Damage identification method for continuous girder bridges based on spatially-distributed long-gauge strain sensing under moving loads

Mechanical Systems and Signal Processing 104 (2018) 415–435

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Mechanical Systems and Signal Processing journal homepage: www.elsevier.com/locate/ymssp

Damage identification method for continuous girder bridges based on spatially-distributed long-gauge strain sensing under moving loads Bitao Wu a, Gang Wu b,⇑, Caiqian Yang b, Yi He b a b

School of Civil Engineering & Architecture, East China Jiao Tong University, Nanchang, Jiangxi 330013, China Key Laboratory of C&PC Structures of the Ministry of Education, Southeast University, Nanjing 210096, China

a r t i c l e

i n f o

Article history: Received 20 December 2015 Received in revised form 17 August 2017 Accepted 30 October 2017

Keywords: Fiber Bragg grating sensor Bearing capacity assessment Macro-strain Damage identification Structural health monitoring

a b s t r a c t A novel damage identification method for concrete continuous girder bridges based on spatially-distributed long-gauge strain sensing is presented in this paper. First, the variation regularity of the long-gauge strain influence line of continuous girder bridges which changes with the location of vehicles on the bridge is studied. According to this variation regularity, a calculation method for the distribution regularity of the area of long-gauge strain history is investigated. Second, a numerical simulation of damage identification based on the distribution regularity of the area of long-gauge strain history is conducted, and the results indicate that this method is effective for identifying damage and is not affected by the speed, axle number and weight of vehicles. Finally, a real bridge test on a highway is conducted, and the experimental results also show that this method is very effective for identifying damage in continuous girder bridges, and the local element stiffness distribution regularity can be revealed at the same time. This identified information is useful for maintaining of continuous girder bridges on highways. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction In recent years, the security of the traffic infrastructure, especially for bridges, has attracted increasingly attention. Bridges can experience structural deterioration as a result of aging, overloading or lack of proper maintenance. The ability to monitor the structural health of existing bridges is crucial for avoiding sudden bridge collapses, which lead to losses of lives and economic losses. Consequently, the structural health monitoring technology has rapidly developed [1–3]. The existing health monitoring systems and methods are primarily designed for long-span bridges [4–6]. By using various sensors, such as accelerometers and strain gauges, it is possible to quantify the response of the structure to static and dynamic loads, to estimate the distribution of extreme loads [7], to identify damages and to estimate the remaining structural capacity [8]. Vibration-based damage identification (VBDI) methods primarily depend on the change in structural parameters for determining whether structural damage has occurred, and the frequency, mode shapes, and mode damping ratio are typically selected as damage indices. Other damage indices include modal flexibility, modal stiffness, modal strain energy, and frequency response function. Extensive literature reviews on VBDI have been reported by Sohn [9] and Goyal [10]. ⇑ Corresponding author. E-mail address: [email protected] (G. Wu). https://doi.org/10.1016/j.ymssp.2017.10.040 0888-3270/Ó 2017 Elsevier Ltd. All rights reserved.

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Although a number of such damage identification strategies have been explored, VBDI techniques still face practicality challenges. The existing methods are based on the traditional accelerometers, strain gauges and displacement meter, and the structural information obtained using these sensors is either too ‘‘macro” or too ‘‘local” to identify local damage [11]. Strain, as a local measurement has been verified to be more sensitive to damage. However, traditional strain gauges cannot effectively reflect the influence of damage unless the gauges are covering the damaged region. Traditional sensors typically possessing a usually short service life are vulnerable to electromagnetic interference and need to be changed frequently. Fiber Bragg grating (FBG) sensors have begun to be widely used for civil structural health monitoring because such sensors are electromagnetic interference resistant, corrosion resistant, light weight, small in size, and easily installed [12]. The multiplexing capabilities of FBG sensors enable many sensors to be installed on a structure with minimal wiring. Villalba applied the optical fiber distributed sensing to health monitoring of concrete structures [13]. Lima et al. [14] presented a structural health monitoring system for one historical building structure, which was based on fiber Bragg gratings. Nineteen FBG displacement sensors and five FBG temperature sensors were used to monitor of the most important points of the structure. Todd demonstrated the sensing capabilities of FBG sensors by installing a number of sensors on a steel girder in a bridge [15]. Schulz reported the application of long- gauge FBG sensors for monitoring civil structures [16]. Wu and Li developed a feasible implementation of distributed long-gauge FBG sensing techniques to use the strain distributions throughout the full or critical regions of structures to detect damage [17,18]. Hong et al. [19,20] investigated the evaluation of bearing capacity and identification of damage based on the distributed strain mode, and the mode macro-strain was selected as a damage index. However, as is the displacement mode, the strain mode is a relative value. The results from different data during short period of time may be different, which will have a certain influence on damage identification. Compared with the monitoring method for long-span bridges, most of the existing highway bridges are using manual detection. Although manual detection can directly evaluate the apparent damage of bridges, this approach has some problems: (1) because of the growing number of bridges, the efficiency of manual detection is too low and the cost is too high; (2) manual detection can only detect apparent damage, and potential damage cannot be detected; and (3) manual inspection requires the use of a bridge inspection vehicle, which will occupy the corresponding lanes and affect the flow of normal traffic. The main purpose of this paper is to investigate how to rapidly and effectively monitor highway bridges without affecting normal traffic. First, the areas distribution regularity of the long-gauge strain of the continuous girder bridge was studied, and the distribution regularity of the area of long-gauge strain history was obtained: when a vehicle passes the monitored span, the area of the strain history of the monitored span is a parabolic distribution; when a vehicle passes other spans, the area of the strain history of the monitored span is a linear distribution. If the stiffness of the monitored element changes, there will be an obvious bulge at the location of the damaged element in the area distribution curve, and this phenomenon can be directly used for the damage identification in continuous beam bridges. The local stiffness distribution and the potential damage can be obtained in a timely manner, and the long-gauge strain history of the monitored span when a single vehicle passes the span is required in this method. Numerical simulations and real bridge tests have confirmed the validity of this method. 2. Theoretical background As shown by Ojio and Yamada, the strain influence line is used primarily for vehicle load identification [21]. However, it is not suitable for bridge damage identification because the information obtained by traditional point strain gauge is too ‘‘local”. Traditional strain gauges cannot reflect the information of damage effectively unless covering the damaged region coincidentally. In this section, the damage identification for continuous girder bridges was studied based on a method which combined the strain influence line and long-gauge strain sensing technology. The relationship between the damage and the area of long-gauge strain histories was investigated. According to influence line theory, the strain can be calculated using Eq. (1)

ei ðxÞ ¼

n X Pk f ðx  dk Þ

ð1Þ

k¼1

where ei ðxÞ is the average strain obtained by long-gauge strain sensors; f ðxÞ is the value of the influence line corresponding to the location of the axis; dk is the distance from the kth axis to the first axis (d1 = 0, the span is L, and the ith axle load is Pi); and x is the distance from the first axis to the left support. Then, Eq. (1) is integrated along the length direction of the structure:

Z 0

L

ei ðxÞdx ¼

Z n X Pk k¼1

0

L

f ðx  dk Þdx ¼

Z n X Pk k¼1

L

f ðxÞdx

ð2Þ

0

RL in which 0 f ðxÞdx is the area of the strain influence line at the location of xi in the x-coordinate. As shown in Eq. (2), the integral value of the strain along the length direction of the structure can be calculated if the influence line function f ðxÞ is known. For continuous girder bridges, the strain influence line function cannot be expressed by a specific function. For

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such bridges, the monitored span is still influenced by the moving load when the load has passed the span. Therefore, the area of the long-gauge strain history cannot be calculated directly. To study the distribution regularity of long-gauge influence line, a three-span 30  30  30 m continuous girder bridge model was established; each span was divided into fifteen elements, and fifteen long-gauge strain sensors were assumed to installed at the bottom of the monitored span, named as S1 to S15, as shown in Fig. 1. A load of F = 1 N was applied with a speed of 1 m/s, and the long-gauge strain histories of the first span were extracted, as shown in Fig. 1. As shown in Fig. 1(a), when the vehicle passes the first span, the maximum value of the long-gauge strain influence line of the first span elements is a parabolic distribution; the location of the maximum value changes with the location of the vehicle along the bridge. When the vehicle passes the second span, the location of the maximum value of the first span does not change with the location of the vehicle; only the amplitude of the maximum value of the first span changes with the location of the vehicle as shown in Fig. 1(b). Therefore, the maximum value of the strain influence line of the first span elements is a linear distribution when the vehicle passes the second span. Similarly, when the vehicle passes the third span, the maximum value of the strain influence line of the first span elements is also linear distribution as shown in Fig. 1(c). As a result, the long-gauge strain histories of the monitored span of the three-span continuous girder bridge can be divided into three sections. Taking the first span as the monitored span as an example. The first section is the part of the strain history where the vehicle is passing the monitored span, and the long-gauge strain influence line function of the monitored span is denoted as f 1 ðxÞ; the second section is the part of the strain history in which the vehicle is passing the second span, and the long-gauge strain influence line function of the monitored span is denoted as f 2 ðxÞ; and the third section is the part of the strain history in which the vehicle is passing the third span, and the long-gauge strain influence line function of the monitored span is denoted as f 3 ðxÞ. f ðxÞ is expressed as follows:

8 2 > < f 1 ðxÞ ¼ a1 x þ b1 x þ c1 f ðxÞ ¼ f 2 ðxÞ ¼ a2 x þ b2 > : f 3 ðxÞ ¼ a3 x þ b3

0 < x < L1 ð3Þ

L1 < x < L2 L2 < x < L3

0.0040 0.0035 0.0025

Long-gauge sensors

0.0020 0.0015

S1-1 S1-4 S1-7 S1-10 S1-13

0.0010 0.0005 0.0000

S1-2 S1-5 S1-8 S1-11 S1-14

Strain (με)

Strain (με)

0.0030

S1-3 S1-6 S1-9 S1-12 S1-15

-0.0005 -0.0010 -10

0

10

20

30

40

50

60

70

80

Location of the vehicle

90

0.0004 0.0003 0.0002 0.0001 0.0000 -0.0001 -0.0002 -0.0003 -0.0004 -0.0005 -0.0006 -0.0007 -0.0008 -10

(a) Long-gauge strain histories of the 1st span when the vehicle passes over the 1st span

S1-1 S1-4 S1-7 S1-10 S1-13

0

10

20

30

40

S1-2 S1-5 S1-8 S1-11 S1-14

50

60

S1-3 S1-6 S1-9 S1-12 S1-15

70

Location of the vehicle

80

90

(b) Long-gauge strain histories of the 1st span when the vehicle passes over the 2nd span

Areas of the strain histories

0.5

Long-gauge sensors

Strain (με)

0.00022 0.00020 0.00018 0.00016 0.00014 0.00012 0.00010 0.00008 0.00006 0.00004 0.00002 0.00000 -0.00002 -10

Long-gauge sensors

S1-1 S1-4 S1-7 S1-10 S1-13

0

10

20

30

40

S1-2 S1-5 S1-8 S1-11 S1-14

50

60

S1-3 S1-6 S1-9 S1-12 S1-15

70

Location of the vehicle

80

90

(c) Long-gauge strain histories of the 1st span when the vehicle passes over the 3rd span

0.4 0.3 0.2

Vehicle on the 1st span Vehicle on the 2nd span Vehicle on the 3rd span

0.1 0.0 -0.1 -0.2 -0.3

0

2

4

6

8

10

12

14

16

Element numbers

(d) Area distribution of strain histories of the first span when the vehicle passes over the different spans

Fig. 1. Long-gauge strain influence line and the area distribution of strain histories of the first span when the vehicle passes over the different spans.

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where a, b and c are constants. Here, we only need to know the form of the function. The area of the long-gauge strain histories of the different sections can be calculated using Eq. (4)

Z

L

0

81 1 2 > < 2 f 1 ðxi Þ  L1 ¼ 2  ða1 xi þ b1 xi þ c1 Þ  L1 f ðxi Þdx ¼ 12 f 2 ðxi Þ  L2 ¼ 12  ða2 xi þ b2 Þ  L2 > :1 f ðx Þ  L3 ¼ 12  ða3 xi þ b3 Þ  L3 2 3 i

ð4Þ

in which, L1 is the length of the first span. The integral value of the strain along the length direction of the structure can be calculated using Eq. (5)

Z 0

where

L

ei ðxÞdx ¼ v

Z

tn t0

ei ðtÞdt ¼ v Ai ðtÞ ¼

n X k¼1

Z

L

f ðxÞdx

Pk

ð5Þ

0

v is the speed of the moving load, ei ðxÞ is the ith long-gauge strain history, t0 is the time when the first axis begins

moving on the bridge, tn is the time when the last axis leaves the bridge, and

R tn t0

ei ðtÞdt ¼ Ai ðtÞ is the area of the ith long-

gauge strain history. By substituting Eq. (4) into Eq. (5), the area of long-gauge strain histories of the different sections can be obtained:

, 8 n X > > 1 2 > 2  ða1 xi þ b1 xi þ c1 Þ  L1  Pk v > > > > k¼1 > > , RL Pn > n X Pk 0 f ðxi Þdx < 1 Ai ðtÞ ¼ k¼1 ¼ 2  ða2 xi þ b2 Þ  L2  Pk v > v > k¼1 > > , > > n > X > > 1 > Pk v : 2  ða3 xi þ b3 Þ  L3 

ð6Þ

k¼1

The area of the long-gauge strain history can be calculated using Eq. (6) when the vehicle passes different spans of the continuous girder bridge. The distribution regularity of the area of the strain history can be obtained from the formula above. When the vehicle passes the monitored span, the area values of the long-gauge strain histories of the monitored span elements follow a parabolic distribution; when the vehicle passes other spans, the area values of the long-gauge strain histories of the monitored span elements follow a linear distribution as shown in Fig. 1(d). If the stiffness of the monitored element changes, an obvious bulge appears at the location of the damaged element in the area distribution map, and this phenomenon can be directly used to identify damage in a continuous beam bridge. In practical engineering, the initial intact state of bridges is unknown, which is the main difficulty in damage extent identification without a reference state. The key point to solve this question is to find a reference state of bridges. Here, the average area value of the two elements adjacent to the damaged element is considered as the ‘‘initial state” and the damage extent can be calculated by Eq. (7)

b ¼ ðAi ðtÞ  Ai ðtÞÞ=Ai ðtÞ

ð7Þ

Ai ðtÞ ¼ ðAi1 ðtÞ þ Aiþ1 ðtÞÞ=2 where b represents the damage extent;

ð8Þ Ai ðtÞ

represents the long-gauge strain history of the identified damaged element;

Ai ðtÞ is the average value of the area value of the two adjacent elements which can be calculated by Eq. (8); Ai1 ðtÞ and Aiþ1 ðtÞ represent the area of the two adjacent elements. 3. Numerical simulation To verify the validity of the proposed method in identifying damage in continuous girder bridges, a three-span continuous girder bridge model, in which each span is 30 m, is established, as shown in Fig. 2. The second span is divided into fifteen elements that are 2 m in length. It is assumed that there are fifteen long-gauge strain sensors with gauge of 2 m, installed on the bottom of the girder, and these sensors are named as S1-S15 from left to right. Ten cases are designed, as shown in Table 1: C0 is the intact case, from C1 to C3 are single damage cases, from C4 to C6 are double damages cases, and from C7 to C10 are triple damages cases. The damage is simulated by reducing the stiffness of the element, and the damage extent and locations are shown in Table 1. A moving vehicle load is simulated by two moving forces, P1 and P2, with a spacing of 4 m, and the value of the forces is 50 kN with a speed of 10 m/s. The long-gauge strain histories of the monitored span elements are shown in Fig. 3. As shown, the strain histories are clearly divided into three sections. The first section is the strain history of the monitored span when the vehicle is passing the first span (t = 0–3.2 s). The second section is the strain history of the monitored span when the vehicle is passing the second span (t = 3.2–6.2 s). The third section is the strain history of the monitored span when the vehicle is passing the third span (t = 6.2–9.2 s). The areas of strain histories of the three sections were calculated, and the distribution of the area of each element is shown in Fig. 4. In Fig. 4, the abscissa is the number of the element. It can be observed

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1

2

3

4

5

6

7

8

9

10 11 12 13 14 15

L

L

L

Intact case: C0

1

2

3

4

5

6

7

8

9

10 11 12 13 14 15

L

L

L

Single damage cases：C1-C3

1

2

3

4

5

6

7

8

9

10 11 12 13 14 15

L

L

L

Triple damages cases：C4-C6

1

2

3

4

5

6

7

8

9

10 11 12 13 14 15

L

L

L

Three damages cases：C7-C9 Fig. 2. Location and extent of the damages.

Table 1 Damage cases. Damage cases

C0 C1 C2 C3 C4

Damage extent (%)

Damage cases

E6

E8

E10

/ /

/ 10 30 50 10

/ / / / 10

/ /

C5 C6 C7 C8 C9

Damage extent (%) E6

E8

E10

/ / 10 30 50

30 50 10 30 50

30 50 10 30 50

that when the vehicle is passing the monitored span, the distribution of the area value is a smooth parabola; when the vehicle is passing other spans, the distributions of the area values are straight lines. A moving load P1 = P2 = 50 kN with a speed of 10 m/s was applied on case C1, C2 and C3, and distributions of the areas of the monitored span elements are shown in Fig. 5. An undamaged element is selected as a reference element, and the regularization of the area values are shown in Fig. 5(b1–b3). The damaged element E8 was identified by the distribution area map; there is an obvious downward bulge at the location of the damaged element in the linear distribution curve, and there is an obvious upward bulge at the location of the damaged element in the parabolic distribution map. The degree of the bulge changes with the extent of the damage, as shown in Fig. 5(a1–a3). In other words, the strain of each section can be used to identify the damage at the same time. For example, the damaged element E8 was identified in Fig. 5(a1), (b1) and (c1) at the same time. The identified result can be verified, thereby improving the reliability of the identified result.

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150

S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14 S15

Strain (με)

100

50

0

0

2

4

6

8

10

-50

-100 vehicle on 1th span

vehicle on 2nd span

vehicle on 3rd span

-150

Time (s) Fig. 3. Strain histories of the 2nd span.

1.2x105

Area values of strain histories

1.0x105 8.0x104 6.0x104 4.0x104 2.0x104 0.0 -2.0x104 -4.0x104 -6.0x104

vehiche on 1th span vehiche on 2th span vehiche on 3th span

-8.0x104 -1.0x105 -1.2x105 0

2

4

6

8

10

12

14

16

Elements of the 2nd span Fig. 4. Area of three sections strain histories.

3.1. The influence of vehicular velocity on the method To investigate the influence of vehicular velocity on the method, velocity is selected as the variable parameter, whose velocities are 10 m/s, 20 m/s and 30 m/s respectively. A moving load P1 = P2 = 50 kN with a spacing of 4 m was applied on C0 and C2. The long-gauge strain histories of element E8 under different speeds are shown in Fig. 6(a). Although the speeds are different, the strain histories are still divided into three sections: two troughs and one peak. Fig. 6(b), (c) and (d) show the distributions of the area values of the monitored span elements when the vehicle is passing the first span, the second span and the third span, respectively (for the case of C0). It can be observed that the distribution of the area values under different vehicular velocities are essentially superimposed, which illustrates that the vehicular velocity has no influence on the distribution of the area values. The damage identification results for case C2 under different vehicular velocities are shown in Fig. 7. Fig. 7(b), (c) and (d) show the distributions of area values of the monitored span elements when the vehicle is passing the first span, the second span and the third span, respectively (in case C2). The damaged element E8 was identified by the distribution area curve. It can be observed that the distributions of the area values under different vehicular velocities are essentially superimposed, which illustrates that the vehicular velocity has no influence on single damage identification.

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C0 C1 C2 C3

2.0x10 4 0.0 -2.0x10 4 -4.0x10 4 -6.0x10 4 -8.0x10

4

-1.0x10 5 0

2

4

6

8

10

12

14

16

Normalized area values of strain histories

Area values of strain histories

4.0x10 4

0.4

C0 C1 C2 C3

0.2 0.0 -0.2 -0.4 -0.6 -0.8 -1.0 -1.2 -1.4 0

2

Elements of the 2nd span

5

1.5x10

5

1.0x10

5

5.0x10

4

C0 C1 C2 C3

0.0 -5.0x10 4 -1.0x10 5 0

2

4

6

8

10

12

14

2 0 -2 -4 2

-2x10 4 -3x10 4 -4x10 4 -5x10 4 2

4

6

8

10

12

4

6

8

10

12

14

16

(b2) Vehicle on the 2nd span (Normalized)

C0 C1 C2 C3

0

16

Elements of the 2nd span

4

-6x10 4

14

C0 C1 C2 C3

0

Normalized area values of strain histories

Area values of strain histories

-1x10

12

4

16

2x10 4

4

10

6

(b1) Vehicle on the 2nd span

0

8

8

Elements of the 2nd span

1x10

6

(a2) Vehicle on the 1st span (Normalized) Normalized area values of strain histories

Area values of strain histories

(a1) Vehicle on the 1st span 2.0x10

4

Elements of the 2nd span

14

Elements of the 2nd span

(c1) Vehicle on the 3rd span

16

0.4

C0 C1 C2 C3

0.2 0.0 -0.2 -0.4 -0.6 -0.8 -1.0 -1.2 0

2

4

6

8

10

12

14

16

Elements of the 2nd span

(c2) Vehicle on the 3rd span (Normalized)

Fig. 5. Area values distribution of the 2nd span elements when vehicle is passing over the different spans (case C0, C1, C2, C3).

3.2. The influence of vehicular weight on the method To investigate the influence of vehicular weight on the method, vehicular weight is selected as the variable parameter, and vehicular weights of P1 = P2 = 20 kN and P1 = P2 = 50 kN with a spacing of 4 m were applied on cases C0 and C5. Fig. 8(b), (c) and (d) show the distributions of area values of the monitored span elements when the vehicle is passing the first span, the second span and the third span, respectively (for the case of C0). It can be observed that the distribution

B. Wu et al. / Mechanical Systems and Signal Processing 104 (2018) 415–435

150

V=10 m/s V=20 m/s V=30 m/s

Strain (με)

100

50

0 0

2

4

6

8

10

-50

Normalized area values of strain histories

422

0.4

v=10m/s v=20m/s v=30m/s

0.2 0.0 -0.2 -0.4 -0.6 -0.8 -1.0 -1.2 -1.4

Time (s)

0

2

1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 0

2

4

6

8

10

12

Elements of the 2nd span

(c) Vehicle on the 2nd span

14

16

Normalized area values of strain histories

Normalized area values of strain histories

v=10m/s v=20m/s v=30m/s

6

8

10

12

14

16

(b) Vehicle on the 1st span

(a) Strain history of element E8 in the 2nd span

2.0

4

Elements of the 2nd span

0.4

v=10m/s v=20m/s v=30m/s

0.2 0.0 -0.2 -0.4 -0.6 -0.8 -1.0 0

2

4

6

8

10

12

14

16

Elements of the 2nd span

(d) Vehicle on the 3rd span

Fig. 6. Area values of the 2nd span elements of C0 under different vehicular velocity.

of the area values under different vehicular weights are essentially superimposed, which illustrates that the vehicular weight has no influence on the distribution of the area values. The damage identification results for case C5 under different vehicular weight are shown in Fig. 9. Fig. 9(b), (c) and (d) show the distributions of area values of the monitored span elements when the vehicle is passing the first span, the second span and the third span, respectively (for the case of C5). The damaged elements E8 and E10 were identified by the distribution area curve. It can be observed that the distributions of the area values under different vehicular weights are essentially superimposed, which illustrates that the vehicular weight has no influence on the identification of double damages.

3.3. The influence of axle numbers on the method To investigate the influence of the number of axles on the method, axle number is selected as the variable parameter. The double-axle vehicle load with a speed of 10 m/s is P1 = P2 = 60 kN with a spacing of 4 m. The three-axle vehicle load with a speed of 10 m/s is P1 = P2 = 50 kN with a spacing of 4 m and P3 = 20 kN (front axle), and the spacing between P3 and P2 is 2 m. Two types of vehicle loads were applied on cases C0 and C8. It can be observed that the distributions of the area values under different numbers of axles are essentially superimposed, which illustrates that the number of axles has no influence on the distribution of the area values(as shown in Fig. 10). The damage identification results for case C8 under different numbers of axles are shown in Fig. 11. Fig. 11(b), (c) and (d) show the distributions of area values of the monitored span elements when the vehicle is passing the first span, the second span and the third span, respectively (for case C8). The damaged elements E6, E8 and E10 were identified from the distribution area curve. It can be observed that the distribution of the area values under different numbers of axles are essentially superimposed, which illustrates that the number of axles have no influence on the identification of damage.

423

3.0

0.4

Normalized area values of strain histories

Normalized area values of strain histories

B. Wu et al. / Mechanical Systems and Signal Processing 104 (2018) 415–435

v=10m/s v=20m/s v=30m/s

0.2 0.0 -0.2 -0.4 -0.6 -0.8 -1.0 -1.2 -1.4

0

2

4

6

8

10

12

14

16

v=10m/s v=20m/s v=30m/s

2.5 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5

0

2

Elements of the 2nd span

Normalized area values of strain histories

(a) Vehicle on the 1st span

4

6

8

10

12

Elements of the 2nd span

14

16

(b) Vehicle on the 2nd span

0.4

v=10m/s v=20m/s v=30m/s

0.2 0.0 -0.2 -0.4 -0.6 -0.8 -1.0 0

2

4

6

8

10

12

14

16

Elements of the 2nd span

(c) Vehicle on the 3rd span Fig. 7. Damage identification of C2 under different vehicular velocity.

3.4. Identification of damage extent It can be obtained by the damage identification results from Section 3.1 to Section 3.3; there is a proportional relationship between the area value surrounded by the long-gauge strain history curve and the damage extent. The area of the long-gauge strain history curve increases with the damage extent. In this section, the damage extent is identified using the area value surrounded by the long-gauge strain history curve. In order to verify the accuracy of damage extent identification, damage extent is calculated using Eq. (7) in the damage case. Damage case: a double-axle vehicle and a three-axle vehicle load are adopted; element E8 is designed as the damaged element with 10%, 30% and 50% decreased in stiffness. The design damage extent is named as ‘‘DE-designed”. The damage extents are identified based on the initial intact state and Eq. (7), which is named as ‘‘DE-initial” and ‘‘DE-average”, respectively. Generally, the initial intact state of the bridge is unknown, the‘‘DE-initial” only could be obtained in laboratory or numerical simulation. The damage extent identification results are shown in Fig. 12; and it can be found that the ‘‘DEaverage” is very close to the ‘‘DE-designed” and ‘‘DE-initial”, and it also illustrates that the number of axles have no influence on the identification of damage extent. Therefore, the ‘‘DE-average” could replace ‘‘DE-initial” to some extent when the ‘‘DEinitial” was unknown, and it also proved the method had a high reliability to identify the damage extent. 4. Real bridge test 4.1. Bridge profile A damage identification experiment was conducted on the Xinyi River Bridge, which is located on the Jiang Huai Expressway in Jiangsu province and crosses the Xinyi River, as shown in Fig. 13. The bridge superstructure uses simple supports and continuous partially pre-stressed concrete box girders, with 72 total spans of 30 m each. Seventy-two spans are divided into

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Fig. 8. Area values of the 2nd span elements of C0 under different vehicular weight.

13 groups, named groups 1–12 from Beijing to Shanghai, and each group contains 6 spans. The bridge was constructed in 2001, and it has been in operation for 15 years. The cross-section of the bridge is shown in Fig. 14. The monitored span is the second span in group 11; there are four box girders named G1, G2, G3 and G4 from outside to inside, as shown in Fig. 15. The left side of the bridge is to Beijing, and the right direction is to Shanghai. 4.2. Establishing the health monitoring system A self-made long-gauge FBG sensor is applied in the health monitoring system (as shown in Fig. 16), and consists of: the sensing part and the connecting optic fiber at the two ends. The sensor is fabricated on a steel calibration instrument. The anchoring section and the gauge section of the sensor are respectively wrapped by a plastic hose with a diameter of 0.9 mm and 1.5 mm, and the plastic hose are packaged by a continuous basalt fiber annular tube. The main process of sensor fabrication: (1) Inserting bare FBG into 1.5 mm and 0.9 mm plastic hose, then coating the basalt fiber sleeve at the outermost layer. (2) Dipping half of the basalt fiber tube and an anchoring section fully with epoxy resin and curing epoxy resin at elevated temperature. (3) Fixing the cured anchorage section and applying a constant pre-stress to another free bare FBG end, then keeping the bare FBG in the gauge section under tension. (4) Dipping the other half of basalt fiber tube and anchoring section with epoxy resin and curing epoxy resin at elevated temperature. The cured epoxy resin basalt fiber tube provides the sensor with certain stiffness, while provides sufficient free space for bare FBG inside.

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(c) Vehicle on the 3rd span Fig. 9. Damage identification of C5 under different vehicular weight.

(5) After the completion of the sensor, a tensile test will be carried out to check whether there is drift in central wavelength of the sensor on the steel calibration instrument. The pre-stressing force has been monitored during the manufacture of the sensor, if the pre-stressing force loss after the sensor completed, which shows that the fabrication of the sensor is failed, and this kind of sensors cannot be used for engineering structure monitoring. In the process of sensor fabrication, the pre-stressing force is used to ensure that the FBG in the central plastic hose is in a free state. There are two types of tubes used in the long-gauge FBG sensors. One is the plastic hose contained 1.5 mm and 0.9 mm in diameter, and the other is a basalt fiber tube coated with epoxy resin in the outermost layer. The cross-section of sensing and anchorage parts are shown in Fig. 17. In the cross-section 1-1, we can easily find that there is enough space between the bare FBG and 1.5 mm inner plastic tube. Therefore, the bare FBG is unconstrained in the sensing part. The space between the bare FBG and 0.9 mm plastic tube is dipped with epoxy resin and the ends of the bare FBG are anchored in the anchorage parts (shown in cross-section 2-2). The characteristic of the sensor is that it uses the hollow sleeve to keep the fiber grating sensor in a free state. The middle tube ensures a uniform strain distribution along the gauge length, and the length of the tube is therefore defined as the gauge length of the sensor. When the sensor is installed on a structure, the average strain of the structure covered by the gauge length can be measured. The gauge length of the long gauge FBG sensors can be designed according to the practical engineering demand. Twenty-five long-gauge FBG sensors with gauges of 1 m were installed on the bottom of G2, as shown in Fig. 18. The long-gauge FBG sensor installation was divided into three steps as shown in Fig. 19. The first step was cleaning the surface with a grinding machine and alcohol. The second step was determining the location of the sensor and then temporarily fixing the ends of the sensors with structure glue. The third step was covering the sensors with structural adhesive after ensuring that every sensor was working.

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Fig. 10. Area values of the 2nd span elements of C0 under different axle numbers.

It should be noted that the attachment pattern of the sensors is divided into two kinds: Point Fixation Bonding (PFB) and Overall Bonding (OB). There are peaks in the macro-strains measure by OB when the crack occurs in the concrete structure. The macro-strain measured by PFB is constant when the crack occurs at the same location. The values measured by PFB and OB are generally identical. Therefore, the attachment procedures of the sensors choose is according to the different measuring purposes and accuracy requirements. With regard to the bridge damage identification, it is recommended to use the overall bonding method, because these peaks are beneficial to improve the accuracy of the damage identification results. At the same time, the overall bonding of the sensors effectively avoids the measure errors as a result of the crack occurring in the fixation end. 4.3. Damage location identification The long-gauge strain response was recorded when a single car passed the bridge, and the sampling frequency was 1000 Hz. It is easy to capture the situations of single vehicle passing bridges, because the safety distance between vehicles and vehicles is more than 150 meters, which is greater than the span of bridges; when a vehicle is passing the bridge, other vehicles are still on the highway. In the test, a total of forty sample data were collected, and each sample contained the longgauge strain histories of the bridge when a single vehicle passing the bridge. Vehicles are random and therefore the speed, axle number and weight of the vehicle are unknown. To avoid the effects of measurement errors, five randomly-selected samples data from a total of forty samples were used in this paper and named as sample 1, sample 2, sample 3, sample 4, and sample 5. Fig. 20 shows the twenty-five long-gauge strain histories of G2. There are five sections in the histories. When the vehicle was passing the monitored span, the

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Fig. 12. Damage extent identification under different vehicle load.

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Fig. 13. Xinyi River Bridge.

Fig. 14. Section of the mid-span and number of girders.

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FBG demodulator

Steel calibration instrument Bare FBG

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Anchoring section

0.9 mm plastic hose

Gauge section

Anchoring section

0.9 mm plastic hose

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Dipping half of the tubers with epoxy resin

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1

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Tube

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Connector 2

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Fig. 17. Cross-section of a long-gauge FBG sensor.

250 900 3000 2-2 Cross section unit: μm

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section1

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amplitude of the histories is the maximum. According to Eq. (6), the areas of the strain section 2, section 3 and section 4 of the long-gauge strain histories were calculated to identify the damages. Fig. 21 displays the area distributions of the monitored span elements, and the area values are calculated using the Section 2. According to the distribution regularity of the area value of the monitored span, the area of the strain histories was linear distribution when the vehicle was not passing the monitored span. The theoretical linear distribution is shown by a blue dotted line with an arrow. It can be observed from the numerical results that there are downward bulges at the location where the damage occurred in linear distribution curve. The elements E5, E8, E13 and E16 are identified as the damaged elements in Fig. 21. Fig. 22 presents the area distributions of the monitored span elements, and the area values are calculated using the strain section 3. Theoretically, the area value of the strain histories is a parabolic distribution. The area values of the strain histories are not a strict parabolic distribution due to the initial defect during the construction process and the pre-stress. It can be observed from the numerical results that there are upward bulges at the location where the damage occurred in parabolic distribution curve. The elements E6, E8, E12, E13, E16 and E18 are identified as the damaged elements in Fig. 22. Fig. 23 shows that the area value distribution that is calculated using the strain section 4, and the elements E6, E8, E13 and E18 are identified as the damaged elements. The numbers of damaged elements identified using the third, fourth and fifth strain sections are 5, 6 and 3, respectively. Synthesizing the damage identification results, the damaged elements are E6, E8, E12, E13, E16 and E18 in G2.

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Area values of strain histories

1.0x10 5 sample1 sample2 sample3 sample4 sample5

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The locations of the damaged elements and stiffness mutation region are shown in Fig. 24. It can be observed that the damaged elements of G2 are located from 1/4 to 3/4 of the span, and there are two continuous damaged elements in the mid-span. Manual inspection of G2 was conducted to verify the correctness of the identification results. The cracks of elements in G2 are shown in Fig. 24, and the comparison between actual and identified damage elements are shown in Fig. 24. A number of transverse cracks in the bottom of the girder and web vertical cracks are found in the elements E12, E13, and E16, which have the width and length ranging from 0.05 mm to 0.15 mm and from 70 mm to 110 mm, respectively (see Fig. 25 (a)). On the other hand, the longitudinal cracks are found in the bottom of the girder of elements E8, E9, and E18, in which the longest longitudinal crack is about 1780 mm (see Fig. 25(b)). Meanwhile, it can be found that the element E9 is not identified by this method. The main reason of the phenomenon could be the direction of the longest longitudinal crack which is parallel to the direction of the long-gauge FBG sensor, and the length of the crack which exceed the gauge of the sensor. Although the results of damage identification could be affected when the direction of the cracks are the same as that of the sensor and the length of the crack exceeds the gauge of the sensor, the most of the damages in G2 can be identified. 4.4. Damage extent identification The damage extent identification is based on the damage identification results in Figs. 21–23. The damage extent of the damaged elements in G2 beam are identified using Eq. (7) and the results are shown in Fig. 26. The damage extent of the first

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Identification damage element Damaged element with vertical creaks by manual inspection

Fig. 24. Location of damaged elements of G2 (bottom diagram).

(a) Web vertical cracks

(b) Longitudinal cracks in the bottom Fig. 25. Web vertical cracks and the longitudinal cracks in the G2.

and last element of the G2 beam cannot be identified using Eq. (7) without lacking of one adjacent element, therefore element E1 and E25 are not identified in this section. It can be seen from the results, the identified damage extent of the damaged element are very stable at the location from 0.25L to 0.75L of the monitored span, and did not appear the positive and negative value alternately (seen in black dotted frame). Element E10 is also stable, but the damage extent value is less than

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Sample data1 Sample data2 Sample data3 Sample data4 Sample data5

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Element number Fig. 27. Damage extent of the identified elements of the bridge.

5%, so it is not identified as a damaged element (seen in red dotted frame). In order to ensure the accuracy of the results, the average value of five samples identified damage extent is considered as the damage extent of the damaged elements (as shown in Fig. 27). The maximum damage element is E8 with damage extent of 21.5%. In this paper, only five randomly-selected samples data from forty samples are used to identify the damage. The more samples datas are acquired, the more reliable of the damage identification results are. It should be noted that this method is mainly used for the medium-small span bridges. The temperature variation in the bridge direction is very small, especially in the bottom of the medium-small span box girder. Specifically, the temperature often changes within 1 °C, which needs to take a long time. Through the experiment calibration, we find that the strains of sensors vary 8 micro-strains/°C. In addition, the strain is approximately 3 micro strains due to the temperature variation in the bridge, which has few effect on the area of long-gauge strain time histories. It is easy to find that the proposed method is based on the area distribution of the long-gauge strain time history curve under a single vehicle load, and the influence of temperature variation on the calculation of the strain time history can be ignored. Meanwhile, the time that some vehicles pass a continuous beam bridge is often not more than 10 s, and the temperature has no great impact on the identification results in such short time. It is recommended to use the temperature compensation when the bridge span is large and the temperature change is obvious. 5. Conclusion The distribution regularity of the long-gauge strain influence line is investigated in this paper, and a damage identification method for continuous girder bridges is proposed, which is based on the distribution of area values of the long-gauge strain histories of different sections. Some conclusions can be drawn, as follows: (1) The damage identification method presented in this paper is suitable for medium-small span continuous beam bridges. The results of numerical simulation show that the vehicle parameters have little effect on the damage identification results. When the method is used for bridge damage identification, the only requirement is to acquire the long-gauge strain histories under a single passing vehicle load, and does not affect the normal traffic.

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(2) When a vehicle passes the monitored span, the area values of the strain histories of the monitored span elements follow a parabolic distribution; when a vehicle passes over other spans, the area values of the strain histories of the monitored span elements follow a linear distribution. If the element stiffness increases, there is a downward bulge at the location of this element; if the element stiffness decreases, there is an upward bulge at the location of this element in the parabolic distribution map. In the linear distribution curve, if the element stiffness increases, there is an upward bulge at the location of this element; if the element stiffness decreases, there is a downward bulge at the location of this element. (3) In the damage extent identification experiment, the damage extent was calculated based on reference values, which were the average value of the two adjacent elements of the identified damaged element. The numerical simulation results show that the identified damage extent have a high accuracy and can be used to evaluate the damage extent of the bridge when the initial condition is unknown. The real bridge test results show that damage identification near the bearing is not stable, the identification accuracy is relatively low, and the damage identification results is very stable in location from 0.25L to 0.75L of the bridge. (4) The long-gauge strain histories are divided into three sections, and the strain of each section can be used to identify damage at the same time. The damaged element can be identified more easily in the parabolic distribution map, and the stiffness mutation region can be identified more easily in the linear distribution map. The identified results can be verified with each other, thereby improving the reliability of the identified result.

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