RJTI - Romanian Journal of Transport Infrastructure

Transcription

TECHNICAL UNIVERSITY OF CIVIL ENGINEERING OF BUCHAREST
ROMANIAN
JOURNAL
OF TRANSPORT
INFRASTRUCTURE
CONSPRESS
ISSN 2286-2218
ISSN-L 2286-2218
ROADS
BRIDGES
RAILWAYS
GEOTECHNICS
This text was elaborated by utilizing the photographic reproduction of originals.
Therefore the editor cannot accept any responsibility for the content nor that of possible
errors in the text.
ROMANIAN JOURNAL
OF
TRANSPORT INFRASTRUCTURE
Vol.2, 2013
No.2, December
Editor-in-chief: Carmen Răcănel
Executive editor: Adrian Burlacu
Editorial Executive Committee (in alphabetical order)
Ştefan Marian Lazăr
Mihai Gabriel Lobază
Claudia Petcu
Ionuţ Radu Răcănel
Publisher: Technical University of Civil Engineering, CONSPRESS Publishing House
ISSN 2286-2218
ISSN-L 2286-2218
ROMANIAN JOURNAL
OF TRANSPORT INFRASTRUCTURE
CONTENT
Viscoelastic model for the rigid body vibrations of a viaduct depending on
the support devices’ rheological model,
Polidor BRATU, Ovidiu VASILE
………
1
Application of GPR and FWD in assessing pavement bearing capacity,
Josipa DOMITROVIĆ, Tatjana RUKAVINA
………
11
The influence of visibility conditions in horizontal road curves on the
efficiency of noise protection barriers,
Tamara DŽAMBAS, Saša AHAC, Vesna DRAGČEVIĆ
………
22
Balanced cantilever girder bridge over the Danube-Black Sea Channel,
Aldo GIORDANO, Giorgio PEDRAZZI, Giovanni VOIRO
………
33
Increase the safety of road traffic accidents by applying clustering,
Goran KOS, Predrag BRLEK, Kristijan MEIC, Kresimir
VIDOVIC
………
45
CONTENT, Romanian Journal of Transport Infrastructure, Vol.2, 2013, No.2
ROMANIAN JOURNAL
VISCOELASTIC MODEL FOR THE RIGID BODY
VIBRATIONS OF A VIADUCT DEPENDING ON THE
SUPPORT DEVICES’ RHEOLOGICAL MODEL
Polidor Bratu, Prof., PhD, Dipl. Eng., Dr. h. c., ICECON S.A., e-mail: icecon@icecon.ro
Ovidiu Vasile, Lect., PhD, Dipl. Eng., ICECON S.A., e-mail: ovidiu.vasile@icecon.ro
Rezumat
Lucrarea abordează comportarea unui model de solid-rigid cu anumite simetrii
structurale. Aceste simetrii permit simplificarea calculelor (ecuaţii de mişcare) şi, deci, a
modelelor matematice. Dacă solidul rigid este conectat la structură prin patru legături elastice,
modelul rămâne încă simplu şi uşor de rezolvat, vibraţiile putând fi decuplate în patru
subsisteme de mişcare.
În final, se prezintă un studiu de caz pentru analiza modală a unui viaduct, modelat
precum un corp solid-rigid, rezemat elastic, de pe autostrada Transilvania (km 29+602.75 m).
Cuvinte cheie: viaduct, aparate de reazem, vibraţii.
Abstract
The paper addresses the behavior of a rigid solid with various structural symmetries.
These symmetries allow the simplification of computations (equations of motion) and, thus,
also of the mathematical models. If the rigid solid is connected to the structure through four
elastic links, the model still remains simple and easy to solve by decomposing the vibrations
into four subsystems of motion: side slipping and rolling, forward motion and pitching, lifting
motion, gyration.
In the end, a case study is presented for the modal analysis of a viaduct, modeled as a
rigid solid, elastically supported, on the Transilvania highway at km 29+602.75 m.
Keywords: viaduct, support devices, vibrations.
1. MATHEMATICAL MODELING OF THE RIGID SOLID WITH
ELASTIC BEARINGS
The mathematical modeling uses the physical model of the rigid solid
with six degrees of freedom (6DOF) with a finite number of viscous-elastic
bearings. Dimensional and inertial characteristics of the rigid solid and
rheological characteristics of the bearings (stiffness and damping) can be
experimentally determined by direct measurements and by static and/or dynamic
testing. According to (7), the differential equations of the movements of the
rigid solid with viscous-elastic bearings are coupled by stiffness and damping
Article No.1, Romanian Journal of Transport Infrastructure, Vol.2, 2013, No.2
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ROMANIAN JOURNAL
Polidor Bratu, Ovidiu Vasile
Viscoelastic model for the rigid body vibrations of a viaduct depending on the support devices rheological model
coefficients. The system of the equations can be write as follows:
Aq  Bq  C q  f ,
(1)
where A is the inertia matrix; B is the viscous damping matrix (damping
coefficients); C is the elasticity matrix (stiffness coefficients); q / q / q are
generalized displacements / velocities / accelerations vector and f is the
generalized forces vector.
If the damping coefficients are small, the differential equations system
becomes:
(2)
Aq  C q  f
Considering the rigid solid no perturbated, the system of differential equations
becomes:
(3)
Aq  C q  0 ,
where 0 is the null vector (where all coefficients are zero).
If the Cartesian coordinates axis system is central and principal, the
quadratic 6  6 inertia matrix becomes diagonal
(4)
A  DIAGm,m,m, J x , J y , J z  ,
where m is the rigid solid mass and J x , J y , J z are the principal inertia
moments.
2. THE RIGID SOLID WITH STRUCTURAL SYMMETRIES. MODAL
ANALYSIS
Considering that the rigid solid has a vertical axis of symmetry (mass
distribution, geometrical configuration, bearings disposal) and the coordinate
system is central and principal, the inertia matrix is diagonal.
z
Mi
kiy
y
kix
kiz
x
Figure 1. Elastic triorthogonal bearing
If the elastic bearing system of the rigid solid is composed from n
supports with triorthogonal stiffness kix , kiy , kiz  like in figure 1, with the
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position done by the coordinates M i xi , yi , zi  i  1, n , the elasticity matrix
becomes:
  k ix
 0

 0
C
 0
 k z
ix i

 0
0
0
0
 k ix z i
 k iy
0
  k iy z i
0
0
 k iz
0
0
  k iy z i

0

k iy z i2
 k iz y i2
0
0
0
0
0
0



0
k iz xi2
 k ix z i2


0


0
 (5)
0


0

 k ix y i2  k iy xi2 
0

0


As the inertia matrix is diagonal, the coefficients outside the main
diagonal of the elasticity matrix C are the coupling terms of the equations of the
system (3). Because there are only four non-zero stiffness coefficients ( c15  c51
and c24  c42 ), the free movements of the rigid solid are decoupled into four
subsystems with coupled vibrations. The subsystems with coupled motion
equations are as follows:
a) subsystem X , y  - side slip movement coupled with rolling
movement

mX  X  k ix   y  k ix zi  0

(6)

2
2


J


X
k
z


k
x

k
z

0



ix i
y
iz i
ix i
 y y
b) subsystem Y , x  - forward-back movement coupled with pitch
movement

mY  Y  k iy   x  k iy zi  0

(7)

 x  Y  k iy zi   x  k iy zi2  k iz yi2  0

J x 
c) subsystem Z  - up-down movement
mZ  Z  kiz  0
(8)
d) subsystem  z  - turning movement (gyration)






 z   z  kix yi2  kiy xi2  0
J z
(9)
In order to determinate the natural frequencies and the eigenvalues we use
the next notations:
• for the pulsations of the no coupled movements of translation
 k iy
 k ix
 kiz
p 
p 
(10a)
p 
X
m
Y
m
Z
m
• for the pulsations of the no coupled movements of rotation
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p x 
p z 

 kiy zi2  kiz yi2

Jx
 kix yi2  kiy xi2


p y 

 k iz xi2  kix zi2

Jy
(10b)
Jz
• the dynamic coupling terms for the X , y  and Y , x  subsystems
1

  1  m  k ix z i

1
 2 
 k ix z i
Jy

1

 1   m  k iy z i

1
 2  
 k iy zi
Jx

(11)
Considering the relations (10) and (11), the natural pulsations and the
eigenvalues of the decoupled subsystems can be determinate with the next
calculus formula:
a) for the subsystem X , y 
p1,2 

2
1 2
 p X  p 2   p 2X  p 2   4 1 2 
y
y 
2





2
1  2
 p X  p 2   p 2X  p 2   4 1 2 
y
y 
2 1 




b) for the subsystem Y , x 
 1,2  
1 2
 pY  p2 
x
2

1  2
 3 ,4  
 pY  p2
x
21 

p3 ,4 

2
 p 2  p 2   4  
1 2
x 
 Y


2
  pY2  p2   41 2 
x 


(12)
(13)
(14)
(15)
3. MODAL ANALYSIS OF A BRIDGE MADE FROM REINFORCED
CONCRETE
Figure 2 shows elevation and the plan view for a bridge made from
twenty reinforced concrete beams jointed through a 300 mm thickness
reinforced concrete plate. Each beam is beared on the piers and on the abutments
of the bridge through four identically viscous-elastic supports made from
neoprene; there a total number of eighty neoprene bearings for the entire bridge.
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Figure 2. Elevation and plan view of the Viaduct Romanian highway
A3 - KM 29+602,75↔KM 29+801,25
The simplified model of the bridge is shown in the figure 3. In order to
calculate the natural pulsations and frequencies and the eigenvalues of the
bridge modeled as in the figure 2, the main characteristics are the next:
• Dimensions (as in detailed engineering drawings and/or measured):
▪for “U” beams: 37100  1700 / 3280  2200 lenght×width×height [mm]
▪for the bridge: 200000  13300  2500 lenght×width×height [mm]
• Stiffness of the neoprene bearings (experimental measurements):
kix  k x  3,15  10 6 N / m
i  1,80
kiy  k y  3,15  10 6 N / m i  1,80
kiz  k z  650  10 6 N / m
i  1,80
• Masses and inertia according to table 1 (calculated):
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Table 1. Inertial characteristics (central and principal axis system)
Arch of the viaduct (4
Denomination Unit
Viaduct (20 beams)
beams)
Mass m
kg
992,000
4,960,000
Products of
J xy  J yz  J zx  0
Kg·m2
inertia
2
120.533×106
16.025×109
Moments J x Kg·m
J y Kg·m2
of
15.133×106
73.270×106
inertia
J z Kg·m2
134.091×106
16.092×109
• Position of the mass center C against the neoprene bearings (calculated):
h  1454 ,4mm
• Positions of the neoprene bearings on the viaduct (related to the centered
coordinate system Cxyz) as in detailed engineering drawings – see table 2.
Table 2. Positions of the neoprene bearings
Bearing and coordinates [m]
i
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
xi
yi
-5,5 -98,05
-4,4 -98,05
-2,2 -98,05
-1,1 -98,05
1,1 -98,05
2,2 -98,05
4,4 -98,05
5,5 -98,05
-5,5 -61,95
-4,4 -61,95
-2,2 -61,95
-1,1 -61,95
1,1 -61,95
2,2 -61,95
4,4 -61,95
5,5 -61,95
-5,5 -58,05
-4,4 -58,05
-2,2 -58,05
-1,1 -58,05
zi
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
i
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
xi
yi
1,1 -58,05
2,2 -58,05
4,4 -58,05
5,5 -58,05
-5,5 -21,95
-4,4 -21,95
-2,2 -21,95
-1,1 -21,95
1,1 -21,95
2,2 -21,95
4,4 -21,95
5,5 -21,95
-5,5 -18,05
-4,4 -18,05
-2,2 -18,05
-1,1 -18,05
1,1 -18,05
2,2 -18,05
4,4 -18,05
5,5 18,05
zi
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
i
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
xi
-5,5
-4,4
-2,2
-1,1
1,1
2,2
4,4
5,5
-5,5
-4,4
-2,2
-1,1
1,1
2,2
4,4
5,5
-5,5
-4,4
-2,2
-1,1
yi
18,05
18,05
18,05
18,05
18,05
18,05
18,05
18,05
21,95
21,95
21,95
21,95
21,95
21,95
21,95
21,95
58,05
58,05
58,05
58,05
zi
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
i
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
xi
1,1
2,2
4,4
5,5
-5,5
-4,4
-2,2
-1,1
1,1
2,2
4,4
5,5
-5,5
-4,4
-2,2
-1,1
1,1
2,2
4,4
5,5
yi
58,05
58,05
58,05
58,05
61,95
61,95
61,95
61,95
61,95
61,95
61,95
61,95
98,05
98,05
98,05
98,05
98,05
98,05
98,05
98,05
zi
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
-1,45
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Table 3. Natural pulsations and frequencies (on the six degrees of dynamic
freedom)
7.13 7.13 102.39 167.67 97.83 11.30
Arch of the viaduct p [rad/s]
(4 beams)
f [Hz]
1.13 1.13 16.30 26.69 15.60 1.80
p [rad/s]
7.13 7.13 102.39 105.49 97.83 7.34
Viaduct
(20 beams)
f [Hz]
1.13 1.13 16.30 16.79 15.60 1.17
Using the relations (10), the natural pulsations p and the natural
frequencies f of the uncoupled vibrations for the six degrees of dynamic
freedom are shown in the table 3.
The figures from table 4 show the values of the natural pulsations and
frequencies and of the eigenvalues for the decoupled subsystems (with coupled
movements) for a bridge section (arche) composed from four „U” beams as in
figure 4 and figure 5.
13,2m
z
x
C
y
Figure 3. The model of the bridge beared on eighty neoprene supports
As it can see, there are the same values for pulsations and frequencies like
in table 3. That means, the movements inside the subsystems X , y  and Y , x 
are very weak coupled, almost uncoupled.
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13200
1700
Figure 4. The model of an arch of the viaduct
13200
C
C2
C1
1650
C4
C3
1650
4950
4950
Figure 5. The model of an arch of the viaduct (transversal section)
Table 4. Modal analyze for an arch (section) of the viaduct (decoupled
subsystems)
Subsystem
Pulsations
Frequencies
Eigenvalues
X , y 
p1  7.13rad / s
p2  97.83rad / s
f 1  1.13Hz
f 2  15.60 Hz
1  0.000509rad / m
 2  128.824rad / m
Y , x 
p3  7.13rad / s
f 3  1.13Hz
 3  0.000002rad / m
p4  167.67 rad / s
f 4  26.69 Hz
 4  379.750rad / m
p5  pZ  102.39rad / s
f 5  f Z  16.30 Hz
-
p6  p z  11.30rad / s
f 6  f  z  1.80 Hz
-
Z 
 z 
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Table 5. Modal analyze for the viaduct (decoupled subsystems)
Subsystem
Pulsations
Frequencies
Eigenvalues
X , y 
p1  7.13rad / s
p2  97.83rad / s
f 1  1.13Hz
f 2  15.57 Hz
1  0.000509rad / m
2  128.824rad / m
Y , x 
p3  7.13rad / s
f 3  1.13Hz
 3  0.000002rad / m
p4  105.49rad / s
f 4  16.79 Hz
4  149.916 rad / m
p5  pZ  102.39rad / s
f 5  f Z  16.30 Hz
-
p6  p z  7.34rad / s
f 6  f  z  1.17 Hz
-
Z 
 z 
The figures from table 5 show the values of the natural pulsations and
frequencies and of the eigenvalues for the decoupled subsystems (with coupled
movements) for the entire bridge composed from five sections (arches)
considered being identical as in figure 3.
As for the arches, the movements inside the subsystems with coupled
movements X , y  and Y , x  of the viaduct are very weak coupled, almost
uncoupled.
4. CONCLUSIONS
a) modeling a rigid solid with elastic or viscous-elastic bearings and
symmetries (structural, inertial, bearings) lead to linear mathematical models
more simple, with differential equations decoupled into subsystems easier to
solve; in this case, we can highlight the influences of different kinds of
characteristics (dimensions, masses, inertia, stiffness) on the dynamic
parameters of the rigid solid (natural pulsations/frequencies, eigenvalues);
b) if the physical model of the rigid solid permits to chose a Cartesian
coordinate system which is central and principal, then the differential equations
of motion are coupled only by the coefficients outside of principal diagonal of
elasticity matrix (elastic coupling of movements), eventually by the dissipation
coefficients from the viscous damping matrix if they are significant;
c) comparing the values of the pulsations/frequencies from the tables 3, 4
and 5, we can say that the movements inside the subsystems are almost
uncoupled on the “directions” ( X , Y , Z ,  x ,  y ,  z ); also the values very small or
very big of the eigenvalues can explain the quasidecoupling of the movements
inside of the subsystems;
d) analyzing the values from table 4 (for the arches), we can find a group
of three natural frequencies in the domain 1.1÷1.2 Hz, another one in the domain
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15.6÷16.3 Hz and the 6-th frequency being much more bigger (26.69 Hz); this
grouping of frequencies and the big differences between the values of domains’
limits can be explained by the significant differences between the bearings
stiffness on vertical axis Cz (compression effort) and on horizontal plane xCy
(shear efforts);
e) analyzing the values from table 5 (for the entire bridge), we can find a
group of three natural frequencies in the domain 1.1÷1.2 Hz and another three in
the domain 15.6÷16.8 Hz; in this case of simulation, the pitch movement  x  of
the viaduct, which is almost decoupled from the forward-back movement Y  ,
has a natural frequency more smaller than the pitch movement of a single arch
because of a bigger value of the moment of inertia J x mainly.
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publicaţiilor pentru construcţii, Bucureşti, 1982.
[3].
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Tehnică, Bucureşti, 1990.
[4].
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Jos” din Galaţi, Fascicula XIV, 1997.
[5].
GH. BUZDUGAN, L. FETCU, M. RADEŞ: “Vibraţii mecanice”, Ed. Didactică şi
Pedagogică, Bucureşti, 1982.
[6].
GH. BUZDUGAN: “Izolarea antivibratorie ”, Ed. Academiei Române, Bucureşti,
1993.
[7].
N. DRAGAN : “Contribuţii la analiza şi optimizarea procesului de transport prin
vibraţii - teză de doctorat”, Universitatea “Dunărea de Jos”, Galaţi, 2001.
[8].
C.M. HARRIS, C.E .CREDE: “Şocuri şi vibraţii” vol. I-III, Ed. Tehnică, Bucureşti,
1967-1969
[9].
D. INMAN: “Vibration with Control”, John Wiley and Sons Ltd., New Jersey, 2006.
[10].
S. RAO: “Mechanical Vibrations” Fourth Edition, Pearson Education Inc., New
Jersey, 2004.
[11].
M. RĂDOI, E. DECIU: “Mecanica”, Editura Didactică şi Pedagogică, Bucureşti,
1977.
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APPLICATION OF GPR AND FWD IN ASSESSING
PAVEMENT BEARING CAPACITY
Josipa Domitrović, MCE, University of Zagreb, Faculty of Civil Engineering, Department of
Transportation, e-mail: jdomitrovic@grad.hr
Tatjana Rukavina, PhD.Prof., MCE, University of Zagreb, Faculty of Civil Engineering,
Department of Transportation, e-mail: rukavina@grad.hr
Abstract
The process of pavement maintenance and rehabilitation starts by collecting the data
which will form the base for evaluation of pavement functional and structural condition.
Collection of data can be performed by destructive and non-destructive testing. Usually
preferred are the non-destructive methods, that do not damage the pavement, and the process
of pavement evaluation is objective and repeatable. Non-destructive testing methods are
becoming more and more popular, especially for assessing the structural condition of the
pavement. Non-destructive testing by a Falling Weight Deflectometer (FWD) and the analysis
of so collected data by the process of backcalculations is today the usual tool for assessing
pavement bearing capacity. One of the basic input parameters for analysis of the data
collected by FWD is pavement layers thickness.
The practice in Croatia is to determine pavement layers thickness by coring. This
destructive method affects pavement integrity, so the number of such tests should be kept to
the minimum. By coring the accurate thickness of all pavement layers is obtained on specific
point locations. Thus, numerous deviations in layer thickness remain unnoticed, and in the
end, use of such data for the process of backcalculations does not provide ac urate values of
layer moduli. Coring can be replaced with non-destructive method of testing by Ground
Penetrating Radar (GPR), which provides continuous information on thickness of all
pavement layers.
The paper shows the method for assessing the bearing capacity of the pavement based
on the data collected by FWD, GPR and coring. The calculation for layer moduli was
performed by the ELMOD software, separately for the layers thickness data obtained by
coring, and separately for the thickness obtained by GPR tests. Analysis and comparison of
the results of calculated elasticity moduli obtained by using various methods for collecting
layer thickness data were performed in the paper.
Keywords: non-destructive testing, FWD, GPR, layer thickness, elastic moduli
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Josipa Domitrović, Tatjana Rukavina
Application of GPR and FWD in assessing pavement bearing capacity
1.
INTRODUCTION
Road is capital investment whose value is gradually reduced within its
lifetime by progression of degradation processes. Pavement degradation can be
slow down or stopped by applying appropriate maintenance and rehabilitation
techniques and for that it is necessary to evaluate pavement structural condition,
i.e. bearing capacity. Nowdays, most common method for determining
pavement bearing capacity is deflection measurement, mostly by Falling Weight
Deflectometer (FWD). FWD determines the full dynamic deflection bowl by
applying known impulse loads on the pavement. Pavement deflections are then
analysed using backcalculation procedure for determing the layer elastic moduli.
The reliability of estimated pavement moduli depends on the accuracy of layer
thickness data.
In Croatia, thickness data is usually obtained from project documentation
or coring. Each of these methods has its advantages and disadvantages. Data
collection based on project documentation is fast and requires minimum effort
but is not very reliable. Coring provides most accurate thickness data, but is
expensive, time consuming, has significant impact on traffic and affects
pavement integrity so the number of such tests should be keep on minimum.
Furthermore, data is obtained only on selected locations that may not be
representative for considered road section so deviations in pavement structure
could easily be missed. This will provide incorrect information for further
analysis and can lead to application of wrong maintenance and/or rehabilitation
techniques.
To address issues mentioned above Ground Penetrating Radar (GPR) was
introduce as non-destructive, fast and reliable technique that provides a
continuous display of pavement layers thickness. Evaluation studies carried out
in the last 20 years show that deviations between GPR and core thickness results
of newly constructed pavement range from 2% to 5% of total thickness [1] and
for old pavements are mostly less than 10% [2]. Based on this it can be conclude
that GPR is suitable non-destructive technique, which can replace coring.
2.
DESCRIPTION OF GPR AND FWD METHODS
Though, integration of non-destructive testing devices, FWD and GPR for
pavement evaluation is not new technology most pavement engineers in Croatia
are not aware of their advantages and still rely on traditional destructive methods
like coring to obtained necessary pavement data. In continuation, components
and basic operating principles of GRP and FWD are explained.
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2.1.
Ground Penetrating Radar (GPR)
The GPR device used in road surveys is vehicle mounted system that
normally consists of following components: 1) antennas (air or ground coupled)
with transmitter and receiver, 2) GPR control/acquisition unit, 3) PC for data
collection and 4) positioning device (Figure 1, left).
antenna
A1
A2
A3
voltage [V]
A0
antenna asphalt unbound
base
reflection reflection
reflection
A0
A1
A2
asphalt
unbound
base
subgrade
subgrade
reflection
A3
time [ns]
t1
t2
t1=travel time through asphalt layer
t2=travel time through unbound base layer
Figure 1. Ground Penetrating Radar (left); Shematic representation of EM
signal (right)
The GPR system is base on the radar principle in which the antenna
transmits pulses of radar energy, i.e. electromagnetic (EM) waves with a central
frequency varying from 10 MHz up to 2.5 GHz [3] into the pavement. EM
waves partly reflect and partly pass through layers of materials with different
EM characteristics. A part of energy that reflects at layers interface is receive by
GPR system and displayed as a plot of amplitude (voltage) and time necessary
for its return to antenna (Figure 1, right) [2].
The speed of passing EM wave through a particular material is under the
influence of its relative dielectric constant (εr). For asphalt pavements materials
relative dielectric constants can be calculated using surface reflection method.
Once the values of materials relative dielectric constants are calculate it is
possible to determine thickness of a particular layer (hi) using equation (1) [4]:
ct i
hi 
(1)
r
where: c – speed of EM wave through vacuum
Δti – time between amplitudes Ai and Ai+1
εr – relative dielectric constant of the material.
EM signal, shown in Figure 1, right, can be send up to 1000 scans/second
[3]. Given that during the measurement vehicle moves along the road, we get
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continuous display of the EM wave’s reflection, the interpretation of which
determines pavement layers thickness.
2.2 Falling Weight deflectometer (FWD)
The FWD device for pavement evaluation is trailer mounte system towed
by the vehicle (Figure 2, left). Basic components of a typical FWD unit are: 1)
control system for data collection, processing and storing, 2) loading weight and
plate, 3) hydraulic system and 4) geophones.
Geophones
Load
cell
Deflection bowl
Figure 2. Falling Weight Deflectometer (left); Schematic representation of
FWD operation (right)
The FWD applies stationary dynamic load, similar to a passing wheel
load, onto the pavement surface. The FWD generates a load pulse by dropping
weight onto 300 mm diameter circular load plate. By varying the mass and/or
drop height, impulse load can be varied between 10 kN to 120 kN [5]. Usually
target peak load is 50 ± 5 kN which matches the standard wheel load. The
pavement responses to applied load pulse are vertical deformations in a shape of
deflection bowl (Figure 2, right). Deformations are measure by geophones
located in the load centre and at several radial distances from the load centre.
Base on the force applied to the pavement and the shape of deflection
bowl, it is possible to estimate the in-situ elastic moduli of the different
pavement layers by the iterative process of backcalculation. In this process, the
deflection values are first calculated for assumed elastic moduli values and
compared with deflection values measured by FWD, and accordingly the
assumed moduli values are further adjust for next iteration. The iteration stops
once predetermined level of tolerance between calculated and measured
deflection have been reach (Figure 3) [6].
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Figure 3. Shematic diagram of backcalculation process
3.
RESULTS OF FIELD TEST ON HIGHWAY A4
A pavement investigation carried out on a section of highway A4, ZagrebGoričan from chainage km 83+000 to km 75+500, in the right wheel path of the
drive lane. The pavement investigation involved determination of pavement
deflection by FWD and pavement layers thickness by extraction of cores and
GPR measurements. Based on cumulative difference method test section was
divided into six homogeneous subsections (Table 1).
Table 1. Division of test section into homogeneous subsections
Homogeneous
1
2
3
4
5
6
subsection
75+500 76+001 78+500 80+201 81+000 82+001
Chainage [km]
–
–
–
–
–
–
76+001 77+224 79+801 81+000 82+001 83+001
3.1. Core data
Six cores (Ø 100 mm) were extracted on selected locations from each
homogeneous subsection to determine pavement layers thickness. Due to
damage of cement treated base layer, which on some locations is completely
destroied, only the cores of asphalt surface and base layers were extracted.
Determinate thickness values are shown in Table 2.
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Table 2. Asphalt layers thickness data obtained by coring
Thickness [mm]
Chainage [km]
Asphalt surface
Asphalt base
Total
75+900 76+900 79+500 80+300 81+800 82+700
50
86
136
49
65
114
63
99
162
58
90
148
59
97
156
61
105
166
3.2 GPR data
GPR measurements were done with two GSSI air-horn antennas, one 2,2
GHz and other 1,0 GHz. Measurements ware taken continuously for the hole
section at vehicle speed between 50 and 70 km/h and with signal speed of 200
scans/sec. The processing and interpretation of gather data were done by
RADAN software. Because of similar dielectric values of asphalt surface and
asphalt base layers, interface between these two layers could not be distinguish,
so only the total thickness of asphalt layers was determinate. Obtained layers
thickness is shown in Figure 4.
3.3 FWD data
Pavement deflection measurements carried out with Dynatest FWD in
accordance with COST 336 Report [7]. Spacing between individual
measurements was 100 m with applied impulse load of 50 kN. For each test
point FWD registers pavement deflections, chainage and air temperature. Based
on measured deflections elastic moduli of individual pavement layers were
determinate by ELMOD6 software, separately for thickness data obtained by
coring and thickness data measured by GPR.
Since only the thickness of asphalt layers were obtained by coring for
purpose of backcalculation process thickness of cement treated and unbound
granular base layers was taken from project documentation (design thickness).
Design thickness of cement treated base layer from chainage km 75+500 to km
79+800 is 200 mm and from chainage km 79+800 to km 83+000 is 250 mm.
Design thickness of unbound granular base layer is 250 mm and is constant over
the entire test section. Pavement layers thickness used in the backcalculaton
process are shown in Figure 4.
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900
Thickness [mm]
800
700
600
500
400
300
200
100
0
Subsection 6
Subsection 5
Subsection 4
Subsection 3
Core data:
asphalt layers
cement treated base
Subsection 2
unbound granular base
GPR data:
asphalt layers
cement treated base
unbound granular base
Subsection 1
Figure 4. Pavement layers thickness used in backcalculation proces
Results of calculated elastic moduli for layers thickness determinate by
core and project data as well as GPR data are shown in Figures 5 and 6
respectively.
Figure 5. Calculated elastic moduli with thickness data from core and project
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Figure 6. Calculated elastic moduli with thickness data from GPR
4. ANALYSIS OF RESULTS
Analysis is done for layer thickness data obtain by coring and GPR
method and for layer elastic moduli calculated by using thickness data obtained
as described above.
4.1. Layer Thickness
Total thickness of asphalt layers measured by GPR, on the entire test
section, ranges from 97 mm to 185 mm with the mean value 136 mm. Mean
values of pavement layers thickness for defined subsections are show in Table 2.
Verification of results of continuous measurement was conducted by comparing
GPR thickness at the location of cores with thickness measured on cores.
Average deviation of the results of continuous measurement was 4,5 mm, thus
confirming the accuracy of the thickness measurement by GPR. From Figure 4 it
can be conclude that cores were not extracted from locations representative for
considered subsection. In fact they were extracted at thickest (subsections 6, 5, 4
and 3) and thinnest (subsections 2 and 1) locations.
Table 2. Mean layers thickness data obtained by GPR for subsections
Mean thickness [mm]
Homogeneous subsection
1
2
3
4
5
6
142
133
145
132
124
139
Asphalt surface+base
212
210
291
301
279
279
Cement treated base
296
320
278
274
295
271
Unbound granular base
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Thickness of cement treated base layer could not be determined by coring.
Layer was completely crushed on entire test section and it was not possible to
extract undisturbed samples based on which the thickness could be determined.
Thickness measured by GPR ranges from 163 mm to 378 mm with mean value
of 263 mm. This data was compared with the data from project documentation.
Mean value on observed sections is close to value from project documentation
but it does not cover wide range of thicknesses obtained by GPR (Figure 4).
Thickness of unbound granular base layer determinate by GPR ranges
from 123 mm to 505 mm and the mean value is 289 mm. Such large range of
thicknesses is result of inability to clearly distinguish the boundary between
unbound granular base layer and subgrade, due to penetration of small particles
of subgrade material into unbound granular material.
4.2 Layer elastic moduli
Elastic moduli of asphalt layers calculated for GPR thickness data range
from 1200 MPa to maximum of 11500 MPa, and for core thickness data from
1300 MPa to 10500 MPa. On the most part of the test section, values of elastic
moduli for both thickness data range from 4000 to 5000. These are characteristic
values of asphalt layers elastic moduli regarding their structure, age and
condition.
Elastic moduli of cement treated base layer calculated for GPR thickness
data range from 500 MPa to 12500 MPa with the mean value of 3000 MPa, and
for design thickness data from 500 MPa to 9500 MPa with the mean value of
3300 MPa. On the entire test section elastic moduli for both thickness data
mostly vary between 1000 MPa and 3000 MPa. This shows that layer has lost its
structural integrity and its characteristics resemble unbound granular layer.
Elastic moduli of unbound granular layer on the entire test section mostly
vary between 100 MPa and 150 MPa. For project thickness data minimum value
is 50 MPa and maximum value is 650 MPa, and for GPR data minimum and
maximum values are 50 and 850 respectively. This wide rane of elastic moduli
indicates uneven layer quality. On some locations quality of unbound granular
material is identical to quality of subgrade material.
Subgrade elastic moduli for both thickness data vary from 40 MPa to 150
MPa. Mean value on entire test section is 80 MPa, which corresponds to CBR of
8% and defines subgrade with good bearing capacity.
From the Table 3, it can be seen that the backcalculated layer moduli for
asphalt layers and cement treated layer based on the GPR thickness data are
generally lower then layer moduli calculated based on the core/design thickness
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data. Elastic moduli of unbound granular base layer are on all subsections higher
for GPR thickness data compared with moduli calculated for design thickness.
Subgrade moduli for both thickness data are similar and put subgrade of each
subsection into same bearing capacity rank.
Core
GPR
Table 3. Calculated mean values of elastic layer moduli for subsections
Elastic moduli [MPa]
Homogeneuos subsection
1
2
3
4
5
6
1786 3935 6229 4167 4006 4657
690
1554 4030 1897 2677 4152
Cement treated base
190
292
126
99
153
229
57
63
97
87
96
113
Subgrade
1936 3650 6657 4088 4736 5443
834
3302 4364 2159 2326 4049
Cement treated base
133
118
115
109
87
194
52
65
86
78
102
99
Subgrade
5. CONCLUSIONS
Estimation of pavement bearing capacity is first step necessary to
calculate pavement remaining life and is main input parameter for most
pavement reinforcement design methods. Contemporary techniques for
estimation of pavement bearing capacity include measurement of pavement
deflections by FWD device and interpretation of so collected data by
backcalculation process to determine layers elastic moduli. Application of this
techniques enabled distance from known empirical pavement reinforcement
design methods. By knowing the in situ elastic moduli of individual layer it is
possible to optimize calculation of pavement remaining life and pavement
reinforcement design.
Main input parameters in backcalculation process are pavement
deflections and layer thickness which can be determinate by coring (localized)
or measured by GPR device (continuous). Comparing values of elastic moduli
obtained through backcalculation process by ELMOD6 software for two cases,
first in which layers thickness was obtained by coring and second in which
layers thickness was obtained by GPR, it was concluded that there are certain
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differences in calculated elastic moduli values but they are not so significant to
discard values obtain based on thickness data from cores.
For design purposes, if the GPR device is not available, it is possible to
use thickness data from cores. However, since there is a tendency in
reinforcement projects to apply recycling methods and use recycled materials,
knowing the continuous thickness of asphalt layers is essential in order to
determine the optimum thickness available for milling and thus achieve
optimization of recycling process.
ACKNOWLEDGMENTS
This study is a contribution to the EU funded COST Action TU1208, "Civil
Engineering Applications of Ground Penetrating Radar".
REFERENCES
[1]. J. WENZLICK, T. SCULLONO, K.R. MASER: “High Accuracy Pavement Thickness
Measurement Using Ground Penetrating Radar”, Missouri Department of Transportation
Research, Development and Technology Division, February 1999.
[2]. M.OŽBOLT, T. RUKAVINA, J.DOMITROVIĆ: “Comparison of pavement layer
thickness measured by GPR and conventional methods”, The Baltic Journal of Road and
Bridge engineering, vol.7, no.1, 2012.
[3]. T. SATTENKETO: “Timo, Electrical properties of road materials and subgrade soils
and the use of Ground Penetrating Radar in traffic infrastructure surveys”, Faculty of
Science, Department of Geosciences, University of Oulu, Finland, 2006.
[4]. S. FONTUL: “Structural Evaluation of Flexible Pavements Using Non-Destructive
Tests”, PhD thesis, LNEC, Lisabon, Portugal, 2004.
[5]. F.ZHOU, T. SCULLION: “Guidelines for evaluation of existing pavements for HMA
overlay”, Report 0-5123-2, Texas Transportation Institute, Texas, November 2006.
[6]. S. ALAVI, J.F. LECATES, M.P. TAVARES: “Falling Weight Deflectometer Usage, A
Synthesis of Highway Practice”, NCHRP Synthesis 381, Sierra Transportation Engineers,
Inc.Reno, Nevada, 2008.
[7]. “Use of Falling Weight Deflectometers in Pavement Evaluation”, COST 336, European
Commission, Directorate General Transport, April 2005.
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THE INFLUENCE OF VISIBILITY CONDITIONS IN
HORIZONTAL ROAD CURVES ON THE EFFICIENCY OF
NOISE PROTECTION BARRIERS
Tamara Džambas, Assistant, MCE, University of Zagreb, Faculty of Civil Engineering, Fra
Andrije Kačića-Miošića 26, 10 000 Zagreb, Croatia, e-mail: tdzambas@grad.hr
Saša Ahac, Sc. novice, MCE, University of Zagreb, Faculty of Civil Engineering, Fra Andrije
Kačića-Miošića 26, 10 000 Zagreb, Croatia, e-mail: sahac@grad.hr
Vesna Dragčević, Prof., PhdCE, University of Zagreb, Faculty of Civil Engineering, Fra
Andrije Kačića-Miošića 26, 10 000 Zagreb, Croatia, e-mail: vesnad@grad.hr
Abstract
Ensuring sufficient visibility on planned roads by sight distance testing is an integral
part of every project, but problems with visibility can emerge when noise barriers are erected
on existing roads. Namely, in order to provide sufficient noise protection, high noise barriers
are often placed at minimum distance from the carriageway edge, and additional visibility
testing in most cases is not carried out.
Research described in this paper consists of stopping sight distance tests conducted by
means of specialized road design software MX Road, and noise barrier optimization
conducted by means of specialized noise prediction software LimA using static noise
calculation method RLS 90. The aim of this research is to establish whether the required
stopping sight distance on road sections where minimum design parameters are applied can be
achieved if the noise barrier is placed at minimum distance from the carriageway edge, and to
establish whether the optimized dimensions of planned noise protection barrier will change if
the barrier is placed on larger distance from the noise source, which is, in this case, the
existing road.
Keywords: visibility, horizontal curves, noise protection barriers
1. INTRODUCTION
Considering the fact that drivers receive 95% of all information from the
environment by sense of sight and that the lack of visibility is direct or indirect
cause of almost 40% of all traffic accidents on suburban roads [1], it can be
stated with certainty that a significant role in road design belongs to sight
distance testing. In this paper stopping sight distance on horizontal curves was
observed. This important safety factor is ensured by removing all obstacles from
visibility field on the inside of a horizontal curve; traffic noise protection
barriers are no exception. Barriers are often placed at minimum distance from
carriageway edge of existing roads while additional visibility testing in most
cases is not carried out.
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Tamara Džambas, Saša Ahac, Vesna Dragčević
The influence of visibility conditions in horizontal road curves on the efficiency of noise protection barriers
In order to increase road traffic safety with simultaneous implementation
of noise protection, necessary to improve the life quality of residents in the
vicinity of roads, tests described in this paper were carried out. Sight distance
testing was conducted by specialized road design software MX Road, and
barrier optimization by specialized noise prediction software LimA. Tests were
performed on eight road models with different curve deflection angles - from
20º to 90º.
2. VISIBILITY CONDITIONS IN HORIZONTAL ROAD CURVES
Term “visibility” implies a certain area in which there are no obstructions
of the driver’s line of sight, [2]. Visibility is determined by infliction of
horizontal and vertical alignment, namely minimum radius of horizontal and
vertical curves. In engineering practice there are two different lengths of
visibility: stopping sight distance and overtaking sight distance, [3]. It is
considered that ensuring of stopping sight distance is basic factor of road traffic
safety.
According to [3], stopping sight distance is equal to the vehicles stopping
distance, and therefore it must be ensured at all road sections, horizontally and
vertically, for both driving directions. This research is focused only on visibility
conditions in horizontal road curves.
Elements of stopping sight distance are sight distance length (P z), sight
distance width (b), and horizontal curve radius (Rmin), which is in direct
correlation with driving speed Vr. Elements of stopping sight distance are shown
in Figure 1. Sight distance length is defined as a tendon that connects the point
of driver’s eye position in vehicle and fixed obstacle which driver must
perceive. Driver’s eye is placed at the height of 1 meter above road surface, and
at the distance of 1.5 m from the edge of the driving lane (“driving line”), [3].
Fixed obstacle is also placed in driving line, at height of 20-25 cm, depending on
driving speed, [3]. Sight distance width is determined at maximum distance
between tendon and driving line, and can be calculated by equation, [3]:
Pz2
[m]
(1)
8R
Values of stopping sight distance length and width, depending on driving
speed Vr, are given in Table 1, [3]. These values refer only for roads with
longitudinal grade 0%.
b
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Figure 1. Elements of horizontal stopping sight distance
Table 1. Values of sight distance elements for driving speed 30-120 km/h
Vr [km/h]
30
40
50
60
70
80
90
100
110
120
Rmin [m]
25
45
75
120
175
250
350
450
600
750
Pz [m]
25
35
50
70
90
120
150
190
230
280
b [m]
2.9 3.6 4.3
5.1
6.0
7.1
8.3
9.9
11.3
13.3
Required horizontal stopping sight distance can be achieved by removing
all obstacles from visibility field - by clearing of vegetation, banning of
construction near the road, additional excavation or placing the supporting wall.
If there are road sections where sight distance cannot be achieved by these
procedures, driving speed must be limited to values where sight distance is
ensured (Table 1).
Ensuring sufficient visibility on planned roads by sight distance testing is
an integral part of every project, but problems with visibility can emerge when
noise barriers, as the most prevalent measures of noise protection, are erected on
existing roads.
Sound barriers are purpose made obstacles placed in areas that must be
protected from traffic (or any kind of) noise. They can be of various types,
design, materials and acoustic performances, depending on required level of
noise protection.
Traffic noise protection barriers are placed between source of the noise
(road) and the receiver (protected object). For the optimal performance of barrier
it is necessary to place it as close as possible to the noise source. This can be
explained as follows. Straight expansion path of sound wave that spreads from
noise source to receiver is changed by placing barrier between them (Fig. 2).
Depending on barrier characteristics, some of the sound waves are reflected,
some are absorbed, part is transmitted, and at the barrier top diffraction occurs.
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With increase of the diffraction angle (angle between direct and diffracted sound
wave shown at Figure 2) i.e. decrease of the distance from noise source, the
energy of the diffracted wave is also decreased, and barrier is more efficient.
This research refers to the examination of whether barrier shifting from
minimum distance from carriageway edge for amount of required sight distance
width has influence on its efficiency apropos optimized dimensions.
Figure 2. Change of sound wave direction caused by barrier [4]
3. VISIBILITY TESTING
Stopping sight distance testing was conducted by specialized road design
software MX Road, using the analysis module „Through Visibility“. This
module is utilised to assess visibility along a road using plan, profile and
perspective views simultaneously. In accordance with input data for driver’s eye
position, target position, required stopping sight distance length and obstacle
beside the road, MX Road determines cross sections with unfulfilled sight
distance.
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3.1. Road models for visibility testing
Visibility tests were performed on eight horizontal curves with the same
(minimum) radii, but different curve deflection angles - from 20º to 90º, with
angle interval of 10º (Fig. 3). In order to simplify the road models, surrounding
terrain was designed as flat surface, and roads were situated on 2 meter high
embankment. Design speed of 80 km/h was presumed, which resulted in
required sight distance length of 120 meters, required minimum radius of 250 m,
transition length of 60 m, and cross section elements as shown in Figure 4. All
analysed road models have longitudinal grade of 0%, and cross section grade of
2.5% in straight sections i.e. 7% in curve sections.
Figure 3. Visibility testing models with various curve deflection angles
Five meters high noise barrier located at minimum required distance of
1.5 meters from the carriageway edge at the inside of a road curve is taken as
input parameter for visibility field restriction. Minimum distance from
carriageway edge is required to provide space for placing the road guard rails
and barrier maintenance. Considering the above, visibility tests are performed
only for ride through the inner side of curve.
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Figure 4. Cross section of visibility testing models
3.2. Visibility test results
MX Road visibility test results are given graphically in a form of visibility
envelope, which represents the border of visibility field (Fig. 5), and numerically
by lengths of road sections on which required sight distance wasn’t achieved.
Figure 5. Visibility test results for road with deflection angle 90º
With barrier placed at minimum distance from carriageway edge, stopping
sight distance was not achieved in any of eight testing models. Visibility tests
also showed that length of road sections with unfulfilled sight distance grow
with increasing deflection angle value (Table 2, Fig. 6). Additionally, maximum
displacements of barrier for every examined deflection angle are smaller than
values defined by regulations (4.1 m).
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Deflection
angle [°]
20
30
40
50
60
70
80
90
Table 2. Visibility test results
Maximum displacement
Length of road sections with
of barrier [m]
unfulfilled sight distance [m]
2.56
80
3.71
130
3.97
170
4.05
220
4.06
270
4.02
310
4.02
350
4.00
390
Figure 6. Relation visibility-deflection angle value
4. NOISE BARRIER EFFICIENCY TESTING
Barrier dimensioning was carried out by optimization procedure through
specialized noise prediction software LimA, using static noise calculation
method RLS 90, as described below.
4.1. Input data for barrier optimization
Traffic noise level calculation model consists of digital 3D terrain model
and acoustic data about noise source, noise spreading direction and barrier
characteristics. 3D terrain model in this research was composed of digital relief
model and digital road model.
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In order to examine the influence of visibility conditions in horizontal
road curves on the efficiency of noise protection barriers, two different digital
terrain models were created. First model consists of eight road models with
same cross sections used for visibility testing in MX Road (Fig. 3). In second
model, in order to take into the account the widening of road bank needed to
achieve sufficient visibility on analysed horizontal curves, all road side banks
were expanded to visibility envelopes. According to this, two groups of barrier
optimization procedures were conducted: for barrier placed at minimum distance
from carriageway edge (1.5 m), and for barrier placed on the outside edge of the
widened road bank (Fig. 7).
Figure 7. Models used for testing of barriers efficiency
For all road models following input data was applied. Noise source is
defined as line source positioned 0.5 m above driving surface in road axis. Road
is described as regional with AADT value 7000, 10% of heavy vehicles and
driving speed of 80 km/h.
Determination of barrier dimensions by optimization procedure is
performed by locating of control receptor and by setting barrier parameters and
initial location. In this research, control receptor was positioned at 25 meters
from noise source at the inner side of a curve (Fig. 7). According to [5], noise
levels used to optimize noise barriers are: 65 dB(A) for day and evening period
(day 07-19 h, evening 19-23 h) and 50 dB(A) for night period (night 23-07 h).
Barrier was erected 200 m along the road at a distance of 1.5 m from
carriageway edge i.e. in visibility envelope. It consists of 4 m long and up to 5 m
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high elements sorted in 20 m long groups of same height (Fig. 8). Height
increment between groups is 0.5 m.
Figure 8. Input parameters for barrier optimization procedure
4.2. Test results
Barrier height and length values, necessary to reduce noise levels in
receptor to prescribed value, are obtained by optimization procedure.
Additionally, optimized barrier areas are calculated, as shown in Table 3. A1 are
dimensions of barriers placed at minimum distance from carriageway edge, and
A2 are dimensions of barriers placed in visibility envelope. Test results indicate
that some dimensions increased, some decreased and some stayed unchanged
due to distancing from a road. Maximum difference between areas A1 and A2 is
approximately 30 m2. Test results also showed that changes in barrier
dimensions are not associated with deflection angle values (Fig. 10).
Figure 9. Graphic result of barrier optimisation procedure
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Table 3. Comparison of barrier optimization results
Deflection angle [°] A1 [m2] A2 [m2] ΔA [m2]
20
220
230
-10
30
190
210
-20
40
190
180
10
50
208
180
28
60
190
190
0
70
196
210
-14
80
180
180
0
90
200
180
20
Figure 10. Relation barrier dimensions-deflection angle value
5. CONCLUSIONS
Considering the fact that visibility is one of the most essential factors of
road traffic safety, stopping sight distance at all road sections must be ensured;
this also applies to sections with noise protection barriers. Lack of visibility is
not an issue at new roads where noise barriers are planned and erected in
accordance with road project that includes visibility testing and determination of
land expropriation width. Problems can emerge at the existing roads, especially
those placed in low profile embankments, where area for road construction is
already redeemed and barrier placement to the outer edge of the visibility field is
often not possible.
The main goal of the research presented in this paper was to establish if
required stopping sight distance in road curves with minimum radius can be
achieved when noise protection barrier is placed at minimum distance from
carriageway edge. Another goal was to determine whether the barrier
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displacement to the outer edge of the visibility field on the inside of a curve, that
should be conducted in order to achieve minimum required visibility, has any
influence on its optimized dimensions.
Visibility test results showed that required stopping sight distance with
barrier placed at minimum distance from carriageway edge isn’t achieved on
any of eight testing models; and secondly that visibility is reduced with
increasing deflection angle value. Barrier optimization results showed that
barrier distancing from carriageway edge has minor impact on its optimized
dimensions.
Based on these results it can be concluded that ensuring the visibility in
horizontal road curves has negligible influence on the efficiency of noise
protection barriers i.e. on barrier construction costs. If barrier is placed at
minimum distance from carriageway edge (mostly due to described problem
with existing roads), additional visibility testing must be carried out and driving
speed should be limited to values where required stopping sight distance is
ensured. In accordance with that, driving speed presumed in this research should
be decreased for approximately 38%. Tests performed in this research should be
carried out on a larger number of models with different input parameters in
order to show whether conclusions obtained in this paper can be applicable to all
cases, or just on particular testing model.
REFERNCES
[1].
LJ. ŠIMUNOVIĆ: „Road visibility”, Faculty of Transport and Traffic Engineering,
Zagreb, 2011.
[2].
„The Law on Road Traffic Safety”, Official Gazette 74/2011.
[3].
„Regulations about basic terms that public suburban roads and their elements must
comply from traffic safety aspects”, Official Gazette 110/2001.
[4].
Environmental Protection Department & Highway Department: „Guidelines on design
of Noise Barriers”, Government of the Hong Kong SAR, Second Issue, 2003.
[5].
„Regulations about highest noise levels in territory where people live and work”,
Official Gazette 145/2004.
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BALANCED CANTILEVER GIRDER BRIDGE OVER THE
DANUBE-BLACK SEA CHANNEL
Aldo Giordano, PH.D. Professor of Structural Engineering, ITALROM Inginerie
Internationala, e-mail: a.giordano@italrominginerie.com
Giorgio Pedrazzi, Chief Structural Engineer, ITALROM Inginerie Internationala,
e-mail: g.pedrazzi@italrominginerie.com
Giovanni Voiro, Structural Engineer, ITALROM Inginerie Internationala,
e-mail: g.voiro@italrominginerie.com
Abstract
This paper describes the design and construction of a “balanced cantilever girder”
bridge over the Danube-Black Sea channel, characterized by a central span of 155m with two
symmetrical side spans of 77.5m. The total length of the bridge, including portions of the
abutments support, is 312.0m.
The bridge main features, from calculation as well as construction points of view, are
in particular the post-tensioning tendons, distributed both a top and bottom sides of the
section along the bridge. The former ones play a key role in the construction phase, for the
need of counterbalancing selfweight while subsequent segments are realized.
Tendons are symmetrical about midspan, with anchors positioned at the end of each
segment.
Bridge deck is supported by two piers outfitted with friction pendulum seismic
bearings, which develop friction both in static conditions to withstand static forces and small
displacements, and in dynamic conditions, causing dissipation. Under severe earthquake load
all structures (deck and piers) develop only elastic behavior.
This papers presents a detailed review of the design process as well as a time journey
during construction
Keywords:, FE non linear analysis, seismic isolation, time-dependent material
properties, staged construction, balanced cantilever bridge
1. INTRODUCTION
This bridge is “balanced cantilever girder” type and it is characterized by
a central 155m span, with two side symmetric 77.5m spans.
The total length of the bridge, including segments at abutments supports,
is 312.0m. The deck shows varying-depth through the spans, provided by a
curved soffit, which characterize the typical parabolic shape of the deck girder.
The depth of the deck cross section varies from a maximum value of
10.0m, at the pier axis, to a minimum value of 2.40m, at the mid span and the
abutments supports.
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Aldo Giordano, Giorgio Pedrazzi, Giovanni Voiro,
Balanced cantilever girder bridge over the Danube – Black Sea channel
The upper slab is 14.75m wide and transversally inclined at 2.5%, same as
the road transverse slope. The upper slab shows a variable thickness from a
minimum of 25cm, at the center of the box girder section, to a maximum of
45cm, at two intermediate web supports.
The box girder section is characterized by a depth of the bottom slab of
variable thickness, which is maximum near the pier to keep the compression at
the bottom fiber compressions below the maximum allowable at this location.
The thickness of the concrete webs is 30cm for the center spans segments and
40cm segments closest to pier segments .
Figure 1. Plan scheme of the bridges
The deck is characterized by internal tendons, positioned in the top and
bottom slab. The upper tendons play an important role during construction
phases because of their counterbalance action against the activation of segments
self-weight, then to reduce the vertical deflection of the free cantilever under
gravity loads.
The upper tendons are symmetric to the pier, with a linear path in the
upper slab and short vertical deviation near the tendon end anchorages. The
tendon anchorages are located at the end of each segment in both web at top
position, where it has been defined a wider thickness zone up to 70cm.The lower
tendons, activated at the end of free cantilever construction stage, are located
along bottom slab. The tendon end anchorages are located in specific r.c.
internal blisters. The lower tendon layout is symmetric at mid central span and
located at end of side spans.The bridge deck is supported by two piers and two
abutments through seismic bearings. At each support there are two bearings type
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“friction pendulum” which develop friction both in static condition, to asses
static forces and small displacements, and dynamic condition, providing
dissipation. Under rare seismic load all structures (deck and elevations) develop
only elastic behavior, because dissipation provided by seismic bearings. As
precaution at piers support a shear key by r.c. is located to prevent deck
overtaking.
Figure 2. The bridges in their final configuration
Peer 1 and 2 are characterized by same shape but different height,
respectively 17.40m and 16.15m. The pier has hollow rectangular section with
8.0m transverse and 6.0m longitudinal external dimensions and 60-80cm web
thickness. At the top of the pier there is a pier cap, of same external dimensions
of pier current section and 2.0m height. At the top of pier cap are located two
bearing r.c. block that transfer the vertical and horizontal deck reactions.
Piers base section is connected to an r.c. massive rectangular footing, of
11.0mx13.0m dimensions and 2.0m thickness, which is founded to a ring of
diaphragm walls able to transfer to the ground, the static and seismic forces
coming from the superstructure.
Both abutments are spill-through type. The reason of this choice of
because of the relevant height of the back embankment, that reach 8.8m in SP1
and 10.5m in SP2, and the high seismic action that could be developed by a
traditional full abutment wall.
The abutment structure has a top beam seat of L shape that is connected to
the back wall. The beam seat collect bridge deck vertical and horizontal
reactions, through bearing seismic devices, and earth backfill pressure of the
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embankment. The beam seat is supported by a number of shear walls of
rectangular section, 1.0m thickness and 4.3m length, aligned with longitudinal
deck axis. Each shear wall is founded, trough an intermediate footing r.c. beam
h=1.5m, to two deep diaphragm walls that transfer to the ground the static and
seismic loading due to superstructure and earth pressures.
The seismic design of the bridge has been assessed through refined
analysis. In details it has been assumed that under extreme seismic actions
(Ultimate Limit State) the bridge develop dissipation at “friction pendulum”
bearings.
2. ANALYSIS
The bridge have been analyzed by detailed finite element models to assess
the structural behavior of the deck, piers and abutments and the different applied
load/boundary condition. The global bridge finite element model is
characterized by “beam” elements of different geometry according to the
variable shape of the bridge deck and piers.
Figure 3. views of the 3D finite element model
Besides the global model of the bridge, different models were created to
analyze every part of the bridge structure, which requires a more detailed
analysis. For this reason, segments and abutments were analyzed separately. The
following figures display the model in the different phases.
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Global finite element model of the bridge is characterized by “beam”
elements with different geometry, suitably variable form of the bridge deck and
piers.
Different phases of construction of the bridge were considered to enable /
disable loading - bridge segments - limits - prestressing and development timedependent material properties.
Figure 4. views of the 3D finite element model during staged construction
analyses
Twenty steps averall have been taken into account, and the time-varing
material properties have been introduced in the constitutive model in order to
account for long term effects. The used model for evaluating time effect is of
course the CEB-FIP one, represente by the following picture:
Of course, thermal effect have been taken into account both for what
concerns daily and seasonal variations.
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Figure 5. CEB-FIP creep model
Special attention have been paid to the modeling of the bearing devices,
which are of the friction pendulum type, as shown in the following pictures.
Figure 6. Friction pendulum isolator with cyclic behavior
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Figure 6. Friction pendulum as modeled in the software program
A very interesting possibility from the computational point of view is the
possibility provided by the software of considering in each construction stage
the presence and/or activation of the post-tensioning cables, which are a special
characteristic of this kind of bridges, with proper constitutive model for the
steel, which also takes into account time effect.
Figure 7. Post tensioning cables
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Figure 8. Post tensioning cables at intrados
Once the finite element model had been set up and analyzed under all the
construction stages, the code-required conventional loads have been applied, as
summarized in the following pictures, which, for paper length limits, cannot
cover each and every load considered.
Figure 9. Some static load conditions
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Figure 10. Additional loading conditions
For the seismic analyses, the model is characterized by the use of bridge
supports of the “friction pendulum” type both at piers and abutment of the
bridge. In the equivalent linear analysis, elastic constraints with the following
stiffness have been taken into account.
Piers K = 16.345 kN / m
Abutements K = 1.960 kN / m
Subsequently, linear analyses using earthquake spectra provided by the
Eurocodes + National annexes have been used performed. In the following
figure, one of the vibration modes is depicted, and the vibration periods are
indicated in the relevant table.
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Figure 11. 8th vibration mode (first vertical mode)
Mod Nr. Fequency
(rad/sec)
Frequency
Period
(cycle/sec)
(sec)
Tolerancy
1
2.581187
0.410809
2.434223
0.00E+00
2
2.68343
0.427081
2.341475
0.00E+00
3
2.693086
0.428618
2.33308
0.00E+00
4
3.451769
0.549366
1.82028
0.00E+00
5
4.049886
0.644559
1.551448
0.00E+00
6
7.689985
1.223899
0.817061
0.00E+00
7
8.134612
1.294664
0.772401
0.00E+00
8
12.54926
1.997277
0.500682
0.00E+00
9
15.06868
2.398254
0.41697
0.00E+00
The global analyses have been completed with more refined ones,
performed on different parts of the structure, for which local models have been
set up and subjected to properly arranged loads.
For space reasons, only a few of such models have been reported in the
following figures, along with some relevant results in terms of stresses and
equivalent internal forces.
Figure 12. Partial model of a segment
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Figure 13. Additional partial models
Figure 14. Some results in terms internal forces and stresses
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4. ERECTION
Once all the design aspect have been suitably treated, a very detailed
method statement for construction, and subsequent testing, has been established
in order to respect the analysis assumption in each phase of the erection, that for
this kind of bridge play a key role.
The following figures show some of the construction phases.
Figure 11. Come construction phases
5. CONCLUSIONS
This paper, within the limits of these few pages, describes the process the
authors have followed in the design of a composite steel-concrete viaduct with
some peculiar characteristics. The approach followed has made possible a
particularly cost effective realization, while at the same time retaining very good
structural performances and beautiful aesthetics. Some concepts, such as shape
effects and extensive use of non-linear analysis, have helped in streamlining the
process balancing the allegedly opposite needs of cost saving and structural
performance.
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INCREASE THE SAFETY OF ROAD TRAFFIC ACCIDENTS
BY APPLYING CLUSTERING
Goran Kos, D Sc, Institute for Tourism, Vrhovec 5, HR-10000 Zagreb, Croatia,
e-mail: goran.kos@iztzg.hr
Predrag Brlek, M Sc, University of Applied Sciences Nikola Tesla, Bana Ivana Karlovica
16, HR-53000 Gospic, Croatia, e-mail: pbrlek@velegs-nikolatesla.hr
Kristijan Meic, B Sc, Ericsson Nikola Tesla d.d., Krapinska 45, HR-10000 Zagreb, Croatia,
e-mail: kristijan.meic@ericsson.com
Kresimir Vidovic, B Sc, Ericsson Nikola Tesla d.d., Krapinska 45, HR-10000 Zagreb,
Croatia, e-mail: kresimir.vidovic@ericsson.com
Abstract
In terms of continual increase of number of traffic accidents and alarming trend of
increasing number of traffic accidents with catastrophic consequences for human life and
health, it is necessary to actively research and develop methods to combat these trends. One of
the measures is the implementation of advanced information systems in existing traffic
environment. Accidents clusters, as databases of traffic accidents, introduce a new dimension
in traffic systems in the form of experience, providing information on current accidents and
the ones that have previously occurred in a given period. This paper proposes a new approach
to predictive management of traffic processes, based on the collection of data in real time and
is based on accidents clusters. The modern traffic information services collects road traffic
status data from a wide variety of traffic sensing systems using modern ICT technologies,
creating the most accurate road traffic situation awareness achieved so far. Road traffic
situation awareness enhanced by accident clusters' data can be visualized and distributed in
various ways (including the forms of dynamic heat maps) and on various information
platforms, suiting the requirements of the end-users. Accent is placed on their significant
features that are based on additional knowledge about existing traffic processes and
distribution of important traffic information in order to prevent and reduce traffic accidents.
Keywords: accident cluster, traffic information system, road traffic safety
1. INTRODUCTION
Even though numerous measures are taken to decrease the number of
accidents, it is still necessary to invent new approaches to tacking road safety.
Based in essence on the Information and Communications Technologies (ICT),
the Intelligent Transport Systems (ITS) collect the information on road traffic
status from various sources, creating general situation awareness in near-real
time.
Road accidents data is currently being collected with traditional methods
for statistical prediction of irregularities and dangers on the roads. Traditional
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Goran Kos, Predrag Brlek, Kristijan Meic, Kresimir Vidovic,
Increase the safety of road. Traffic accidents by applying clustering
methods that are based on various detectors require additional infrastructure
investment and maintenance along transport corridors. Ease of Internet
information access on different platforms significantly expands the available
information and the ultimate benefit is much higher.
Therefore, it is necessary to develop new methods of analysis to perform
sanation of dangerous spots by changing driver’s perspective. In this way,
participants in traffic can promptly, clearly and unambiguously, in adverse
conditions, spot the danger on the road and thus avoid accidents.
The development of information technology and the development of
precise radio navigation systems have opened a wide range of possibilities of
implementing geographic information systems and have made GIS-oriented
applications available to a wider circle of users. GIS-oriented applications
enable connecting of different types of data in order to realize complex analyses.
2. INFORMATION SYSTEMS FOR COLLECTING AND ANALYZING
DATA ON TRAFFIC ACCIDENTS
The main purpose of the service for the collection and analysis of traffic
and other information relevant to safe traffic is to make mobility safe and
controlled traffic on all sequences.
Intelligent Transportation Systems inform participants about the
upcoming traffic situation, such as tips for drivers or passengers, personal
navigation, congestion on the road, information on incidents or toll. The primary
purpose of the integration of information systems and the traffic itself is to
increase safety of all participants in road traffic.
At the end of the process chain to raise awareness of passengers and / or
drivers of the need for increased road safety is user focused distribution and
visualization of traffic information.
Information systems for traffic management must be capable of adaptive
activity in real time in order to be maximally effective. Good and dynamic
adaptive control of traffic flow reduces the possibility of incidental events that
significantly increases safety on the roads. Such information systems consist of
the following components:
• The transmission system (the fiber optic transmission system)
• A system for collecting and processing information
• Multimedia system for disseminating information
• Center management.
These components should support the process of collecting, processing
and distributing traffic information. The system for collecting and processing the
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collected information gives accurate and relevant information on traffic
accidents and adjusts format delivery information form to be useful and
understanding to the end user. This system involves the availability of traffic
information to end users through the following media:
- Television, radio and internet portals
- Mobile devices (WEB / WAP, SMS, MMS)
- Electronic displays.
3. DATA RELATED ACCIDENT CLUSTER ESTIMATION
Highway engineers and traffic police generally know of the tendency for
road accidents to cluster together at certain locations, commonly termed
“accident black spots”. Two common methods for tracking high risk sites are:
• List – based on accident statistics, a list is drafted indicating concentrations
with the highest frequency of accidents involving injury. The list is then divided
into junctions and road links, the latter specifying the number of accidents
involving injury per kilometer.
• Inventory map – usually managed by the road owner or road authority, this
is regularly updated map with a record of all accidents. Each new accident is
located on the map with a color pin and the color of the pin varies according to
the seriousness (injury/fatality) of the accident. This provides a quick way to
visualize the most dangerous spots and sections of roads.
In the context of traffic management, an accident cluster is a group of
clustered data points which are indicative of high accident locations. Accident
clusters are used to present a group of geospatially organized traffic data based
on traffic accident dataset. The main part of an accident cluster is based on
historic traffic accident reports collected through defined time period. The
cluster is constantly updated with new reports which are collected using the
semantic web. It searches specified web sites which announces new traffic
accidents daily and collects needed data; street address, accident description and
type. The cluster is being updated with new data, latitude and longitude are
matched and map is refreshed.
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Figure 1. Inventory maps
The result is a constantly evolving map that can be visualized with
markers or heat map (Fig 1) reflecting near real-time traffic conditions, which
can considerably enhance spatial and situational awareness through the
distribution in various ways and platforms, such as dynamic heat maps
themselves, plain text, IPTV broadcasts, still images, location-based services
based on mobile communication networks, RDS, electronic panels along the
roads etc [4]. Accident cluster map can be visualized either using mobile devices
or on desktop computers.
Heat maps are especially useful in presenting the results of cluster
analysis where observations are assigned into subsets so that observations in the
same cluster are similar in some sense. Accordingly, accident clusters are used
to present a group of geospatially organized traffic data based on historic
knowledge of traffic accidents. Accident clusters have been traditionally used
alongside with heat maps to gradually improve traffic safety and increase the
awareness my marking dangerous roads with road signs limiting speed, alerting
to sharp turn and similar. Since accident clusters have always been considered a
component of traffic statistics due to their long-term nature, their use in dynamic
traffic conditions has been questionable due to ever evolving nature of traffic
conditions [3].
Heat maps and accident clusters cannot predict potentially dangerous
dynamic conditions based on historical statistics alone. Therefore it is necessary
to include a variety of near real-time traffic data such as location of accident
data received from various sources or the estimation of the accident clusters.
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Figure 2. Accident cluster presented using heat map for the City of Zagreb
4. METHODS FOR SANATION OF DANGEROUS SPOTS
After collecting data on traffic accidents, it is necessary to choose a
dangerous location and approach to it’s sanation. If we look at the locations of
accidents in relation to road locations, we observe the following:
• There are road sections with an extremely low accident rate (from the
statistical point of view) in long periods of time;
• There are short road sections with maximum traffic accident rates, in relation
to equal traffic intensity;
• Research of geometrical road components (situational elements: courses,
curves, transitions, elements of longitudinal and transversal profiles) shows the
presence of the same elements both on sections with low (zero) and on those
with high accident rates).
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General perspective, based on the total road environment information,
might not be in proportion with the information indicating danger. This mostly
boils down to three characteristic situations:
1)
The driver does not recognize clearly enough the road extension
perspective, does not slow down and is a potential, or sometimes even the actual
cause of the accident
2)
The driver does not recognize, or does not recognize soon enough, a
traffic priority situation at the crossroads, which causes an accident due to
disrespecting of the right way, passing through the red light or sudden braking
3)
Insufficient perceptibility of a moving vehicle (with bad or no lights at all,
at night, at sunset, but also during the day), and various obstacles between a
vehicle and a pedestrian.
Up to now, this problem has been solved with the use of mathematical,
graphic, field and photographic method. The new sanation method, using georeferenced video, lowers field costs, increases accuracy and raises safety.
To obtain the right information on a possible relationship between the
driver and his environment, it is necessary to take video movie with GPS
coordinates of the danger spot according to the prepared plan. A detailed
analysis of the area outlook and the road environment from driver’s point of
view, point at the possible perception “defects”, which prevent the driver from
realizing a danger on the road clearly and on time. Modern computer technology
theoretically enables simulation of the road’s outlook and it’s environment from
the driver’s point of view, based on the data gathered from the road project
documentation.
Analysis of video, from various distances on accesses to the danger spot,
from driver’s point of view, provides the opportunity for impartial judgment on
some or most of the probable causes of an accident.
These methods helped improve eight extremely dangerous spots on the
main road network in Croatia. The improvements needed to make an entire road
network or hazardous site safer often cost little but can result in huge benefits in
terms of reduced incidence of road crash and injury. The injured rate and the
total number of accidents were reduced by 30 - 70%.
5. CONCLUSION
On a wide range of transport systems, from road and public transportation
to major traffic infrastructure systems, information systems play a very
important role in the prevention, early warning, and reduce the effects of traffic
accidents.
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The development of intelligent transport systems, as well as the
application of information and communication technologies, will certainly
contribute to the increase in road safety. In the near future it is necessary to
consider wider use of modern safety systems such as the exchange of
information between vehicles in motion, the exchange of information between
vehicles and infrastructure and information exchange infrastructure and
advanced support systems drivers (ADAS - Advanced Driver Assistance
Systems).
The implementation of these systems will contribute to creation of
database containing latest data on road conditions and accidents in real time.
This would allow the development of algorithms that will automatically
processed and distribute traffic information to end users.
REFERENCES
[1].
R FILJAR, M DUJAK, B DRILO, D SARIC, Z KLJAIĆ: Road traffic status
estimation using network-based location intelligence. Automation in Transportation,
29th Conference on Transportation Systems 2009.
[2].
D FILIPOVA, J LEE, A OLEA, M VANDANIKER, K WONGSUPHASAVAT:
Exploring clusters in geospatial datasets. Human-computer interaction lab,
University of Maryland. 2008
[3].
M KARASAHIN, S TERZI: Determination of hazardous locations on highway
through GIS: A case study-rural road of Isparta-Antalya. International Symposium
on GIS, Istanbul- Turkey. 2002.
[4].
C HECHT, K HEINIG: A map based accident hot spot warning application. Concept
from the MAPS&ADAS vertical subproject of the 6FP integrated project PReVENT.
2006
[5].
K VIDOVIC, M DUJAK, K MEIC: Accident Clusters Estimation as part of Traffic
Information Services. Road Accident Prevention 2010, 10th International Symposium
Novi Sad 2010.
[6].
J. MILLER HARVEY, Shaw Shih LUNG: Geographic Information Systems for
Transportation. Oxford University Press, 2001
[7].
P BRLEK: Methods of central projection of traffic signs on the roads. Master Thesis,
Faculty of Traffic Sciences, Zagreb, 2004.
[8].
P BRLEK, K VIDOVIC, M SOSTARIC: The Use of Geo-referenced Video in the
Increase of Traffic Safety. 9th Symposium with international participation
„Prevention of Traffic Accidents of Roads 2008“, Novi Sad, 2008.
51

RJTI - Romanian Journal of Transport Infrastructure

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