New Approach for Evaluation of Longitudinal
Evenness of Pavement Surfaces on Newly
Constructed Roads
Željko Vojni , M.Sc.C.E.
Asaf Cvijeti , B.Sc.C.E.
Viadukt,d.d. Kranjceviceva 2, 10000 Zagreb, Croatia
Darko Kokot, B.Sc.C.E.
Zavod za gradbeništvo Slovenije, Dimi eva 12, Ljubljana
Abstract
This paper primarily presents information on a new approach in evaluating the
longitudinal profile of pavement surfaces on the newly constructed roads, based on Index IRI and
a developed methodology founded on the following design parameters:
(I) the road class, (II) the relevant values of Index IRI, (III) the criteria of the longitudinal
evenness and (IV) the category of longitudinal evenness.
The road class is determined in accordance with the effective legal categorization of roads
in Croatia in function of the traffic on roads expressed in AADT (Average Annual Daily Traffic)
The relevant values of the Index IRI have been defined on the basis of the processed data
of the measured pavement longitudinal evenness values and on the established model of the
statistical analysis. The model calculates frequencies of distribution of longitudinal profile
results measured at pavement surfaces as well as the confidence of the obtained data.
On basis of the performed analysis criteria for the acceptability limit state have been
determined, as well as the acceptability limit state and the limiting area (interval) of usage (fit
for use) (critical area). Accordingly, proposed categorization of the longitudinal evenness values
for certain road classes was produced in relation to the calculative values of the characteristic
basic variables of IRI values within the defined confidence intervals.
Povzetek
V lanku je opisan nov pristop vrednotenja vzdolžnega profila novozgrajenih cestnih
odsekov. Pripravljen pristop temelji na štirih parametrih: kategoriji ceste (po hrvaški
kategorizaciji glede na PLDP), relevantni vrednosti izra unanih indeksov IRI, kriterijev za
ocenjevanje vzdolžne ravnosti in kategoriji vzdolžne ravnosti cest. Relevantne vrednosti indeksov
IRI so opredeljene na podlagi statisti ne analize, s katero pridobimo frekven no distibucijo
indeksov IRI in interval zaupanja izra unanih podatkov. Na podlagi analiz so bile opredeljene
mejne vrednosti in opozorilno ter mejno obmo je stanja. Glede na intervale zaupanja in
izra unane vrednosti karakteristi nih spremenljivk vrednosti IRI so bile opredeljene še
kategorije vzdolžne neravnosti cest.
Vojni , Ž., Cvijeti , A., Kokot, D.: Nov pristop vrednotenju vzdolžnega profila novozgrajenih cestnih odsekov
Vojni , Ž., Cvijeti , A., Kokot, D.:
New Approach for Evaluation of Longitudinal Evenness of Pavement Surfaces on Newly Constructed Roads
1 Introduction
1.1 General
Evenness is an important performance
indicator of road pavement surfaces,
especially as concerns the aspects of their
safety and the riding comfort at the prescribed
speeds. An ideal road pavement surface as
envisaged by the Design practically cannot be
obtained. In practice, the road pavement
surfaces are usually constructed with smaller
or larger discrepancies from the designed
height values, resulting in the longitudinal or
cross directional wave bands. The evenness of
road pavement surfaces is a spatial problem.
In the technical sense this problem is
identified with the plane problem; most often,
the longitudinal and the transverse evenness
are observed individually. Unevenness of
road pavement surfaces has an adverse effect
over the vehicle, the driver, the passengers as
well as the transported cargo, and indirectly,
on the pavement structure because od the
increased dynamic load. The latter directly
leads to distresses of pavement structure
ahead of time that was predicted. Presently
there are various devices for measuring of
pavement evenness all over the world, as well
as various procedures (methods) of evaluating
the obtained evenness [1].
1.2 Evaluating approaches for
analyzing longitudinal
pavement evenness
The first attempts of unifying the
existing measuring methods for evaluating of
the evenness of the longitudinal pavement
surfaces date some twenty years ago when
under the sponsorship of the World Bank an
extensive investigation project was carried
out in Brazil [2, 3, 4]. As a result of
performed comparison of various measuring
equipment, a new analising procedure for the
longitudinal evenness of the pavement
surfaces was expressed by the so called the
IRI (International Roughness Index),
calculated on the basis of the adopted
mathematical model [5].
After the project in Brazil was
completed, on the basis of the obtained results
of measured pavement evenness, the World
Bank proclaimed the IRI Index values
2
recommended for certain category of road,
type of pavement and speed of vehicles.
In 1998, the World Road Association
coordinated by PIARC, Committee C1 on
Surface Characteristics conducted an
international experiment to harmonize
longitudinal and transverse profile and
reporting procedures.
This experiment was carried out in
Europe, in Japan and in the United States
(EVEN project), and it enabled almost every
type equipment in the world to participate [6].
The European part of this project
(FILTER Experiment) was jointly conducted
by some ten member laboratories of the
Forum of European National Highway
Research Laboratories (FEHRL) [7]. It
comprised an inventory of existing methods, a
theoretical study to assess the methods of
analysis, and a comparative experiment with
the measuring methods and different
measuring equipment in European countries
under actual field conditions.
The final results of the FILTER and
EVEN research projects were presented in
2001 and 2002; [8, 9], and were used as a
basis for harmonizing the existing European
measuring methods for determination of
longitudinal
evenness
indices,
under
European roads surface characteristics
standardization activities.
European attempts on standardization,
method harmonization, not only measuring,
but also in
assessing of pavement
characteristics of roads as well as airfield
pavements
–
including
longitudinal
unevenness of pavement – are essentially
carried out within the Technical Committee
CEN/TC 227 ˝Road materials˝ by the working
group WG5 ˝Surface Characteristics˝.
For the purpose of unifying and
harmonizing the methods of measuring the
longitudinal evenness of road pavements,
CEN/TC 227/WG5 has published during this
year, final version of the standard draft EN
13036-5 [10], where characteristics of the
road profile unevenness are expressed using
also the IRI Index (International Roughness
Index)
A complete computation of the IRI Index
is based on a procedure recommended by the
World Bank as well as on a complete
computer code provided in ASTM Standards
[11].
8. SLOVENSKI KONGRES O CESTAH IN PROMETU, Portorož, 25.-27. oktobra 2006
Vojni , Ž., Cvijeti , A., Kokot, D.:
New Approach for Evaluation of Longitudinal Evenness of Pavement Surfaces on Newly Constructed Roads
1.3 Current criteria for
evaluation of longitudinal
pavement evenness
The existing current criteria for
evaluation of the longitudinal pavement
evenness are not unique all over the world;
they are based on the assumptions of certain
institutions or state road authorities that
prescribe different measurement procedures
and methods.
It can generally be stated that in the
majority of the European countries, as well as
in the world, a deterministic approach is
applied when assessing the longitudinal
pavement evenness usually based on a
simplified application of the empirical data
for two limiting, accepted (fixed) values of the
IRI Index, such as:
acceptability limit value, and
allowance value.
Within such deterministic system, the
interacting relations are precisely defined.
The analysis of the deterministic system is
generally based on the mathematic models.
When assessing the longitudinal pavement
evenness, expressed by the IRI Index, as per
the valid Technical Specifications for Roads
in Slovenia [12] and the General Technical
Conditions for Roadworks in Croatia [13], the
concept of such deterministic approach has
also been applied.
2 Basic principles of the
new approach
2.1 Initial encouragement
An initial encouragement to this paper
was generated by the relevant technical
information based on the specific provisions
resulting from the effective technical
regulations applied in Spain: PG-3, ˝Pliego de
Prescripciones Técnicas Generales para
obras de carreteras y puentes˝ (˝General
Technical Prescriptions for road and bridge
works˝), Artículo 550 [14].
In Chapter 5 (Article 550.7.3), technical
regulations specify the minimal percentage of
the road length (P50%, P80% and P100%) in
function with the required limiting values of
the IRI Index, for two road categories
(motorways and higher ranked roads, and
other roads).
The respective regulations have aroused
an interest to start changing the perception of
evaluating the longitudinal pavement profile
as presently applied (deterministic approach),
and that the prediction of the relevant values
of the profile (as relevant basic variables) be
conducted on the basis of certain statistical
probability analysis.
2.2 Formulation of the
Analysis Procedure –
major parameters
The process of evaluating the
longitudinal evenness of newly constructed
road pavement surfaces expressed by IRI
Index includes following major parameters:
Road class,
Relevant values of the IRI Index,
Criteria for evaluation of longitudinal
surface evenness, and
Categories of evenness.
2.2.1 Road Class
Within the proposed new model the
assessment of the road pavement longitudinal
evenness, road class is treated as one of major
parameters. In accordance with the legal
classification of public roads in Croatia and
the defined type of the traffic ranks, in
function of the roads category and the traffic
level on roads, expressed in AADT (Average
Annual Daily Traffic) [15], the roads are
divided into three classes as presented in table
1.
Table 1: Road classes in function of the road
category / traffic level (AADT)
Road
Class
Road Category / Traffic level
(AADT)
I
Motorways and 1st category
roads (State Roads)/
AADT > 12.000 vehicles/day
II
Roads of 2nd category (State
Roads)/
AADT 7.000 – 12.000
vehicles/day
III
Lower ranked roads of 3rd, 4th
& 5th category (State, County
and Local roads)/
AADT < 7.000 vehicles/day)
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Vojni , Ž., Cvijeti , A., Kokot, D.:
New Approach for Evaluation of Longitudinal Evenness of Pavement Surfaces on Newly Constructed Roads
2.2.2 Relevant values of the IRI
Index
a) Definition of particular IRI value
According to the definition, single values
of the IRI Index summarize the quality of the
longitudinal road profile and riding comfort
and are calculated by applying the
corresponding computer model [5]. Within
the scope of this methodology, for single
values of the IRI Index, a representative
longitudinal road segment was adopted in the
length of 100 meters. It was defined as IRI100.
b) Typical IRI values of characteristic basic
variables
As known from the theory of probability,
when processing the data on continuous
random variables of the obtained data,
knowledge of the basic pattern is not
sufficient. An additional analysis is necessary
on conformity of possible deviation. The
confidence analysis makes it possible to
predict the probability of occurrence of
certain values of the basic variables obtained
by testing.
During statistical modeling of the
obtained data on testing the evenness
expressed by the IRI100, the following is
applied:
Definition of empirical distribution
(arranging of quality and quantity
data)
Description of distribution (shape,
central tendencies, variability);
Theoretical curve of frequencies in
relation to distribution of the measured
data – retrieval of the most suitable
theoretical probability distribution.
By determining the acceptability limit
value and fit for use interval (area), the
criteria for selection of characteristic basic
variables were also defined (IRIk.gr, IRId.gr. and
IRIgr.up.).
While determining the characteristic
basic variables of the relevant calculated IRI
values during statistical processing of
evaluating the measured profile, particular
limiting
confidence
levels
were
recommended, as presented in table 2.
Table 2: Characteristic basic variables and recommended confidence levels
Characteristic basic variables
Recommended confidence levels(g)
Symbol
Definition
Percentile(Pi)
Quantile(pi)
IRIk.gr.
Characteristic acceptability limit
value
P1 = 75-85%*
p1 = 15-25%
IRId.gr,
Upper limit value of a confidence
interval
P2 = 95%
p2 = 5%
IRIgr.up
Fit for use - limit value
P3 = 100%
p3 < p2
* Recommended limit confidence levels (P1) generally depending on road class
Note: For road class I the recommended upper confidence level is P1=85%, while for road classes II and
III lower quoted confidence levels could be applied.
c) Recommended limit values of
characteristic base variables for the
particular road class
The recommended limit values of the
characteristic base variables for a particular
road class - expressed by the IRI Index - were
applied on the basis of the recent knowledge
acquired when measuring the evenness of
4
road pavements in Croatia and Slovenia, as
well as the comparative analysis and
comparison of data that refer to such values
obtained
from
the
actual,
relevant
specifications for the motorways and highly
ranked roads in various countries of the world
(USA, Canada, Australia and some European
countries) [16].
8. SLOVENSKI KONGRES O CESTAH IN PROMETU, Portorož, 25.-27. oktobra 2006
Vojni , Ž., Cvijeti , A., Kokot, D.:
New Approach for Evaluation of Longitudinal Evenness of Pavement Surfaces on Newly Constructed Roads
Table 3: Recommended limit values of certain characteristic base variables for the particular road class
Characteristic basic variables
Road Class
I
II
III
Characteristic acceptability limit
value - IRIk,,gr., [m/km]
1,50
1,80
2,25
Upper limit value of the confidence
interval - IRId, gr., [m/km]
1,80
2,25
2,75
Fit for use - limit value
IRIgr.up., [m/km]
2,00
2,50
3,00
d) Theoretical curve of frequencies in
relation to distribution of actually
measured data – retrieval of the most
suitable theoretical probability
distribution
When analyzing the distribution of
relative frequencies of IRI100 Index on several
selected, typical newly constructed road
sections in Slovenia and Croatia, the exact
theoretical function of distribution was
attempted to be identified, optimal for
approximating the histogram of relative
frequencies for IRI values. The statistical data
processing was done by the software
˝Statistica˝, ver. 6.1˝ (StatSoft Inc). The
functional modulus Distribution Fitting was
used for determination of the theoretical
distribution function best suited for the
distribution of the measured data and the
Probability Calculator for calculation of the
required IRI limit values for certain typical
base variables and the required confidence
levels, expressed by the values of percentile
(Pi) and quantile (pi). As most suitable
theoretical curves for approximation of
relative frequency histogram for the actually
measured data of the longitudinal pavement
evenness
the
following
asymmetric
distributions were taken into consideration:
Gamma distribution (corresponding to
Pearson type III distribution), Lognormal
distribution, Weibull distribution, Chi-square
distribution. Testing results pursuant to the
Smirnov-Kolmogorov test and Chi-square test
have shown that for approximation of the
actually measured data, in a particular case,
the Lognormal distribution is the most
suitable function.
In figure 1, the following is indicated –
on the assumed (typical) continuous,
asymmetric theoretical distribution curve
(Probability density function):
characteristic basic variables (IRIk.gr,
IRIgr,up)
with
specified
IRId.gr,
characteristic
confidence intervals
among such basic variables,
categories of evenness.
8. SLOVENSKI KONGRES O CESTAH IN PROMETU, Portorož, 25.-27. oktobra 2006
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Vojni , Ž., Cvijeti , A., Kokot, D.:
New Approach for Evaluation of Longitudinal Evenness of Pavement Surfaces on Newly Constructed Roads
Figure 1.- Typical probability density function for performed analyses, characteristic basic variables and
description of typical confidence intervals
2.2.3 Criteria for evaluation of
longitudinal surface
evenness
The essential criteria have to be fulfilled
for particular road class of newly constructed
road. Three criteria (conditions) have been
established in evaluation of calculated IRI
values of certain characteristic basic variables
obtained on the basis of the statistical
processing of the actually measured data. The
established criteria are based on comparison
of the calculated IRI values with the adopted
limit values for particular characteristic basic
variables, in relation to the required
confidence levels (table 4). The limit values
adopted for certain characteristic basic
variable - depending on the road class - are
used pursuant to the data shown in table 3.
Table 4: Criteria for evaluation of longitudinal surface evenness
Criteria for evaluation of
longitudinal surface evenness
Condition
Required confidence level
(Pi)
Criterion 1
IRIk,pr. < IRIk.gr
P1 = 75 - 85%
Criterion 2
IRId.pr. < IRId.gr
P2 = 95%
Criterion 3
IRIgr.up
P3 = 100%
2.2.4 Categories of longitudinal
evenness
The categories of longitudinal pavement
evenness are presented for road classes in
relation to the calculative values of the
characteristic basic variables of IRI values
within the defined confidence intervals (see
figure 1 and table 5). Table 5 also shows
6
categorization into classes in evaluating the
quality of works, based on calculated index
IRI. In relation to the adopted acceptability
limit values the financial penalties were
quoted subject to the degree of deviation from
the recommended limit IRI values. The
respective model of financial penalties should
be treated separately; however, this is not the
subject of this paper.
8. SLOVENSKI KONGRES O CESTAH IN PROMETU, Portorož, 25.-27. oktobra 2006
Vojni , Ž., Cvijeti , A., Kokot, D.:
New Approach for Evaluation of Longitudinal Evenness of Pavement Surfaces on Newly Constructed Roads
Table 5: Categorization of longitudinal pavement subject to calculated IRI values of characteristic
basic variables corresponding to the adopted limit values
Evenness category
Condition
Evaluation of measured longitudinal
evenness - Financial penalties
R1
IRIk,pr. < IRIk.gr.
No financial penalties
Interval/area of tolerance I
R2
IRIk.gr < IRId1,pr< IRId.gr
R3
IRId.gr < IRId2,pr < IRIgr,up.
R4
IRI.pr > IRIgr.up
Financial penalties due to partially
reduced quality of evenness on
constructed asphalt layer
(up to 5% of the contracted asphalt
layer price)
Interval/area of tolerance II
Financial penalties due to partially
reduced quality of evenness on
constructed asphalt layer
(from 5 to 15% of the contracted
asphalt layer price)
Unacceptable quality of the obtained
evenness
Corrective measures are to be
undertaken depending on the
deviation from the limit
3 Verification of model proposed for evaluation of
longitudinal pavement evenness
3.1 General data on analyzed motorway sections
For verification of the proposed approach for evaluation of the longitudinal pavement
evenness (expressed with index IRI), a statistical analisys for selected representative sections of
the newly constructed motorways in Slovenia and Croatia was performed. These are shown in
table 6.
Table 6: List of selected representative segments for a statistical analysis
Analyzed segment at
motorway section
a) Slovenia
1.
Blagovica-Šentjakob
2.
Vransko-Blagovica
3.
Kozina-Klanec ( rni Kal)
4.
Bi -Korenitka (Trebnje)
5.
Smednik-Krška Vas
b) Croatia
1.
Pirovac-Skradin-Šibenik
Župnja-Lipovac
2.
(Subsection: Županja-Spa va)
3.
Rijeka-Rupa
Designation of
motorway
A1
A1
A1
A2
A2
Total under a):
Total number of analyzed IRI100
values
(traffic lane and overtaking lane)
591
348
289
193
640
2061
A1
382
A3
198
A7
Total under b):
176
756
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Vojni , Ž., Cvijeti , A., Kokot, D.:
New Approach for Evaluation of Longitudinal Evenness of Pavement Surfaces on Newly Constructed Roads
Within the statistical processing of the
actually measured data, the calculated IRI
values were processed and systemized into
tables. Accordingly, the results are
graphically presented in the form of a
histogram showing distribution of the relative
frequencies, as well as the distribution curve
of cumulative relative frequencies. In order to
perform the confidence analysis of some basic
variables experimentally obtained data were
approximated. The most suitable theoretical
curve (probability density function) was
selected by the Distribution Fitting Software
(software program ˝Statistica˝).
For the majority of cases the probability
density function type Lognormal distribution
curve appeared to be most suitable. From the
adopted Lognormal probability density
function, on the basis of the confidence
analysis, it was possible to foresee the
probability of appearance of percentile
variable in accordance with the criteria
presented in table 4.
3.2 Examples of performed
analysis
As an illustration the statistical analysis
of the experimentally obtained data for the
two selected typical motorway sections in
Slovenia and Croatia are presented. The
graphical presentation of the fitted probability
density function approximated to the relative
distribution of the actually measured data, is
shown in figures 2 and 3. In this particular
case, the relevant selected representative
segments on the newly constructed motorway
sections are as follows:
Smednik – Krška Vas
Motorway
A2: Tunnel ˝Karavanke˝ - Ljubljana –
Obrežje (Slovenia)
Skradin-Šibenik-Pirovac Motorway
A1: Motorway Zagreb - Bosiljevo –
Split (Croatia)
3.2.1 Motorway A2, Section: Smednik – Krška Vas
Figure 2: Graph of fitted density function to the input data (histogram of relative frequencies of
calculated IRI values) for Motorway A2, Section: Smednik-Krška Vas
8
8. SLOVENSKI KONGRES O CESTAH IN PROMETU, Portorož, 25.-27. oktobra 2006
Vojni , Ž., Cvijeti , A., Kokot, D.:
New Approach for Evaluation of Longitudinal Evenness of Pavement Surfaces on Newly Constructed Roads
Evaluation of performed statistical
analysis
On the basis of the performed,
previously described statistical analysis the
summarized evaluation of obtained pavement
surface evenness at the Motorway A2:
Section: Smednik -Krška Vas is shown in
table 7 – in accordance with the criteria
quoted in table 4.
Table 7: Evaluation of obtained pavement evenness at Motorway A2: Section Smednik – Krška Vas
Required level of
confidence
(Pi)
Calculated values
of characteristic
base variables
IRIpr [m/km]
Limit values of
base variables
IRIgr. [m/km]
Calculated value
of confidence
Pi
Evaluation
85%
IRIk.pr. = 1,46
IRIk.gr. = 1,50
---
Acceptable
95%
IRId.pr. = 1,63
IRId.gr. = 1,80
---
Acceptable
100%
---
IRIgr.up. = 2,00
P2 = 98,81 %*
Unacceptable
(quantile: p3 =
1,19%)
* Calculated value of confidence for IRIgr.up.=2,0 [m/km], obtained from the diagram of cumulative relative frequencies
3.2.2 Motorway A1, Section: Skradin-Šibenik-Pirovac
Figure 3: Graph of fitted density function to the input data (histogram of relative frequencies calculated
IRI values) for Motorway A1, Section: Skradin-Pirovac-Šibenik
8. SLOVENSKI KONGRES O CESTAH IN PROMETU, Portorož, 25.-27. oktobra 2006
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Vojni , Ž., Cvijeti , A., Kokot, D.:
New Approach for Evaluation of Longitudinal Evenness of Pavement Surfaces on Newly Constructed Roads
Evaluation of performed statistical
analysis
Evaluation of the performed statistical
analysis was carried out pursuant to the same
methodology as in the previous example, and
the summarized relevant results are shown in
table 8.
Table 8: Evaluation of obtained pavement evenness at Motorway A1, Section: Skradin-Pirovac-Šibenik
Required level of
confidence
(Pi)
Calculated values
of characteristic
base variables
IRIpr [m/km]
Limit values of
base variables
IRIgr. [m/km]
Calculated value
of confidence
Pi
Evaluation
85%
IRIk.pr. = 1,33
IRIk.gr. = 1,50
---
Acceptable
95%
IRId.pr. = 1,57
IRId.gr. = 1,80
---
Acceptable
100%
---
IRIgr.up. = 2,00
P = 98,40 % *
Unacceptable
(quantile: p3 =
1,60 %)
3.2.3 Processing of data for
other motorway sections
For the other selected representative
segments on the newly constructed motorway
sections in Slovenia and Croatia (shown in
table 6) the analysis of the actually measured
data was performed following the same
methodological approach – respecting the
established criteria. Due to the limited scope
of this paper, the report of the performed
detailed analysis of each section could not be
provided. As evident from the performed
computation, all analyzed segments show
confident accuracy of the established criteria
what verifies the acceptability of the applied
conceptual approach.
4 Conclusion
This paper describes the basic postulates
and the main characteristics of the proposed
new model for evaluation of longitudinal
pavement evenness on newly constructed
roads expressed by the IRI Index.
The subject model is founded on a semiprobabilistic concept. During the analysis
procedure one of the dominant input
parameters – the relevant values of
longitudinal
evenness
(expressed
as
appropriate basic variables), are statistically
processed and determined following the
probabilistic evaluation approach. Limit
values of the characteristic base variables are
still determined on the basis of the adopted
10
(fixed) variables following the deterministic
concept.
For the purpose of the most selective
evaluation of the results obtained on the
measured longitudinal pavement evenness,
several typical confidence intervals were
introduced into the analysis on the basis of
which the characteristic basic variables were
specified.
For evaluation of the achieved
longitudinal surface evenness, three criteria
have been provided based on limit values for
particular characteristic basic variable.
The categories of longitudinal pavement
evenness are presented for road classes in
relation to the calculative values of the
characteristic basic variables of the IRI values
within the defined confidence intervals.
Verification of a model proposed for
evaluation of the longitudinal pavement
evenness – on the basis of the actually
measured longitudinal evenness data at
several selected representative segments of
the newly constructed motorway sections in
Slovenia and Croatia – confirmed the
acceptability of the applied conceptual
approach.
As a conclusion, it should be stressed
that the applied conceptual approach, as
compared to the usual evaluation procedures
of measured longitudinal profile, offers better
quantitative and qualitative insight into
obtained evenness data in accordance with the
relevant technical specifications or design
requirements.
8. SLOVENSKI KONGRES O CESTAH IN PROMETU, Portorož, 25.-27. oktobra 2006
Vojni , Ž., Cvijeti , A., Kokot, D.:
New Approach for Evaluation of Longitudinal Evenness of Pavement Surfaces on Newly Constructed Roads
Acknowledgments
This is to acknowledge the help received
from DARS d.d. (Družba za avtoceste v
Republiki Sloveniji) and HAC d.o.o.
(Hrvatske autoceste) regarding the provided
database of results of the longitudinal
pavement evenness, at particular segments of
the newly constructed motorway sections in
Slovenia and Croatia which served for
verification of the proposed model.
Furthermore, we express our personal
gratitude for useful suggestions and the
relevant information concerning the subjected
issues received from Mr. Bojan Leben, –
ZAG (Zavod za gradbeništvo Slovenije,
Slovenia).
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