Transactions on Modelling and Simulation vol 16, 1997 WIT Press, ISSN X

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1 Dynamic testing of a prestressed concrete bridge and numerical verification M.M. Abdel Wahab and G. De Roeck Department of Civil Engineering, Katholieke Universiteit te Leuven, Belgium Abstract In this paper, different dynamic tests carried out on bridge B15 over the highway E19 connecting Brussels and Antwerpen in Belgium are described.two Different excitation types are considered: a drop weight and ambient vibrations due to the traffic under and over the bridge. Finite element model is constructed to support and verify the dynamic measurements. The current measurements are a part of a research project for diagnostic inspection and detection of damages for bridges. By repeating the dynamic test after a certain time of use, the bridge's dynamic parameters such as natural frequencies, mode shapes and modal damping ratios could be used to detect and quantify damages. The modal parameters are extracted from the response time series using the data dependent system (DDS) approach. Good correlation between the finite element simulation and the experiments is obtained. 1 Introduction Nowadays, the application of dynamic testing to civil engineering structures, especially bridges, for damage detection and diagnostic inspections increases. In general, the costs of maintaining and repairing existing structures are much lower than building new structures or reconstructing old ones. To minimize the costs of repair, it is important to detect damage at an early stage. The classical visual inspections techniques have a limited possibility for the quantification of damage. On the other hand, dynamic parameters such as modal frequencies, mode shapes and damping ratios can be easily determined from experimental measurements. Due to damage, the stiffness of the structure reduces and consequently the natural frequencies decrease. The creation of additional friction surfaces causes an increase of damping ratios. Thus, the dynamic parameters can be used to detect and quantify damages. This concept has been successfully applied to bridges in references [1,4]. Experimental modal analysis can be divided into frequency and time

2 196 Computer Methods and Experimental Measurements domain methods. Frequency domain analysis is mostly based on curve fitting of frequency response functions, obtained by dividing the fast fourier transform (FFT) of the response and the force functions. The disadvantages of the FFT are: low frequency resolution, leakage, aliasing and contamination by noise. The data dependent system (DDS) method, originally developed by Pandit [5], is a time domain identification method which doesn't require measurement of input forces. An autoregressive moving average vector model ARV(n) or ARMAV(n) [5] is supposed to represent the measured response data. From the identified model, modal characteristics can be derived. Two different excitations, namely impact weight and ambient vibrations due to the traffic under and over the bridge, are considered and the dynamic response of the bridge is measured. An ARV-model is used to extract the modal parameters for both tests. First, the autoregressive vector (ARV) model is briefly reviewed. A brief description of the bridge and the dynamic tests are presented. Then, the finite element model is described. Finally, the results obtained from each test are presented and compared to the finite element results. 2 DDS method - ARV model For the second dynamic test (ambient vibration test), the dynamic loading can not be measured. Thus, the classical technique for data processing of frequency response functions in the frequency domain is not applicable. On the other hand, the DDS method does not required knowledge about loading because the modal parameters can be extracted directly from the response time data. The simplest AR (1) model relating two successive observation of data is; X, = < >, X,_, + a, (1) where X^ and X^ are the observed output data, (j) is the autoregressive parameter, a^ expresses the residual and t refers to the sequence index of observations. For an ideally deterministic system, the dependence would be perfect and \ would be zero. Equation (1) is called autoregressive model of order 1, AR(1). The order is 1 because X< depends only on X^. To be able to calculate X<, we need initial values, i.e.; X = X at f=0 (2) By a straightforward substitution, the solution of the differential equation (1) can be found as follows: X, = 4) X, + 4) a 7-0 The first term of equation (3) is called the deterministic part and the second

3 Computer Methods and Experimental Measurements 197 term the stochastic part. Now, consider the case of simultaneous measurement of response data at p different locations (X,(i), i=l,p). The vector X, (Xj=[X^, X2p...Xp<) can be written in the following form: X, Where a,=[a^(l) a,(2)... a,(p)] and fy (j=l,n) are p x p matrices. This model is known as a vector autoregressive model of order n, ARV(n). If Xo denotes the vector containing the initial values, one can obtain the modal decomposition for the ARV model analogous to equation (3) as follows: %, = /, #-"+' f.<"-'> + Z G/z,_. (5) 7=0 with!,=[! ], I=pxp unit matrix, X^»=[X^ X^ X^... X^], O is the autoregressive parameter matrix and Gj is the Green's function. If we assume that O is diagonalizable, its spectral decomposition may be written as: O = L A, L -' (6) where X is the diagonal spectral matrix of O and L is the matrix of eigenvectors. The eigenvalues A and the modal vectors 1* can be determined by solving the following autoregressive characteristic polynomial [6]: [A? / - AT 4>, -...4>J /. =0, i = l,2,...,nxp (7) After obtaining the solution, the important question arises how to select the modes and separate them from those arising from the measurement noise, computation,etc... The first criteria for selection of the physical modes are the eigenfrequencies and the damping ratios. Knowledge of the frequency range of interest can be used to reject modes of lower or higher frequencies. Modes with high damping ratio may also be rejected as they damp out quickly. A second criterion is the average modal amplitude (AM) [5] which characterizes the strength of each mode in the deterministic part of the measured data X<. Computational modes usually have small amplitude and can be rejected. The last criterion is the modal signal-to-noise ratio (MSN) which is defined as the ratio of AM to V~MV, where MV is the summed up variance of the stochastic part of X,. In addition to the above selection criteria, the results of a finite element simulation may also be used during the selection procedure of the relevant modes. The ARV(n) model described in this section is implemented in a computer program DDS [7] developed at the department of Civil Engineering, Katholieke Universiteit te Leuven.

4 198 Computer Methods and Experimental Measurements 3 Description of the bridge The bridge under consideration B15 is located between the villages Peutie and Perk and crossing the highway E19 between Brussels and Antwerpen. The bridge B15 is shown in figure 1.B15 built in 1971, is a box-girder bridge and has three spans with overall length of 124.6m (53.0m mid-span and 2x35.8 side-spans). The box-girder is 9.4m wide and varies in height between 1.0m and 2.5m. B15 is 13.0m wide and has two traffic lanes. The superstructure is supported by neoprene bearings which allow for lateral movements at the two outside abutments. An important feature of B15 is that it is a skew-symmetric bridge so that its mode shapes are not expected to be clearly separated into bending and torsion modes but rather a combination of them. 4 Description of the dynamic tests Dynamic tests can be subdivided into forced vibration and ambient vibration tests. In the first method, the structure is excited by artificial means such as shakers or drop weights. The disadvantage of this method is that the traffic has to be shut down for a rather long time, especially for large structures, e.g. long bridges. This can be a serious problem for intensively used bridges. In contrast, ambient vibration testing does not affect the traffic on the bridge because it uses the traffic as natural excitation. This method is cheaper than the first one because no extra costs are needed for exciting the structure. However, it requires relatively long records of response measurements. It should be noted that in our case, the considered bridge has characteristics which enable the use of a reasonable small impact weight system (mass of 120 kg and drop height of 1m). It can be installed on the side walk, so minimizing the disturbance to traffic. In the following subsections, the methods used to excite the bridge are briefly described. 4.1 Impact weight Impact force was applied to the bridge using a weight of 120 kg falling from a height of about 1.0 m. The place of this weight was chosen according to the preliminary finite element results. The response of the bridge at selected points is measured in the vertical direction using accelerometers (PCB type 393A, 393A03, 393C, Schaevitz sch-x-o). Because it was not possible to close the bridge due to its heavy traffic, the impact weight and the accelerometers are placed on the side walk and the bicycle lane. A total of 86 points (43 points x 2 sides) are considered as shown in figure 2. Eight series, each of them consisting of nine points, in addition to two other series of seven points, are recorded for the whole bridge. Two reference points are fixed during the overall test setup. For most bridges, the frequency range of interest is lying between 0 and lohz containing at least the first ten eigenfrequencies. The sampling frequency on site was chosen to be 500Hz. Afterwards, the data are resampled at 62.5Hz

5 Computer Methods and Experimental Measurements Figure 1: Bridge B15 Figure 2: B15 - measurement locations

6 200 Computer Methods and Experimental Measurements eliminating frequency components above 0.8 times the Nyquist frequency (cutoff frequency of 25Hz). 4.2 Ambient vibration test B15 has intensive traffic so that the traffic over this bridge is the main cause of vibrations. During a relatively long time interval, the vibrations of the bridges are registered at points mentioned under 4.1. The total acquisition time varied between 2 to 5 minutes at a sampling rate of 200Hz. Afterwards, the data were resampled to 25Hz resulting in a cutoff frequency of lohz. 5 Finite element model The bridge is simulated using the finite element program ANSYS [8]. The whole bridge should be modeled to account for the skew-symmetric configurations. Therefore, Four-noded shell elements with 6 degrees of freedom per node are used to model the bridge. Figure 3 shows the finite element mesh. The model consists of 3637 nodes and 3828 elements. An extra mass is added at the deck of the bridges to account for the cover (asphalt, side walk, ). The finite element model is built before performing the dynamic tests. Its preliminary results are used to determine the location of the impact weight and that of the reference points. Afterwards, the model results are compared to the test results. Figure 3: F.E. mesh for B15 - shell elements

7 Computer Methods and Experimental Measurements Results and comparisons The results of the impact and ambient tests are given in table 1 and compared to the untuned finite element results. In total eight modes are identified. For the impact test, by using the DDS technique, the shapes of all modes shown in table 1 are clearly found except some irregularities in mode shape 2. However, the DDS technique was unable to find accurate mode shapes resulting from the ambient vibration test. Only the fist mode shape was identified and is shown in figure 4. From table 1, we can see that the AM value for the first mode obtained from the ambient test is much higher than the rest of the modes. This means that mode 1 is more dominant present in the response measurement. In contrast, the AM values of the impact test are more or less equal for the different modes. Figures 5 to 12 illustrate the computed and the measured (impact test) mode shapes for the first four modes (modes 1,3,4 and 5 in table 1). To evaluate the correlation between the computed and the measured mode shapes, the 'Modal Assurance Criterion' is calculated. The MAC-value is a correlation factor for each pair of analytical and experimental mode shapes. It is defined as [9]: 4>* Yl MAC(ij) = ' ' _ (8) Where Y is an eigenvector en * denotes its complex conjugate. De MAC-value always lies between 0 and 1. A MAC-value of 1 indicates excellent correlation, while a MAC-value of 0 indicates that the modes do not show any correlation. The diagonal of the matrix MAC(ij) should have a high value (>0.8) for good correlation. The MAC-matrix is computed for the impact test and is given in table 2. It is clear that the correlation between the computed and the measured mode shapes is very good. Figure 4: mode 1 - B15 - ambient test

8 202 Computer Methods and Experimental Measurements Table 1: Test Results - B15 mode Impact test Ambient test F.E. Freq. Damp.% AM% Freq. Damp.% AM% Freq Table 2: MAC-matrix -B Figure 5: mode 1-B15-F.E. results Figure 6: mode 1-B15-impact test

9 Computer Methods and Experimental Measurements Figure 7: mode 3-B15-F.E. results Figure 8: mode 3-B15-impact test Figure 9: mode 4-B15-F.E. results Figure 10: mode 4-B15-impact test I I I 1 >' Figure ll:mode 5-B15-F.E. results Figure 12: mode 5-B15-impact test

10 204 Computer Methods and Experimental Measurements 7 Conclusion Dynamic tests were performed on bridge B15 crossing the E19 highway in Belgium using two different excitations, impact weight and ambient conditions. The data dependent system (DOS) approach based on a vector autoregressive model (ARV), was used to extract the dynamic parameters from the recorded data. Finite element model was constructed to support and validate the dynamic measurements. The results show good agreement between the measured and computed natural frequencies and mode shapes, even without supplementary tuning. For the impact test, at least seven modes in the range of 0-10 Hz are completely identified. For the ambient test, the higher mode shapes could not be identified when using ARV-model. Acknowledgement: This research work is a part of the research project supported by the Flemish Government Institute IWT. IWT 8 References [1] Flesch, R., A dynamic method for the safety inspection of large prestressed bridges, CEEC, TH - Aachen, March, [2] Flesch, R. and Kernbichler, K., Diagnostic dynamic testing of bridges on Brenner motorway, International Conference on Bridge Management, University of Surry, Guildford, U.K., March, [3] Deger, Y., Cantien, R. and Pietrzko, S., Modal analysis of an arch bridge: experimental, finite element analysis and link, Proceedings of the 12* International Modal Analysis Conference, Honolulu, Hawaii, February, [4] Flesch, R. et al., The significance of system identification for diagnostic dynamic testing of bridges, Proceedings EURODYN 90, European conference on structural dynamics, [5] Pandit, S., Modal and spectrum analysis: data dependent system in state space, John Wiley & Sons, [6] Pandit, S.W. and Metha, N.P., Data dependent systems approach to modal analysis via state space, ASME paper n 85 -WA/DSC- 1,1985. [7] De Roeck, G, Abdel Wahab, M. and Claesen, W., System identification using the data dependent system method, Version 1.1, Department of Civil Engineering, Katholieke Universiteit te Leuven. [8] ANSYS, revision 5.0, Swanson Analysis Systems, 1992 [9] Heylen, W., Lammens, S. and Sas, P., Modal analysis theory and testing, Department of Mechanical Engineering, K.U.Leuven, 1995.