IOMAC'13 5 th International Operational Modal Analysis Conference 2013 May 13-15 Guimarães - Portugal RELATIONSHIP BETWEEN DAMAGE AND CHANGE IN DYNAMIC CHARACTERISTICS OF AN EXISTING BRIDGE Takeshi Miyashita 1, Kazuya Tamada 2, Hidenori Iwasaki 3 and Masatsugu Nagai 4 ABSTRACT The objective of this study is to understand the relationship between damage and changes in the dynamic characteristics of an existing bridge as a contribution toward vibration-based structural health monitoring. The bridge that is the focus of this study is a demolished pedestrian bridge composed of a composite steel girder with two main girders. The first case of damage that was examined involved slits that were made by gas cutting on a lower flange in the lateral direction. Next, an outstanding in the lower flange was removed along the span. Vibration measurement was carried out for each case of damage. Our results confirmed that the natural frequencies decreased depending on the degree of damage. The rate of reduction of this decrease was greater in those modes that were without torsion. As a form of reproducible analysis, finite element analysis was carried out, whose results showed a similar reduction in the natural frequency measurements. Keywords: Steel bridge, Vibration,, Dynamic characteristics, System identification, FEA 1. INTRODUCTION The deterioration of bridges has progressed rapidly. There is a strong need, therefore, to develop effective quantitative techniques that can be applied to bridge maintenance. A great deal of research has been conducted on ways of diagnosing the structural integrity of a bridge or detecting damage, by focusing on changes in a bridge s dynamic characteristics, such as its natural frequency or mode shape, as identified by vibration measurements [1]. Remarkable advances have been made in hardware related to the measurement of bridge vibrations. Examples of this include laser devices [2] and a wireless network [3], among others. On the other hand, very little research has been done on the relationship between structural damage and changes in the dynamic characteristics of an existing bridge [4]-[6]. In such research, however, since the number of damage to the study bridges is comparatively a little, it makes difficult to generalize the results. It is for this reason that the present research is based on an existing bridge that has experienced substantial 1 Associate Professor, Nagaoka University of Technology, mtakeshi@vos.nagaokaut.ac.jp 2 Professor, Maizuru National College of Technology, tamada@maizuru-ct.ac.jp 3 Director, Office of Civil Engineering, Chutan East, Kyoto Prefecture, h-iwasaki74@pref.kyoto.lg.jp 4 Professor, Nagaoka University of Technology, nagai@nagaokaut.ac.jp
100 100 520 ~743 4000 4000 30 100 T. MIYASHITA, K. TAMADA, H. IWASAKI, M. NAGAI Figure 1 The bridge analyzed in this study West 28480 40 28400 40 East 14.900 3300 400 2500 400 Asphalt pavement t=30~49 mm Slab t=140 mm 1.5 % 1.5 % PC pile Φ500 L=14.50 m 10.800 10.800 PC pile Φ500 L=14.50 m -3.500 750 1800 750 (a) Side view Figure 2 Schematic drawing (unit: mm) (b) -section lot damage, in order to investigate the correlation between damage and changes in the bridge s dynamic characteristics. Moreover, analytical investigation is carried out in order to provide a reproducible form of analysis, using finite element analysis (FEA). 2. OUTLINE OF MEASUREMENT PROCESS 2.1. The study bridge The bridge considered in this study is a pedestrian bridge located in Maizuru City, Kyoto Prefecture. A photo of the bridge is shown in Fig.1, and a schematic drawing is shown in Fig.2. Demolition of this bridge was planned in relation to the widening of a neighboring road bridge. Structurally, the bridge, which was constructed in 1985, is a composite steel girder bridge with two main girders. It consists of a single span that has a length of 27.9 m and a width of 3.3 m. The bridge is supported by line bearings, which are a fixed-end type on the west side and a roller-end type on the east side. Vibration measurement was conducted from September 9 to 11, 2010. 2.2. Arrangement of sensors After removing the asphalt pavement on the bridge, fourteen servo accelerometers were installed on an RC slab above the main girders, as shown in Fig.3. The accelerometers were equidistantly positioned over the length of the span. Ambient vibration measurements were then conducted for each case of damage, as is explained in the next section. The measurement axis was in the vertical direction. The sampling frequency was 200 Hz, and the measurement time was 20 min for each damage case. 2.3. Cases of The damage cases explained below are referenced in Fig.4 and Table 1. The types of damage are divided into two cases, which are called damage series 1 and damage series 2. In damage series 1, slits were made by gas cutting on an outstanding of a lower flange in a main girder on the downstream side, as shown in Fig.5. The width of the slit was about 10 mm, and the 2
5 th International Operational Modal Analysis Conference, Guimarães 13-15 May 2013 Figure 3 Arrangement of sensors (unit: mm) Downstream 28400 8400 11600 8400 250 130 1480 1520 1520 1520 1300 15 665 665 485 1550 1550 1550 1550 1550 1550 485 665 665 15 1300 1520 1520 1520 1480 130 250 Web 9 10 1 3 4 5 6 7 8 11 12 13 14 15 16 2 1 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 15 19 2 1 3 4 5 6 7 8 9 10 11 12 13 14 15 16 2 20 22 23 24 25 26 27 28 29 30 31 32 33 34 35 21 7 6 5 4 3 2 1 Lower flange Gusset Gusset West East Gusset Gusset Web Lower flange 14 13 12 11 10 9 8 Figure 4 Locations of damage (unit: mm) (Non-italicized numbers: sensor numbers; italicized numbers: damage numbers; Numbers enclosed within a circle: damage cases) completely off the edge after removal of the slag produced by the gas cutting. First, this damage was inflicted on both ends of the girder (damage cases 1 and 2), since damage in an existing bridge frequently appears on the girder ends. Next, slits were cut from west to east at intervals, as shown in Fig.4, in order to avoid the gusset s. In damage cases 8 and 9, however, two and three slits, respectively, were made at one time, because of time constraints. The total number of damage cases was 16. In damage series 2, the outstanding was removed by gas cutting in order to increase the degree of change in the dynamic characteristics. This assumes the loss of a cross-section by corrosion. New slits were made along the welding line on the lower flange between the slits made in damage series 1, as shown in Fig.6. However, for purposes of work safety, the outstanding was not completely cut off. The length of the connection between the outstanding and the web was about 100 mm. In this damage series as well, the outstanding completely off the edge after the removal of the slag produced by the gas cutting. The total number of instances of this damage case was also 16. In summary, 32 instances of damage were inflicted on the study bridge, step by step, and the ambient vibration was measured in each case. The temperature of the bridge was not measured in the vibration measurement process. As a reference, then, Table 1 includes the temperatures on the dates of measurement, as recorded at the Maizuru Japan Meteorological Agency observatory, which is near the bridge site. 3
T. MIYASHITA, K. TAMADA, H. IWASAKI, M. NAGAI # series case Location of damage 1) (mm) Date Meas. end time Table 1 cases Temp. 2) ( ) # series case Location of damage 1) (mm) Date Meas. end time 0 - - - 8:37 26.8 20 130 ~ 1,610 10:27 28.4 1 130 11:28 28.3 21 26,290 ~ 27,770 11:39 30.1 2 27,770 12:05 27.9 22 1,610 ~ 3,130 12:39 32.2 3 1,610 13:12 28.9 23 3,130 ~ 4,650 Sept. 10 13:30 32.5 4 3,130 13:28 28.9 24 4,650 ~ 6,170 2010 14:13 32.4 5 4,650 13:48 29.3 25 6,170 ~ 7,470 14:48 31.7 6 6,170 14:06 29.1 26 9,300 ~ 10,850 15:32 31.2 7 7,470 Sept. 9 14:25 28.8 27 10,850 ~ 12,400 16:19 30.0 2 8 9,300 2010 14:44 28.4 28 12,400 ~ 13,950 16:59 29.3 9 10,850 29 13,950 ~ 15,500 9:11 28.5 10 1 12,400 15:14 28.2 30 15,500 ~ 17,050 10:12 31.7 11 13,950 31 17,050 ~ 18,600 Sept. 11 10:53 32.8 12 15,500 32 20,430 ~ 21,730 2010 11:49 34.2 15:38 28.6 13 17,050 33 21,730 ~ 23,250 13:28 31.9 14 18,600 15:57 27.9 34 23,250~ 24,770 14:04 32.6 15 20,430 16:13 28.0 35 24,700 ~ 26,290 14:54 31.0 16 21,730 16:32 27.7 17 23,250 Spet. 10 8:57 25.1 18 24,770 2010 9:12 26.1 19 26,290 9:26 26.7 1) Distance from fixed-end on the west side 2) Maizuru Japan Meteorological Agency observatory Temp. 2) ( ) Figure 5 series 1 Figure 6 series 2 3. MEASUREMENT RESULTS 3.1. Identification of dynamic characteristics In order to understand the dynamic characteristics statistically, datasets for durations of 100 s were extracted from the raw data, with 10 s of overlap between each case. In each case, the number of datasets was 20. The NExT-ERA [7] and [8] method was adopted for the identification of dynamic characteristics, using MATLAB. The reference point in NExT was set to be measurement point 2, as shown in Fig.3, when calculating the cross-correlation function. Here, the auto-correlation function was calculated for the reference point. Then, output-damped free vibrations in 90 s intervals from NExT became inputs to the ERA method. Fig.7 shows the mode shapes without damage that were identified. 3.2. Relationship between damage and dynamic characteristics 3.2.1. Natural frequency Fig.8 shows the changes in natural frequencies that were identified. Here, the horizontal axis in Fig.8 indicates the numeration of the damage cases presented in Table 1. On the vertical axis, f n0 and f nd indicate the natural frequencies in the nth order without and with damage, and the ratio of change in the natural frequencies, respectively. From the figure, the following observations can be made. 4
5 th International Operational Modal Analysis Conference, Guimarães 13-15 May 2013 East 東側 Down stream 下流側 西側 West (a) 1st mode (around 3.5 Hz) (b) 2nd mode (around 6.0 Hz) (c) 3rd mode (around 9.0 Hz) (d) 4th mode (around 13.5 Hz) (e) 5th mode (around 20.0 Hz) (f) 6th mode (around 22.5 Hz) Figure 7 Identified mode shapes indicating no damage Figure 8 Change in the ratio of natural frequencies ( : mode with torsion, : mode without torsion) Figure 9 3rd mode The natural frequencies decrease as the damage progresses. The ratio of change in damage series 2 is large, since the loss of a cross-section in that series is larger than is the case in damage series 1. However, we are still able to recognize an increase in the natural frequencies, despite the damage inflicted, as shown in Fig.8. This reason for this will be discussed later. The ratio of change in the natural frequencies is larger in the mode without torsion. The reason for this is that the damage inflicted upon the lower flange does not affect the torsional rigidity of the pseudo-box section, which consists of a slab and a lower cross-. The ratio of change in the natural frequencies is largest in the 3rd mode. The reason for this is that this mode is easily excited, as is known from the Fourier spectral amplitude that was calculated from the acceleration response. 5
T. MIYASHITA, K. TAMADA, H. IWASAKI, M. NAGAI We next investigated in detail the natural frequency in the 3rd mode, which shows the largest correlation with damage. Fig.9 shows the change in the ratio of the natural frequency in the 3rd mode, with a standard deviation of ±1σ. As a reference, the figure also includes the temperature on the study dates, as recorded at the Maizuru Japan Meteorological Agency observatory. From Fig.9, we can make the following observations. (a) Full model Figure 10 FEA model of the study bridge (b) floor system The natural frequency decreased by about 8.2% relative to the initial state, following the complete removal of the outstanding on the lower flange in damage series 2. The natural frequency increased slightly up to approximately 0.03 Hz, despite the damage that was inflicted. This change corresponds to the change in the date of measurement. Since the temperature at the time when measurement began was lower than it was at the end of measurement on the previous day, the decrease in temperature could be one reason for the increase in the natural frequency. Other factors could be the influence of traffic-induced vibration from the neighboring bridge, or the numerical parameters used in the NExT-ERA method. 3.2.2. Damping ratio and mode shape The identified damping ratios reveal no correlation between the damage cases and the damping ratios. Since the slits that were made by gas cutting were about 10 mm in width and the outstanding was completely cut off, it seems that the damping ratios did not change. This behavior is not similar to that in fatigue cracks, in which the friction force is increased by the opening of the crack. In addition, as reported in references [4] and [5], there was no correlation between the damageand the damping ratios, since the slits in a bridge that were made by gas cutting were similar to those made in this research. Moreover, we cannot recognize any obvious changes in the mode shapes that resulted from the damage. As was also reported in references [4] and [5], the change in mode shape was small, after calculating the modal assurance criterion (MAC) for the mode shapes without and with damage. However, we also hypothesize that the curvature of the mode shapes is an effective means of damage detection in bridges. This will be the subject of future research. 4. ANALYTICAL STUDY BY FEA 4.1. Outline of analysis In the creation of an FEA model of the study bridge, its main girders, cross-s, lateral bracings, and its RC slab, including its curb-stones, sole s at the points of support, and gusset s were considered, using Diana 9.3. Here, the shape of the main girders was accurately modeled as a 3.2% parabola that is convex on the upper flange. The asphalt pavement was not considered, though, because it had already been removed when vibration measurement was carried out. The handrails were also not considered, even though they had not been removed, because their mass constituted about 2.4% of the total mass, so their influence on the dynamic characteristics was negligible. The following elements were utilized for the FEA model: a four-node shell element for the main girders, vertical stiffeners, cross-s, and gusset s. We also utilized an eight-node solid 6
5 th International Operational Modal Analysis Conference, Guimarães 13-15 May 2013 (a) 1st mode (b) 2nd mode (c) 3rd mode (d) 4th mode (e) 5th mode element for the RC slab, and the truss element for the lateral bracings. The connection between the upper flange of the main girder and the slab was modeled by sharing the nodal points of the shell and the solid elements. Fig.10 shows the FEA model that was constructed. The numbers of nodal points and elements were 44,643 and 40,302, respectively. The position of the boundary condition of the FEA model is at the nodes that connect the vertical stiffeners at the point of support with the lower flanges. A preliminary analysis shows that when the boundary condition is set to be fixed-fixed ends with regard to displacement, with only rotations in the lateral direction being allowed, the analytical results for the case without damage agree well with the measurement results. This is the reason why the roller bearings did not move longitudinally, since the amplitude of vibration was small under the ambient vibration. We therefore adopted this boundary condition for the FEA model. Next, eigenvalue analyses were carried out, by applying the same damage as would occur in an actual scenario to the FEA model. 4.2. Relationship between damage and dynamic characteristics (f) 6th mode Figure 11 Comparison of FEA with measurement results Fig.11 shows the change in the ratio of the natural frequencies for each damage case, together with the measurement results. As can be seen in Fig.11, both sets of results are generally in agreement. The FEA also reveals that the change in the ratio of the natural frequency with torsion became small, a finding that is similar to the measurement results. In the 2nd mode, however, there was a difference between the measurement results and the FEA. When the boundary condition of the FEA model was 7
T. MIYASHITA, K. TAMADA, H. IWASAKI, M. NAGAI set to be roller-end at the fixe-end, the change in the ratio of the natural frequency became about 2.6%, and was close to the measurement results. Although this difference is the result of the difference in the boundary condition, we have not yet been able to identify the cause of this. 5. CONCLUSIONS The aim of this research was to understand the relationship between damage and the dynamic characteristics of an existing bridge. Ambient vibration measurement was carried out for a demolished pedestrian bridge. Moreover, finite element analysis (FEA) was carried out as a form of reproducible analysis. From our research, we were able to draw the following conclusions. 1) The largest correlation was found between the change in the ratio of the natural frequency in the 3rd mode and damage. The change in the ratio from the initial to the final states was about 8.2%. The reason for this is that the 3rd mode is easily excited, as was deduced from the measurement results. This generalization, however, is a subject for future research, since the excited mode is dependent on the structural form or the length of the span. 2) The change in the ratio of the natural frequency with torsion was larger than it was without torsion. The reason for this is that the damage inflicted on the lower flange does not affect torsional stiffness of the pseudo-box section, which consists of the slab and the lower lateral bracings. 3) The natural frequencies increased slightly, despite the damage that was inflicted. One reason for this could be the decrease in temperature. Other factors could be the influence of traffic-induced vibration from the neighboring bridge, or the numerical parameters used in the calculation. 4) No correlation was found between the damping ratio and the damage inflicted, a finding that is similar to that of previous research. Moreover, a change in mode shapes due to the inflicted damage was not confirmed. 5) A detailed FEA model was constructed for the study bridge. Eigenvalue analyses were then carried out for the same damage as would be experienced in a real situation. A preliminary analysis shows that when the boundary condition was set to be fixed-fixed ends with regard to displacement, with only rotations in the lateral direction being allowed, the analytical results for the case without damage agreed well with the measurement results. Thus, the FEA results are consistent with the measurement results. REFERENCES [1] Boller, C. et al. (Editors) (2009) Encyclopedia of structural health monitoring, Wiley. [2] Nagayama, T., Urushima, A., Fujino, Y., Miyashita, T., Yoshioka, T. and Ieiri, M. (2012) Dense vibration measurement of an arch bridge before and after its seismic retrofit using wireless smart sensors, Proc. SPIE 8345, 834536, Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems, San Diego, California. [3] Miyashita, T., Ishii, H., Kubota, K. and Fujino, Y. (2007) Advanced vibration measurement system using laser Doppler vibrometers for structural monitoring, Proc. Int. Conf. Experimental Vibration Analysis for Civil Engineering Structures, Porto, Portugal, 132-133. [4] Farrar, C. R. and Jauregui, D. A. (1998) Comparative study of damage identification algorithms applied to a bridge: I. Experiment, Smart Materials and Structures, 7(5), 704-719. [5] Maeck, J. and De Roeck, G. (2003) Description of Z24 benchmark, Mechanical Systems and Signal Processing, 17(1), 127-131. [6] Peeters, B. and De Roeck, G. (2001) One-year monitoring of the Z24-Bridge: Environmental effects versus damage events, Earthquake Engineering and Structural Dynamics, 30(2), 149-171. [7] Farrar, C. R. and James III, G. H. (1997) System identification from ambient vibration measurements on a bridge, Journal of Sound and Vibration, 205(1), 1-18. 8
5 th International Operational Modal Analysis Conference, Guimarães 13-15 May 2013 [8] Juang, J. N. and Pappa, R. S. (1985) An eigensystem realization algorithm for modal parameter identification and model reduction, Journal of Guidance, Control and Dynamics, 8(5), 620-627. 9