3-D Modelling of the Confederation Bridge Using Data of Full Scale Tests

doi:10.4236/ojce.2013.33B004

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Open Journal of Civil Engineering, 2013, 3, 18-25

http://dx.doi.org/10.4236/ojce.2013.33B004 Published Online September 2013 (http://www.scirp.org/journal/ojce)

3-D Modelling of the Confederation Bridge Using

Data of Full Scale Tests

Lan Lin

Department of Building, Civil and Environmental Engineering, Concordia University, Montreal, Canada

Email: [email protected]

Received July 2013

ABSTRACT

Long-span bridges are special structures that require advanced analysis techniques to examine their performance. This

paper presents a procedure developed to model the Confederation Bridge using 3-D beam elements. The model was

validated using the data collected before the opening of the bridge to the public. The bridge was instrumented to con-

duct fullscale static and dynamic tests. The static tests were to measure the deflection of the bridge pier while the dy-

namic tests to measure the free vibrations of the pier due to a sudden release of the static load. Confederation Bridge is

one of the longest reinforced concrete bridges in the world. It connects the province of Prince Edward Island and the

province of New Brunswick in Canada. Due to its strategic location and vital role as a transportation link between these

two provinces, it was designed using higher safety factors than those for typical highway bridges. After validating the

present numerical model, a procedure was developed to evaluate the performance of similar bridges subjected to traffic

and seismic loads. It is of interest to note that the foundation stiffness and the modulus of elasticity of the concrete have

significant effects on the structural responses of the Confederation Bridge.

Keywords: 3-D Numerical Modeling; Finite Element Technique; Static Tests; Dynamic Tests; Acceleration Time

History; Fourier Analysis; Full Scale Tes t; Seis mic Evalu ation; Confederation Bridge

1. Introduction

The Confederation Bridge was built in June 1997 to con-

nect the province of Prince Edward Island and the prov-

ince of New Brunswick in Canada. The length of the

bridge is 12.9 km, which makes it one of the longest re-

inforced concrete bridges in the world. The bridge is lo-

cated in a region known for severe and harsh environ-

mental conditions. In fact, the bridge is covered by ice

approximately three to four months every year; this be-

side the heavy storms with winds in excess of 100 km/h,

which is often experienced at the bridge site.

The Confederation Bridge was designed for a lifespan

of 100 years, which is twice the life span suggested by

the Canadian Standard Association(CSA) [1], and the

Ontario Highway Bridge Design Code (OHBDC) [2].

This is because of the strategic importance of the Con-

federation Bridge to the community.

A comprehensive research program was undertaken to

monitor and study the behaviour of the bridge during

construction and during its operation. The objective of

this program was to record valuable data on the per-

formance of the bridge under dynamic loads including

seismic, wind, traffic, and ice loads.

This paper presents a 3-D numerical model, developed

to simulate the performance of the Confederation Bridge

under static and dynamic loads. The data collected from

the full scale tests were used to validate the model. The

methodology presented in this paper can be followed for

evaluation of existing condition for similar and other

bridges subjected to these sever loading conditions.

2. Description of the Bridge

Figure 1 presents a sketch showing the layout of the

Confederation Bridge. The bridge consists of two ap-

proach bridges at its ends and a main bridge between

them. The approach bridge at the Prince Edward Island

end (i.e., the east end) is 555 m long and has 7 piers,

andhas 7 piers, and that at the New Brunswick end (i.e.,

the west end) is 1 275 m long and has 14 piers. The long-

est span of the approach bridges is 93 m. The main

bridge is 11,080 m long and has 44 piers, designated P1

to P44. Out of the 45 spans of the main bridge, 43 spans

are 250 m long and the two end spans are 165 m long.

The height of the columns of this part of the bridge

ranges from 38 to 75 m. The cross section of the bridge

girder is a single-cell trapezoidal box. The depth of the

girder of the main bridge varies from 4.5 m at mid spans

to 14 m at piers. The width of the bridge deck is 11 m.

L. LIN

Figure 1. Configuration of the confederation bridge.

The structural system of the main bridge, which is the

subject of this paper, consists of a series of rigid portal

frames connected by simply supported girders, which are

called drop-in girders. Every second span is constructed

as a portal frame, and all other spans are constructed us-

ing drop-in girders. In total, there are 21 portal frames in

the main bridge. This structural system was selected to

prevent progressive collapse of the bridge due to extreme

wind, ice, seismic, traffic loads, and ship collisions. Fig-

ure 2 presents a typical portal frame of the main bridge.

The girder consists of two 192.5 m double cantilevers

and a 55 m long segment between them. The connections

between this segment and the cantilevers are detailed to

behave as rigid joints. The drop-in girders that connect

the frames are shown in the spans adjacent to the portal

frame span. The length of the drop-in girders is 60 m.

Each of the drop-in girders sits on the overhangs of the

two adjacent portal frames. Four specially designed elas-

tomeric bearings are used as supports. One of the bear-

ings is fixed against translations and the remaining three

allow translations of the girder only in the longitudinal

direction. All four bearings allow rotation s about all axes.

This configuration of the bearings provides a hinge con-

nection at one end, and longitudinal sliding connection at

the other end of the drop-in girder.

The piers are constructed of two precast concrete units

each, i.e., the pier base and the pier shaft (see Figure 2).

The pier base is a hollow unit and has a circular cross

section in plan with an outer diameter of 8 m at the top

and 22 m at the footing. The pier shaft is also a hollow

unit and consists of a shaft at the upper portion and an ice

shield at the bottom portion of the pier. The cross section

of the pier shaft varies from a rectangular section at the

top to an octagonal section at the bottom of the shaft.

Both the pier base and the pier shaft have very complex

shapes. Detailed explanations for these and the geomet-

rical properties of the piers are given in [3].

3. Numerical Modeling

Figure 3 presents the finite element model developed

inthis study to simulate the case of a three-span frame

which represents the bridge segment between piers P29

and P32 (Figure 1). It consists of two rigid portal frames

(P29-P30 and P31-P32), and one drop-in span (P30 -P31).

This segment was modelled since it was the instru-

mented portion of the bridge, and the data recorded will

be used extensively in this study in the calibration of the

model. The model consists of 179 beam elements and

180 joints. The bridge girder is modelled by 123 ele-

ments, and each pier is modelled by 14 elements. The

longitudinal axis (X) of the bridge is at the centroids of

the cross section areas along the bridge girder. The geo-

metrical properties at the end sections of the eleme nt s

L. LIN

Figure 2. Typical portal frame.

Bearin gs

-21.7 m

P32

-29 .3 m

P31

-28.4 m

P30

Drop -in girder (6 0 m)

-33.6 m

P29

0.0 Water level

+39 .24 m

250 m

95 m

250 m

95 m

Mas s

Figure 3. Model of two portal frames and one drop-in span using 3-D beam elements.

including the cross-sectional area, moment of inertia, and

torsional constant, were determined from the dimen-

sions given in the bridge drawings. Since the elements

are non-prismatic, the variation of the bending stiffness

along each element was taken into account in developing

the model. These were based on the variations of the

cross section dimensions along the elements. A cubic va-

riation about the transver s e axis (Y) and a linear variation

about the vertical axis (Z) were used to determine the

bending stiffness of the bridge girder elements and a cu-

bic variation of the stiffness about the longitudinal and

the transverse axes of the cross sections were used for the

pier elements. The interaction with the adjacent drop-in

girders (left of P32, and right of P29) was modelled by

adding equivalent masses at the ends of the overhangs, as

shown in Figure 3. Half the mass of each drop-in girder

was added at the end of the supporting overhang in

transverse and vertical directions, full mass was added in

the longitudinal direction for a hinge connection, and no

mass was added in the longitudinal direction for a sliding

connection. Similarly, vertical forces from one half of the

weight of each drop-in girder were applied at the ends of

the overhangs. The model was conducted using the com-

puter program SAP 2000 [4].

4. Calibration of the Model Using Data of

Full Scale Tests

The model shown in Figure 3 was calibrated using re-

cords of vibrations and tilts of the bridge collected from

the results of the full scale tests on the bridge, which are

referred to herein as the pull tests. Also, measured data

for the modulus of elasticity of the concrete were also

used in the calibration process. The data collected and

the analyses conducted in the calibration of the model are

provided and discussed in detail hereafter.

4.1. Recorded Data during Pull Tests

Full scale pull tests were conducted on April 14, 1997,

about two months before the official opening of the

bridge to the public. The objectives of the tests were: 1)

to measure the deflection of the bridge pier under static

loads, and 2) to measure the free vibrations of the pier

due to a sudden release of the static load.

The instrumentation of the bridge shown in Figure 4

was used to measure the bridge response during the pull

tests. It consists of 76 accelerometers and 2 tiltmeters.

The accelerometers were used to measure acceleration

time histories of the response of the bridge. The two tilt-

meters installed at locations 3 and 4 of pier P31 were

used to measure the tilts of the pier.

The first pull test was a static test, by using a steel ca-

ble, a powerful ship pulled pier P31 in the transverse

direction of the bridge. The pulling was at the top of the

ice shield, approximately 6 m above the mean sea level.

The force was increased steadily up to 1.43 MN, and

then released slowly. The tilts at locations 3 and 4 were

measured continuously dur ing the test. T he tilt at location

3 per unit applied force was 46.57 µR/MN, and that at

L. LIN

Figure 4. Locations of accelerometers: (a) instrumented sections of the bridge girder and piers, and (b) locations of accelero-

meters in the girder.

location 4 was 42.99 µR/MN. The second pull test was a

dynamic test. In this case, the load was applied at a slow

rate up to 1.40 MN and then suddenly released. This

triggered free vibrations of the bridge, which were re-

corded by several accelerometers. Figure 5 shows the

acceleration time history of the transverse vibrations re-

corded at the middle of span P31-P32 (location 9 is

shown in Figure 4). These records and those of the tilts

were used in the calibration of the model.

4.2. Predominant Frequencies of the Recorded

Vibrations

The predominant frequencies of the recorded vibrations

were essential for the calibration of the model. These

frequencies were determined using Fourier analysis. The

Fourier amplitude spectrum of the vibration recorded at

location 9 is shown in Figure 6. Since the record consists

of N = 12,000 acceleration data points at equal time in-

tervals of Δt = 0.0034 s, the frequency resolution of the

Fourier amplitude spectrum is Δf = 0.0245 Hz (Δf =

1.0/(N·Δt)). From Figure 6, it was found that the domi-

nant f requencies of the vibrat ion are f1 = 0.466 Hz and f2 =

1.30 Hz. These two frequencies were used in the calibra-

tion of the model.

4.3. Damping Ratios of the Recorded Vibrations

In order to determine the damping ratios of the modes

with frequencies of f1 = 0.466 Hz and f2 = 1.30 Hz, the

time histories of the vibrations at these two frequencies

were extracted from the record using numerical band-

pass filters. In numerical filtering, it is important that the

band-width of the filter is wide enough to avoid distor-

tions of the time history, but at the same time to exclude

effects of adjacent modes. In this study, a band from

0.346 Hz to 0.586 Hz was used to extract the modal vi-

brations at 0.466 Hz, and a band from 1.0 Hz to 1.5 Hz

for the vibrations at 1.30 Hz. The damping ratios ob-

tained from the analysis were ξ1 = 0.038 for the modal

vibrations at f1 = 0.466 Hz, and ξ2 = 0.032 for the vibra-

tions at f2 = 1.30 Hz. The average value of these two

damping ratios is 0.035, and this value was used in the

-150

-100

-50

100

150

05 10 15 20 25 30 35 40

Acceleration (mm /s

)

Time (s)

Figure 5. Acceleration time history of the transverse vibra-

tion at location 9.

100

120

140

0246810

Amplitude (mm/s)

Frequency (Hz)

Figure 6. Fourier amplitude spectrum of the acceleration

timehistory of the transverse vibration at location 9.

calibration of the model.

4.4. Modulus of Elasticity of the Concrete

During the construction of the bridge, cylinders were

taken from the concrete used for the monitored part of

the bridge between P31 and P32. The modulus of elastic-

ity of concrete was measured at specified concrete age.

Results from measurements taken at concrete age t = 2, 7,

14, 28, 90 and 180 days are reported in [5]. Based on the

measured data, Reference 5 proposed the following equa-

tion for the prediction of the average modulus of elastic-

ity of the concrete:

L. LIN

Ec(t) = Ec(28){exp[s(1 - (28/t)1/2)]}1/2 (1)

in which Ec(t) is the elastic modulus at age t, Ec(28) =

38.7 GPa is the average elastic modulus at age t = 28

days, and s = 0.25 is a coefficient for normal hardening

cement assumed for the concrete used in the bridge.

4.5. Calibration of the Model

The calibration was conducted using the model shown in

Figure 3. Since the calibration was based on the meas-

ured data during the pull tests, it was important that the

masses of the bridge model correspond to those of the

bridge during the pull tests. As reported by [6], the barri-

ers and the pavement had not yet been in place at the

time of the pull tests. Therefore these masses were not

included in the calibration of the model. Given the avai-

lable data described in Sections 4.1 to 4.4, the following

parameters were used as reference parameters in the ca-

libration of the model:

• Tilts at locations 3 and 4 of pier P31 recorded during

the static pull test,

• Acceleration time history of the transverse vibrations

at location 9 (Figure 5) recorded during the dynamic

pull test,

• Predominant frequencies of the recorded vibrations at

locati on 9,

• Damping ratios of the predominant modes of the re-

corded vi br a t ions, and

• Modulus of elasticity of the concrete of 40,000 MPa

corresponding to the age of the concrete at the time

when the pull tests were conducted. It was determined

by using Equation 1.

The parameter that was varied in the calibration of the

model was the foundation stiffness. While the soil under

the foundations of the piers is designated “rock” in the

design drawings, it is believed that they may have certain

soil-structure interaction effects, which is appropriate to

consider them in analyzing the dynamic behaviour of the

bridge. Rotational springs (at the bases of the piers) in

the longitudinal and transverse directions were intro-

duced in the model to represent the foundation stiffness.

The calibration consisted of iterative performing the fol-

lowing sequence of tasks:

1) The selection (in the first iteration), or the adjust-

ment (in the subsequent iterations) of the rotation al stiff-

ness of the springs;

2) Static analysis of the model by applying a horizon-

tal force of 1 MN to pier P31, 6 m above the mean sea

level, in the transverse direction of the model;

3) Using the results from 2), the tilts at locations 3 and

4 of pier P31 were computed, and compared with the

values measured during the static pull test;

4) Time-history analysis of the model by applying a

loading representative of that used in the dynamic pull

test. The loading was applied to pier P31, 6 m above the

mean sea level, in the transverse direction of the model;

5) Fourier analysis of the response time history of the

model at location 9 to compute the Fourier amplitude

spectrum. This spectrum was compared with that of the

vibrations recorded at location 9 during the dynamic pull

test (Figure 6).

It should be mentioned herein that in case of differ-

ences between the computed and measured tilts in task 3)

of a given iteration were larger than those in the previous

iteration, then tasks 4) and 5) were not proceeded, and a

new itera t ion was undertake n.

4.5.1. C om parison of Tilts

Results for the tilts of selected iterations of the calibra-

tion process are given in Table 1. The table shows the

rotational stiffness used in the iterations and the corre-

sponding tilts at locations 3 and 4 resulted from the static

analysis of applying a horizontal force of 1 MN to pier

P31, 6 m above the mean sea level. For comparison, the

tilts measured during the static pull test are also given in

the table. It can be noted that the stiffness of the founda-

tion between 3.35 MN·m/µR and 4.45 MN·m/µR pro-

vides tilts that are quite close to the measured tilts. The

differences between the computed and the measured tilts

were less than 3%. Tabl e 1 also sho ws t hat the computed

tilts corresponding to fixed-base conditions are signifi-

cantly smaller than the measured values. This was ex-

pected since the bridge structure with rigid bases is stiffer

than that with flexible bases.

4.5.2. Time-History Analysis of the Model

For each of the foundation stiffness considered in the

calibration process, a time-history analysis was con-

ducted to compute the response time histories of the mo-

del. The load was assumed to increase linearly from 0 to

1.4 MN in 15 s, and then it was kept constant for 10 s,

Table 1. Foundation stiffness used in selected iterations and

computed tilts at locations 3 and 4.

Foundation

stiffness

(MN·m/μR)

Computed tilts (in μR) and differences (in %)

between computed and measured values

Location 3 Difference Location 4 Difference

∞(Fixed-bases) 34.78 −19.1(1) 38.15 −18.1

5.05 40.71 −5.3 44.72 −4.0

4.45 41.70 −3.0 45.54 −2.0

4.05 42.29 −1.6 46.36 -0.5

3.35 43.77 +1.8 48.00 +3.0

2.65 46.34 +7.8 50.67 +8.8

Measured values 42.99 46.59

(1)Difference wi th negat ive sig n indicates t hat the co mputed v alue is small er

than the measured value.

L. LIN

and then was decreased linearly to zero in 0.13 s. The

load was applied to pier P31, 6 m above the mean sea

level, in the transverse direction of the model. The

time -history analysis was conducted using a modal

damping of 3.5%. A time interval of integration of 0.005

s was used in the time-history analysis. Note that the

loading used in the analysis was representative of that

applied load during the dynamic pull tests. Figure 7

shows the computed acceleration time history of the re-

sponse of the bridge girder at location 9. Comparing this

time history with the recorded vibrations (Figure 5), it

can be noted that the computed response was in a good

agreement with the measured response.

4.5.3. C om parison of F ou r i er Amplitude Spe c tra

For each of the foundation stiffness, Fourier amplitude

spectrum was computed for the acceleration time history

of the transverse response at location 9 obtained from the

dynamic analysis. This spectrum was compared with the

spectrum of the measured vibrations (Figure 5). It was

found that the foundation stiffness of 3.35 MN·m/µR

provided satisfactory match of the predominant frequen-

cies of the computed and measured responses at location

9. Figure 8 shows the Fourier amplitude spectrum of the

-150

-100

-50

100

150

0510 15 20 25 30 35 40

A ccelerat ion. (mm/s

)

Time (s)

Figure 7. Computed acceleration time history of the trans-

verse response at location 9.

100

120

140

012345678910

A mpl i tude ( mm/s)

Fr equency (Hz)

Figure 8. Fourier amplitude spectrum of the acceleration

time history of the transverse response at location 9.

computed response for found ations tiffness of 3.35

MN·m/µR. It can be seen that this spectrum is quite close

to that of the measured vibrations (Figure 6). The first

two predominant frequencies of the computed response

are fr1 = 0.513 Hz and fr2 = 1.277 Hz, which are very

close to the corresponding predominant frequencies of f1 =

0.466 Hz and f2 = 1.30 Hz of the measured vibration.

Based on the analyses of the Fourier amplitude spectra

and those of the tilts, the foundation stiffness of 3.35

MN·m/µR was adopted to represent the foundation con-

ditions of the bridge. This value was used in the further

analyses in this study.

4.6. Dynamics Characteristics of the Evaluation

Model

An evaluation model was developed in this study using

the results from the calibration process. In this model, a

foundation stiffness of 3.35 MN· m/µR was incorp orated,

and a modulus of elasticity of the concrete of 40,000

MPa was used. Also the masses of the barriers and the

pavement were included also in the model.

Table 2 shows the natural periods of the first ten

modes obtained from dynamic analysis of the model. For

illustration, the vibrations of th e first five modes are pre-

sented in Figure 9. It can be noted that all the five modes

represent transverse vibrations. In the study it was found

that the vibrations of one of the rigid frames are domi-

nant in the majority of the modes. For example, the vi-

brations of frame P29-P30 are dominant in the 1st, 4th and

5th modes (See Figure 9). This is due to the fact that the

connection between the frames is relatively week, and

each frame may vibrate independently at its own fre-

quency. Detailed discussion on the dynamic characteris-

tics of the evaluation model is given in [7]. It is neces-

sary to report here in that a similar model was developed

by Lau et al. [8] using the computer program COSMOS

[9]. The natural periods and mode shapes of that model

are very close to those of the model developed in this

study.

It is useful to mention that certain variations of the

dynamic properties of the model are expected due to dif-

ferent effects. For example, the modulus of elasticity

increases with the age of concrete and varies due to tem-

perature changes. Also, the responses used in the calibra-

tion of the model are substantially smaller than those

from expected seismic motions at the bridge location. A

comprehensive inv estigation of the possible variations of

the dynamic properties due to the foregoing effects con-

ducted by [7] showed that these variations are insignifi-

cant from the practical point of view, therefore, the

model developed as described above is considered ap-

propriate for the evaluation of the bridge under seismic

loads. The results from a comprehensive seismic analysis

of the bridge are given in [7].

L. LIN

Table 2. Natural periods of the first 10 modes of the bridge

model.

Mode No. Period (s) Mode type

1 3.13 Trensverse

2 2.99 Trensverse

3 2.72 Trensverse

4 2.48 Trensverse

5 2.22 Trensverse

6 2.13 Longitudinal

7 2.08 Trensverse

8 2.01 Longitudinal

9 1.54 Vertical

10 1.43 Vertical

Figure 9. Mode shapes of the bridge model.

Figure 9. Mod e shape s of the bridge model.

5. Conclusions

3-D numerical model was developed using the beam

elements to simulate one of the longest reinforced con-

crete bridges in the world under dynamic loading. The

model was validated using the results of full scale static

and dynamic tests conducted on Confederation Bridge

connecting the province of Prince Edward Island and the

New Brunswick in Canada.

Tilts at two locations along the height of pier were

measured during the static test and the acceleration time

history of the deck in the transverse direction at the mid-

dle span was recorded during the dynamic test. The pa-

rameters used in the calibration of the numerical model

include the dominant frequencies of the recorded vibra-

tions, damping ratio, modulus of the elasticity of the

concrete, tilts of the pier, and the rotational stiffness of

the foundation. In this study it was found that the model

with the damping ratio of 3.5%, modulus of elasticity of

concrete of 40,000 MPa, and rotational stiffness of the

foundation of 3.35 MN·m/µR provided similar tilts, ac-

celeration time history, and Fourier amplitude spectra

like those based on the measured data. This model has

been further used for the assessment of Confederation

Bridge for seismic loads. The following can be con-

cluded from this study:

• The damping ratio, modulus of the elasticity of con-

crete, and the rotational stiffness of foundation are

important parameters in developing numerical models

of long-span bridges.

• The modulus of the elasticity of concrete has larger

effect on the natural periods of the bridge than the

foundation stiffness. Therefore, a value representative

the current condition of the concrete is appropriate in

the evaluation of the performance of an existing

bridge.

• The results of the present investigation showed that

the vibration of one of the rigid frames in the bridge

dominating the modes has given the bridge configura-

tion. This observation is valuable for modelling part

or the entire bridges.

The procedure presented in this paper may be used to

model and evaluate the performance of a new or an ex-

isting bridge subjected to dynamic loads.

REFERENCES

[1] CSA, “Design of Highway Bridge,” Standard CAN/CSA-

S6-88, Canadian Standard Association, Rexdale, Ontario,

1988.

[2] MTO, “Ontario Highway Bridge Design Code,” Ministry

of Transportation of Ontario, Downsview, Ontario, 1991.

[3] G. Tadros, “The Confederation Bridge: An Overview,”

Canadian Journal of Civil Engineering, Vol. 24, No. 6,

2001, pp. 850-866.

http://dx.doi.org/10.1139/cjce-24-6-850

[4] CSI, “SAP2000 Integrated Software for Structural Analy-

sis and Design,” Computers and Structures Inc., Berkeley,

California.

[5] A. Ghali, M. Elbadry and S. Megally, “Two-Year Deflec-

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http://dx.doi.org/10.1139/l00-050

[6] T. G. Brown and K. R. Croasdale, “Confederation Bridge

Ice Force Monitoring Joint Industry Project Annual Re-

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L. LIN

[7] L. Lin, “Seismic Evaluation of the Confederation Bridge,”

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[8] D. T. Lau, T. Brown, M. S. Cheung and W.C. Li, “Dy-

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Bridge,” Canadian Journal of Civil Engineering, Vol. 31,

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http://dx.doi.org/10.1139/l03-106

[9] SRAC, “COSMOS-Finite Element Analysis Software,”

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Santa Monica, California.