VIBRATION-BASED DAMAGE DETECTION IN A CABLE STAYED-BRIDGE.

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1 VIBRATION-BASED DAMAGE DETECTION IN A CABLE STAYED-BRIDGE More info about this article: Zahrasadat Momeni a, Ardalan Sabamehr b, Ashutosh Bagchi c and Mazdak Nik-Bakht d a,b PhD student, b Professor, c Assistant Professor a, b, c Department of Building, Civil & Environmental Engineering, Concordia University Montréal, QC, H3G 1M8, Canada (514) ABSTRACT a zahra.momeni24@yahoo.com b sabamehrardalan875@gmail.com c ashutosh.bagchi@concordia.ca d mazdak.nikbakht@concordia.ca Cable-supported bridges, such as cable suspension bridges and cable stayed bridges, are critical lifeline structures. Cable stayed bridges have a structural system, effectively composed of cables, the main girder and towers. Such systems are characterized by a long fundamental period; and are also flexible and lightweight structures with a low structural damping; a combination which makes this type of bridges vulnerable in large amplitude vibrations due to earthquake or wind excitation. A strong earthquake could heavily damage different parts of such bridges. Vibration monitoring and modal analysis play an important role in identifying structural conditions of such structures and aid in detection of damage or distress. Modal analysis involves the field measurement of vibration response, and estimation of natural frequency and mode shape vectors through a process of system identification. On the other hand, dynamic characteristics of a structure change when damage occurs in the structure. Vibration-based damage detection technic is an important tool for cable-stayed bridge due to its efficiency, cost-effectiveness and ease of application. Damage detection in a reliable way in order to facilitate effective maintenance that helps keeping the structure in good condition and extending its service life. In this study, one of the mode shape based technique which is called Mode Shape Curvature (MSC) method has been used to detect the damage. One of the main goals of this study is to consider the seismic response of the bridge under multiple support excitations for identifying the extent of the inflicted damage to the bridge caused by strong ground motion. In this study, the Quincy Bayview Bridge on the Mississippi river, Illinois, US has been studied. This bridge was designed in 1983 and its construction was completed in Total length of the bridge is 542 m including the 274 m main span and two equal 134 m side span. The bridge consists of two H-shaped concrete towers, double-plane fan type cables, and a composite concrete-steel girder bridge deck. There are a total of 56 cables and the width of the deck from center to center of cables is 12 m. Nonlinear dynamic time history analysis has been performed by the of ABAQUS software, through applying displacement time history corresponding to a set of spectrum compatible artificial ground motion records to the supports of the bridge. The results indicate that the Mode shape curvature method is efficient for detecting

2 damages. Knowing that the dynamic characteristics of the bridge are continuously changing while the main supports of the bridge are undergoing different motions during the earthquake event and consequent damage. The results of modal analysis of bridge under extreme displacements of the supports have been used for damage estimations of the bridge. Keywords: Cable-Stayed Bridge, Health Monitoring, Vibration Based Damage Identification, Mode Shape Curvature method 1. Introduction Due to aesthetic appeal, effective usage of structural materials and other advantages of a cablestayed bridge, construction of this type of structure increased tremendously worldwide [1]. Also, By the advent of new design and construction technology, the cable-stayed bridge is constructed lighter and longer [1, 2]. Since the construction of this type of bridge with longer span length is increasing, having strong structural performance under natural disaster and adverse condition besides, economic design and confirmation of safety and durability are necessary for the cablestayed bridge. These three-dimensional, flexible long span of these structures make them vulnerable to environmental and service loadings such as wind, rain, earthquake, and traffic [3]. Variations in phase and amplitude of seismic motions during long distances are defined as a spatial variation of seismic ground motions. Cable-stayed bridge s supports experience different motion during an earthquake since this type of structure has a long span length over the ground. This different motion causes a dynamic response of the structure increase. Spatial variation of seismic ground motions can have a detrimental effect on the dynamic response of the structure and cannot be ignored. So, in this study, the artificial earthquake records is considered taking into account the distance between the piers of the considered bridge [4, 5]. Structural health monitoring is a process aimed to assess the condition and performance of structure as well as detecting damage after exposing natural disaster. It is defined as the use of in situ, non-destructive sensing, and analysis of structural characteristics, including the structural response, for the purpose of estimating the severity of damage and evaluating the consequences of damage on the structure in terms of response, capacity, and service-life. More simply, SHM represents the implementation of a Level IV non-destructive damage evaluation [6]. Vibration-based damage detection technic for cable-stayed bridge is an important tool due to its efficiency, cost-effectiveness and ease of application [7]. Natural frequencies, mode shapes and modal damping which are modal parameters are functions of physical properties of the structure such as stiffness, mass and damping. So, having change in frequency lead to change in modal parameters. Damage that is defined as any changes introduced to system which adversely affect the current or future performance of that system, reduces the stiffness of the structure and change its vibration characteristics. Therefore, by using vibration measurement the location and severity of damage can be detected. [8, 9, 10] McCuskey et al detected the damage in Tilff Bridge by using the lateral vibration frequency and mode shape in [7]. C. H. Jenkins et al [11] work on the sensitivity of parameter changes in structural damage detection. They believe static deflection can be a more sensitive predictor of 2

3 structural damage than frequency. Also, they mention static deflection measurements are often easier to make, with higher levels of accuracy than dynamic measurements. S. Choi and N. Stubbs [12] used the time domain response to identify location and intensity of damage. From their study, They conclude: (1) the time-domain response data may be used directly to localize and size damage in a structure; (2) the numerical simulation of a continuous beam reveals that the proposed methodology can identify single and multiple damage locations consistently and accurately even using the data with simulated noise; (3) the false negatives can be reduced using the lowered significance level of test for damage localization at the expense of increasing the number of false positives; and (4) the proposed methodology consistently produces lower damage severity estimations [12]. S. Caddemi and A. Greco [13] found out location and intensity of damage by using static test on damaged beam based on displacement measurement. S.M. Seyedpoor and O. Yazdanpanah [14] found multiple locations of damage and establish an indicator for it by using the change of static strain energy method. With considering measurement noise in numerical result the location of damage is identified with high accuracy. J.-T. Kim and N. Stubbs [15] used frequency data to detect the location and severity of crack in beam-type structure non-destructively with high accuracy. Ricardo Perera and Ronald Torres [16] used a genetic algorithm to detect the structural damage via modal data. They consider the influence of noise in the modal data. In spite of high safety measures for the system, structure may deteriorate during its performance or even collapse over period of time. These events cause financial and human losses. Therefore, structural health monitoring methods have drawn a lot of attention in order to identify damage at early stage and preventing collapsed in the structure. 2. Case Study In this study, the Quincy Bayview Bridge on the Mississippi river in Illinois, US was modeled in ABAQUS software. The ABAQUS software is used for 3D modeling and frequency analysis of the considered cable-stayed bridge. The artificial earthquake records are considered taking into account the distance between the piers of the considered bridge in two directions. 2.2 General Description of the bridge The Quincy Bayview Bridge was designed in 1983 and was constructed completely in Chicago of the USA in1987. The bridge consists of two equal side spans with the length of 440 ft and one main span with the length of 900ft. also, it has two concrete towers in the shape of H, and doubleplane cable in the type of fan. The tops of the tower from waterline are 71m. A total number of cables are 56 with 28 of them support the main span and remain 14 cables support the side span of the bridge. The width of the deck from center to center of cables is 12m. The diameter wires of the cables are 0.25 in and the ultimate strength of the cables is 240ksi [17]. 3

4 Figure 1. The Quincy Bayview Bridge [17] Figure 2. shows the bridge details deck cross section, cable type and tower elevation view. (a) (b) (c) Figure 2. Details of the Bridge: (a) Cross Section of the Bridge Deck, (b) Detail of the Cable System, (c) Elevation View of the Bridge Tower [17] 2.3 Finite Element Modeling of Quincy Bayview Bridge All the elements in this model have a linear elastic behavior. Linear elastic beam elements are used for finite element modeling of the towers and deck and truss elements are used for modeling the cables. Figure 3. shows the line geometry-diagram of the model. A single central spine with offset links to accommodate lumped masses and cable anchor points is used for finite element modeling. The spine consisted of 29 beam elements with the length of 60 ft in main span and 63 ft inside span. a couple of rigid links, each having a length of 20ft, are horizontally placed. They have a 90 angle between their longitudinal spinal axis at each cable location to satisfy the required offset of the cables from the deck center line. The finite element modeling of the cross-section of the deck is shown in figure 4. [17]. 4

5 Figure 3. Line Diagram of Finite Elements[17 ] Figure 4. Finite Element Modeling of the Cross-Section of the Deck [17] The details description of the physical properties of the different components of the bridge required for the development of three-dimensional finite element model is prepared as follows Deck Material properties of the deck and the required properties for finite element model of the deck are shown in table 1. and table 2. respectively. Table 1. Material Properties of the Deck [17] Modulus of elasticity steel 4.32 x lo 9 (lb/ft 2 ) concrete 643 x lo 8 Unit weight (lb/ft 3 ) steel 490 concrete 150 Poisson's ratio steel 0.3 concrete 0.25 Table 2. Properties for Finite Element Model of the Deck [17] Model Parameters Section properties of spine: Vertical (Iyy) Transverse ( Izz) Torsion ( Jgq) Cross-section area (A) Translational weights: Main span (M) Side span (M) Corrections applied to rotational inertia: Main span Δx Δy Δz Side span Δx Δy Δz Numerical Values 39.5 ft ft ft ft lb Ib x lo7 lb. ft x 10' lb.ft x lo7 lb. ft x lo' lb.ft x lo* lb.ft x lo7 Ib*ft 2 5

6 2.3.2 Tower As it was mentioned, the bridge has two concrete towers. Each tower consists of 28 beam elements which have linear behavior. The concrete material properties of the towers are as same as material properties of the deck. Table 3. summarized the geometric information of three-dimension finite element model of towers [17]. Table 1. Properties of Finite Element Model of Towers [17] Column sections Area(ft 2 ) Ixx(ft 4 ) Iyy(ft 4 ) J(ft 4 ) Struts lower Struts Upper Cables Figure 3. Finite Element Model of Tower[17] The cables were modeled as a linear elastic truss element with a modulus of elasticity of Es=30x106 psi. The properties for finite element model of cables are summarized in the table below [17]. Table 2. Properties for Finite Element Model of Cables [17] Cable Number Cable Cross-Section Area Cable Weight (Ib/ft) (in 2 )

7 2.3.4 Deck-Tower Bearings Rotation in y-direction is the only relative motion between the deck and the towers. Four bearing links was used for finite element modeling as it was shown in figure 8. Two vertical and two horizontal links to connect the deck to the lower strut and tower column were used respectively [17] Piers and Abutment Tower bases are fixed in all degree of freedom at the piers. The east and west ends of the deck rotate freely in z and y directions.[17] Verification of Finite Element Model Result The article introduces the first vertical bending mode and first mode consists of coupled transverse and torsional motions of the deck as its result of its modeling the bridge with ANSYS. the first vertical bending mode of the article is equal to Hz and the other mode is Hz [17]. These modes in this model in Abaqus are Hz and Hz that this error is negligible. 3. Vibration Based Damage Identification The main purpose of nondestructive damage identification methods is related to facilitate effective maintenance of the structure and keep it in the safe condition. A large variety of nondestructive techniques are available for damage detection in a structure such as penetrating liquids, ultrasound, visual inspection, etc. however, all these techniques are localized, implying long and expensive inspection time. The shortcomings of these techniques have made engineers investigate new methods based on vibration responses of the structure, that allow continuous monitoring and global condition assessment of structures [18]. Damage to physical properties of the structure such as mass, stiffness, and damping can change modal properties of the structure including natural frequencies, mode shapes, and modal damping. So, with analyzing the changes in the dynamic characteristic of the structure, damage can be detected. For damage identification [8]. In this study, two elements of the main span are chosen, and their stiffness is reduced by 10%. 3.1 Natural Frequency-based Method Figure 4.Modeling of bearings at Deck-to-tower Connection [17] Natural frequency-based methods is based on natural frequency change for damage identification. Natural frequency can be measured from few accessible points on the structure, it is also less affected by noise; hence, Natural frequency-based method has attracted a lot of attention [6]. 7

8 Scaled Einenvectors Scaled Einenvectors However, some limitations make this method impractical; for one, extremely precise frequency measurements are required to detect small levels of damage. Moreover, environmental parameters, especially temperature, have an important effect on frequency changes. This method is only applicable to a slender beam-type structure with small cracks [8]. Table 5 shows frequencies of the undamaged and damaged bridge. It is seen that all frequencies are reduced after damage, but the differences are negligible and location of damage cannot be identified. Table 3. Frequencies of undamaged and damaged bridge Mode no. undamaged (Hz) damaged (Hz) Difference (%) 1 st nd th th th th th th Methods based on mode shape changes Compared to natural frequencies approach, mode shapes consist local information and are sensitive to local damages. So, they can be used for multiple damage detection. Also, mode shapes are less affected by environmental condition parameters such as temperature. However, this method has its own drawbacks, such as the requirement of series of sensors for measuring mode shapes. Also, it is contaminated by more sensitive to noise more than compared to the natural frequency. When damage is subtle, this method is impractical. In this study, the mode shapes of the structure are extracted and plotted in excel. The first and second mode shapes are shown here. As it is obviously seen, the mode shapes of the intact and damaged structure are the same [6]. Mode Shape1 Before Damage After Damage 1.5 Before Damage Mode Shape3 After Damage Distance Along Deck (M) Distance Along Deck (M) (a) (b) Figure 5. Comparison of Two Mode shape of Intact and Damaged Structure: (a) Comparison of First Mode Shape Between Intact and Damaged Structure, (b) Comparison of Third Mode Shape Between Intact and Damaged Structure 8

9 3.3 Methods based on Mode Shape Curvature/ Strain Mode Shape Changes Mode shape curvature is an alternative approach to determine vibration changes. The curvature at a point is given by: = =. It is stated that absolute changes in mode shape curvature can be a good indicator by damage for the FEM beam structure. The curvature value can be computed from the lateral displacement components of the measured mode shapes by using a central difference approximation for mode i and Degree of Freedom q = Ф, 2Ф, +Ф +,. h Where h is the length of each of the two elements between the DOF (q-1) and (q+1) [7]. The curvatures of extracted mode shapes are calculated. For example the first and third mode shape curvature are presented here. As it is seen, the location of damage in this method is identified. Difference Between Intact and Damaged Structure in First Curvature Mode Shape Difference Between Intact and Damaged Structure in Third Curvature Mode Shape Distance Along Deck(m) Distance Along Deck(m) Figure 6. Differences of Mode Shapes Among Intact and Damage Structure 4. Conclusion This study investigated the effectiveness of three damage identification methods: natural frequency-based method, methods based on mode shape changes and methods based on mode shape curvature. Natural frequency-based method and method based on mode shape change are not reliable for detecting the damage in complex and huge structure such as cable stayed bridge. The differences in frequencies and mode shapes are negligible and location of damage cannot be identified. These methods are impractical in subtle damages. Mode shape curvature method, however, is sensitive to damage and the location of damage can be identified. Damage in the 9

10 structure increases the curvature so, the differences between the curvature of mode shapes of intact and damages structure are used for identifying the location of damage. 5. References [1] R. Karoumi, Some modeling aspects in the nonlinear finite element analysis of cable supported bridges, Computers and Structures, Vol 71, No 4, pp , [2] R. Karoumi, Modeling of Cable-Stayed Bridges for Analysis of Traffic Induced Vibration, Proceedings of IMAC-XVIIII on Structural Dynamics, Vol. 4062, pp 842, [3] I. E. Harik, J.D. Hu, S.W. Smith, W.X. Ren, T. Zhao, J.E. Campbell and R.C. Graves, Baseline Modeling of the Maysville Cable-Stayed Bridge Over the Ohio River, University of Kentucky, [4] A. Zerva, V. Zervas, Spatial variation of seismic ground motions: An overview, American Society of Mechanical Engineers, Vol 55, No 3, pp , [5] F.R.Rofooei, Aghababaii Mobarake,G. Ahmadi, Generation of artificial earthquake records with a nonstationary Kanai-Tajimi model, Engineering Structures, Vol 23, No 7, pp , [6] Ch. Lim, A. Sabamehr, A. Bagchi (2016), System Identification and Damage Detection Technique in Pre-stress Concrete Box Bridge, CSCE [7] Zhao-Dong Xu et al (2011), Energy Damage Detection Strategy Based on Strain Responses for Long-Span Bridge Structures, Bridge Engineering, Vol 16, No 5, [8] W. Fan and P.Qiao, Vibration-based Damage Identification Methods: A Review and Comparative Study, Structural health monitoring, Vol 10, No 1, pp 83-29, [9] E. Peter Carden and P.Fanning, Vibration Based Condition Monitoring: A Review, Structural health monitoring, Vol 3, No 4, pp , [10] S. W. Doebling, C. R. Farrar, M. B. Prime, and others, A summary review of vibration-based damage identification methods, Shock Vib. Dig., Vol. 30, No. 2, pp , [11] C. H. Jenkins, L. Kjerengtroen, and H. Oestensen, Sensitivity of parameter changes in structural damage detection, Shock Vib., Vol. 4, No. 1, pp , [12] S. Choi and N. Stubbs, Damage identification in structures using the time-domain response, J. Sound Vib., Vol. 275, No. 3 5, pp , Aug [13]. Caddemi and A. Greco, The influence of instrumental errors on the static identification of damage parameters for elastic beams, Comput. Struct., Vol. 84, No , pp , Oct

11 [14] S. M. Seyedpoor and O. Yazdanpanah, An efficient indicator for structural damage localization using the change of strain energy based on static noisy data, Appl. Math. Model., Vol. 38, No. 9 10, pp , May [15] J.-T. Kim and N. Stubbs, CRACK DETECTION IN BEAM-TYPE STRUCTURES USING FREQUENCY DATA, J. Sound Vib., Vol. 259, No. 1, pp , Jan [16] R. Perera and R. Torres, Structural damage detection via modal data with genetic algorithms, J. Struct. Eng., Vol. 132, No. 9, pp , [17] J. C. Wilson and W. Gravelle, Modeling of a Cable-Stayed Bridge for Dynamic Analysis, Earthquake Engineering and Structural Dynamics, Vol 20, No 8, pp ,1991. [18] R. P. C. Sampaio, N. M. M. Maia and J. M. M. Silva (1999), Damage Detection Using the Frequency Response-Function Curvature Method, Journal of Sound and vibration, Vol 226, No 5, Pages ,