puente atirantado

10NCEE
Tenth U.S. National Conference on Earthquake Engineering
Frontiers of Earthquake Engineering
July 21-25, 2014
Anchorage, Alaska
ESTIMATION OF SOME DYNAMIC
PARAMETERS OF THE HIGHEST CABLESTAYED BRIDGE IN THE WORLD
L. M. Arenas-García1, M. A. Mendoza-Salas1,
R. Sánchez-García1, R. Gómez2, J. A. Escobar2 and O. RosalesGonzález1
ABSTRACT
Mexico is a country where there is significant seismic activity, therefore any civil structure (such
as a bridge) being constructed must consider actions of earthquakes during all stages of design,
construction and service life. The newly constructed Baluarte Bridge, located at the border of
Durango and Sinaloa states in Mexico, has been recognized by the Guinness Book of World
Records as the tallest cable-stayed bridge in the world. This paper presents the results of ambient
vibration studies conducted on this bridge to determine parameters such as fundamental
frequencies of vibration and mode shapes, in order to create a database representing the current
state of the bridge that could be used to evaluate the structure after an earthquake occurs. It also
presents a comparison of analytical results of a mathematical model developed for this purpose,
which is calibrated using records from a permanent monitoring of the bridge superstructure.
It is well known, that in most cases, direct measurements from instrumentation is the most
effective, reliable, and time efficient mean to monitor the structural integrity of a bridge during
and after an earthquake. Instrumentation of a bridge for the purpose of structural health
monitoring in correlation with ordinary and extraordinary loads is of great importance when
trying to identify, in real time, effects and damages of seismic events.
1
Research Assistant, Institute of Engineering, National Autonomous University of Mexico, 04510 Mexico
[email protected],[email protected],[email protected],
[email protected]
2
Researcher, Institute of Engineering, National Autonomous University of Mexico, 04510 Mexico
[email protected], [email protected]
Arenas-García, L.M., Mendoza-Salas, M.A., Sanchez-Garcia, R., Gomez, R., Escobar, J.A. and Rosales-González,
O. Estimation of Some Dynamic Parameters of the Highest Cable-Stayed Bridge in the World. Proceedings of the
10th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK,
2014.
10NCEE
Tenth U.S. National Conference on Earthquake Engineering
Frontiers of Earthquake Engineering
July 21-25, 2014
Anchorage, Alaska
Estimation of Some Dynamic Parameters of the Highest Cable-Stayed
Bridge in the World
L. M. Arenas-García1 M. A. Mendoza-Salas1,
R. Sánchez-García1, R. Gómez2, J. A. Escobar2 and O. Rosales-González1
ABSTRACT
Mexico is a country where there is significant seismic activity, therefore any civil structure (such
as a bridge) being constructed must consider actions of earthquakes during all stages of design,
construction and service life. The newly constructed Baluarte Bridge, located at the border of
Durango and Sinaloa states in Mexico, has been recognized by the Guinness Book of World
Records as the tallest cable-stayed bridge in the world. This paper presents the results of ambient
vibration studies conducted on this bridge to determine parameters such as fundamental
frequencies of vibration and mode shapes, in order to create a database representing the current
state of the bridge that can be used to evaluate the structure after an earthquake occurs. It also
presents a comparison of analytical results of a mathematical model developed for this purpose,
which is calibrated using records from a permanent monitoring of the bridge superstructure.
It is well known, that in most cases, direct measurements from instrumentation is the most
effective, reliable, and time efficient mean to monitor the structural integrity of a bridge during
and after an earthquake. Instrumentation of a bridge for the purpose of structural health monitoring
in correlation with ordinary and extraordinary loads is of great importance when trying to identify,
in real time, effects and damages of seismic events.
Introduction
Bridges are the most important structures in the road systems of a country. It is of vital
importance that these structures are designed and built according to the most current safety and
behavior criteria. Furthermore, Ambient Vibration Testing (AVT) is an accurate and costeffective technique for obtaining modal parameters of large structures such as airplanes, bridges,
dams, buildings, and other manmade structures. AVT consists of measuring the structure
response, at different locations, to ambient forces such as wind, traffic, human activities, etc. [1]
The Baluarte Bridge is located less than seventy kilometers from the Pacific Ocean and is
prone to earthquake and wind action mainly. For this reason a complete knowledge of its
1
Research Assistant, Institute of Engineering, National Autonomous University of Mexico, 04510 Mexico
[email protected],[email protected],[email protected],
[email protected]
2
Researcher, Institute of Engineering, National Autonomous University of Mexico, 04510 Mexico
[email protected], [email protected]
Arenas-García, L.M., Mendoza-Salas, M.A., Sanchez-Garcia, R., Gomez, R., Escobar, J.A. and Rosales-González,
O. Estimation of Some Dynamic Parameters of the Highest Cable-Stayed Bridge in the World. Proceedings of the
10th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK,
2014.
structural response by combining experimental and analytical techniques is desirable. In the next
paragraphs results obtained from ambient vibration measurements are presented and compared
with those from a mathematical model developed for this purpose. This model is calibrated with
parameters obtained from a permanent instrumentation system installed on the superstructure of
the bridge, based on optical fiber technologies.
Description of the Bridge
The Baluarte Bridge is one of more than sixty bridges that were constructed as part of the largest
road project in Mexico’s history. The bridge is located at Km 157 on the Durango- Mazatlan
Highway, segment Santa Lucia- Rio Baluarte, at the border of the Sinaloa and Durango states in
Mexico (Figure 1).
Figure 1. The Baluarte Bridge.
The bridge has a total length of 1,124 m, and a total width of 20 m comprising four lanes
for commuter and commercial traffic. The cable- stayed superstructure consists of 152 cables, is
supported on one abutment and 11 reinforced concrete piers including two main pylons. With a
height of 402.77 m from the bottom of the ravine to deck, this structure has been certified by the
Guinness Book of World Records as the tallest cable-stayed bridge in the world. Regarding its
length, it is ranked 23rd worldwide, with a 520 m central span (the longest being the Russky
Island Bridge in Vladivostok, Russia, with a 1104 m span).
Experimental Vibration Tests
The experimental vibration testing technique involves measuring the structural response, at
different locations, to ambient forces. Data is processed through an analysis by signal pairs [2],
in an attempt to obtain the modal parameters of the structure: natural frequencies, damping, and
mode shapes. The main advantages of AVT are:
(A)- Equipment for exciting the structure is not required.
(B)- Testing does not interfere with normal operations of the structure.
(C)- The measured response is representative of real operating conditions of the structure.
The Baluarte Bridge dynamic behavior program included measuring the accelerations
produced by vibrations induced by the surrounding medium to the superstructure of the bridge,
such as transit of vehicles, machinery, people, wind, earthquakes, etc. Acceleration sensors
placed at specific points along the main span (between pylon 5 and 6), as well as the two spans
adjacent to this one (Figure 2) provided acceleration records. Through the use of this
implementation, acceleration graphs were obtained in three orthogonal directional components:
longitudinal (L), transversal (T) and vertical (V). 3-D accelerometers, manufactured by Guralp
Systems, were installed to gather these records.
Figure 2. Location of accelerometers for ambient vibration tests.
Presentation of the Experimental Data
To determine the natural frequencies of vibration of the structural system under study, analysis
was carried out using pairs of signals. This methodology is based on the interpretation of
spectral density, transfer, coherence and phase angle functions, calculated from sets of two
records of acceleration. Figure 3 shows spectral density, phase angle, transfer and coherence
functions corresponding to points 12 and 16 for the transverse component. The frequency
associated to the first peak of the spectral density function has a value 0.29 Hz, which coincides
with the first maximum ordinate of the transfer function shown; for this value the coherence
ordinate is 0.96.
Figure 3. Spectral density, phase angle, transfer and coherence functions, at points 12 and 16,
component T.
Figure 4 shows another example of this analysis, which involves points 3 and 4 located in
the span adjacent to central span, next to the pylon 5. In this case, the identified frequency was
3.15 Hz.
Figure 4. Spectral density, phase angle, transfer and coherence functions of points 3 and 4,
component V.
A summary of the results of the ambient vibration tests is presented in Table 1. The data shown
correspond to both pure and coupled vibration modes, namely, the former are those whose
frequencies are associated with pure translational motions that match the trajectory of any of the
recording components (L, T or V), whereas the latter are those occurring simultaneously in two
or all three orthogonal directions mentioned. This is to be expected, since this dynamic behavior
is characteristic of cable-stayed bridges [4]. Tables 2 and 3 show the frequencies obtained for
the adjacent spans.
Table 1. Frequency values and periods obtained for components L, T and V of the cable-stayed
bridge superstructure, main span.
Mode
1
2
3
4
5
6
7
8
9
10
Component
T-V
T
V
L
L
T(Pylons 5 y 6)
Torsion
T-V
L (Pylons 5 y 6)
Torsion
Frequency [Hz]
0.29
0.63
0.73
0.83
1.03
1.07
1.12
1.22
1.51
1.61
Period [s]
3.45
1.59
1.36
1.20
0.97
0.93
0.89
0.82
0.66
0.62
Table 2. Frequency values and periods, span adjacent to pylon 5.
Mode
1
2
3
4
Component
T
L
V
Torsion
Frequency [Hz]
0.29
0.83-0.87
2.39
3.15
Period [s]
3.4
1.14-1.20
0.41
3.20
Table 3. Frequency values and periods, span adjacent to pylon 6.
Mode
1
2
3
4
Component
T
L
V
Torsion
Frequency [Hz]
0.29
0.83
2.29
3.51-3.61
Period [s]
0.34
1.20
0.43
0.27-0.28
Mathematical Modelling
The mathematical model was developed with SAP2000 software. Columns, piers, girders and
cross beams were modeled with bar-type elements, the deck was modeled with shell elements
and for the stays a cable type element was used (Figure 5).The model allows simulations with
greater certainty of events such as earthquake and wind loading, as well as loads produced by
vehicle models either for research or proposed in design codes.
Figure 5. 3-D view of the mathematical model.
Permanent Instrumentation
In recent years, Fiber Bragg Sensors (FBG) have attracted much interest and are being used in
numerous applications, including bridges similar to Baluarte, and in the longest suspension
bridge in the world: Tsing Ma Bridge, in Hong Kong.
As in the Tsing Ma, FBGs were used for monitoring the Baluarte bridge in order to detect
changes in temperature or strain based on the variation of the wavelength of the reflected light.
Physical principle of operation of FBGs is the phenomenon of reflection of light through the
fiber, which allows placing several sensors in series and only few channels to collect signals
from many sensors. At the Baluarte brideg only two channels were used for 28 sensors. In
addition to this feature, the system benefits from the properties of the fiber optic cables which are
immune to environmental noise, providing a significant advantage over electrical sensors or
transducers that use copper wires.
The monitoring system in the Baluarte bridge basically consists of 3 parts: a) Set of
sensors and Fiber Optic (FO), b) Monitoring system and c) Embedded software [5] (Figure 6).
Some of the installation activities are observed in Figure 7.
Figure 6. Monitoring System.
a) Fiber optic splicing
b) Spot welding of sensor
c) Protection and final check
Figure 7. Installation of fiber optic sensors in the superstructure of the bridge.
Enligth Pro is the program that controls data acquisition and allows easy integration of
optical sensor systems. It works by detecting wavelengths (distance from pulse to pulse of
radiation of light) of each sensor in units of nanometers (nm) and transforms them through
mathematical expressions into units of pressure, deformation or temperature depending on the
type of sensor. Equation (1) was used to calculate the total microstrain (um/m), and equation (2)
to determine the microstrain by thermal induction [6].
∆ ⁄
Δ
1 10 /
(1)
⁄
(2)
where ε is in microstrains, Δλ is the variation of the wavelength in nm, λ0 is the nominal
wavelength in nm, FG is a sensor factor, ΔT is the temperature variation in ° C, C1 and C2 are
constants of each sensor and CTEs is the material constant.
Load Testing
Load tests have been widely used to evaluate the structural behavior and strength of bridges, to
assess the damage state or even for determining the efficiency of repair works. Field tests are
also useful to determine more accurately the capability of a bridge to distribute live loads [7].
After the construction of the Baluarte bridge, several load tests were carried out using
five axles T3-S2 type trucks (Figure 8) to represent mobile and static loads.
Figure 8. Truck type used in load testing.
Below, some of the experimental results of static load tests in the bridge superstructure
are presented. For each test, truck configurations are shown as well as two graphs: one with the
strain records and the other with the calculated stresses considering a structural steel A572 gr50.
These graphs only show the results for the sensors at the center of the main span, since this is the
place where the largest deformations and stresses occur. Test E2 consisted of static loads (4 T3S2 trucks) placed at midspan in the downstream side of the superstructure; Figure 9 shows the
configuration and the corresponding measurements. Test E3 test is illustrated in Figure 10. In
addition to the static tests, dynamic tests were conducted comprising the passing of trucks at
different speeds; Figure 11 shows an example of records obtained during a dynamic test.
Figure 9. Static load test E2, Baluarte bridge.
Figure 10. Static load test E3, Baluarte bridge.
Figure 11. Dynamic load test D4, Baluarte bridge.
Experimental and Analytical Results
The implementation allowed verifying the structural behavior of the bridge under static and
dynamic loads, as well as comparing experimental and analytical data obtained from the
developed mathematical model. Table 4 shows test results from actual and simulated loads and
the difference between them. It is observed that major differences are around 16 and 13 %,
ensuring a considerable reduction of uncertainties related to instrumentation. Also, it was
observed that the structure showed a reasonable elastic recovery capacity when loads were
removed.
Table 4. Results of experimental data and mathematical model.
N°
Test
E2
E3
D4
Mathematical Model
stress
microstrain
(Mpa)
(µm/m)
78.9
383
22
108
53
262
Experimental
stress
microstrain
(Mpa)
(µm/m)
68
330
23
111
49
243
stress
(%)
16
-4.3
7.5
Difference
microstrain
(%)
13
-2.7
7.2
Conclusions
The first modes of vibration of the superstructure of the Baluarte Bridge were identified,
specifically in the central span. The most important modes were associated to the vertical and
transverse component, and coupling of these two modes of vibration. The first fundamental
frequency was 0.29 Hz, corresponding to a 3.45s period; the following frequency modes
identified were 0.63 Hz (transverse), and 0.73 Hz (vertical); these same modes were identified
with the mathematical model. The first mode shapes identified with accelerometers were very
well correlated with those of the model. With respect to the longitudinal vibration mode
frequencies, they were 0.83 and 1.03 Hz; a torsional frequency was identified near 1.12 Hz. It is
worth to mention that some of the frequencies and mode shapes obtained from the analysis of the
model were not displayed during the field tests, probably due to the limited number of
accelerometers and large dimensions of the bridge.
The results presented show that experimental techniques are reliable and are useful to
identify structural aspects that otherwise would be impossible to determine. Furthermore, it was
shown that the system will be able to provide long-term monitoring alerts related to situations
that could risk the integrity of the bridge. It is necessary to have systems designed to identify in
real time potential areas of stress concentration during seismic events
By obtaining records during seismic events, that often occur in Mexico, we will know
more about the behavior of complex structures such as large cable-stayed bridges. Records will
be an important contribution to the study of the seismic behavior of large cable-stayed bridges.
Acknowledgments
The Ministry of Communication and Transportation of Mexico provided the funds for the
development of the work carried out by the personnel of IIUNAM and IST (JC Velasquez and
Cody Carter)
References
1.
Carlos Ventura, Juan C. Carvajal, Jose Centeno, Bishnu Pandey. Identification of modal propierities of the
Ironworkers Memorial second Narrows Crossing: testing on the deck. IOMAC'09 – 3rd International
Operattional Modal Analysis Conference
2.
Bendat, J. S.; Piersol, A.G. 1989. Random data: analysis and measurements procedures. 2ª edicion, Wiley
Interscience. New York.
3.
Aly S. Nazmy and Ahmed M. Abdel-Ghaffar. 1992. Effects of ground motion spatial variability on the response
of cable-stayed bridges. Ltd. Issue. Earthquake Engineering & Structural Dynamics. Volume 21, Issue 1,
pages 1–20, 1992.
4.
Gómez, R., Arenas-García, L. M., Sánchez-García, R., Mendoza-Salas, M.A., Escobar, J.A. and RosalesGonzález, O. N., Pruebas Bajo Cargas Estáticas, Dinámicas, de Impacto y de Frenado en el Tramo Principal del
Puente Atirantado, in Spanish, Institute of Engineering, UNAM. Mexico.
5.
Micron Optics Inc, 2005. Optical Fiber Sensor Guide: Fundamentals and Applications. Operating Manual,
Atlanta, GA, EEUU.
6.
Andersson A., Karoumi R. y Sundquist H. 2006. Static and Dynamic Load Testing of the New Svinesund Arch
Bridge. Hong Kong, China, International Conference on Bridge Engineering-Challenges in the 21st Century,
Hong Kong, China 2006.