sensors
with a measuring accuracy of ±0.1 mm. The four sensors are mounted on an aluminium
profile with a length of two metres (see Figure 1).
3.4
Calculation of true profile
The calculation of the true profile is based on the profilometer method. The measurement
system is divided into a symmetric system (sensors 1, 3 and 4 – see Figure 1) and a
asymmetric system (sensors 1, 2 and 4 – see Figure 1). The symmetric system is used for
capturing the long wave unevenness; the asymmetric system is used for capturing the short
wave unevenness.
DI Roland Spielhofer
Vienna, 2004-04-24
Measurement values of the four laser sensors are collected every five millimetres. Ten of
these measurement values are averaged for a resulting value each five centimetres. For the
filtering of spikes, a median filter of ± 2 values is applied. A superposition of the symmetric
and asymmetric profile adds up to the true longitudinal profile. The profile is high pass
filtered to contain only wavelengths ranging from 0.5 to 50 metres according to [1]
Figure 2: Measurement system for longitudinal evenness
4. Data analysis
Starting from the true profile of all thirty test sections, several calculations were done for each
test section. At first, the true profile was plotted in sections of 100 m. As we discovered, just
by looking on the actual profile, it is possible to do a rough characterization of the section.
The different longitudinal evenness phenomena can clearly be seen in the plots.
4.1
Statistical parameters
Mean values and variances for 100 m sections were calculated and a histogram was plotted
for every test section (see Figure 3).
DI Roland Spielhofer
Vienna, 2004-04-24
Figure 3: Mean value and variance for 100 m sections
4.2
Power spectral density (PSD)
General
The power spectral denisty was computed for every 1000 m section according to ##. It is
plotted with a log/log. The PSD diagram shows the “intensity” of every wavelength in the
spectrum. A regression line is computed; the value of the regression line at Ω= 100 rad/m is
called the “Allgemeine Unebenheit” (AUN) – a parameter used in Germany – that gives an
indication for the general “niveau” of the longitudinal evenness of the actual section. The
absolute value of the slope of the regression line is called the “waviness”. The value of the
waviness depends on the relation between long wavelengths and short wavelengths. Dominant
higher wavelengths in the spectrum lead to a higher waviness. For the interpretation of the
PSD, lines for the ISO road classes were implemented. These classes show – quite similar to
the AUN the general quality of the longitudinal evenness of a road.
DI Roland Spielhofer
Vienna, 2004-04-24
Figure 4: Sample PSD for a road with a high proportion of longh wavelengths
Interpretation
The PSD gives a good characterization of the road section concerning general unevenness (the
higher the AUN, the worse is the evenness). Periodic unevenness is clearly shown with peaks
in the spectrum. The classification with ISO road classes show the distribution of wavelengths
in the spectrum – if the whole spectrum fits in one class the distribution is equivalent through
the whole spectrum. And last but not least: the PSD is a completely geometric parameter for
the description of evenness. There is no assumption about the effects of the evenness for
vehicles or road durability made. Some weaknesses of the PSD as a parameter describing
longitudinal evenness has been detected as well:
•
The PSD cannot discover singular obstacles as it is computed in frequency domain.
•
The PSD has to be computed for a minimum length of about of 1000 m. Using smaller
section lengths lead to higher uncertainties. For acceptance tests, a minimum section
length of 1000 m is too long.
•
Singular obstacles cannot be localized.
•
The PSD gives visually a good overview about the evenness characteristics of a road and
the picture is quite intuitive, but it can’t be described by just one parameter. Furthermore,
a judgement of the PSD (peaks for periodic unevenness etc) is difficult.
DI Roland Spielhofer
Vienna, 2004-04-24
4.3
Wave band analysis and Notes par Bandes d´Ondes
Wave band analysis is the name of a method described in [1]. The signal is filtered in three
wavebands: Short wavelengths from 0.781 to 3.125 m, medium wavelengths from 3.125 to
12.5 m and long wavelengths from 12.5 to 50 m. Then, for every band the square mean value
is computed for a presentation length of 100 m. The result of the wave band analysis itself
doesn’t give a clear image of the unevenness problems of a road section. Due to the higher
amplitudes of the longer wavelengths, the derived values are always higher for the long
wavelengths – see Figure 5. What is missing is a normalization that brings a relation into the
values of the three bands. One possibility for this relation is the French method Notes par
Bandes d´Ondes [6]. The splitting of the signal into three bands is the same as in the wave
band analysis, but it adds a weighting function to get a dimensionless value for the evenness
for the three wavebands. These values range from 10 (best) to 0 (worst) – see Figure 6. The
values were calculated for presentation lengths of 50 m. A deeper analysis showed good
results for the characterization of road unevenness. Singular obstacles showed a significant
decline in the short waveband value, and general unevenness was good represented in lower
values in all three bands. There is a rating for acceptance test and one for pavement
management purposes (target value, threshold value and critical value).
Figure 5: Wave band analysis of test section 12
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Vienna, 2004-04-24
10
9
8
Bew ertung [0-10]
7
6
5
4
3
2
Short Wavelength
Medium Wavelength
1
Long Wavelength
0
0
250
500
750
1000
1250
1500 1750
2000 2250
2500
2750
3000 3250
3500 3750 4000
4250 4500
4750
5000
5250 5500
5750
Stationierung [m]
Figure 6: Noted par Bandes d´Ondes for test section 13 –through the normalization the
dominant short wavelenght are highlighte
4.4
Effective longitudinal evenness index (LWI)
The LWI focuses on the effects of longitudinal evenness on. The parameter is split into three
domains:
•
strain of road and driving safety
•
strain of driver
•
strain of cargo
The rating is done with a filtering in three wavebands, one representing “the human”, one for
wheel load and one for cargo. The filter results are normalized and the highest value of the
three components is the final index. The presentation length is set to 100 m.
For the refinement of the LWI calculation, different truck models were investigated. At last, a
rather detailed truck model with ten degrees of freedom was chosen to catch the different
effects and interactions of tractor and semitrailer. The same model was chosen to calculate the
actual wheel load described below. The LWI showed good results in finding and rating
singular obstacles and also the judging of general unevenness was found to be good. Periodic
unevenness was underrated. An advantage of the LWI is the good localisation of the evenness
problem along the section. A disadvantage is the merging of the three values, so that from the
result one cannot tell if the value comes from a singular obstacle (wheel load filter) or from
long wavelengths (human filter). Furthermore, the results of the LWI are dependent on the
speed that is considered for the human or truck that is moved along the profile.
DI Roland Spielhofer
Vienna, 2004-04-24
Figure 7: Example for LWI calculation. The first diagram shows the result of the human filter,
the second one the result of the wheel load filter, the third one shows the result of the
cargo filter and the last graph shows the maxima of the three filters above.
4.5
Dynamic wheel loads and pavement loading
To calculate the effects of unevenness on the road itself, a sophisticated truck model with ten
degrees of freedom was introduced (see Figure 8). In a simulation environment, the truck was
driven with 80 km/h over the calculated longitudinal profile and the (dynamic) wheel loads
were calculated for every point of the profile. Furthermore, three parameters for pavement
loading [2, 3 and 4] were calculated for presentation length of 50 m. The decisive value for
the pavement loading is the ratio between the standard deviation of the dynamic wheel loads
and the static wheel load. The static wheel load is constant, so an analysis of the standard
deviations gives a hint on the pavement loading itself. The analysis showed a good correlation
to what was expected from the visual inspection of the true profile. Singular obstacles were
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Vienna, 2004-04-24
rated with high values for pavement loading, and periodic unevenness showed raised values
as well. Very long wavelength (≥30 m) had – as expected – almost no impact on pavement
loading. So from a road operator’s point of view, these parameters seem to be sufficient to
describe the effects of unevenness properly. A shortcoming of these values is the disregard of
the longer wavelengths, that are mainly a riding comfort issue – important for the road user,
but not that important for the road operator.
Figure 8: Truck model with ten degrees of freedom for dynamic wheel load calculation
Figure 9: Calculation of pavement loading according to [3]. A value of 1 is equivalent to the
damage an axle of 10 tons does.
4.6
Weighted longitudinal profile
A new parameter developed in Germany was investigated as well – the weighted longitudinal
profile [5]. As with other parameters, the true profile is transformed into the frequency
DI Roland Spielhofer
Vienna, 2004-04-24
domain. Then, the spectrum is weighted in ten consecutive octavos. The weighting function is
derived from the PSD analysis. Through a retransformation into space domain a weighted
profile is calculated that amplifies singular obstacles as well periodic unevenness. The
describing parameters are range and standard deviation that are usually calculated for a
presentation length of 100 m. The weighted longitudinal profile has some advantages: It rates
the singular obstacles very well and also the periodic unevenness. Furthermore, the longer
wavelengths are rated well and through modification of the weighting function one can give
special emphasis on short or long wavelengths. Noticeable high values can easily be located
along the section as the profile is an output of the calculation as well. Range and standard
deviation are of good use in pavement management systems whereas the weighted profile
itself is useful on project level.
Figure 10: Principle of calculation of the weighted longitudinal profile [5]
5. Conclusions and further research
Until now, several parameters for the description and rating of the different phenomena of
longitudinal evenness were examined and calculated for thirty road sections in Austria.
Keeping the true profile, pavement loading and hence road detoriation in mind, the weighted
longitudinal profile showed to fulfil the needs for a sufficient description of longitudinal
evenness. The weighting function can be adjusted to reflect the specific characteristics of a
road network. The next step is to calculate the weighted longitudinal profile for the whole
Austrian high level road network (about 4.000 km) with different weighting functions to get a
distribution of values on network level. After that, a rating background has to be defined for
pavement management systems and limits for acceptance tests have to be defined.
DI Roland Spielhofer
Vienna, 2004-04-24
6. Literature
[1]
prEN 13036-5 Surface Characteristics of Road and Airfield Pavements. Test methods
– Part 5: Determination of Longitudinal Uneveness Indices.
[2]
EISENMANN J,. Betonfahrbahnen. Handbuch für Beton-, Stahlbeton- und
Spannbetonbau, Verlag von Wilhelm Ernst & Sohn, München, 1979
[3]
MITSCHKE M., Dynamik der Kraftfahrzeuge. Springer-Verlag, Berlin, 1984
[4]
MITCHELL C.G.B., GYENES L., The Spatial Repeatability of Dynamic Pavement
Loads caused by Heavy Goods Vehicles. Proceedings of the Third International
Symposium on Heavy Vehicle Weights and Dimensions, Cambridge, 1992
[5]
UECKERMANN A.: Das bewertete Längsprofil, Straße und Autobahn, Heft 1,
Kirschbaum Verlag, Köln, 2005
[6]
Laboratoire Central des Ponts et Chaussées: Mesure de l’uni longitudinal des
chaussées routières et aéronautiques ; Méthode d’essai No. 46
DI Roland Spielhofer
Vienna, 2004-04-24