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Road and airfield surface characteristics - Test methods - Part 5: Determination of
longitudinal unevenness indices
Oberflächeneigenschaften von Straßen und Flugplätzen - Prüfverfahren - Teil 5:
Bestimmung der Längsunebenheitsindizes
Caractéristiques de surface des routes et aérodromes - Méthodes d'essais - Partie 5:
Détermination des indices d'uni longitudinal
Ta slovenski standard je istoveten z: prEN 13036-5
ICS:
17.040.20 Lastnosti površin Properties of surfaces
93.080.10 Gradnja cest Road construction
93.120 *UDGQMDOHWDOLãþ Construction of airports
oSIST prEN 13036-5:2006 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
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oSIST prEN 13036-5:2006
EUROPEAN STANDARD
DRAFT
prEN 13036-5
NORME EUROPÉENNE
EUROPÄISCHE NORM
January 2006
ICS
English Version
Road and airfield surface characteristics - Test methods - Part 5:
Determination of longitudinal unevenness indices
Oberflächeneigenschaften von Straßen und Flugplätzen -
Prüfverfahren - Teil 5: Bestimmung der
Längsunebenheitsindizes
This draft European Standard is submitted to CEN members for enquiry. It has been drawn up by the Technical Committee CEN/TC 227.
If this draft becomes a European Standard, CEN members are bound to comply with the CEN/CENELEC Internal Regulations which
stipulate the conditions for giving this European Standard the status of a national standard without any alteration.
This draft European Standard was established by CEN in three official versions (English, French, German). A version in any other language
made by translation under the responsibility of a CEN member into its own language and notified to the Management Centre has the same
status as the official versions.
CEN members are the national standards bodies of Austria, Belgium, Cyprus, Czech Republic, Denmark, Estonia, Finland, France,
Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania,
Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom.
Recipients of this draft are invited to submit, with their comments, notification of any relevant patent rights of which they are aware and to
provide supporting documentation.
Warning : This document is not a European Standard. It is distributed for review and comments. It is subject to change without notice and
shall not be referred to as a European Standard.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
Management Centre: rue de Stassart, 36 B-1050 Brussels
© 2006 CEN All rights of exploitation in any form and by any means reserved Ref. No. prEN 13036-5:2006: E
worldwide for CEN national Members.
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Contents Page
Introduction .3
1 Scope.3
2 Normative references.4
3 Terms and definitions .4
4 Symbols and abbreviations .6
5 Computation of unevenness indices.7
5.1 General overview of the computation .7
5.2 Pre-filtering and re-sampling.8
6 Computation of unevenness indices.11
6.1 International Roughness Index (IRI) .11
6.1.1 General.11
6.1.2 Moving average length.12
6.1.3 Presentation base length .12
6.2 Wave bands analysis.12
6.2.1 Computation of the indices .12
6.2.2 Filters.13
6.2.3 Filtering algorithm.14
6.2.4 Wave band indices.15
6.3 PSD analyses.16
6.3.1 Segmentation and windowing.16
6.3.2 PSD Computation.16
6.3.3 De-colouring.16
6.3.4 Smoothing.16
6.3.5 Fitting and computation.16
7 Test report.18
Annex A (informative) Re-sampling.19
Annex B (informative) Wave bands analysis.20
B.1 Re-sampling and three bands filtering .20
B.1.1 Re-sampling and three bands filtering process detailed algorithm.22
B.2 Detailed characteristics of filters .24
Annex C (informative) An illustration of PSD computation .26
C.1 General.26
C.2 Segmentation and windowing.26
C.3 PSD Computation.27
C.4 De-colouring.27
C.5 Smoothing.27
C.6 Fitting and computation.30
Bibliography .35
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Foreword
This document (prEN 13036-5:2006) has been prepared by Technical Committee CEN/TC 227 “Road
materials”, the secretariat of which is held by DIN.
This document is currently submitted to the CEN Enquiry.
Introduction
The road profile unevenness through road/vehicle dynamic interaction and vehicle vibration affects safety (tyre
contact forces), ride comfort, energy consumption and vehicle wear. The road profile unevenness is
consequently a key information for road maintenance management systems.
The measurement of road unevenness has been a subject of numerous researches for more than 70 years.
Methods developed can be classified into two types:
those based on response type devices and
those based on profiling devices or profilometers.
Assessing the condition of a road using a profilometer usually involve to record its profile, then computing a
limited set of numbers or indices characterising the unevenness, and eventually comparing these indexes to a
reference scale. Only profilometers able to digitise and record under a digital format a road profile from which
different indices can be computed are considered in this prEN 13036-6.
The purpose of this document is to standardise various possible characterisations of the road profile
unevenness such as the International Roughness Index (IRI) computation procedure, wave bands analyses
as well as Power Spectral Density (PSD) analyses. The objective of the document is not to impose a single
specific procedure but to insure that when applying one of the possible procedure exactly the same steps are
carried out with the aim of facilitating the comparison of unevenness measurements carried out with different
profiling instruments in European countries.
It is beyond the scope of this document to provide reference values for these indices, or to provide detailed
information about the characteristics of profilometers.
1 Scope
This document defines different possible methods for processing digitised road profiles:
Computation of the International Roughness Index (IRI); based on the Golden car characteristics,
Spectral analyses: Wave band analysis and Spectrum analysis, based on the Power Spectral Density
(PSD)
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2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
prEN 13036-6, Road and airfield surface characteristics — Test methods — Part 6: Measurement of
transverse and longitudinal profiles in the unevenness and megatexture wavelength ranges.
ISO 2041, Vibration and shock — Vocabulary.
ISO 8608, Mechanical vibrations — Road surface profiles — Reporting of measured data.
ANSI – S1. 11-2004-07-27, Specification for octave band and fractional octave band, analog and digital filters.
IEC 61260, Octave-band and fractional-octave-band filters.
ISO TS 13473-4, Characterisation of pavement texture by use of surface profiles. (in preparation)
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
3.1
profile
is the intersection between the surface of the pavement and the plane which contains both the vertical of the
measured pavement and the line of travel of the measuring instrument; when the measuring instrument
travels in a curve the line of travel is the tangent to that curve, when travelling in a straight line it is this line. In
this plane, a point of the profile can be adequately described by its coordinates x (abscissa) and z (elevation),
in any orthonormal reference system (X, Z), where Z is parallel to the aforementioned vertical
3.2
spatial sampling interval
is the absolute value of the difference of abscissa between two adjacent points of the digitised longitudinal
profile line. This definition assumes that the distance measured by the profilometer, which is usually related to
the curvilinear abscissa, is close enough to the abscissa in the mathematical sense
3.3
longitudinal road profile
is one of the profiles obtained when the measuring instrument travels in the same direction as the usual traffic.
Usually one of the profiles measured in the wheel tracks is used
NOTE Strictly speaking the digitised profile given by a profilometer, is a distorted image of the real profile, usually
referred as a pseudo-profile ; in order to make the remaining part of this standard more easy to read the word profile is
used to denote this image.
3.4
Longitudinal unevenness
is the deviation of the longitudinal profile from a straight reference line in a wavelength range of 0,5 m to 50 m.
The reference line, is usually the intersection of the profile plane and the horizontal plane.
The range from 0,5 m to 50 m is the common range for roads. This limit can be extended to 100 m for
runways. Higher values don’t deal with unevenness but depend on road geometry
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3.5
raw profile
is the profile given by a profilometer when measuring a longitudinal road profile. Characteristics of raw profile,
depend on the profilometer used
3.6
pre-processed profile (re-sampled and filtered profile)
is obtained by applying the re-sampling and filtering procedure described in clause 6. The pre-processing
procedure aims to harmonize the profile provided by various devices
3.7
wavelengths
in most cases the profile can be adequately described as a sum of sine functions, when this is possible one
such sine function is
2π
Asin ()x − x
0
Λ
Where
Λ is the wavelength of the sine in metres (m);
A is the amplitude of the sine in metres (m);
x is the abscissa of the current point, in metres (m);
x is the phase of the sine, in metres (m).
0
3.8
spatial frequency
is the reciprocal of a wavelength in cycles per metre. The spatial frequency N defines the number of waves, of
wavelength Λ, per metre:
1
N =
Λ
3.9
spatial sampling interval
is the horizontal distance between two adjacent points of the digitised longitudinal profile line
3.10
standard reference sampling interval
is the spatial sampling interval which must be used when computing the indices defined in this standard, its
value is 0,05 m
3.11
measuring track
is the intersection of the envelope of the profile plane and the horizontal plane
3.12
profile measurement length
is the length of an uninterrupted profile measurement. It is the length over which the profilometer continuously
and accurately digitises and records the profile (from point B to C in Figure 1). Most profilometers need to run
for some minimum distance before and after the very profile they are to measure, these starting (from point A
to B in Figure 1) and ending phases (from point C to D in Figure 1) should not be included in the profile
measurement length
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Key
1 road
2 l . . . l sample reporting length
0 n
3 profile measurement length
4 overall profilometre route
Figure 1 — Profile lengths definitions
3.13
evaluation or reporting length
are the measurements made over the profile measurement length which are often analysed using shorter
parts or samples (l to l in Figure 1) to allow for a more precise description of the measured profile. The
0 n
evaluation or reporting length is the length of such a sample
NOTE In the case of consecutive samples such as l and l in Figure 1, over the profile measurement length, the
0 1
word “segment” is used.
3.14
PSD (Power Spectral Density)
Is the limiting mean-square value of a signal spectrum per unit bandwidth, i.e. the limit of the mean-square
value in a rectangular bandwidth divided by the bandwidth, as the bandwidth approaches zero. In the
unevenness measurement field, the signal used is usually the road profile. In practice the PSD spectrum is
characterised by fitted straight regression line[s] and expressed by indices related to the location of these
line[s]
4 Symbols and abbreviations
Symbols, which are used in equation are written using normal characters, abbreviations are written using bold
characters.
B is the base used for IRI computation in metre (m). It is the length over which the IRI computation
is performed (or reporting length using the terminology of this document).
G(x) is the displacement PSD value for the spatial frequency x;
3
L denotes the measurement length, in metres (m), provided the conversion factor (1 km = 10 m) is
given, kilometres can be used as an alternative;
1
N is the spatial frequency, in cycles per metre (m): N = ; N is usually called a wave number;
Λ
X is the abscissa of the sampled point i, in metre (m).
i
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z is the elevation of the profile determined at the sampling point i, in metre (m), provided the
i
–3
conversion factor (1 mm = 10 m) is given, millimetres can be used as an alternative;
δ is the spatial sampling interval for the digitisation of the profile, in metre (m), provided the
x
–3
conversion factor (1 mm = 10 m) is given, millimetres can be used as an alternative;
Λ is the wavelength, in metre (m);
2π
Ω is the spatial frequency, in radian per metre (rad/m) Ω = ;
Λ
G(Ω ) is the unevenness index; where Ω = 1 rad/m;
0 0
IRI is the International Roughness Index;
PSD is the Power Spectrum Density of a signal spectrum;
WB is the wave band index calculated by using root mean square analysis applied to the pre-
processed profile elevations for the wave band W, in metre (m), provided the conversion factor
–3
(1 mm = 10 m) is given, millimetres can be used as an alternative;
SW is the Root Mean Square value of the short waves band;
MW is the Root Mean Square value of the medium waves band;
LW is the Root Mean Square value of the long waves band;
w is the waviness of the signal spectrum
5 Computation of unevenness indices
5.1 General overview of the computation
The computation of unevenness indices, involves three steps:
the measurement and pre-processing of the profile, the output of which is a filtered and re-sampled (or
pre-processed) profile,
the computation of one or more index(es),
the creation of a report (see Figure 2).
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Figure 2 — General overview of the computation
The pre-processing is essential in the case of wave band analysis is strongly recommended to homogenize
the profiles and facilitate comparisons.
5.2 Pre-filtering and re-sampling
In order to allow for meaningful comparisons all the analyses described below, should be carried out using
exactly the same algorithms which must be applied to signals sampled with exactly the same sampling interval.
As indicated in Figure 2, the output of a profilometer measurement is a raw profile, which makes use of a
sampling interval which depends on the profilometer used.
NOTE The profilometer used should at least have a class 2 vertical definition and traveled distance accuracy, and a
class 3 acquisition sampling interval, larger wavelength cutoff and reporting sampling interval as defined in the
prEN 13036-6
As it is very unlikely that all profilometers will natively report results using the same sampling interval, one of
the first step of the spectrum analysis must consist in re-sampling the original data to the standard reference
sampling interval which is defined to be 0,05 m. This re-sampling process must be preceded by a bandpass
filtering of the original signal, in order to insure that no unwanted distortion of the profile can be introduced
(see Figure 3).
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The result of this procedure is the pre-processed profile, which has a sampling interval of 0,05 m, and a
wavelength bandwidth limited to the 0,781 m to 50,0 m band. For certain applications the limitation of
bandwidth is not applied.
Unless the used profilometer and the computations made afterward make use of a spatial sampling interval
which is an integer multiple of the standard reference sampling interval, carrying out this the pre-processing is
mandatory.
Profile analysis can afterward be carried out using either limited wave bands and derived associated indices
or the full frequency content of the signal in which case the spectral density must be adequately estimated and
described.
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Key
1 elevations, in millimetre (mm)
2 measured originals profile (x = sampled points)
3 filtered originals profile (x = sampled points)
4 resampled profile (x = original points, • = resampled points)
Figure 3 — Filtering and Re-Sampling illustration
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6 Computation of unevenness indices
6.1 International Roughness Index (IRI)
6.1.1 General
The IRI is an index computed from a longitudinal road profile measurement using a virtual response type
system, quarter-car simulation, running at a speed of 80 km/h, (see Figure 4). The quarter-car simulation
applied on the digitised road profile calculates the accumulated suspension motions divided by the distance
travelled. Using a continuous road profile this is illustrated in formula (1). Time is related to longitudinal
distance by the simulated speed of the quarter-car simulation, t = x/V, where x is the longitudinal distance and
V is the simulated forward speed.
T
1
& &
IRI = z − z dt (1)
s u
∫
B
0
In practise all road profiles are sampled and the formula thus follows
n
1
IRI = s − s (2)
∑ s,i u,i
n
i=1
The IRI has the unit of slope, e.g. mm/m or m/km. A complete computation of IRI is described in World Bank
Technical Papers 45 and 46, [1], [2] and additional information in [3] and [4] as well as a complete computer
code that is provided in [5].
Key
1 spring mass 4 unspring mass
2 suspension damping rate C 5 tyre spring rate k
s t
3 suspension spring rate K 6 longitudinal profile Z(x)
s
Figure 4 — Quarter car (virtual response type system)
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6.1.2 Moving average length
IRI should be calculated using the state transition matrix principle, see reference [4]. A smoothed profile height
determined with a moving average length of L = 250 mm should be used as input into the calculations. The
s
sampling interval should be 125 mm or less. If the moving average is already applied when the road profile is
measured it should not be done again. The averaging should only be done once.
By using the specific parameter values, Golden Carsee Table 1) and the speed of 80 km/h the output from the
quarter-car simulation is defined as the International Roughness Index, IRI. The IRI scale starts at zero for a
road with no unevenness and covers positive numbers that increases in proportion to unevenness.
Table 1 — The Golden car parameter values
–2 –2
K = k / M = 653 s k = k / M = 63,3 s
1 t s 2 s s
–2
u = m / M = 0,15 c = C / M = 6,0 s
u s s s
6.1.3 Presentation base length
The base length, B in formula (1), can be any length from the sample length and up; this is decided by the use
of the IRI-value. For international comparison of IRI it is found, that a length of 100 meter is suitable [6]. The
presentation base length must be reported together with the IRI value. It is important to remember that
intervention thresholds depend on the presentation base length.
6.2 Wave bands analysis
6.2.1 Computation of the indices
In order to perform wave band analysis, the pre-processed profile is splitted into different wave band limited
profile using filters (see Figure 5). The definition of the wave bands used as well as the characteristics of the
filters used to obtain band limited signals, from the original longitudinal profile must be given. How indices are
derived from the band limited signals must also be defined.
NOTE The chosen indices and associated computations are directly derived from the ones used in the FEHRL
FILTER experiment at the European level, and the PIARC EVEN experiment at the world-wide level [7], [8], [9], [10].
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Key
1 elevation, in millimetre (mm) 5 highpoass filter
2 pre-processed profile 6 long waves filtered profile
3 lowpass filter 7 medium waves filtered profile
4 bandpass filter 8 shortwaves filtered profile
Figure 5 — Wave bands splitting
6.2.2 Filters
6.2.2.1 Octave filters (according to ANSI-S1-11-2004-07-27)
Octave filters are constant relative band filters defined by
f
h
= 2 (3)
f
l
where
f is the high cutoff spatial frequency at – 3 dB, in cycles per metre;
h
f is the low cutoff spatial frequency at – 3 dB, in cycles per metre.
l
The central spatial frequency of such a filter is defined as f = f f .
c
l h
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6.2.2.2 Bi-octave band
The bi-octave bands used for the determination of band limited unevenness indices group together two
consecutive octaves.
NOTE These bands have been defined for the FEHRL FILTER [9] and PIARC EVEN [10] projects.
These bands are defined below:
short wave SW band grouping together the octaves having a central spatial frequency of 1,280 cycle per
metre and 0,320 cycle per metre;
medium wave MW band grouping together the octaves having a central spatial frequency of 0,320 cycle
per metre and 0,080 cycle per metre;
long wave LW band grouping together the octaves having a central spatial frequency of 0,080 cycle per
metre and 0,020 cycle per metre.
Table 2 summarises these values showing wavelengths as well as spatial frequencies.
Table 2 — Characteristics of the filters
Band Spatial filtering in wavelengths Spatial frequencies in
cycles per metre
Bi-octave Octave
m m
Short waves (SW)
low limit 0,781 0,781 1,280
1,105 0,905
central value 1,563
1,563 0,640
2,210 0,453
high limit 3,125
3,125 0,320
Medium waves (MW)
low limit 3,125 3,125 0,320
4,419 0,226
central value 6,250
6,250 0,160
high value 12,500 8,839 0,113
12,500 0,080
Long waves (LW)
low limit 12,500 12,500 0,080
17,678 0,057
central value 25,000
25,000 0,040
35,355 0,028
high values 50,000
50,000 0,020
6.2.3 Filtering algorithm
The filters used to break the original longitudinal profile into the previously defined bands, should be carefully
chosen in order to introduce as little distortion as possible in the filtered signals, a common technique in that
view is to use by digital forward and reverse filtering associated with measured section extending beyond the
profile which is to be assessed.
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6.2.4 Wave band indices
6.2.4.1 General
Different indices can be used in order to characterise the different wave band filtered profiles. These indices
are denoted WB , where WB denotes the wave band, i and j are the profile sample numbers corresponding
ij
respectively to the beginning and the end of the reporting length (for instance LW , is the long waves
1024,2048
Root Mean Square of the pre-processed profile elevations for the reporting length containing profile samples
1024 to 2048)
6.2.4.2 Root Mean Square value of the pre-processed profile elevations per wave band
The Root Mean Square value per wave band of the pre-processed profile elevations over a section S , where i
ij
and j are respectively the indices of the first and last point of the profile to be considered, is defined as:
k= j
1
2
WB z (4)
=
ij ∑ wb,k
j − i +1
k=i
The index per wave band WB can determined for each of the three wave band limited profiles z , by
ij wb
applying the above formula to the digital files obtained by filtering the pre-processed profile using the by the bi-
octave filters described above.
These formulas applied to the three wavelength ranges give the indices:
SW : short waveband (0,78125 m to 3,125 m) Root Mean Square value :
ij
k= j
1
2
SW = z (5)
ij sw,k
∑
j − i +1
k=i
MW : medium waveband (3,125 m to 12,5 m) Root Mean Square value :
ij
k= j
1
2
MW = z (6)
ij ∑ mw,k
j − i +1
k=i
LW : long waveband (12,5 m to 50 m) Root Mean Square value :
ij
k= j
1
2
LW = z (7)
ij ∑ l w,k
j − i
...