Tenth U.S. National Conference on Earthquake EngineeringFrontiers of Earthquake Engineering July 21-25, 2014 Anchorage, Alaska 10NCEE

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 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 LArenasG@iingen.unam.mx,MMendozaS@iingen.unam.mx,RSanchezG@iingen.unam.mx, OrosalesG@iingen.unam.mx 2 Researcher, Institute of Engineering, National Autonomous University of Mexico, 04510 Mexico RGomezM@iingen.unam.mx, jess@pumas.ii.unam.mx 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.

Tenth U.S. National Conference on Earthquake EngineeringFrontiers of Earthquake Engineering July 21-25, 2014 Anchorage, Alaska 10NCEE

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 cost-effective 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 LArenasG@iingen.unam.mx,MMendozaS@iingen.unam.mx,RSanchezG@iingen.unam.mx, OrosalesG@iingen.unam.mx 2 Researcher, Institute of Engineering, National Autonomous University of Mexico, 04510 Mexico RGomezM@iingen.unam.mx, jess@pumas.ii.unam.mx 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 Component Frequency [Hz] Period [s] 1 T-V 0.29 3.45 2 T 0.63 1.59 3 V 0.73 1.36 4 L 0.83 1.20 5 L 1.03 0.97 6 T(Pylons 5 y 6) 1.07 0.93 7 Torsion 1.12 0.89 8 T-V 1.22 0.82 9 L (Pylons 5 y 6) 1.51 0.66 10 Torsion 1.61 0.62

Table 2. Frequency values and periods, span adjacent to pylon 5.

Mode Component Frequency [Hz] Period [s]

1 T 0.29 3.4 2 L 0.83-0.87 1.14-1.20 3 V 2.39 0.41 4 Torsion 3.15 3.20

Table 3. Frequency values and periods, span adjacent to pylon 6.

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.

Mode Component Frequency [Hz] Period [s] 1 T 0.29 0.34 2 L 0.83 1.20 3 V 2.29 0.43 4 Torsion 3.51-3.61 0.27-0.28

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].

∆ ⁄ 1 10 / (1) Δ ⁄ (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 T3-S2 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

Mathematical Model Experimental Difference stress

(Mpa) microstrain (µm/m)

stress (Mpa)

microstrain (µm/m)

stress (%)

microstrain (%)

E2 78.9 383 68 330 16 13 E3 22 108 23 111 -4.3 -2.7 D4 53 262 49 243 7.5 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)

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