DYNAMIC TESTING AND MODEL UPDATING OF CABLE-STAYED ...

DYNAMIC TESTING AND MODEL UPDATING OF CABLE-STAYED BRIDGES

Joan R. Casas Technical University of Catalunya Civil Engineering Deparment Gran Capitan s/n. Modulo C 1 08034 Barcelona Spain

ABSTRACT. The paper shows the different dynamic tests peiformed in two-cable-stayed bridges: the Alamillo bridge in Spain and the General Belgrano (Chaco-Corrientes) bridge in Argentina. The first is a nwly constructed bridge and the dynamic tests peifomred just after completion of the construction were justified to update the mathematical model and the scaled model used in the wind tunnel tests. The second corresponds to an existing cable-stayed bridge where a repair and strengthening work had to be undertaken. In this case, the model updating and correslation was mandatory to know some of the mst important parameters involved in the design of the most effective repair (deck properties, cable forces, ... ). The vibration data is used in the identification of the model of the complete bridges as well as in the updating of the actual forces in the stays. The experiences show how with a minimum instrumentation and recording set-up. and with very simple excitation techniques, it is possible to derive important conclusions regarding the reliability and structural peifonnance of cable-stayed bridges through dynamic testing.

Jeronimo meander of the river Guadalquivir and is bounded by the ringroad of Sevilla (Spain) in the west. It was also used as an access to the Island of La Cartuja, seat of the Expo '92 Universal Exhibition. The originality of the design, lies in the fact that the load borne by the cables supporting the deck over the river is compensated not by traditional back stays, but by the considerable backward inclination (32 o from vertical) of a massive reinforced concrete tower, so that the resultant of its self weight, composed with the resultant of the stay forces follows the direction of the tower (Figure 1). The deck of the bridge, with a 200m span, is supported every 12m by a pair of stays. A total of 13 pairs of cables are used. Twelve pairs of cables consist of 60 steel strands with diameter of 15.24 mm (0.6 in). The longest pair of stays are formed only by 45 strands. The individual strands are protected by an epoxy resin coating and the cables are encased in a two-layer high density polyethylene sheath with a white outer and an interior coated with matt black to increase resistance to ageing.

1. INTRODUCTION For many years, model updating and correlation has been used in bridge engineering to check feasibility of structural models used during design and stability of final construction. Many works were developed in the range of short and medium span bridges by using experimental modal analysis techniques which require an important and large test set-up both to excite the bridge vibrations and to measure in different locations. However, less investigations have been devoted to the field of cable-stayed bridges because of the required experimental resources. This paper wants to show, by means of two examples, how even in the case of using limited experimental resources it is feasible to perform calibration techniques oriented to updating the dynamic models of existing cable-stayed bridges.

In the transverse section (Fig. 2), the deck is composed of a large steel girder with a hexagonal box section 4.4 m high and 5.6 m wide, from which 12 m long transverse steel ribs arise every four metres, supporting a 230 mm thick concrete slab. The deck is 32m in width, and the pedestrians walk on the middle of the box girder, at a higher plane than the vehicles. The deck supports 6 lanes of traffic (3 in each direction). The part of the deck closest to the tower is made of reinforced concrete and there is a transition zone (composite action) to translate the internal forces from the standard steel deck to the concrete.

2.1 Alamillo cable-stayed bridge

The tower is a reinforced concrete element of considerable thickness that is inclined thirty-two degrees from the vertical and runs from benchmark 7.0 m to benchmark 141.25 m. Its transverse section varies constantly and has an irregular, roughly hexagonal shape, with average dimensions on the order of 12x8 metres. Additional information regarding the bridge design and construction is available in [1]

The Alamillo bridge is a cable-stayed bridge that crosses the San

The objectives of the dynamic test were:

2. DESCRIPTION OF THE BRIDGES AND DYNAMIC TESTS

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1) to check the agreement between natural frequencies of the real bridge and mathematical and wind-tunnel models. That was important to validate the dynamic models used in the design. 2) to check if the damping in the real bridge is greater than or equal to the damping in the wind-tunnel model. That was very important concerning the conclusions drawn from the wind-tunnel test about vibrations due to vortex shedding. 3) To determine the final cable forces after completion of the bridge and to check if they were within the tolerance limits stated in the design. 4) to evaluate the dynamic increment (impact factor) due to traffic. The equipment consisted of 4 accelerometers (Figure 3 ). One of them was placed at the top of the tower and was monitoring accelerations in 3 orthogonal directions. The rest were placed in different crosssections of the deck and measuring in the vertical direction. In addition, one displacement transducer was placed in the deck. The dynamic tests were performed before the bridge was open to traffic, and the dynamic excitation was provided by two 2-axle trucks of 196 kN crossing the bridge at different speeds from 5 to 15 rnls. To excite mainly bending or torsional modes in the deck and transverse and longitudinal modes in the tower, different crossing arrangements were chosen (symmetric and eccentric load). Also several passages were performed over the undisturbed pavement and other, with the trucks passing over and artificial unevennes provided by a plank placed at midspan. A complete description of the tests can be found in [2]. A dynamic test in the cables was also used to derive the final forces in the cables after construction according to the vibrating chord theory. An accelerometer was attached to the lower end of the cable-sheating pipe. The excitation was achieved by releasing a hanging weight in a rhythm similar to the natural frequency of the cable. 2.2 General Belgrano bridge

The Chaco-Corrientes cable-stayed bridge is the central link of a major roadway connection across the Parana River in Argentina. Inaugurated in 1973, its structure consists of two main longitudinal box girders of segmental precast prestressed concrete. Pylons are cast-in-place concrete space frame rigidly connected to the box girders at deck level and supported by thirty two 1.80 m diameter concrete piles. A general view is given in Figure 4. The static scheme of the bridge consists of two independent half bridges, connected between them and to the access viaducts with simply supported spans of 20 m length. Each half bridge is approximately symmetric about the vertical plane containing the axis of the pylon. The central span measured at centerlines of pylons is 220 m (Figure 5). The main box girders within the pylons are also of cast-in- place reinforced concrete with rigid connections to the other members of the pylon. The box girders outside the pylons are made of precast prestressed concrete segments. The deck slab and transverse beams that connect the box girders are also made of precast prestressed concrete elements. The original cables are of locked-coil type with external layers of galvanized wires. The cables are organized in sets of 6 cables for the longer stays and of 4 cables for the shorter ones. All cables have a centering collar between 2 to 3 m from the ends to reduce bending at the anchor sections.

In this case, the objective of the dynamic test was the reconstruction of the current state of stress in the different elements of the bridge (model updating). That was necessary to decide and design the repair and strengthening works to be carried out. The works consist basically in the replacement of all cables due to the damage present as well as in the resitution of the correct profile of the bridge deck that showed a large and unpleasant deflection after some years of operation due to concrete creep and cables relaxation. The updating was possible by direct measurement of cable forces and vertical deck accelerations recorded over time. Determination of the current stiffness of the concrete deck was accomplished through interpretation of ambient vibration records of the bridge deck under traffic and wind forces. This procedure provided an alternative to the conventional static method based on level measurements of the deck for known concentrated loads, which are strongly affected by uncertainties in the transient thermal changes. Measured natural frequencies are used to calibrate the effective stiffness of a numerical model, which in turn is used to determine the additional forces in cables and girders associated with restitution of the longitudinal profile. The ambient vibration records, taken before any repair work was done on the bridge, consist of a series of vertical acceleration time histories of three points at the curbs of the roadway. These points, located above the longitudinal axis of the main girders and very close to the vertical plane containing these axes, are in correspondence with three characteristic cross sections: • Sensor I: Cross section passing through the intersection of the longitudinal axis of the girder and the resultant force of the groups of 6 stays. • Sensor 2: Cross section passing through the intersection of the auxiliary stays (not yet installed when the records were made) and the longitudinal axis of the girder. • Sensor 3: Cross section passing through the intersection of the longitudinal axis of the girder and the resultant force of the groups of 4 stays. These sets of3 simultaneous records, made along both main girders in the two half bridges, were repeated several times at each location to provide a variety of forcing functions during intervals with large oscillations induced by traffic and wind. 3. RESULTS AND DISCUSSION 3.1. Alamillo bridge

The FFT technique was used to identify frequencies and mode shapes. The frequency resolution achieved with the part of the total recorded signals suitable for post-processing was 0.025 Hz. The main results concerning the dynamic parameters of the bridge and their comparison with theoretical ones are summarized in table 1. The range in the values of percentage of critical damping ( 0 indicates the maximum and minimum values obtained from records with different maximum vibration amplitudes depending on the test. Only the transverse vibrations of the pylon were measured. The excitation due to the two trucks over the deck plus wind is enough to produce a level of transverse acceleration at the top of the tower suitable for acquisition and post-processing. As deduced from the table, the agreement between dynamic parameters of the real bridge and theoretical and scaled models (tested in wind-tunnel) was completely satisfactory. This validates the results of the wind-tunnel

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tests either for the maximum non-divergent displacements (vortex shedding) or for the flutter or torsional divergence. It also confirms the good agreement of mass and stiffness, and their spatial distribution into the bridge, between completed bridge, aerolastic model and designed bridge. Also in the table is shown how, in spite of the scatter,

Vibration mode

Theoretical model

the actual measured damping ratio is always greater than damping in the aerolastic model. Therefore the conclusion was that the vibration level because of vortex shedding will not derive in unpleasant (from the pedestrian point of view) or dangerous (from the fatigue point of view) vibrations.

Aerolastic model

Actual bridge (acceleration)

Actual bridge (displacement)

f(Hz)

f(Hz)

( (%)

f(Hz)

( (%)*

f(Hz)

( (%)

Transverse pylon 1

0.292

0.30

0.41

0.30

--

--

--

Longitudinal (pylon + deck) 1

0.373

0.39

0.21

0.40

1.9-4

0.40

1.9

Longitudinal (pylon + deck) 2

0.610

0.65

0.37

0.66

1.1-4

0.65

1.6

Transverse deck 1

1.088

1.20

0.72

--

--

--

--

Longitudinal (pylon + deck) 3

1.191

1.19

--

1.205

0.6-2.6

1.20

--

Torsion deck I

1.235

1.11

0.25

1.155

0.5-1.5

1.16

--

Transverse pylon 2

1.583

1.67

--

1.537

--

--

--

Longitudinal (pylon + deck) 4

2.196

1.97

--

2.155

0.6-3.7

2.06

--

Torsion deck 2

2.298

2.19

--

2.295

0.5-0.8

--

--

Longitudinal (pylon + deck) 5

2.312

--

--

2.78

--

--

Transverse deck 2

3.244

3.4

--

--

--

--

---

Table 1 Summary of results in the dynamic test of the Alamillo bridge Concerning the measurement of actual forces in the cables through dynamic vibration, the most important differences between design and real forces are those of the last two couple of cables (table 2). This is due to the fact that the fmal design of the last segment of the tower (with the shape of a Trojan horse) translated into a lighter segment, and consequently, in a lower force in the closest cables. The correct knowledge of these values is of great interest regarding the bridge stability and monitoring during the service life. The test results and process of derivation of the cable forces and the problems encountered are fully described in [3].

3.2 General Belgrano bridge A numerical model of a half bridge was prepared following the design documents. The mass of the main structural elements was modified in order to take into account as-built conditions from thickness measurements of the box girder , pavement layer and structural modifications introduced at the simply supported 20m spans at both ends introduced in a previous repair program (1986-87). The modulus of elasticity of concrete was retained as the single parameter to be adjusted in the model updating to conform with the measured dynamic properties of the bridge. Three procedures were applied to identify the natural frequencies of the bridge from the recorded accelerograms: Spectral Density Function To eliminate peaks of these individual records due to the

Cable (couple)

Design force at jacking (kN)

Design force after end of construction (kN)

Measured force (kN)

I

11642

11534

11556

2

12025

11809

11694

3

12495

12103

12224

4

10839

10231

10614

5

11182

10457

10810

6

10849

10094

10164

7

10996

10280

10478

8

10849

10153

10242

9

10506

9967

10026

10

9820

9379

9280

II

9398

9094

9124

12

8977

8859

8398

13

9398

9349

8730

Table2 Design and measured cable forces using vibration method in the AlamiUo bridge

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characteristics of the forcing function for each record, and to retain only the common ones associated with the natural frequencies, the average power spectral density function was calculated for each sensor normalizing the amplitude of all records to the same root mean square value [4].

higher frequencies. The value of the modulus of elasticity of concrete leading to a minimum error was found to be 42500 MPa with both forms of the error function. The value derived via the measurement of the static deflection through levelling of the deck when a cable stay was removed was found to be 45000 MPa.

Phase Dispersion The natural frequencies were also be identified by means of the Phase Dispersion of the records as defined by Ceballos et al. [5], which is itself a normalized function. The frequencies identified by these two procedures from sensor 2 are given in Table 3.

Vibrations of the cables were also induced in this case to derive the actual forces in the cables to be replaced. Because the technology of stays and anchorages in this bridge was much older and simpler than in the case of the Alamillo bridge, the actual forces were easily derived from the records without requiring additional information and correction procedures as in the other bridge [3]. In this way, the actual forces to be introduced in the new cables was easily obtained. More information on the tests results can be found in [6].

Freguency of peaks 1 2 3 4 5 6 7 8 9

ANPSD 0.567 1.621 2.404

4.058

11.810 13.013

-

Phase Dispersion 0.540 1.648 2.384 2.948 4.043 9.208 11.826 13.104 14.173

4. CONCLUSIONS

Table 3 Natural frequencies from accelerometer 2 in Belgrano bridge Peak;s of FFT (fast Fourier Transform) In order to get longer records in time and, therefore, to achieve a better resolution in frequency, the different individual records acquised in different times in the same sensor location, were added. The record TORI corresponds to the experimental set-up disposed to measure the torsional accelerations. Two sensors were located in the same cross-section, and the corresponding records were added in order to give more importance to the torsional movements. In figure 6 are shown the FFT values of accelerometers 2 and 3. In table 4, the values of frequency for each record are obtained analysing the corresponding peak frequencies in the 3 sensors. A value is identified as a natural frequency of the bridge only if it is present as a peak in the 3 records. In the same way, comparing the peak amplitudes of each record, the vibration mode corresponding to each frequency is identified. The mode numbers in table 4 are related to the corresponding vibration modes derived with the theoreTical model. As can be seen there, the mean value of the natural frequencies obtained averaging all records are in good agreement with those derived with the theoretical model and also with those obtained by the other two procedures (ANPSD and Phase Dispersion). The differences are in the range of the corresponding standard deviations and the frequency resolution available (0.04 Hz). Table 5 gives a comparison between computed and measured natural frequencies and mode shapes at sensor locations 1 and 2. The effective modulus of elasticity of the concrete deck was determined by minimizing the difference between calculated and measured natural frequencies of the 3 dominant modes of response. The error to be minimized was defined as the sum of the absolute values of the difference between measured and computed frequency of modes a), b) and c), weighted by the square root of the amplitude of the PSD function of the corresponding mode. This was intended to assign more weight to those modes with larger amplitudes in the records. Alternatively, a variant involving the difference of frequency divided b.y the frequency was also used to avoid a bias towards the

For the Alamillo bridge, the results have confirmed the possibility of performing dynamic tests in long-span bridges even with relatively low excitation means consisting of two trucks if the measurement setup is accurate enough. Therefore, this excitation technique (passage of trucks over obstacle) becomes a useful alternative to the ambient vibration test (by wind or traffic) when the on-site characteristics of the bridge or the fact that the bridge is not yet open to traffic do not permit their reliable performance. The correlation between experimental and theoretical dynamic parameters has provided a strong confidence on the models (both mathematical and wind-tunnel) used during the design and in the safety level of the finished bridge. The correct dynamic behaviour of the bridge in response to traffic and wind (vortex shedding, flutter, etc.) can be deduced jointly with the correct alignment and expected internal forces in the permanent state (self-weight plus permanent loads) in tower and deck. Moreover, the measurements in the cables permits the updating of their dynamic modeL being the basis of future inspections of the cable structural performance based on the vibrating method. In the case of the actual anchorage devices some problems may arise in the interpretation of the test results due to the distance between the effective anchorage plate and the dampers [3]. In the case of the Chaco-Corrientes bridge, the model updating by the ambient vibration measurements performed before initiation of the bridge repairs have shown to yield valuable data to control the process of repair and to introduce effective changes in the strengthening process. The ambient vibration technique has shown again as very useful in its application to cable-stayed bridges, where wind actions are of importance. Moreover, in this case to work with the traffic induced vibrations was of great importance because the bridge was already in operation and was not possible to close it at any time due to its location in one of the main commercial links between Argentina and Brasil. Calculations to determine the schedule for profile correction were performed on the basis of the effective modulus of concrete derived via the model updating procedure. Actual forces in the cables to be replaced were also found in the dynamic tests. Only in this way the correct force to be introduced in the new cables can be deduced. In this bridge, a static test was also carried out. The static test consists on the measurements of displacements in the deck during the process of removal of old cables, that may be considered as the application of a static load equal to the cable force. The comparison of the values obtained in the static measurements permits to validate the results of the dynamic test. A new dynamic tests will be also carrried out in the new cables to check their final force after finishing of the repair works.

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Record

Mode 4 (Bending) 9 (Bending) 12 (Torsion) 14 (Bending) 28 (Bending) CN 0.64 1.64 4.09 13.15 CN' 1.59 13.20 0.51 3.99 cs 0.62 4.07 13.20 CS' 1.58 0.50 3.88 13.03 HN 1.62 0.65 4.04 13.18 HN' 0.65 1.62 12.99 HS 0.62 1.69 4.00 13.10 HS' 0.47 1.57 3.87 13.11 TOR1 0.58 1.67 3.72 4.03 13.09 Mean 0.58 1.62 3.72 4.00 13.12 Standard dev. 0.067 0.040 0.076 0.069 Numerical model 0.57 1.616 3.80 4.071 13.048 Table 4 General Belgrano bridge. Theoretical and experimental frequencies derived by FFT. The various records correspond to different sensor locations within bridge. Each record is the sum of several records of large ambient vibration (wind and traffic)

Sensor Mode (a) Mode (b) Mode (c)

1 2 1 2 1 2

Freq. [Hz] 1.616 4.071 13.048

Computed Norm. amp. 0.201 1.000 0.328 1.000 0.931 1.000

0

Phase [ 0 180 0 0 0 180

]

Freq. [Hz] 1.621 4.058 13.013

Measured Norm. amp. 0.679 1.000 0.326 1.000 1.204 1.000

Phase [0 ] 0 175 0 0 0 165

TableS Comparison of modal shapes at sensors 1 and 2 in the General Belgrano bridge 5. ACKNOWLEDGEMENTS

The dynamic tests in the Chaco-Corrientes bridge were performed by the team of the Universidad Nacional de Cordoba (Argentina), under the supervision of Professor Carlos A. Prato who also provided some of the results presented in the paper. The financial support of the Regional Government of Andalucia regarding the execution of the tests on the Alamillo bridge and from the Spanish Ministry of Education (Direcci6n General de Ensefianza Superior) through Research Project PB95-0769 is greatly acknowledged.

[3) Casas, J.R. A combined method for measuring cable forces: the cable-stayed Alamillo bridge, Spain. Structural Engineering International, Vol. 4, No.4, 235-240. 1994. [4) Cantieni, R. Updating of Analytical Models of Existing Large Structures Based on Modal Testing, RECENT ADVANCES IN BRIDGE ENGINEERING: Evaluation, Management and Repair, Edit. J.R. Casas, F.W. Klaiber and A. R. Mari, Proceedings of the US-Europe Workshop on Bridge Engineering, Barcelona, 153-177, July 1996.

6. REFERENCES

[1) Aparicio, A.C. and Ca~as. J.R. The Alamillo cable-stayed bridge: special issues faced in the analysis and construction. Proceedings of the Institution of Civil Engineers, Journal of Structures and Buildings, Vol 122., November 1997. [2) Ca,as, J.R. Full-scale dynamic testing of the Alamillo cable-stayed bridge in Sevilla (Spain). Earthquake Engineeering and Structural Dynamics. Vol. 24,35-51, 1995.

[5] Ceballos, M.A. et al. E-1:perimental and Numerical Determination of the Dynamic Propenies of the Reactor Building of Atucha II NPP, SMIRT13 Post Conference Seminar 16: Seismic Evaluation of Existing Nuclear Facilities. Iguazu, Argentina, 311-327, August 1995. [6) Prato, C.A.; Ceballos, M.A.; Casas. J.R. and Aparicio, A.C.lnterpretation of ambient vibration records for restitution of deck profile of the Chaco-Corrientes cable-stayed bridge. Proceedings of Structural Faults and Repair-97, 387-394, Edinburgh, 1997.

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Figure 1.- View of the Alamillo cable-stayed bridge (Sevilla, Spain)

y

I

16000

1200 250

250

10500

II

325 608

II 1oooll I

: 1875

.. N

Figure 2.- Half cross-section of deck (Alamillo bridge, dimensions in mm)

180cm

·t--+·

DISPLACEMENT TRANSDUCER

Figure 3.- Instrumentation used and location in the Alamillo bridge

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Figure 4.- View of the Chaco-Corrientes bridge (Argentina)

Auxiliary cables

Set of 6 cables

Figure 5.- Structural model of the Chaco-Corrientes bridge

~~~--~~~-4---+---+--~~~--+

i

~ ~+----1---1

.. frequency(llz)

"·

Figure 6.- FFT of records in accelerometers 2 and 3 from all tests (General Belgrano bridge)

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