23rd Australasian Conference on the Mechanics of Structures and Materials (ACMSM23)
Byron Bay, Australia, 9-12 December 2014, S.T. Smith (Ed.)
ASSESSMENT OF A SEGMENTAL POST-TENSIONED BOX GIRDER
BRIDGE USING AMBIENT VIBRATION TESTING
X.H. Chen*
Department of Civil and Environmental Engineering, The University of Auckland
Auckland 1010, New Zealand. xche210@aucklanduni.ac.nz (Corresponding Author)
P. Omenzetter
The LRF Centre for Safety and Reliability Engineering, The University of Aberdeen
Aberdeen, AB24 3UE, UK. piotr.omenzetter@abdn.ac.uk
S. Beskhyroun
Department of Civil and Environmental Engineering, The University of Auckland
Auckland 1010, New Zealand. s.beskhyroun@auckland.ac.nz
ABSTRACT
The condition and load carrying capacity of a bridge needs to be properly assessed to operate the
structure safely and efficiently. The conventionally utilized static and quasi-static loading tests with
weight-controlled heavy trucks have shown distinct limitations in practical applications for the
assessment of existing bridges. New and efficient approaches are thus required. In this paper, the
assessment of condition and load carrying capacity of the 12-span Newmarket Viaduct, situated in
Auckland, New Zealand was conducted using finite element modelling and vibration testing. A finite
element model was built to predict the response of the bridge. The ambient vibration testing provided
the real properties of the full-scale structure and improved the accuracy of the finite element model of
the bridge via model updating process. The significant parameters in calibrating the model were the
stiffness of the deck and the boundary conditions at the bearings. The load capacity of the structure
was then studied under dead and live loading through the analysis using the calibrated finite element
model. The availability of the calibrated, reliable finite element model enhanced the effective
structural assessment.
KEYWORDS
Load carrying capacity, ambient vibration test, modal identification, model updating, bridge.
INTRODUCTION
Highway bridges, as critical components of any nation’s transportation network infrastructure and are
normally designed to have a long life span. In order to reach a sustainable development of the society,
it is of great importance that the huge investments that are made in the infrastructure can be utilized
during the entire lifetime of the structures. However, because of increasing traffic volumes and speeds,
harsher environments and accelerated aging of materials, bridges nowadays begin to deteriorate
quicker that it was once the case. Consequently, the structural capacity of an existing bridge is
typically less than the structural capacity of a new structure designed to the same targets. Even though
the deterioration very rarely leads to the direct failure of a bridge, it may weaken the structure, making
it more vulnerable to dynamic loadings resulting from earthquakes, winds and moving vehicles and
decreasing its load carrying capacity (LCC). Therefore, the condition and LCC of bridges in service
needs to be properly assessed to operate the structure safely and efficiently. However, the
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conventionally utilized static and quasi-static loading tests with weight-controlled heavy trucks have
shown distinct limitations in practical applications for the assessment of existing bridges (Aktan et al.
1997). Ambient vibration techniques, on the other hand, provide new and efficient experimental
approaches capable of assessing the working condition of bridge structures without incurring traffic
interruption (Cunha et al. 2001). This identifies the structural dynamic print of the bridge which is
unique for a specific structure and involves all the ingredients of its behaviour such as the mass,
stiffness, damping, boundary conditions, etc., and presents them in the form of natural frequencies,
mode shapes and damping ratios. This unique print can then be used to evaluate a theoretical design,
refine an analytical model, or evaluate a change of the state for the bridge structure (Zaki and AbuHamd 2007). The application of ambient vibration based evaluation techniques in the past decades
(Chen et al. 1995; Brownjohn and Xia 2000; Ren et al. 2004; Costa et al. 2014) have demonstrated
that these methods are powerful and have many advantages. These are low cost, easiness of execution
(Ren et al. 2004), ability of simultaneous evaluation of motion in different directions, long duration of
excitation and frequency content suitable for long-span and flexible bridges (Hsieh et al. 2006). This
paper proposes a LCC evaluation method for estimating the bridge load-carrying capacity on a realtime basis by using the ambient traffic-induced vibration. This approach does not require knowledge
of the excitation, so it is applicable to the general problem where the excitation is from ambient
sources and is, generally, unmeasurable. The 12-span Newmarket Viaduct, situated in Auckland, New
Zealand was used as a case study for the proposed approach. The first step was to identify the
structural dynamic properties in ambient vibration. Model identification of the bridge structure was
obtained by using the measurement data from ambient vibration tests. Following this step, a refined
finite element (FE) model of the bridge was generated based on test results via model updating process.
The significant parameters in calibrating the model were the bridge deck stiffness and the boundary
conditions at the bearings. Finally, the load capacity of the structure was studied under dead and live
loading through the analysis using the calibrated finite element model.
BRIDGE DESCRIPTION
The bridge under investigation is the Newmarket Viaduct (Figure 1) located in Auckland, New
Zealand. It is a curved 12-span post-tensioned concrete bridge, comprising two parallel, twin bridges
(Northbound and Southbound). The bridge is supported by two abutments at both ends and 11
concrete piers. The total length of the bridge is 690 m, with twelve different spans ranging in length
from 38.67 m to 62.65 m and average length of approximately 60 m. The superstructure of the bridge
is a continuous twin-cell box girder of a total width of approximately 30 m. The Northbound and
Southbound Bridges are supported on independent pylons and only joined together via a cast in-situ
concrete ‘stitch’ at the deck girder upper flange level. At the abutments and four interior supports, the
bridge deck is supported on bi-directional elastomeric seismic devices. For the other supports, the
bridge bent bearings were fixed in all directions.
Figure 1. Side view of Newmarket Viaduct.
AMBIENT VIBRATION TEST
The ambient vibration testing reported herein was conducted on November 29 and 30, 2012 under
operational conditions and did not interfere with the normal flow of traffic over the bridge as the
testing personnel worked exclusively inside the box girder. The accelerometers used for the test were
two models of wireless USB accelerometers produced by the Gulf Coast Design Concepts
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(www.gcdataconcepts.com): X6-1A and X6-2. A total of 288 measuring points (144 for each span) on
both sides inside the box girders were chosen for placing the accelerometers in order to map accurately
mode shapes. The accelerometers were ‘lightly’ glued to the internal surface of the bridge deck using a
silicone adhesive. Six test setups were used to cover the planned testing locations of both bridges. The
sampling frequency was 160Hz and corresponding recording times were all approximately 1 hour for
each setup.
The modal frequencies and mode shapes were identified using the Frequency Domain Decomposition
(FDD) algorithm. This allowed the identification of 6 transverse, 6 torsional and 8 vertical modes. The
standard deviations associated with the identified natural frequencies between the different setups are
very small (between 0 and 0.04 Hz). Figure 2 shows selected mode shapes and the calculated
frequencies values from the experiment.
H1*: f=1.25 Hz
V1: f=2.03 Hz
T1: f=3.17 Hz
H2: f=1.56 Hz
V2: f=2.15 Hz
T2: f=3.34 Hz
Figure 2. Selected mode shapes and frequencies identified by FDD (*H1: H1 = transverse mode 1 (V =
vertical, T = torsional)).
Southbound
SA
Northbound
PA
Figure 3. FE model of Newmarket Viaduct.
FE MODEL CALIBRATION
A detailed three-dimensional (3D) FE model of the as-built bridge was developed using SAP2000
finite element software to simulate realistic responses of the bridge. A view of the FE model of the
bridge is shown in Figure 3. The concrete deck and all the piers were represented using solid elements.
The elastic modulus of the concrete solid elements was initially computed based on the compressive
strength of 60 MPa, which was first determined by the authors by testing 100×200 mm cylinder
specimens that were cast during construction of deck slab and piers and then supplemented by the
analogous tests conducted by the contractor. The prestressing tendons were modelled using link
elements.
Using the extracted modal properties from the ambient tests, the initial model was updated. A
sensitivity based method was employed as the updating algorithm in a MATLAB script and SAP2000
was called to calculate the modal properties of the updated FE model iteratively. The objective
function was constructed by using the difference between the measured and estimated natural
frequencies, and the constraint equations were considered to limit the differences between the
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measured and estimated mode shapes ( α ) as well as the lower bounds (b1) and upper bounds (bu) of
the parameters used for updating the FE model:
  f a,i  f e,i
J    wi 
i 1 
  f e,i
n
2
 
  subject to MACup,i  MAC0,i  α and b1  b  bu
 
(1)
where fi represents the i-th frequency, wi is the weighting factor for the i-th mode, subscripts a and e
refer to analytical and experimental, respectively, and n is the total number of frequencies considered.
The difference in mode shapes is expressed in terms of the modal assurance criterions (MACs) where
subscripts ‘up’ and 0 refer to updated and initial i-th mode shape, respectively.
The selected parameters for the model updating based on sensitivity analysis were deck flexural
stiffness for vertical and horizontal bending, deck torsional stiffness and horizontal stiffness of the
bearings. After updating the FE model, the natural frequencies from the experiment, initial FE model,
and updated FE model were compared, as shown in Figure 4. As can be seen the natural frequencies of
the updated FE model became closer to the measured values than those of the initial FE model. The
MAC values, shown in Figure 5, did not improve significantly for all the twenty modes. As the
dynamic test was carried out just before the construction completion of the Newmarket Viaduct and
the calibrated 3D FE model reflects the as-built bridge conditions and achieves a good correlation with
the measured modal parameters identified from field ambient vibration tests. Therefore, this model can
serve as a baseline in structural dynamics for further in-service condition assessment.
Figure 4. Natural frequencies of the bridge.
Figure 5. MACs of the bridge model before and after updating.
BRIDGE LOAD CARRYING CAPACITY
The basic load carrying capacity can be obtained by analysing the bridge response under the design
live load including the rating factor. However, this value may not represent the current state of a
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bridge because the differences between the FE model of the structure and true structure. The FE model
of the Newmarket Viaduct, having been calibrated to correlate with the field dynamic test results, is
capable of predicting the global load capacity more accurately. Evaluation of bridge LCC is comprises
the prediction of the deflected shape and girder internal forces due to dead load (DL) and the imposed
live load (LL) on the bridge. The applied live-load patterns are two extreme live-load cases of the 20%
of DL (LL1=0.20DL) and 40% of the dead load (LL2=0.40DL), respectively. The results reported
herein include maximum deck deflection, and load capacity of the deck sections for various load
combinations.
Maximum Deck Deflection
Figure 6 shows the deck deflected shapes of the deck under dead load (DL) and two live load cases
(DL+LL1=1.20DL and DL+LL2=1.40DL). The increased deflections due to live loading are a
measure of the bridge stiffness. The maximum positive deck deflections of the bridge for all three
loading cases are at the mid-span of the Span 2, and the maximum negative deck deflections of the
bridge are at the mid-span of Span 1. It can be observed that the negative deflections increase (or
positive deflections decrease) proportionately to the load.
Figure 6. Deck deflections under various loadings.
LCC of Deck Sections
Deck capacity factor (DCF) is one of the key parameters that define the status of a bridge and its
response to various loads. In this study, the overload and live load capacity for each critical location in
the deck of Newmarket Viaduct are defined as the following ratios (NZ Transport Agency 2013):
M LL 
ΦM i  γ DL M DL
γ LL
Mo 
ΦM i  γ DL M DL
γo
(2)
where Φ is strength reduction factor, Mi is the section moment strength, γDL and γLL are the dead load
and live load factors, M DL is the moments under design dead load, γo is the overload capacity,
M LL and M o are the live load and overload capacities. The DCF can be calculated by dividing the
overload capacity by the load effect. Table 1 summarizes the maximum moments and moment
capacities in one of the critical deck sections of the model. An investigation of the moments reveals
that the moments induced under a severe uniformly distributed live load equal to 40% of the dead load
are well within the maximum capacity of the section. Note that the change of live loads increase the
moments in the deck sections, and therefore the DCF are reduced dramatically.
Table 1. Load capacity of a deck section
Load
Maximum Moment [kN.m] Mi [kN.m] MLL [kN.m] Mo [kN.m] DCF
DL
39,880
143,600
52,490
66,935
1.68
DL+LL1=1.20DL
45,850
143,600
52,490
66,935
1.46
DL+LL2=1.40DL
51,818
143,600
52,490
66,935
1.29
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CONCLUSIONS
A method for the evaluation of the condition and load capacity of a bridge is studied. The method uses
ambient vibration tests. During tests, the normal traffic is not suspended. Model identification of the
bridge structure was conducted using the ambient vibration test data. A calibrated model of the bridge
was generated based on the test results and this model was used for structural assessment and
evaluation of the bridge structure load carrying capacity. From the results, it can be shown that the
studied bridge, Newmarket Viaduct, has the capability to withstand the proposed live loads with
considerable safety as a new built bridge. However, due to the importance status of this type of
structure, the continuous periodic dynamic monitoring of the bridge in the future should be
implemented to assess the real impact of the different adverse effects on its condition. Furthermore,
the advanced optimization techniques for modal updating should be used to verify or improve the
adopted numerical models.
ACKNOWLEDGMENTS
The authors would like to express their gratitude to their supporters. Research work at the University
of Auckland was supported by the Earthquake Commission Research Foundation grant UNI/578. Piotr
Omenzetter’s work within the Lloyd’s Register Foundation Centre for Safety and Reliability
Engineering at the University of Aberdeen is supported by Lloyd’s Register Foundation. The
Foundation helps to protect life and property by supporting engineering-related education, public
engagement and the application of research. NGA Newmarket facilitated the field testing and New
Zealand Transport Agency allowed the use of Newmarket Viaduct for research. Gewei Chen and
Shahab Ramhormozian, PhD students at the University of Auckland, assisted with the ambient tests.
Xinghua Chen’s PhD study at the University of Auckland is funded by Chinese Scholarship Council
(CSC).
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