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
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.

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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

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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
250 m
95 m
Mas s
X
Y
Z
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

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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
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-50
0
50
100
150
05 10 15 20 25 30 35 40
Acceleration (mm /s
2
)
Time (s)
Figure 5. Acceleration time history of the transverse vibra-
tion at location 9.
0
20
40
60
80
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
22
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.

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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
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-50
0
50
100
150
0510 15 20 25 30 35 40
A ccelerat ion. (mm/s
2
)
Time (s)
Figure 7. Computed acceleration time history of the trans-
verse response at location 9.
0
20
40
60
80
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].

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24
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.
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