Dynamic Analysis of Bridges

7/27/2019 Dynamic Analysis of Bridges

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Dynamic analysis of a bridge repaired by CFRP: Experimental and

numerical modelling

M. Abdessemed a,c, S. Kenai b,, A. Bali c, A. Kibboua d

a Public Works Ministry, Algiers, Algeriab Civil Engineering Department, Geomaterials Laboratory, University of Blida, Algeriac Construction & Environment Laboratory, Polytechnic National School of Algiers, Algeriad National Earthquake Engineering Centre (CGS), Algiers, Algeria

a r t i c l e i n f o

Article history:

Received 8 May 2009

Received in revised form 27 July 2010

Accepted 2 September 2010

Available online 28 September 2010

Keywords:

Bridge

Reinforced concrete

Strengthening

Carbon fibres

Ambient vibrations

Modelling

Finite element

a b s t r a c t

A significant number of existing reinforced-concrete bridges all over the world require maintenance and

repair. Hence, the need for a rapid evaluation procedure for the diagnosis of existing bridges. This paper

presents the application of a dynamic analysis methodology for structural evaluation of reinforced-con-

crete bridges. The methodology is based on the application of ambient vibrations non-destructive testing

method and theidentificationof thestructure total responseusing finite element method. A case study of

a three span reinforced concrete bridgein a strong seismic activity area in thenorthof Algeria is analysed.

The ambient vibration testing was carried out on the bridge, before and after its repair by the application

of carbon fibre composites. The tests were conducted using an acquisition system made up of four accel-

erometers with three components placed at specific locations on the bridge. The finite element model

gave comparable results to the experimental ambient vibrations tests. The modal parameters of the

bridge before and after repair were identified by this in situ testing. The applicationof composite material

to strengthen the structure increases the transverse rigidity of the structure and thus its modal frequency.

2010 Elsevier Ltd. All rights reserved.

1. Introduction

A significant number of existing reinforced-concrete bridges

require maintenance and repair. In Algeria there are more than

4850 road bridges of which more than 40% require repair. Many

of these structures have suffered cracking and various damages

during their life span [1]. The causes of these damages are either

due to errors in design, detailing, calculation or construction and

also due to ageing and fatigue. In addition, Algeria is located in a

high activity earthquake zone and its infrastructure is often dam-

aged by seismic actions. Therefore, there is a need to evaluate

and diagnosis these structures in order to repair and strengthen

them when necessary. Bridge inspection is currently conducted

mainly based on visual inspection and hence there is a need to im-

prove bridge assessment techniques. The evaluation procedure

should be a quick method that could detect any damage at its early

stage and propose repair and/or strengthening method to reinstate

the initial transverse rigidity of the structure and improve its per-

formance and durability. The non-destructive testing methods

(NDT) that permit the evaluation of the materials properties and

the performance of the structure without interfering with its use

and without affecting its carrying capacity are the most recom-

mended for this kind of evaluation. The mostly used NDT tech-

niques are optical fibres, ambient excitation or forced vibrations

[2].

Vibrations testing on bridges are not recent and several studies

are reported by various researchers and testing laboratories [3].

This technique has gained recently a widespread use for structural

evaluation. This technique could be divided into two main catego-

ries: the category of testing by measurement of inputs generally

called measured-input testing intended for large structures such

as stayed-girder bridges, suspension bridges or structures with

large lattice road surface, and a second category known as ambi-

ent testing intended for medium and small scale structures, such

as reinforced concrete or steel beam bridges with reinforced con-

crete slab deck [4].

Ambient vibration testing could be applied using excitation by

vehicles. For bridges with heavy traffic that cannot be interrupted,

another form of ambient vibration testing is applied which is that

of the excitation of the circulating traffic itself on the structure in

use that could be associated with other sources of ambient excita-

tion such as wind. This type of excitations was applied on 57 large

bridges in California in 1982. Ambient excitation by wind and

waves as well as pedestrians was also applied on the Oakland

0950-0618/$ - see front matter 2010 Elsevier Ltd. All rights reserved.doi:10.1016/j.conbuildmat.2010.09.025

Corresponding author. Tel.: +213 25 433939; fax: +213 21404921.

E-mail address: [email protected] (S. Kenai).

Construction and Building Materials 25 (2011) 12701276

Contents lists available at ScienceDirect

Construction and Building Materials

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c o n b u i l d m a t
http://dx.doi.org/10.1016/j.conbuildmat.2010.09.025mailto:[email protected]://dx.doi.org/10.1016/j.conbuildmat.2010.09.025http://www.sciencedirect.com/science/journal/09500618http://www.elsevier.com/locate/conbuildmathttp://www.elsevier.com/locate/conbuildmathttp://www.sciencedirect.com/science/journal/09500618http://dx.doi.org/10.1016/j.conbuildmat.2010.09.025mailto:[email protected]://dx.doi.org/10.1016/j.conbuildmat.2010.09.025


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Bay Bridge and the Golden Gate Bridge of San Francisco [2]. Themain objective of the ambient excitation tests is the determination

of the modal parameters such as Eigen frequencies, the distortion

and the damping coefficients of the structures.

Most ambient excitation tests for the structural evaluation of

bridges were carried out to check the numerical modelling and

comparing it with the experimental data and also to monitor

changes in the modal properties due to changes in the structural

conditions after induced defects [26]. However, the application

of such test method on rehabilitated and strengthened structures

remains scarce.

The objective of this paper is the structural evaluation of an old

three span reinforced concrete bridge in Algeria before and after

strengthening by a carbon fibre composite material. The tested

bridge is described as well as the instrumentation used. The effect

of the composite materials on the modal characteristics of the

structure by using ambient excitations testing was quantified.

2. Case study

2.1. Description of the structure

The structure is a road bridge crossing Oumazer River located

near the old city of Tipaza at about 80 km west of Algiers. The area

is situated in a strong seismic activity zone classified as zone III [7].

The bridge is a hyperstatic three span bridge built in 1927. The

deck consists of a reinforced concrete slab supported by four rein-

forced concrete longitudinal beams, while the infrastructure ismade up of two piles each made of four posts connected by shear

walls, and two supports (Fig. 1). The geometrical characteristics ofthe bridge are:

Total length 70.0 m.

Length of access span 15.0 m.

Intermediate span 40.0 m.

Length of road surface 6.0 m.

Length of shoulders 1.0 m.

Height of pile 10.0 m.

2.2. Diagnosis of degradation

The degradations are visible on the bridge structural elements,

with cracking in the concrete cover and corrosion of the reinforce-

ment in the beams and piles (Fig. 2). Corrosion of the piles affectedthe concrete cover with a loss of steel and concrete section proba-

bly due to the aggressive marine environment. The diagnosis also

reveals cracks inclined at 45 near the support of the main beams

indicating an increase in shear stress mainly due to road traffic

increase. These damages were probably exacerbated by the

Fig. 1. Overview of the bridge.

Fig. 2. A view of pile degradations.

Slab

Girders

Beam strengtheningby composites

Fig. 3. Applications of carbon fibres CFRP on the bridge beams.

M. Abdessemed et al. / Construction and Building Materials 25 (2011) 12701276 1271


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earthquake that struck the region in 1989 at a 6.1 magnitude on

the Richter scale.

2.3. Strengthening of the structure

The analysis of the degradation and their causes enabled the

proposition of rehabilitation and strengthening solution of the

deteriorated elements to restore their initial load capacity and

gives to the structure its initial performance. The procedure used

to strengthen the bridge was as follows:

Strengthening of the piles by reinforced concrete jacketing. Repair of the cover concrete by a cement ready mix repair

mortar.

Injection of the cracks by epoxy resin.

Strengthening of the beams by applying carbon fibre sheets

(CFRP).

In order to restore the initial rigidity of the deteriorated ele-

ments and strengthen them to be able to withstand the new traffic

overloads, the choice of appropriate repair materials is important.

The repair techniques used are reinforced concrete jacketing of

piles and flexural and shear strengthening by carbon fibre compos-

ite materials for beams (Fig. 3). Unidirectional Sika wrap sheets

(80 mm in width and 0.13 mm in thickness) were applied to the

side faces of the main beams to increase their shear strength, whilethe carbon fibre laminate Sika carbohard (80 mm in width and

1.2 mm in thickness) were applied to the lower faces of these same

beams to increase their flexural strength. The characteristics of

the repair and strengthening materials used are summarised in

Table 1.

The repair and strengthening of the structure lasted 10 months.

Information on the existing bridge was lacking. Calculation note,

concrete and steel drawings were not available either. However,

the necessary data for testing and modelling were collected on site,

from the client and other intervening engineers or companies.

3. Numerical modelling by finite elements

3.1. Data

Data used to calculate the mass and the transverse rigidity, be-

fore and after repair and strengthening of the structure are given in

Table 2. These values show that the percentage of mass increase of

the repaired structure (before and after repair) is 16%, while the

transverse rigidity (K= EI) increase is of 23.6%.

3.2. Numerical modelling

Three-dimensional modelling was realised by finite elements

using the commercial structural package SAP 2000 [8]. Soil-struc-

ture interaction was neglected. The non-linear behaviour of con-

crete and steel was also neglected as well as the P-delta effect.

Two types of elements were selected for the modelling of the

bridge, the frame elements for the beams, girders and piles and

the shell elements for the surface elements such as the slabsand shear walls. The bridge is flat with a bias angle of 100 grades.

The material used is concrete with a linear elastic, isotropic and

homogeneous behaviour.

The composite materials were introduced into the calculation of

the Young modulus and the transverse rigidity Ky of the structure.

It is considered that the concrete reinforced by carbon fibre sheets

retains its linear elastic behaviour, but with a new higher Young

modulus. The supports are embedded in the road surface, consid-

ering that the existing old apparatus are with fixed supports. The

deterioration is taken into account, in the modelling by the finite

element method, through the choice of the value of the longitudi-

nal modulus of elasticity (Youngs modulus) E. The value ofEof the

damaged concrete (before repair of the bridge) is distinctly lower

to that of the concrete after its repair.The girders are simply supported and the piles are anchored in

the foundations. Modelling was carried out by modal analysis of

the structure [9], where the aim is to determine the frequencies

and the fundamental modes and to compare them with those ob-

tained experimentally by ambient vibration tests. The number of

modes taken into account is six (6), in such a way that the sum

of the modal masses chosen represents the total mass of the struc-

ture (approximately 90%) in our case of study [6]. For the calibra-

tion, the values given by the numerical three-dimensional finite

elements model (3DFEM) are calibrated by the experimental val-

ues found by ambient vibration measurements before repair and

strengthening of the bridge.

4. Experimentation by ambient excitation

An adequate evaluation of the bridge, before and after its repair,

requires an exact estimate of its modal identification (Eigen fre-

quencies, fundamental modes) based on the measurement of the

Table 1

Mechanical characteristics of the materials used.

Used material Modulus E (GPa) Density Tensile strength (MPa) Compressive strength (MPa) Extension at failure (%) Thickness (mm)

Concrete 35 2.5 3.0 33.5

High strength steel 210 550

Mild steel 210 400

Epoxy Sikahard 30 12.8 1.8 30 55

Sika wrap sheet 230 3500 1.5 0.13

Laminate Sika carbohard 165 1.5 2800 1.7 1.2

Table 2

Comparison between weight and transverse rigidity of the bridge before and after repair.

Elements Weight (t) Total weight (t) Moment of Inertia (m3) Elasticity modulus (GPa)

Before repair Deck (slab + beams + equipment) 1295 1470 2.416 25.0

Infrastructure (piles) 174.9

Additional material after repair Concrete jacketing (piles level) 250

Lining steel 12.2

Crack injection 0.235 280.2 2.432 32.5

Protective mortar 17.1

CFRP sheets 0.612

1272 M. Abdessemed et al. / Construction and Building Materials 25 (2011) 12701276


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excitation response. For such structures, testing using ambientexcitation with the sole introduction of geometrical dimensions

is preferred compared to testing using forced excitation where

the excitation and response are measured [3]. The reason is that

the response measured in an ambient excitation testing is repre-

sentative of the real service conditions of the structure which vi-

brates under the effects of natural excitation such as traffic,

wind, and micro-quakes and other ambient noises.

4.1. Experimental setups and apparatus

Experimental tests by ambient excitation were directed on the

bridge from its centre (C1 and C2) towards the south side on one

hand, and from the centre to the north side on the other hand

(Fig. 4). Other background noise measurements at the piles level

were taken. The same positions of the accelerometers were kept

before and after repair, in order to compare the results in terms

of modes and Eigen frequencies of the structure. Vertical, longitu-

dinal, and transverse bridge movements were measured using 04

accelerometer channels with three components x, y and z.

The positions of the stations (Fig. 4) were also imposed by the

accessibility of the structure. Apart from the background noise to

the bottom of the piles; all the other positions are on the two

shoulders and on the road surface.

4.2. Data acquisition and recording

The ambient excitation tests were carried out on the bridgeusing the acquisition equipment and four sensors (accelerometers

tri-axes). The recording of the background noise was carried out

using a recording station CityShark Ii-6 and four Lennartz seis-

mometers at 5 s. The CityShark station can simultaneously record

signals from six sensors. For this study, only four sensors were

used. While the Lennartz sensors are equipped with three compo-

nents: a vertical component, and two horizontal components per-

pendicular to each other. The duration of the recordings is 15 min.

The signal was sampled at 200 Hz.

The recordings of the background noise were carried out on the

bridge road surface, using four sensors. Sensors 1 and 2 are fixed

and placed in the middle of the bridge and are moved by steps of

6 m in one direction and later in the other direction. Sensors 3

and 4 are placed on both sides of the road surface. Recordings werealso carried out on the ground close to the piles of the bridge

simultaneously with recordings on the road surface, in order toestimate the transfer functions of these piles.

4.3. Data analysis

All of the collected background noise recordings are analysed

and treated using Geopsy software [10]. The data-processing meth-

od and programs were developed at the Internal Laboratory of Geo-

physics and Tectonophysics LGIT) of Grenoble, and validated by the

European project SESAME. The 15 min recordings were divided

into 40 s frames. The ambient vibrations are random and the anal-

ysis of the response of the bridge to such actions consists of the

computation of Fourier Spectra of different windows taken from

the response signal, compute their mean and evaluate the standard

deviation. However, to do so and to be able to analyze the dynamicresponse, the selected windows, from the total recorded signal,

must approach as much as possible the characteristic of a white

noise record. Consequently, not all windows on the record can be

used. The spectral amplitude for each window is computed

through a Fourier transform. Then, all computed spectra are

smoothed through a sliding window of which the form and the

width depend on the frequency [11]. Finally, the obtained spectra

are averaged and their standard deviation determined. The Fourier

transforms of the recorded signals enable the assessment of the

natural frequencies of the bridge and are extractedsimply by locat-

ing the peaks corresponding to the maximum responses [12].

5. Results and discussions

5.1. Numerical modelling calibration

The three-dimensional finite elements model was validated

against the natural excitation frequencies and the fundamental

modes obtained from the ambient excitation tests. Exact calibra-

tion is not easy as real values of the mechanical characteristics of

concrete and the loss of the corroded steel sections before its repair

are not reliably known. Thus the values used for numerical calcu-

lation are an approximate estimation of the real characteristics of

the bridge that may have experienced some repair during its

history.

In order to elaborate the complex computational model based

on finite elements, several approximations attempts were adopted.

These approximations took into account the properties of materi-als, the stiffness of the bridge bearing elements, the influence of

C3 C4

C1 C3 C2 C4

Fig. 4. Location of the accelerometers.



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composite materials and the mode of their application on the

beams as well as the bridge supports model. The finite elements

model chosen permits the calibration and the adjustment of se-

lected parameters until reasonable values for natural frequencies

and modal forms were obtained [13,14].

5.2. Experimental results of the ambient excitation testing

The most unfavourable experimental values recorded are those

of the sensors of reference (C1 or C2) in their three directions.

Accelerations and frequencies records before and after repair of

the structure are presented, in spite of inexistence of great differ-

ences between the values obtained (Figs. 5 and 6).

The most unfavourable values of the mobile stations are ob-

tained from C4 position located at 24 m from the centre of the

bridge, with vertical accelerations (z), horizontal in the transverse

direction (Northern) and in the longitudinal direction (East). Verti-

cal accelerationszare definitely more dominating than those in the

horizontal x and y directions. Hence, we can conclude that the

structure is very rigid horizontally and rather flexible with vertical

bending due primarily to the tensile forces, whose accelerations

are about 0.045 g (g: gravity acceleration).The vertical and horizontal signals of the excitations of the

structure, before and after its repair, by composite materials CFRP,

always give a clear reduction in amplitudes of the excitations, and

consequently a damping of the structure. This is one of the funda-

mental characteristics of carbon fibres CFRP [15]. However, when

the repair of the structure is modified through a material addition

(jacketing) and an additional reinforcement by CFRP, the variation

by excess of the mass on this structure gives an increase in ampli-

tudes of resonance from 7.5% to 33%.

Table 3 illustrates the results found for the first six fundamental

modes of the structure concerning the dominating values of the Ei-

gen frequencies, before and after repair.

The experimental results (Table 3) showed that the added mass

of the repaired bridge resulted in a slight increase of the bending

longitudinal frequencies (F1, F3 and F5) considerably with varying

rates from 2% to 3%. However, it has increased the transverse rigid-

ity of the bridge which results in slight changes in the longitudinal

horizontal modes (F4) and also increased the frequencies of the

associated modes of longitudinal transverse bending (F2, F6).Carbon fibre composite materials increase the Eigen frequencies

of the dominating modes of reinforced concrete structures by up to

8%, and that is due possibly to the variation of the transverse rigid-

ity Ky of the structure (since there is a proportionality between the

0.04

0.00

0 5 10 15 20 25 30 35 40

Time (sec.)

Vertical signal Z from point C1 (middle of bridge)

0.04

0.00

-0.04

0.04

0.00

-0.04

0 5 10 15 20 25 30 35 40

Time (sec.)

Horizontal signal N from point C1 (middle of bridge)

0 5 10 15 20 25 30 35 40

Time (sec.)

Horizontal signal E from point C1 (middle of bridge)

-0.04

Fig. 5. Accelerations before strengthening.

0 5 10 15 20 25 30 35 40

Time (sec.)

Vertical signal Z from point C1 (middle of bridge)

0 5 10 15 20 25 30 35 40

Time (sec.)


0 5 10 15 20 25 30 35 40

Time (sec.)


Fig. 6. Accelerations after strengthening.

Table 3

Experimental frequency values of the fundamental mode.

No. Frequency before

repair (Hz)

Frequency after

repair (Hz)

Discrepancy

(%)

Mode of

excitation

1 3.94 4.05 2.8 Vertical (z)

2 4.55 4.67 2.20 Horizontal (E)

3 4.89 5.00 2.25 Vertical (z)

4 5.03 5.07 0.08 Horizontal (N)

5 6.72 6.93 3.10 Vertical (z)

6 7.23 7.36 1.80 Horizontal (E)

Table 4

Frequency values obtained by MEF analysis.

No. Frequency before repair

(Hz)

Frequency after repair

(Hz)

Mode of

excitation

1 2.85 4.00 Horizontal (N)

2 3.16 4.16 Vertical (z)

3 3.89 4.54 Torsion

4 8.23 10.11 Vertical (z)

5 13.02 13.37 Torsion

6 13.22 16.66 Horizontal (E)



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Eigen frequencies Fand rigidity Ky) [16]. Bridges damaged and then

repaired by reinforced concrete addition (jacketing) during their

evaluation have shown frequencies which vary according to the

mode of excitation. The frequency of a bridge was shown to de-

crease after its repair for the mode of vertical bending (z) (the in-

crease in the mass of the bridge decreases the frequency F),

while the horizontal modes (x andy) and mode of torsion influence

directly and proportionally the frequency of the structure [17,18].

5.3. Numerical results of the selected model

The dynamic analysis of the calibrated model has led to modalparameters of the bridge. The modal frequencies obtained by MEF

analysis are given in Table 4, with the corresponding modes illus-

trated in Fig. 7.

The first six dominating modes were distinguished for both

cases before and after bridge strengthening. The dominating mode

is the longitudinal mode of translation (N) with a clear increase

(from 2.85 to 4 Hz) in frequency due to the increase of transverse

rigidity Ky. The dominating frequency before repair for the selected

computational model is about 2.85 Hz, while the frequency

obtained by the experimental testing is 3.94 Hz. The same

observation could be generalised for all other modes. However,

after strengthening of the bridge, the agreement becomes excellent

(difference of 1.25%) with values of 4.00 Hz and 4.05 Hz for the first

mode for the FE model and the experimental results respectively.This was obtained despite that a linear and elastic behaviour of

the materials (concrete, steel and composite) was considered in

the model.

5.4. Comparison and comments

A reasonable correlation between the experimental and numer-

ical model was obtained. The parameters that most influence the

dynamic behaviour of the bridge and consequently the modes

and Eigen frequencies, are the Young modulus of the composite

element (concrete CFRP), after its strengthening and jacketing.

The results of the dynamic testing show an increase in the mod-

al frequencies (Table 5). The increase in the frequency of the first

mode is very small (only 1.2%). The increases at the second and

third modes are respectively about 12% and 10%. The dispersion

becomes large from the fourth mode probably due to the fact that

the non-linear behaviour of materials making up the composite

material (concrete, steel and CFRP) is not taken into account.

Fig. 7. The different modes obtained.

Table 5

Comparison of FE & experimental frequencies after repair.

Mode no. Model MEF (Hz) Experimental tests (Hz) Relative error (%)

1 4.00 4.05 1.2

2 4.16 4.67 12.3

3 4.54 5.00 10.1

4 10.11 5.07

5 13.37 6.93

6 16.66 7.36



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6. Conclusions

An evaluation of the performance of an old bridge before and

after repair and strengthening of piles by reinforced concrete jac-

keting and the beams by a composite material was performed

using ambient excitation tests. An attempt to calibrate the experi-

mental results obtained by MEF modelling was made allowing the

comparison between the calibrated model (modal analysis) andthe ambient excitation method. The conclusions to be drawn from

this work are as follows:

It is possible to evaluate the dynamic behaviour of a repaired

bridge through the application of ambient excitation tests. The

modal parameters of the bridge before and after repair are iden-

tified by this in situ testing.

The value of the elasticity modulus E indicates the real state of

the material and possible damage on the bridge. The transverse

rigidity Ky, before and after reinforcement, reflects changes of

the structure.

The predominant mode of the bridge is the vertical bending

with a frequency of 3.98 Hz before CRFP reinforcement and

4.05 Hz after. The composite material increases the transverse

rigidity of the structure and thus its modal frequency (propor-

tionality between the frequency f and the rigidity Ky).

Increases in resonance amplitudes of about 7.5% for the vertical

excitations (Z), 25% for the longitudinal excitations (N) and 33%

for the transverse excitations (E) were observed. This is proba-

bly due to the jacketing of the piles which increased the mass

of the structure (by 16%).

Computational modelling by finite elements enabled the cali-

bration of the experimental results with a small dispersion of

only about 1.2% for the first mode and 10% and 12% for the

two following modes.

Acknowledgments

The authors are thankful to the local authorities of the public

work ministry in Tipaza (DTP), SAPTA company, SIKA as well as

the researchers at the centre for earthquake engineering (CGS) in

Algiers for their help in conducting the site testing.

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