Tracking behaviour in time of the bridge over the Danube ...

Tracking behaviour in time of the bridge over the Danube - Black Sea

Channel from Cernavoda

DUMITRU ONOSE , ADRIAN SAVU,

AUREL NEGRILĂ

Faculty of Geodesy

Technical University of Civil Engineering Bucharest

B-dul Lacul Tei, nr. 122-124, sector 2, Bucharest

ROMANIA

[email protected]; [email protected]; [email protected]

Abstract: The article presents the theoretical considerations in the tracking behaviour of bridges and their

application in practice. For the bridge over the Danube-Black Sea Channel from Cernavoda was made a

tracking network consisting of 9 studs and 5 marks, and in the bridge structure: pillars, ledges, decks were

embedded 130 tracing marks. The results of the first stage of measurement are also presented.

Key-Words: Monitoring, Geodetic, Tracking Network, DATUM, Fischer Test, STUDENT (“t”) Test

1 Introduction The bridge over Danube-Black Sea Channel in

Cernavoda (Fig. 1) was inaugurated in 2003 as an

objective of vital importance for the city of

Cernavoda and as any work of art it requires

tracking behaviour and creating a tracking network.

Fig. 1

2 General principles In general, the network design principles are

applicable to the tracking network and the special

characteristics that must be followed further on are:

the results that depend on the period of observation,

the major features that are the precision of points,

not the characteristics of the points themselves. We

must make the distinction between support points

and object points, the networks having limited

scope and being dependent on the existence of

areas with stable points.

Outside the followed target, better said, outside the

deformation target a number of support points must

be present which can be considered in terms of

technique and construction as stable. In this case

we speak about an absolute tracking model, if the

movements of construction are determined from the

outside support points.

The number and the arrangement of the network

tracking points are given by certain rules that

should be set according to the specific problem of

tracking; the goal is to solve the following issues:

the choice of representative points and the

delimitation of the field influenced by deformation.

Equally important as the choice of the

representative points is the setting time (time of

observation). For stabilizing the moment of

measurements we must study the annual

movements that can be caused by the water level or

the variation of temperature and the possible daily

movements resulting from temperature. Choosing

randomly the moments of measurement for

deformation, has led, after a few steps, to a wrong

practice model; practice showed that such

measurements must be determined vith a view to be

included in the maximum and minimum stages of

the construction. The bridge from Cernavoda is

composed of three independent parts, i.e.: the

viaduct on the right bank, the viaduct on the left

bank and the main bridge (metal) (Fig. 1). The

viaduct on the right bank sits on the ledge and two

pillars, the viaduct on the left bank sits on the ledge

and seven pillars, the main bridge sits on the last

Proceedings of the 11th WSEAS International Conference on Sustainability in Science Engineering

ISSN: 1790-2769 207 ISBN: 978-960-474-080-2

pillar of each viaduct. To create the tracking

network of the time behaviour of the bridge, in the

bridge stable areas were planted six studs with

concrete foundation, three studs embedded in the

infrastructure of the pillars (fig. 2), and five marks

of reinforced concrete type A.

In the platform of support the studs were embedded

by levelling benchmarks (Fig. 3).

The object points have been materialized in parts of

the bridge (ledges, pillars, decks, the main metal

structure) by tracking marks with a diameter of 50

mm (Fig. 4).

On the pillars number 2, 3, and 4, the right bank

pillar and the left bank pillar, were placed four

tracking marks, two on the up stream face and two

on down stream face. On the pillars 1, 5, 6 and 7

were placed four tracking marks on the channel

side. On the two ledges were placed four marks on

the superior part, where the decks merge. On the

nine decks of the viaducts were placed forty

tracking marks, thirty on the left bank viaduct and

ten on the right bank viaduct (fig.5) The position of

tracking marks was chosen to define the possible

movements and deformations which may occur in

the constructive elements of the bridge. On the

main bridge were installed 16 tracking marks, eight

down stream and eight up stream (Fig. 6) taking

into consideration its metal structure and the fact

that much higher deformations and movements

may appear in comparison with other elements of

the bridge.

LEDGE 2

PILLAR 1LEDGE 1

Dan

ube - B

lack S

ea

PILLAR 1LEDGE 1

PILLARLEFT BANK

PILLAR 1LEDGE 1

Ch

an

nel

PILLAR 1

PILLAR 7

PILLAR 7

PILLAR 2

PILLARRIGHT BANK

PILLAR 3

PILLAR 5PILLAR 4

PILLAR 6

PILLAR 3PILLAR 2 PILLAR 5 PILLAR 6PILLAR 4 LEDGE 2

PILLAR 7PILLAR 5 PILLAR 6

RIGHT BANKPILLAR

RIGHT BANKPILLAR

LEFT BANKPILLAR

LEFT BANKPILLAR

PILLAR 2 PILLAR 3 PILLAR 4 PILLAR 5 PILLAR 6 PILLAR 7 LEDGE 2

Fig. 2

Fig. 3

Fig. 4

Fig. 5


ISSN: 1790-2769 208 ISBN: 978-960-474-080-2

A8V

A4VA5V A3V A2V

A7V

A6V

A1V

A8M

A4MA5M A3M A2M

A7M

A6M

A1M

Fig. 6

3 Principles of measurement There are two distinct possibilities in determining

the constructions movements and strains:

a. with measuring devices installed inside the

building;

b. with measuring devices installed outside the

building.

In the second case the measurements will be

reported to a network of fixed points located

outside the influence zone of factors acting on the

object pursued and the land on which it is located.

Through this process we determine absolute values

of horizontal or vertical movements, in this

category also entering the geodesic methods.

To realize the tracking network for the bridge of

Cernavoda the last method was used:

measurements of horizontal directions and zenith

angles of each stud were performed to the visible

tracking marks with a total station Leica TCR

1102; the difference between the levelling marks

embed in the studs with NI 007 level. In Fig. 7 the

planimetric tracking network is shown in which the

measured directions and ellipse errors obtained

after processing are highlighted, and in Fig. 8

altimetry tracking network, with routes and

levelling closure in polygons are presented.


ISSN: 1790-2769 209 ISBN: 978-960-474-080-2

Dan

ube - B

lack S

ea

Ch

an

el

Fig. 7

Main Bridge

P1C1

PF2

1.5501 - level difference (m)

- number of stations

- polygon closure (m)

1

Right Bank Viaduct

-21.08938

CUI

PF1

2- 4

.121

21.55011

PMD

-5.3

55

73

4.04

18

10

24.8939

PF3

PA5

1. 6

29

42

3

PF4

P4P3P2 - 1.4123

BA11

4.2788

Left Bank Viaduct

4.2

705

2.91431

4

PF8

PMS

2.04

874

1

BA142

P7

10.39

89

P5

C2

2.2

252

2

1.3180

PA6

Dan

ube

- B

lack

Sea

Ch

ann

el

- 2.91831

0.9

534

- 4.4

923

BA9

2

1

PF7

2

BA13

BA12

4- 7.5373

STUD

MARK

Fig. 8

4 Results of measurements

Measurements made at the t0 were processed

independently for planimetry and altimetry by

using indirect measurements. The results obtained

from processing are:


ISSN: 1790-2769 210 ISBN: 978-960-474-080-2

1. for planimetry

Number of points of the network 15

Mode of compensation network free

Horizontal directions measured 62

Zenith angles measured 62

Average standard deviation “a

priori” 1 cm


posteriori” 0.65 cm

STANDARD

DEVIATION

Min. Max. Average

on X 0.18 0.86 0.47

on Y 0.24 0.62 0.39

(cm) (cm) (cm)

2. for levelling

Number of points of the network 15

Mode of compensation network free

Difference level measured 62

Zenith angles measured 42


priori” 1 mm


posteriori” 1.01 mm

STANDARD

DEVIATION

Min. Max. Average

0.28mm 0.89mm 0.61mm

After performing the measurements for stage t1,

with global matching test we can determine

whether the network, measured at different stages,

forms or not congruent figures. The difference

between the network parameters points to

determine the two stages of measurement must fall

within a "safety limit", being based on the

empirical standard deviation of measurements. If

this difference does not fall within the "safe limit",

the comparison indicates that the network has

deformations.

For both stages of the same measure provisional

coordinates should be introduced with a view to

refer to the same DATUM.

After processing the measurements we obtain the

following items which will be used to the global

matching test:

- t0 phase measurements:

1

∧

X +−

= 1

1

1 NQxx 01s (1)

- t1 phase measurements:

2

∧

X +−

= 2

1

2 NQxx 02s (2)

1

∧

X = Vector of parameters in stage t0

2

∧

X = Vector of parameters in stage t1

1xxQ = Cofactor matrix in stage t0

2xxQ = Cofactor matrix in stage t1

01s = Empirical standard deviation in stage t0

measurements

02s = Empirical standard deviation in stage t1

measurements

Determination of movements and deformations will

be done under the scheme below.

4.1 Global matching test: ∧∧

−= 12 XXd (3)

21 xxxxdd QQQ += (4)

+++= 21 NNQdd (5)

2

02

2

010 sss +±= (6)

2

0sh

dQdF dd

T

⋅

⋅⋅=

+

(7)

d = Discrepancy vector

Qdd = Cofactor matrix of the model of deformation

0s = Empirical standard deviation of the model of

deformation

F = Calculated Fischer test value

h = Rank of the Qdd matrix

Etapa 1 Etapa 2

11,LL

QL 22 ,

LLQL

2

01111 ,,,ˆ sfQX xx

2

02222 ,,,ˆ sfQX xx

ddQd ,

TG≡

Da Nu

Localizare Stop

DATUM

Stage 1 Stage 2

Localization

NO YES


ISSN: 1790-2769 211 ISBN: 978-960-474-080-2

Decision of the Fischer test: F = Calculated Fischer test value

Flim = Theoretical value of Fischer test

α = confidence coefficient (safety threshold),

%5=α

1. If

α,,lim fhFFF =≤ ⇒ hypothesis )( 0H true (9)

=

∧∧

21 XEXE ⇒We don’t have

deformations (10)

2. If

α,,lim fhFFF => ⇒ hypothesis )( 0H false (11)

hypothesis )( 1H true (alternative hypothesis)

≠

∧∧

21 XEXE ⇒We have deformations(12)

Decision determined by the application test is true

within the safety threshold α. The global matching

test discloses that the two networks are matching or

not, if deformation exist, they were not emphasized

(not localized). The localization is made by

applying other specific statistical tests.

4.2 Locating deformations using STUDENT

TEST ( "t"):

This test checks each parameter of the vector d

and if the discrepancy falls within the safety limit

established.

jjj Qss0

= (13)

With the above formula we can determine the

practice of statistics "t" to point j.

j

j

js

dt = (14)

α−= 1,lim ftt (15)

js = Individual empirical standard deviation (each

point j)

jt = Calculated value of the localization

deformation test

limt = Theoretical value of the localization

deformation test

At this test the points that have the empirical

standard deviation smaller than the individual

standard deviation of the empirical model of

deformation are considered stable.

Decision of the test:

1. If

lim1, ttt fj =≤−α ⇒ hypothesis )( 0H true (16)

{ } 0=jdE ⇒ dj point considered stable (17)

2. If

lim1, ttt fj =>−α ⇒ hypothesis )( 0H false (18)

hypothesis )( 1H true (alternative hypothesis)

{ } 0≠jdE ⇒ dj point considered unstable (19)

This test is not quite stable (under the hypothesis

H0 should have most stable points),and it gives

good results if the number of points moved is much

smaller than the number of fixed points, the test not

taking into account also the correlations that

appear.

4.3 Locating deformations using Multiple

STATISTICAL TEST "F"

With this test we check the situation of each

component point of the network, whether or not the

points are moved.

k

k

kdy

dxd =

yykyxk

xykxxk

ddk QQ

QQQ = (20)

k = 1,2 ... n / 2

We calculate the test by analogy with the global

practice of matching statistics with the relationship:

22

0 ⋅=

+

s

dQdF

kddk

T

k

k (21)

k = 1,2 ... n / 2

Flim = F2,f,1-α (22)

Decision of the test:

1. If

Fk ≤ Flim = F2,f,1-α ⇒ hypothesis (H0) true (23)

E{dk} = 0 ⇒ k point is stable (24)

2. If

Fk > Flim = F2,f,1-α ⇒ hypothesis (H0) false (25)

- hypothesis (H1) true

E{dk} ≠ 0 ⇒ k point is unstable (26)

It gives good results when we have many stable

points, when we consider the coordinates of a point

and not take into account the correlation between

points, providing information about points and not

with the X, Y, H; it can be tested at several points

in the network, which forms a group.


ISSN: 1790-2769 212 ISBN: 978-960-474-080-2

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