DAMAGE IDENTIFICATION ON THE Z24-BRIDGE USING VIBRATION MONITORING

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1 DAMAGE IDETIFICATIO O THE Z4-BRIDGE USIG VIBRATIO MOITORIG Johan Maeck, Bart Peeters, Guido De Roeck Department of Civil Engineering, K.U.Leuven W. de Croylaan, B-300 Heverlee, Belgium johan.maeck@bwk.kuleuven.ac.be SUMMARY: In the frame of developing a non-destructive damage identification technique, vibration monitoring is a useful evaluation tool that relies on the fact that occurrence of damage in a structural system leads to changes in its dynamic properties. The damage identification techniques are based on the observed shifts in eigenfrequencies and modeshapes and relate the dynamic characteristics to a damage pattern of the structure. The presented technique makes use of the calculation of modal bending moments and curvatures to derive the bending stiffness at each location. Damage identification results are compared with results from a classical sensitivity based updating technique. The basic assumption in both techniques is that damage can be directly related to a decrease of stiffness in the structure. Damage assessment techniques are validated on the progressively damaged prestressed concrete bridge Z4 in Switzerland, tested in the framework of the BriteEuram project SIMCES. A series of full modal surveys are carried out on the bridge before and after applying a number of damage scenarios. KEYWORDS: damage identification, vibration monitoring, prestressed concrete bridge ITRODUCTIO As an alternative for damage identification by updating of a finite element model, a method of damage detection and quantification is developed, called direct stiffness determination. The direct stiffness calculation is based on the relation that the bending stiffness in each section of a structure can be written as the quotient of the bending moment to the corresponding curvature. Besides experimental eigenfrequencies, also modeshapes are needed to calculate curvatures. The method is explained and then applied to experimental data. For a more in-depth explanation of the method is referred to Maeck & De Roeck [4], Maeck et al. [3]. In the framework of Brite Euram project BE SIMCES (System Identification to Monitor Civil Engineering Structures), the technique is applied to a prestressed concrete bridge in Switzerland to detect, localise and quantify artificially applied damage.

2 The test set-up and damage scenarios are described, and the solution procedure and experimental validation results are given, and compared to results from finite element model updating. DIRECT STIFFESS CALCULATIO The direct stiffness calculation uses the experimental eigenfrequencies and modeshapes in deriving the dynamic stiffness. The method makes use of the basic relation that the dynamic bending stiffness (EI) in each section is equal to the bending moment (M) in that section divided by the corresponding curvature (second derivative of bending mode ϕ b ). Firstly the moment in each section of the structure has to be determined. The eigenvalue problem for the undamped system can be written as: EI d M b ϕ dx = () K ϕ = ω M ϕ () in which K is the stiffness matrix, M the (analytical) mass matrix, ϕ the measured modeshape and ω the measured eigenpulsation. This can be seen as a pseudo static system: for each mode internal (section) forces are due to inertial forces which can be calculated as the product of local mass and local acceleration (= ω.ϕ). The mass distribution is assumed to be known. A lumped mass matrix is used in Eqn.. As the measurement mesh is rather dense, this is acceptable. To calculate the modal internal forces (i.e. modal bending moments) needed to evaluate Eqn., a (hyper)static analysis with the pseudo-static forces from Eqn. as load has to be carried out e.g. with a finite element package. The next step in deriving the dynamic bending stiffness consists of the calculation of the curvatures along the beam for each modeshape. Direct calculation of curvatures from measured modeshapes e.g. by using the central difference approximation, results in oscillating and inaccurate values. A smoothing procedure, which accounts for the inherent inaccuracies of the measured modeshapes, should be applied. Therefore a weighted residual penalty-based technique is adopted which closely resembles the finite element approach. The structure is divided in a number of elements separated by nodes that correspond to the measurement points. Each node has 3 degrees of freedom: the modal displacement v a, the rotation ψ and the curvature κ, which are approximated independently (Fig. ). Linear shape functions i are used. Fig. : Finite element variables v = v + v = + = + The approach is analogous to the Mindlin plate element, for which the rotations are approximated independently from the bending deflection.

3 The objective function, which has to be minimised, contains the difference between approximate and measured modeshapes. Two penalty terms are added to enforce continuity of rotations and curvatures in a mean, smeared way. e (v ϕ = m ) / dv / d dx + ( ) dx + ( ) dx dx dx ϕ m denotes the measured modeshape, and L e is the length of a finite element. Elements are chosen in such way that nodes coincide with measurement points. The first term expresses that the average difference between approximation and measurement has to be minimised. Without any other terms in the objective function one will find a (piecewise linear) approximation through all measurement points. In order to obtain a filtering of experimental errors and so a smoothing of the deflection, two extra terms are added. Differences between the independent approximations of rotations and curvatures with respectively the first derivatives of displacements and rotations are minimised. The coupling between the independently approximated unknowns is established by these constraint conditions. The weight of these extra conditions is set by the dimensionless penalty factors α and β. Deriving Eqn.3 to the unknown variables v, ψ and κ gives a system of dimension three times the number of nodes. As α and β are penalty terms, they are not unknowns in the system but must be chosen by the user. Advantages of this Mindlin approach are that directly curvatures are available, that boundary conditions can be imposed easily and that the approximated modal deflections have not to go through all measurement points. A drawback is that penalty factors must be chosen in an allowable range: large enough to be effective and not too large to avoid numerical difficulties (locking of the system). The direct stiffness calculation uses the experimental modeshapes in deriving the dynamic stiffness. For hyperstatic systems, the reaction forces and consequently the internal forces are dependent of the stiffness of the structure. Therefore an iterative procedure is needed to find the EI distribution of the structure. e 4 (3) Bridge description TEST SET UP The bridge used for validation is bridge Z4 in Canton Bern, Switzerland, connecting Koppigen and Utzenstorf. The bridge is a highway overpass of the A, linking Bern and Zürich (Fig. ). Z4 is a prestressed bridge, with three spans, two lanes and 60m overall length. The geometry is plotted in Fig. 3. Fig. : View of Z4 bridge

4 Damage scenarios Fig. 3: Top view, cross section, elevation (Krämer et al. []) Within the SIMCES project a series of progressive damage tests have been carried out during the summer of 998. For a full description of all damage scenarios, instrumentation and safety considerations is referred to Krämer et al. []. The first 8 scenarios are summarised in Table. # Date Scenario st reference measurement nd reference measurement settlement of pier, 0mm settlement of pier, 40mm settlement of pier, 80mm settlement of pier, 95mm tilt of foundation rd reference measurement Table Damage scenarios on Z4 The settlement is simulated by cutting the Koppigen pier and removing about 0.4m of concrete. Lowering and lifting was done by 6 hydraulic jacks. During the tests the pier rested on steel sections with similar stiffness as the uncut concrete section. Other damage scenarios (spalling of concrete, landslide, cut of concrete hinges, failure of anchor heads, rupture of tendons) are not considered here as they caused no or a minor degradation of bending stiffness. Solution procedure The experimental eigenfrequencies and standard deviations for the first five modes are summarised in Table for the different reference measurements and damage scenarios.

5 Processing of the measurements is done by the stochastic subspace identification method (Peeters & De Roeck [6]). # Mode Mode Mode 3 Mode 4 Mode 5 f σ f f σ f f σ f f σ f f σ f Table : Eigenfrequencies and standard deviation for bridge Z4 (PDT) In order to find the internal bending moments in the bridge, a hyperstatic analysis is needed. Therefore an ASYS [] beam model is used. The model consists of beam elements for the girder, piers and abutment piers. The cross-section area, area moment of inertia and torsional moment of inertia are precalculated and given as input for the elements. An angle of rotation is defined to account for the skewness of the bridge. Soil under the pier foundation and cantilever ends at the abutments are represented by spring elements. The boundary conditions (soil spring stiffnesses) which can change for different scenarios are found by sensitivity based updating (SIMCES report [8]). This is done for reference measurements and 3. Due to the tilting operation, a change in soil springs under the Koppigen pier is found after updating. MATLAB ASYS experimental eigenfrequencies experimental modes Mindlin approach: curvatures inertia forces:.m. EI distribution F.E. model: mass distribution M hyperstatic analysis: internal forces Fig. 4: Direct stiffness calculation scheme For hyperstatic systems, the reaction forces and consequently the internal forces are dependent on the stiffness of the structure. Therefore an iterative procedure is needed to find the internal moments with the adjusted EI distribution of the structure in the case of damage. The smoothing of the modeshapes using the Mindlin approach and the curvature calculation is done within the package MATLAB [5]. The procedure for the direct stiffness calculation is given in Fig. 4. The EI distribution is calculated using the first bending mode of the bridge. Fig. 5 shows the st mode of Z4 for the nd reference measurement.

6 Mode f = 3.98Hz xi = 0.93% z y x Fig. 5: First modeshape of Z4 (SIMCES report [7]) EXPERIMETAL VALIDATIO In the visualisation of the bending stiffness the inaccurate zones due to zero by zero division (see Eqn.) are omitted. For the first mode four inaccurate zones are present: at the bridge abutments and at two points of the central span, close to the bridge piers. It turned out that higher modes with more inaccurate zones give unsatisfactory EI estimations. The direct stiffness calculations for damage scenarios are compared with the scenarios without any damage. Also the bending stiffness from the ASYS finite element model of the undamaged bridge is given. Firstly the nd reference test carried out after cutting the Koppigen pier and installing the steel plates, and the settlement scenarios are compared. The dynamic bending stiffness distribution for the nd reference test and the scenario with 40mm settlement (Fig. 6a) corresponds well along the length of the bridge, except at the inner side of the pier which was subjected to the settlement (Koppigen pier at 46.7m). Curvatures are rather small in the side spans, which causes numerical difficulties to calculate EI. Also the higher stiffness of the girder box beam at the girder-pier connections due to the increased thickness of the lower slabs, is clearly detectable from the direct stiffness determination. Another observation is that the Koppigen pier seems to be stiffer than the Utzenstorf pier. bending stiffness EI 3.0E+0.8E+0.6E+0.4E+0.E+0.0E+0.8E+0.6E+0.4E+0 Ansys Reference.E+0 Settlement 40mm.0E bending stiffness EI 3.0E+0.8E+0.6E+0.4E+0.E+0.0E+0.8E+0.6E+0.4E+0 Ansys Reference.E+0 Settlement 80mm.0E Fig. 6: EI for scenario &4 (a) & &5 (b)

7 From Fig. 6b, the stiffness degradation due to the settlement of 80mm is clearly visible. It seems that the largest decrease of stiffness is localised in the mid-span, although it remains difficult to conclude something from the side span calculations. Also the stiffness of the pierbridge connection itself at the Koppigen side has substantially changed (7%). When considering the results for the settlement of 95mm (Fig. 7a), the stiffness degradation is even more pronounced. Also the region of the affected zone of the girder in the mid-span is wider. A maximum stiffness decrease of about 30% is noticed. bending stiffness EI 3.0E+0.8E+0.6E+0.4E+0.E+0.0E+0.8E+0.6E+0 bending stiffness EI 3.0E+0.8E+0.6E+0.4E+0.E+0.0E+0.8E+0.6E+0.4E+0.E+0 Ansys Reference Settlement 95mm.4E+0.E+0 Ansys Reference Reference 3.0E Fig. 7: EI for scenario &6 (a) & &8 (b).0e After the settlement is reversed and the bridge is brought back in its initial position, a new reference measurement is done. From application of updating it turned out that the spring support under the Koppigen pier was changed due to the tilting operation of the pier. However the bending stiffness should be again the initial one (as in reference ) as the cracks close by removing the settlement. This is illustrated by Fig. 7b, which proves that cracks can only be detected when they remain opened. FIITE ELEMET MODEL UPDATIG The used method (SIMCES report [8]) minimizes in an iterative manner the differences between numerical and experimental modal parameters. The resulting least-square problem is solved by the Gauss-ewton method. Practical implementation of the Gauss-ewton method relies upon the application of the singular value decomposition. The Gauss-ewton equation is similar to the truncated Taylor series used in the penalty function method (Friswell & Mottershead [9]). The penalty function equation can be written in the following form: S δθ - δz = 0 (4) where δz is the discrepancy between the measured modal data and the finite element solution. δθ is the perturbation in the unknown parameters to be updated. S is the Jacobian or sensitivity matrix containing the first derivative of the calculated modal parameters (z) with respect to the unknown parameters (θ). The sensitivity matrix S is defined as the first derivative of the modal parameters (z) with respect to the unknown parameters (θ). A finite difference approximation is used to calculate the elements of the sensitivity matrix.

8 To reduce the number of update parameters a function is proposed that can describe a damage pattern by only few representative parameters and that has the flexibility to represent small as well as large damage zones. Assuming that the reduction in the bending stiffness can be simulated by a reduction of the E-modulus, the following function is proposed. Details are found in Maeck et al. [0]. Fig. 8: Damage function The stiffness decrease along the beam is represented in Fig. 9, and shows that the decrease is at maximum 5% of the initial bending stiffness, which corresponds with the results from direct stiffness calculation (Fig. 7a). The damage function is implemented in a nonsymmetrical way. The biggest decrease is observed at the left side of the settled pier (pier at 46.5m). 0.9 EI/EIo distance along bridge (m) Fig. 9: Relative stiffness decrease along bridge While the modeshape information is explicitly used in the case of direct stiffness calculation, it is also implicitly used in updating. Changes of modal displacements are needed to determine at which side the damage in the structure occurred, what is impossible by using only eigenfrequency information as the bridge is point-symmetrical. To illustrate the important influence of damage, results are presented for the 5 th modeshape, which can be characterised in the undamaged case (Fig. 0a) as a symmetrical bending mode with high modal displacements of the sidespans. In Fig. 0b one notices that the symmetrical character of the modeshape disappears in the mid-span as well as the side-spans.

9 Mode 5 f =.69Hz xi =.4% z y x Mode 5 f =.Hz xi =.3% z y x Fig. 0: Fifth modeshape of undamaged bridge (a) and after settlement (b) COCLUSIO Direct stiffness calculation seems to be a good alternative for other detection methods like sensitivity based updating techniques. Despite of numerical inaccuracies at some locations of the bridge, damage was clearly observed and localised for settlements of 80mm and 95mm. Also the recovery of stiffness by removing the settlement and thus closing the cracks at the Koppigen pier is clearly demonstrated. For the considered bridge higher modes seem to give bad results due to more numerical inaccuracies. As a manner of improving the method, curvatures could be determined experimentally, which is under investigation at the moment. Eigenfrequencies as well as modal displacements (and its derivatives) are useful damage indicators. ACKOWLEDGEMET The research has been carried out in the framework of the BRITE-EURAM Program CT SIMCES with a financial contribution by the Commission. Partners in the project are: K.U.Leuven (Department Civil Engineering, Division Structural Mechanics) Aalborg University (Insitut for Bygningsteknik) EMPA (Swiss Federal Laboratories for Materials Testing and Research, Section Concrete Structures) LMS (Leuven Measurements and Systems International.V., Engineering and Modeling) WS Atkins Consultants Ltd. (Science and Technology) Sineco Spa (Ufficio Promozione e Sviluppo) Technische Universität Graz (Structural Concrete Institute)

10 REFERECES [] ASYS revision 5.5., Swanson Analysis System, 999 [] Krämer C., De Smet C.A.M., De Roeck G., Z4 Bridge Damage Detection Tests, Proceedings of IMAC XVII, Kissimmee, Florida, USA, 999 [3] Maeck J., Abdel Wahab M., De Roeck G., Damage detection in reinforced concrete structures by dynamic system identification, Proceedings of. ISMA3, pp , Leuven, Belgium, 998 [4] Maeck J., De Roeck G., Dynamic bending and torsion stiffness derivation from modal curvatures and torsion rates, J. Sound & Vibration, V.5(), pp.53-70, 999 [5] MATLAB revision 5.3, The Mathworks Inc., 999 [6] Peeters B., De Roeck G., The performance of time domain system identification methods applied to operational data, Proceedings of DAMAS 997, pp , Sheffield, UK, 997 [7] SIMCES Task B Internal report Dec.998, Peeters B., De Roeck G., Stochastic subspace identification applied to progressive damage test vibration data from the Z4 bridge, KUL, Leuven, Belgium. [8] SIMCES Task D Internal report Feb.998. Updating applied to bridge Z4, KUL, Leuven, Belgium. [9] Friswell, M.I. and Mottershead, J.E., Finite element model updating in structural dynamics, KLUWER Academic Publisher, Dordrechts, The etherlands, 995. [0] Maeck J., Abdel Wahab M., De Roeck G., Damage detection in reinforced concrete structures by dynamic system identification, Proceedings ISMA 3, oise and Vibration Engineering, pp , Leuven, Belgium, 998