Acoustic emission monitoring and damage assessment of FRP-strengthened reinforced concrete columns under cyclic loading

Construction and Building Materials 144 (2017) 86–98

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Acoustic emission monitoring and damage assessment of FRPstrengthened reinforced concrete columns under cyclic loading Gao Ma a,b,⇑, Hui Li c a

College of Civil Engineering, Hunan University, Changsha 410082, China Hunan Provincial Key Lab on Damage Diagnosis for Engineering Structures (Hunan University), Changsha 410082, China c School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, China b

h i g h l i g h t s
AE hits analysis reveals the crack process of the strengthened column effectively.
The trend of b-values can reflect the variation of concrete crack magnitude.
The accumulative AE energy and hysteretic energy exhibit a good correlation.
The fractal theory based damage index predicts the column damage levels effectively.

a r t i c l e

i n f o

Article history: Received 16 May 2016 Received in revised form 6 March 2017 Accepted 18 March 2017

Keywords: Acoustic emission Crack process Fiber-reinforced polymer Reinforced concrete column Cyclic tests

a b s t r a c t Fiber-reinforced polymers (FRPs) have been widely used for the seismic strengthening of reinforced concrete (RC) structures in seismic regions across the world during the last decades. However, the crack states of concrete inside the strengthened regions are wrapped by FRP sheets and are not visible to inspectors after earthquakes. Aiming to solve this problem, the crack process of FRP-strengthened large-sized RC column under lateral reversed cyclic loading was investigated based on acoustic emission (AE) techniques in the present study. It was found that AE techniques were effective in revealing the crack process of both FRP-strengthened and unstrengthened RC columns. The AE hits analysis revealed that the damage process of the FRP-strengthened column could be divided into four damage levels qualitatively, and the distribution of AE amplitudes had an obvious relationship with the peak displacements of the strengthened column under cyclic loading. The b-value analysis showed that the variation of the crack magnitude during the cyclic test could be reflected effectively by the trend of b-values. The accumulative AE energy exhibited a good correlation with the accumulative hysteretic energy dissipated during the cyclic test for the FRP-strengthened column. Based on fractal theory, a concise but reliable damage index was proposed to predict the damage levels of FRP-strengthened RC columns and the efficiency of the damage index has been verified through the test results. Ó 2017 Published by Elsevier Ltd.

1. Introduction Fiber-reinforced polymers (FRPs) have been widely studied and used for the seismic strengthening of reinforced concrete (RC) structures in seismic regions across the world during the last decades, due to their high strength-to-weight ratio, high corrosion resistance, and ease of in situ application [1,2]. The FRPstrengthened RC structures in seismic regions may be damaged after earthquake striking. Hence, determination of the damage

⇑ Corresponding author at: College of Civil Engineering, Hunan University, Changsha 410082, China. E-mail addresses: [email protected] (G. Ma), [email protected] (H. Li). http://dx.doi.org/10.1016/j.conbuildmat.2017.03.169 0950-0618/Ó 2017 Published by Elsevier Ltd.

levels of these damaged structures is needed before rehabilitation. After earthquakes, the damage levels of unstrengthened RC structures can be determined by in-situ observation of crack states and sample inspection. However, for FRP-strengthened structures subjected to earthquake loads, most of the cracks are covered by FRP sheets, and it is difficult to determine the damage levels of these structures. In addition, in-situ observation highly depends on experience and sample inspection could be costly and timeconsuming. Therefore, it is necessary to develop a new alternative method to assess the damage levels of FRP-strengthened RC structures subjected to earthquake loads. Acoustic emission (AE) is the elastic wave generated by irreversible changes in internal microstructure of solid material, such

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as crack, plastic deformation, and friction. In the last decades, AE techniques have undergone considerable development and have been widely used in metal industry, civil engineering, rock excavation and mining industry, owing to its no disturbance to equipment operation, better reliability and more convenience, compared with other nondestructive evaluation methods [3]. In the AE field, the methods of analyzing the data collected by AE acquisition system can be classified into two types: AE parameter analysis and AE waveform analysis. AE parameters include event, hit, frequency, energy, amplitude and so on. AE parameter analysis is widely used for its simplicity and high calculation efficiency [4,5]. AE waveform analysis uses the entire signal information and is time-consuming. Because AE signals are sensitive to geometry boundary conditions, material heterogeneity, propagation path, and sensor characteristics, the application of AE waveform analysis is limited [6]. The micro-fracture in the AE field is similar to the fault activity in earthquakes and hence the well known magnitude-frequency relationship (MFR) proposed by Gutenberg and Richter [7] can be used for fracture analysis in the AE field [8]. Because a constant (usually represented by the symbol b) can be obtained from the MFR analysis of AE signals, this method is termed as the b-value method. The b-value method has been used to study the crack process of rocks and it was found that the b-values had a good relationship with the crack levels [9–11]. Colombo et al. [12] investigated the crack process of RC beams under bending test using AE techniques and the results confirmed that the b-values were correlated to the crack process of concrete. For RC beams strengthened with carbon fiber-reinforced polymer (CFRP), Yun et al. [5] found the b-values related strongly to the crack process and the localization of damage. Ma et al. [13] revealed that the crack process of FRP-confined concrete columns under axial compression loading was quite different from that of plain concrete columns through b-value method. For RC structural components, most of the literature focuses on the AE technique based crack monitoring of RC beams [12] and FRP-strengthened RC beams [5,14,15] under bending test. Research studying the crack monitoring of FRP-strengthened RC columns under cyclic loading using AE techniques has not been reported. The crack process of the concrete at the plastic hinge regions of RC columns is more complicated under cyclic loading, compared with the crack process of RC beam under bending test. Furthermore, for an FRP-strengthened RC column, the crack process of concrete at the plastic hinge region is covered by FRP sheets, which remain intact even after the failure of the column, indicating that it is impossible to assess the damage levels of the concrete at the plastic hinge under cyclic loading. In addition, the columns of RC frame structures in earthquake regions are more vulnerable to the lateral force induced by earthquake shaking, compared with the axial load applied by weight. Therefore, it is meaningful to extend AE techniques to monitor the crack process and assess the damage levels of FRP-strengthened RC columns under cyclic loading. In this paper, the crack process and damage levels of FRPstrengthened RC column under lateral reversed cyclic loading were investigated based on AE techniques. Two large-sized RC columns were fabricated, including one unstrengthened column (as the reference specimen) and one FRP-strengthened column. Cyclic loading (to simulate earthquake loads) was conducted on the columns to generate cracks at the plastic hinge region, and AE signals were collected simultaneously by AE sensors pasted on the surface of the columns. The crack process of the concrete at the plastic hinge regions was analyzed through AE characteristic parameter analysis and b-value analysis. Finally, a fractal theory based damage index was proposed to assess the damage levels of FRP-strengthened RC columns.

2. Lateral cyclic tests of RC columns 2.1. Specimen fabrication In order to make the test more convincing and to provide guidance for practical application of AE technique based crack monitoring and damage assessment, two large-sized identical RC columns, with a cross section of 300  300 mm, were designed and fabricated. One column was unstrengthened and used as the reference specimen, and the other column was strengthened with basalt fiber reinforced polymer (BFRP) sheets. Detailed information of the columns is shown in Fig. 1, where the longitudinal reinforcement and hoop reinforcement ratios of the columns were 1.79% and 0.87%, respectively. In order to facilitate FRP retrofitting, four chamfers with a radius of 45 mm at the plastic hinge region of the columns were made during the construction. The mechanical properties of the reinforcement bars and BFRP laminates after being cured in epoxy are listed in Table 1. Commercial concrete, with a maximum diameter of coarse aggregates of 20 mm, was used to construct the columns. The average compression strength of the 150  150  300 mm standard concrete prisms was 47.5 MPa after 28 days of curing at room temperature. Eleven layers of BFRP sheets were used to strengthen the columns to ensure the ductility ratio reached l ¼ 8, through the design method proposed by Seible et al. [16]. 2.2. Cyclic loading program In order to simulate earthquake damage, the columns were tested under lateral reversed cyclic loading. The cyclic loading system is shown in Fig. 2, where an MTS electro-hydraulic testing machine (Model 244), with a maximum load capacity of 1000 kN and a maximum static stroke of 508 mm, was used to conduct the cyclic tests, and a hydraulic jack was installed on the top of the column to apply the axial compression load. A compression ratio of 0.3 was considered in the tests and the actual compression strength of concrete was used to calculate the axial compression ratio. The reversed cyclic loading program is shown in Fig. 3, where one cycle was conducted at 0.5 F y and 0.75 F y respectively before the column yielded, and then the loading step was set to be multiples of the yield displacement and two cycles were conducted at each step. The yield capacity F y of the unstrengthened column was 174.8 kN, after calculation based on the theory of reinforced concrete structures [17]. Because few improvement of the column flexural capacities could be achieved after FRP wrapping around

3-3

50

8@60 R45

400 400

38

300 400 3-3

2-2

4 25

300

8 16

1-1

8@100

925 1-1 Hoist rings 450

8@100

Hole for anchor

38

300 300

8 16

2-2

500

1400 Fig. 1. Geometry and reinforcement details of the column (units: mm).

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Table 1 Mechanical properties of reinforced bars and BFRP. Material type

Elastic modulus (GPa)

Yield strength (MPa)

Ultimate strength (MPa)

Strain at ultimate strength (%)

8 mm hoop (plain bar) 16 mm rebar (deformed bar) BFRP

192 202 92

272 361 –

391 580 1848

20.8% 17.3% 2.1%

column was also set to 5.15 mm. For the unstrengthened and FRP-strengthened columns, the load step increased to 5Dy and 11Dy respectively, and then the cyclic tests ended, because the lateral load reached 0.85 F p (F p was the peak load strength of the column specimen) in the descending branch of the column loaddisplacement curves and the columns were heavily damaged, according to the specification of testing methods for earthquake resistant building in China [18]. In the following paragraphs, URC and BRC were used to nominate the unstrengthened and FRPstrengthened column respectively for conciseness.

Steel rollers Load cell

Hydraulic jack

MTS actuator Specimen LVDTs

2.3. Measurement systems

(a)

Axial force

Cyclic force

(b) Fig. 2. The cyclic test system of the columns: (a) photo of the test devices and (b) sketch of the test devices.

Δ

F 0.75Fy

Yielding point

nΔ y …

AE signals emitted from the crack process of concrete were collected by a PAC-DiSP system (manufactured by Physical Acoustics Corporation, USA). PAC’s products have been widely used in the AE research fields due to its high reliability and accuracy [3,10– 13,19,20]. PAC R15 sensors, with an effective operation frequency ranging from 50 to 400 kHz (reported by PAC), were used here to gather AE signals. The R15 sensor was also used by Yuyama et al. [19] and Mirmiran et al. [20] to study the crack process of concrete. Schematic diagram of the AE acquisition system is shown in Fig. 4. Two AE sensors were used for each column and the location of the sensors was 490 mm high from the pedestal. Silicon grease was used as the coupling agent between the sensors and concrete surface. The gain of the preamplifier was 40 dB. The acquisition threshold was set to 40 dB to ensure the background noise was not gathered. Before cyclic tests, lead break test was carried out to verify the responses of the sensors and the PAC-DiSP system. During the cyclic tests, the strain responses of concrete, BFRP sheets, and reinforced bars were also measured. Because the concrete strain gauges pasted on the bottom of URC failed after the concrete tensile cracks occurred, only the locations of the strain gauges on rebars (the same for URC) and BFRP sheets for the BRC specimen are shown in Fig. 5 for conciseness. The FRP strain gauges were along the hoop direction of the column. The displacement responses of the columns were measured by linear variable differential transformers (LVDTs), as shown in Fig. 2(b).

2Δ y

Δy

0.5Fy Time

Fig. 3. Cyclic loading program.

the columns [1], the yield capacity of the FRP-strengthened column was also set to 174.8 kN. When one of the longitudinal reinforced bars entered into yield stage (based on the readings of the strain gauges), it was determined that the yield displacement Dy of the reference specimen was 5.15 mm. In order to facilitate comparison of the results, the yield displacement of the FRP-strengthened

Fig. 4. AE acquisition system setup (units: mm).

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Fig. 5. Locations of the strain gauges (units: mm).

3. Load-displacement curves and damage patterns Fig. 7. Final damage patterns of the BRC specimen.

3.1. FRP-strengthened column The load-displacement curve and final damage patterns of BRC are shown in Fig. 6 and Fig. 7, respectively. It is obvious that the FRP-strengthened column exhibited good ductility and energy dissipation capacities (Fig. 6) and the concrete cracks at the plastic hinge region was unseen due to the FRP cover (Fig. 7). During the cyclic tests, concrete cracks were observed and photographed at the maximum displacement (including push and pull directions) in the second hoop of the control displacement. Since the column was symmetrical along the loading direction, only the crack patterns on the surfaces S1 and S2 (shown in Fig. 8) were given here. These cracks were observed at the points from a to e, which were marked on the load-displacement curve in Fig. 6, when the lateral force was along the push direction. The points a–e corresponded to 2Dy  10Dy , respectively. At the point a, the first crack appeared at the interface of the column and the pedestal. Then several cracks began to appear on S1 and S2 above the FRP sheets at the point b, and these cracks developed further at the points c, d, and e. At the point c, a horizontal crack appeared on the FRP sheets and extended at the points d and e. This crack was along the fiber

300 a

Load (kN)

200

b c d e

100

Push

0

Pull -100 -200 -300 -80 -60 -40 -20

0

20

40

60

Lateral displacement (mm) Fig. 6. Load-displacement curve of the BRC specimen.

80

direction and had no effect on the tensile strength of FRP. During the cyclic test, the maximum tensile and compressive strains of the steel strain gauges were 13,613 le and 13,956 le, respectively. The maximum tensile strain of the FRP strain gauges was 5246 le, which was much below the ultimate FRP tensile strain (= 2.1%, as shown in Table 1). The final failure model of the FRPstrengthened column was the interface failure of the column and the pedestal and no FRP breakage was observed after the test. The concrete cracks at the plastic hinge region were cover by the FRP sheets and could hardly be observed during the cyclic tests. Therefore, it is meaningful to develop a nondestructive method to detect the crack process and assess the damage levels of the inside concrete for FRP-strengthened columns. 3.2. Unstrengthened column The load-displacement curve and final damage patterns of URC are shown in Fig. 9 and Fig. 10, respectively. It was found that the lateral load entered into an obvious descending branch (Fig. 9) and the column was heavily damaged (Fig. 10). Fig. 11 shows the crack patterns observed at the points from a0 to e0 , which were marked on the load-displacement curve in Fig. 9. The points a0 –e0 corresponded to Dy  5Dy , respectively. The crack patterns of the unstrengthened column were obviously quite different from those of the FRP-strengthened column. At the point a0 , some horizontal cracks began to appear on S2, which was under tensile stress state when the force was along the push direction. With the increasement of the control displacement, more horizontal cracks appeared on S2 and several of these cracks extended to S1. When the lateral load reached the point c0 (nearly to the peak load capacity point of the column), diagonal cracks were observed on S1, because both tensile and shear stress became notable at the plastic region of S1 in this loading step. The crush of cover concrete appeared on the bottom of S2 at the point d’ and the decrease in the loaddisplacement curve can be observed in Fig. 9. At the point e0 , severe concrete crush occurred on S2 and the chamfered region, and the load capacity decreased further, indicating that the column entered

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Fig. 8. Crack patterns of the BRC specimen at different peak loading displacements.

300 b' c' d' a' e'

Load (kN)

200 100

Push

0

Pull -100 -200 -300

-60

-40

-20

0

20

40

60

Lateral displacement (mm) Fig. 9. Load-displacement curve of the URC specimen.

into the failure stage. During the cyclic test, the maximum tensile and compressive strains of the steel strain gauges were 3129 le and 7559 le, respectively. It can be determined that the failure model of the unstrengthened column was typical flexural failure. 4. Analysis of AE characteristic parameters 4.1. Introduction of AE parameters During the cyclic tests, the columns underwent a process of accumulated damage, as seen from Figs. 8 and 11. Meanwhile, AE signals were generated from concrete cracking and were collected by the AE acquisition system. A waveform of typical AE signal is shown in Fig. 12, where the common AE characteristic parameters are also illustrated, including rise time, duration time, count, amplitude, and energy. One AE hit corresponds to one AE waveform. The number of AE hits per unit time is usually used to represent the degree of crack activity. AE amplitude corresponds to the peak point of the signal and is expressed on a decibel scale. AE energy of a waveform is the area under the envelope curve of an AE waveform and above the threshold and is measured in attojoule (1018 J). The amplitude and AE energy can be used to describe the magnitude of the crack. AE peak frequency is the frequency corresponding to the peak value on the power spectrum of an AE waveform obtained through Fourier transform. AE peak frequency is closely related to the material type and cracking characteristics [13,21]. In this paper, only AE parameters were utilized to analyze the crack process of the specimens, because AE waveform analysis could lead to unreliable results for large-sized column specimens,

Fig. 10. Final damage patterns of the URC specimen.

due to its sensitive to many factors (e.g. geometry boundary conditions, material heterogeneity, propagation path, and sensor characteristics) [6]. 4.2. AE source analysis Figs. 8 and 11 show that there are a very small number of cracks on the column surfaces above the AE sensors for both the FRPstrengthened and unstrengthened RC columns. Furthermore, the crack width of these cracks (less than 0.15 mm) was much smaller compared with the cracks generated at the plastic hinge region. For the FRP-strengthened RC column, the AE signals can be generated from concrete crack, debonding between concrete and FRP sheets, and crack of FRP sheets. The debonding between concrete and FRP sheets was unobvious for FRP-strengthened columns [1], and no FRP breakage was observed during the cyclic test. Hence, the

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Fig. 11. Crack patterns of the URC specimen at different peak loading displacements.

Fig. 12. Schematic diagram of AE parameters.

majority of the collected AE signals were emitted from the concrete cracks at the plastic hinge region, and it was reasonable to use these signals to evaluate the damage process of the FRPstrengthened RC column. In addition, an AE wave generated in concrete propagated as a bulk wave, while a wave generated in FRP sheets propagated as a guided wave with frequency dispersion effect [22]. Because of the complexity of AE sources and wave propagation, distinguishing these AE sources was difficult. For the unstrengthened column, it was unavailable to distinguish whether the AE signals were emitted from the plastic hinge region or the region above the sensors, because only two sensors were used to collect the signals. The location of cracks can be determined through AE location analysis, provided that more AE sensors (4 sensors or more) are mounted on the column.

4.3. AE hits analysis of the FRP-strengthened column Compared with the unstrenghened column, the FRPstrengthened column exhibited excellent ductility and energy dissipation capacity. However, the crack process of the concrete in the FRP wrapped plastic hinge region is unknown to inspectors, because the inside concrete is invisible due to the FRP cover. The AE activities of the FRP-strengthened column during the cyclic test are shown in Fig. 13(a), where the control displacement is also given. Because the AE signals collected by the two sensors were similar, only one sensor’s data was used here for conciseness. The time was normalized for comparison convenience. The crack process of the FRP-strengthened RC column can be divided into

three stages qualitatively (marked in Fig. 13(a)), based on the distribution of AE hits during the cyclic test. Stage 1 (initial stage): the specimen was in the elastic stage; AE hits were rare and the damage was negligible, because the displacement of the column was small and the crack activity of the concrete was weak. Stage 2: the specimen entered into yield stage, and it was observed that most of the AE hits occurred around the peak displacements and a relatively small number of AE hits occurred at other displacements, because the concrete at the bottom of the column cracked more severely around the peak displacement compared with other displacements at this stage. Stage 3 (from the twice yield displacement till the end of test): at the early part of Stage 3, it was observed that the peak of AE hits exhibited a relationship with the peak points of the control displacement, similar to that in Stage 2; at the latter part of Stage 3, the relationship became unobvious. There were two reasons for this: (1) most of the concrete cracks had formed before this stage, hence fewer new concrete cracks occurred at this stage compared with the former stages; (2) large amounts of AE hits were also generated from the opening and surface friction of the massive existing cracks during the cyclic loading at this stage. Fig. 13(a) shows that the boundary between the early part of Stage 3 and the latter part of Stage 3 is not clear. For practical application of AE technique based crack monitoring of RC columns, the peak points of displacement are always unavailable, and hence, the latter part of Stage 3 becomes difficult to identify. Fig. 13(a) also shows the strain responses of LS1 and BS1, which were measured at the peak points of the control displacement. Because of the symmetrical arrangement of the strain gauges (as shown in Fig. 5), the results of LS2 and BS3 are not shown in Fig. 13 for conciseness. Though the tensile strains of LS1 reached 13,613 le at the final loading stage, the strain responses of LS1 were mainly in the compressive state during the cyclic test owing to a large compression ratio of 0.3. The strain responses of the FRP strain gauges were in the tensile state due to the expansion of concrete at the plastic hinge region, and hence the FRP sheets can provide confinement stress for the inside concrete. For both LS1 and BS1, the strain responses showed an obvious fluctuation trend with the changes of the control displacement and increased with the increasement of the control displacement. However, the crack process of concrete during the cyclic test cannot be revealed by the strain variations of LS1 and BS1. In earthquake engineering, the damage levels of RC columns are always divided into five levels through the criterion proposed by Park et al. [23], including slight, minor, moderate, severe and collapse. Based on the distribution of AE hits during the test and the observed damage states of the FRP-strengthened column (as shown in Fig. 8), it can be inferred that Stages 1, 2 and 3 in the distribution of AE hits can be related to four different damage levels of the FRP-strengthened column qualitatively (as shown in

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(a) the BRC specimen

(b) the URC specimen Fig. 13. Distribution of AE hits and strain responses of the tested specimens.

Table 2): Stage 1 corresponded to slight damage; Stage 2 corresponded to minor damage; the early part of Stage 3 corresponded to moderate damage, and the latter part of Stage 3 corresponded to severe damage. Therefore, it can be concluded that the crack process of FRP-strengthened columns can be monitored by AE techniques and the damage levels can be determined qualitatively and conveniently based on the distribution of AE hits. 4.4. AE hits analysis of the unstrengthened column The distribution of AE hits of the unstrengthened column during the cyclic test is shown in Fig. 13(b), along with the strain

responses of LS1. The concrete strain gauges failed after the concrete tensile cracks appeared at the plastic hinge region, and hence the strain results are not given in Fig. 13(b). The steel strain responses of URC at the end of the test were evidently smaller than those of BRC, because the deformation capacity of BRC was great larger compared with URC. The strain responses of LS1 also showed a fluctuation trend with the changes of the control displacement. Based on the distribution of AE hits in Fig. 13(b), the crack process of the unstrengthened column can also be divided into three stages (marked in Fig. 13(b)). The distribution of AE hits in Stage 1 and Stage 2 was similar to those of the FRP-strengthened column. The difference was observed in Stage 3, where the corresponding

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G. Ma, H. Li / Construction and Building Materials 144 (2017) 86–98 Table 2 Damage levels of RC columns determined based on AE hits. Damage levels

AE hits stage

Observed damage states FRP-strengthened column

Unstrengthened column

Slight Minor

Stage 1 Stage 2

No cracks No cracks

Moderate

Early part of Stage 3 Latter part of Stage 3

Some horizontal cracks above FRP sheets, cracks between column and pedestal Horizontal cracks on FRP sheets, interface failure between column and pedestal.

Few tiny cracks Small horizontal cracks Many horizontal cracks, diagonal cracks Obvious plastic hinge, cover concrete peeled off

Severe

(a) the BRC specimen

relationship between the peak of AE hits and the peak displacements was unobvious compared with that of the FRPstrengthened RC column. The main reason was that the concrete damage of the unstrengthened column developed quickly at this stage compared with that of the FRP-strengthened column, due to no FRP confinement. The damage process of the unstrengthened column during the cyclic test can also be divided into four damage levels qualitatively (as shown in Table 2), based on the relationship between the distribution of AE hits during the test and the observed damage states of the unstrengthened column (Fig. 11). It should be noted that the damage levels of unstrengthened RC columns can be determined just based on the observed concrete crack states, because there are no FRP sheets on the concrete surface. 4.5. AE amplitude analysis In order to analyze the intensity of the crack process, the distribution of AE amplitudes of the FRP-strengthened and unstrengthened columns is shown in Figs. 14(a) and (b) respectively, in which the above-mentioned three stages are also marked for the sake of comparison convenience. Since there were huge numbers of AE hits released during the cyclic test for the specimens, each circle dot shown in Fig. 14 was an average amplitude value obtained from 50 AE hits. For the BRC specimen, it is obvious that large AE amplitudes occurred around the peak points of the control displacement at Stage 1, Stage 2 and the early part of Stage 3 (as shown in Fig. 14(a)), indicating that larger cracks appeared around the peak displacement compared with other displacement. At the latter part of Stage 3, this phenomenon became unobvious. The main reasons were: (1) fewer new concrete cracks occurred at this stage compared with the former stages, because most of the concrete cracks had already formed; (2) the amplitude of AE singles emitted from the opening and surface friction of the existing cracks was lower compared with new concrete cracks, as reported by Ma et al. [13]. Similar phenomenon was also observed for the URC specimen, as shown in Fig. 14(b). Based on the above findings, the distribution of AE amplitude can provide an alternative method to identify the peak displacements of RC columns under cyclic loading or earthquake loading for practical engineering, when the displacement responses are unavailable. 5. AE technique based crack magnitude assessment 5.1. B-value method The magnitude-frequency relationship (MFR), proposed by Gutenberg and Richter [7], was used in earthquake seismology to describe the relationship between the occurrence frequency and the magnitude of earthquakes. The magnitude-frequency relationship is depicted by the following formula [7]:

(b) the URC specimen Fig. 14. Distribution of AE amplitude of the tested specimens.

log10 N ¼ a  bML

ð1Þ

where ML is Richter magnitude of earthquake; N is number of earthquakes with magnitude greater than ML , and a and b are constants varying from region to region. The equation reveals the phenomenon that earthquakes with larger magnitude occur less frequently than those with smaller magnitude. In fact, acoustic emissions and earthquakes have similar mechanisms from the perspective of crack. The magnitude-frequency relationship was also used in the AE field after the pioneering work of Sammonds et al. [9]. The following equation can be derived from Eq. (1) to account the MFR of AE activities:

log10 NAE ¼ aAE  bAE AdB

ð2Þ

where N AE is number of AE hits with magnitude greater than AdB ; AdB is peak amplitude of AE hit in decibel unit, obtained from AE acquisition system; aAE and bAE are constants related with the crack process characteristic, and bAE is called the b-value of these AE hits. As similar to earthquakes, when micro-cracks are dominant in a crack process, a bigger bAE value is obtained; otherwise, a smaller bAE value is obtained when macro-cracks are dominant in a crack process. AdB can be determined by the magnitude of an AE waveform, through the following equation:

AdB ¼ 20log10 Amax

ð3Þ

where Amax is peak value of an AE waveform in lV unit. Therefore, the b-value calculated from Eqs. (2) and (3) should be multiplied by a factor of 20 to be consistent with the b-value used in seismology [10]. Shiotani et al. [24] proposed the improved b-value (Ib-value) analysis to take into account the statistical characteristics of the MFR of AE hits, in order to obtain more reasonable b-values. The b-value and Ib-value method were found to be effective and

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G. Ma, H. Li / Construction and Building Materials 144 (2017) 86–98

reliable in the evaluation of the crack process of rock [9–11], RC beams [12], FRP-strengthened RC beams [5], and FRP-confined concrete columns [13]. Until now, research addressing the crack process of FRP-strengthened RC columns under cyclic loading using b-value or Ib-value method has not been performed. In this study, it was found that the results obtained from bvalue and Ib-value analysis were close to each other when sufficient AE hits were used to calculate b-values and Ib-values. Similar phenomenon was also reported in Ref. [13]. Therefore, only b-value analysis was used here to analyze the crack process of the FRPstrengthened and unstrengthened RC columns. The b-value analysis of all the specimens was conducted according to the following steps: (1) the AE hits from the entire crack process of a specimen during the test were divided into several groups according to the time sequence. In this test, 800 AE hits of each group were found to be sufficient for calculating a reasonable b-value; (2) for each group, the b-value was obtained utilizing the method of linear least-square fitting and (3) repeat step (2) until all the AE groups were analyzed. Because each b-value corresponded to 800 AE hits, the density of b-values was correlative to the number of AE hits in a certain range of time. High b-value density indicated a large number of AE hits (high degree of crack activity), and low bvalue density meant a small number of AE hits (low degree of crack activity), as shown in Figs. 16(a) and (b) and discussed in the following Subsections 5.2 and 5.3. Fig. 15 represents the results of b-value analysis of two groups of AE hits to illustrate the magnitude-frequency relationship of AE hits and the effectiveness of b-value analysis. Group 1 and Group 2 were selected from the above-mentioned Stage 2 and Stage 3 crack process of the BRC specimen, respectively. There were no groups of AE hits from Stage 1, because the total AE hits were less than 800 in Stage 1 for both the BRC and URC specimens. During the b-value analysis, the range of amplitude (from 40 dB to 100 dB) was divided by an interval of 2 dB, in order to obtain a b-value with high accuracy and reliability, which can be demonstrated by the well fitting results shown in Fig. 15. The b-values decreased obviously from Stage 2 to Stage 3, indicating that the crack magnitude increased in Stage 3. 5.2. B-value analysis of the FRP-strengthened RC column The b-value analysis results of the FRP-strengthened RC column is shown in Fig. 16(a). Because of the inhomogeneous mechanical properties of concrete, the crack process of the concrete in the plastic region was essentially non-uniform, resulting in that the entire b-value curve along the time axis was not smooth. However, it is obvious that the distribution of b-values can be divided into three stages, which has also been used to divide the distribution

Fig. 15. Example of b-values of two AE groups from Stage 2 and Stage 3 of the BRC specimen.

(a) the BRC specimen

(b) the URC specimen Fig. 16. Variations in the b-values of the tested specimens.

of AE hits in the previous section. In Stage 1, no b-value was obtained at this stage because AE hits were rare at this stage (less than 800). In Stage 2, b-values were sparse (low density of b-values) along the time axis, because the control displacement was not large enough to generate large numbers of AE hits at the plastic hinge region. The obvious decrease of b-values was observed in Stage 2, indicating the increase of crack magnitude at this stage. In Stage 3, b-values became dense along the time axis compared with those in Stage 2, because the crack activity of concrete became more severe and the number of AE hits increased. It was obvious that the b-values became smaller at this stage compared with those in Stage 2, indicating that the crack magnitude of concrete at this stage was greater than that in Stage 2. At the beginning of Stage 3 (the loading step was 2Dy ), because the peak strength of the FRP-strengthened column was reached at the loading step of 2Dy (as shown in Fig. 6), large cracks occurred at this phase and the b-values showed an abrupt decrease. Then, the b-values increased to some extent, indicating the decrease of crack magnitude after the peak strength. After this, the b-values exhibited a fluctuation of up and down with the changes of the control displacement. The main reason was that the crack intensities at the plastic hinge region were more severe when the control displacement reached the peak value (resulting in smaller b-values), and the crack intensities became weak at the unloading stage (resulting in larger b-values). However, at the latter part of Stage 3, this phenomenon was unobvious. The main reason was that fewer new concrete cracks occurred at this stage compared with the former stages (as discussed in the previous Subsection 4.5). It should be noted that each b-value in this study was calculated by a group containing 800 AE hits. The number of AE hits in a group had a certain effect on the size of b-value, while had little effect on the trend of b-values during the crack process of a specimen [13].

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5.3. B-value analysis of the unstrengthened RC columns The b-value analysis results of the unstrengthened RC column is shown in Fig. 16(b). The trend of b-values can also be divided into three stages, similar to that of the FRP-strengthened RC column. In Stage 2, the b-values decreased obviously, indicating that the crack magnitude increased significantly with the increase of control displacement. After this stage, the b-values exhibited an abrupt decrease, and then showed a fluctuation of up and down with the changes of the control displacement at the early part of Stage 3, this phenomenon was more obvious compared with that of the FRP-strengthened column. At the latter part of Stage 3, this phenomenon became unobvious. 5.4. Comparison of b-values between cyclic and bending loading In cyclic test, the concrete crack process can be quite different from that in bending test, because the loading directions (push and pull) keep reversing along with the control displacement in the cyclic test (as shown in Fig. 3) compared with the monotonic loading method in bending test. Therefore, the above-mentioned trends of b-values of the FRP-strengthened and unstrengthened RC columns during the cyclic loading test are quite different from those of RC beams under bending test. For RC beams under bending test, the evolution of b-values can be divided into three stages, including the 1st stage (from beginning to 25% peak load strength Fp, b values showed a decrease trend), the 2nd stage (from 25% Fp to 75% Fp, b values exhibited no considerable changes), and the 3rd stage (from 75% Fp to failure, b value increased after a rapid drop at the yielding point) [5]. The fluctuation trend of values with the changes of the control displacement cannot be observed for RC beams under bending test. 6. Fractal theory based damage assessment 6.1. AE energy analysis The cumulative AE energy of the FRP-strengthened and unstrengthened RC columns is shown in Figs. 17(a) and (b) respectively, where the accumulative hysteretic energy dissipated during the cyclic test is also given, and the AE energy and hysteretic energy have been normalized for comparison convenience. Though a certain number of AE hits were observed in Stage 2, the cumulative AE energy was very low compared with the entire AE energy released during the test. The main reason was that only small concrete cracks were observed in Stage 2, though the columns entered into yield state at this stage. In Stage 3, the cumulative AE energy started to increase much faster compared with that in Stage 1 and Stage 2, and the cumulative AE energy in Stage 3 accounted for 98.8% and 95.3% of the entire AE energy for BRC and URC, respectively, indicating that the majority of the damage was accumulated in Stage 3. For both the FRP-strengthened and unstrengthened RC columns, the plastic hinge region formed and developed with the increasement of the control displacement in Stage 3, and the number and the size of the cracks also increased (as shown in Figs. 8 and 11). After the test, it was found that most of the concrete at the plastic hinge region cracked. Therefore, it can be inferred that the AE energy had a relationship with the volume of the cracked concrete for RC columns. This phenomenon is further discussed in the Subsection 6.2. In Figs. 17(a) and (b), it is obvious that the trend of the accumulative AE energy and hysteretic energy exhibited a good correlation for both FRP-strengthened and unstrengthened columns. Hence, an approximate formula can be proposed to describe this relationship as follows:

EAE EAE end

¼

Ehys

ð4Þ

Ehys end

where EAE and Ehys are accumulative AE energy and hysteretic energy from the start point to a given instant, respectively; EAE end and Ehys end are total AE energy and hysteretic energy at the end of the test, respectively. Eq. (4) shows that the AE energy can be treated equivalent to the hysteretic energy in earthquake engineering. 6.2. Fractal theory based damage prediction During the cyclic loading, the RC columns dissipated the input energy through hysteretic deformation and hence underwent accumulated damage in the plastic hinge regions. The dissipated energy can be used to describe the damage level of RC columns at a given instant during the cyclic test as follows:

Dhys ¼

Ehys

ð5Þ

Ehys end

Eq. (5) is a typical energy based damage index in earthquake engineering. The above Subsection 6.1 has shown that the accumulative AE energy had a good relationship with the hysteretic energy dissipated during the test, as shown in Eq. (4). Therefore, an AE energy based damage index DAE can be written as:

DAE ¼ Dhys ¼

EAE

ð6Þ

EAE end

Eq. (6) is concise in concept. However, in practical engineering applications, it is difficult to obtain the total AE energy EAE end of a RC column loaded from start to failure through AE acquisition system. Hence, it is necessary to derive EAE end based on theory analysis. For rock and concrete materials, the AE energy during the crack process shows a fractal characteristic based on fragmentation theory [25–27]. The relationship of AE energy and specimen volume can be defined as follows [27]:

C¼

EAE end

ð7Þ

V D=3

where C is the critical value of fractal energy density; EAE end is entire AE energy of the specimen till failure; V is specimen volume and D is the fractal exponent, which is comprised between 2 and 3. Based on experimental results of concrete under compression loading, D ¼ 2:3 was suggested by Carpinteri et al. [27] and was adopted tentatively here. The value of C can be treated as a sizeindependent parameter [27]. Hence, C can be considered the same for specimens of the same shape. Based on this rule, AE energy of practical FRP-strengthened columns can be predicted based on the experimental results obtained in this paper, written as follows:

EAE end;p EAE end;r

¼

 D=3 Vp Vr

ð8Þ

where EAE end;p is total AE energy of practical FRP-strengthened column under cyclic loading till failure; EAE end;r is AE energy of the FRPstrengthened specimen tested in this paper and is used as the reference column; V p is the volume of a practical column; V r is volume of the reference column. A damage index for practical FRPstrengthened columns under cyclic loading can be defined as:

DAE ¼

EAE p EAE end;p

¼

EAE p EAE end;r



Vr Vp

D=3 ¼

EAE p

Cr V D=3 p

ð9Þ

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(a) the BRC specimen

(b) the URC specimen Fig. 17. Cumulative AE energy of the tested specimens.

where EAE p is accumulative AE energy of practical FRP-strengthened column at a given instant and Cr is the critical value of fractal energy density of the reference specimen. Cr can be estimated from Eq. (7) when EAE end;r and the volume of the cracked concrete V r are known. For the reference FRP-strengthened column, the volume V r can be derived as follows:

V r ¼ hc b c L p

ð10Þ

where hc and bc are height and width of the column transverse section respectively, and Lp is length of the plastic hinge region. For unstrengthened RC columns, Lp can be obtained using the following formula proposed by Priestley et al. [28]:

Lp ¼ 0:08Lc þ 0:022f yl dl

ð11Þ

where Lc is column length; f yl and dl are yield strength and bar diameter of longitudinal reinforcement rebar, respectively. For FRP-strengthened square columns, the plastic hinge length is affected by the FRP confinement and Eq. (11) should be modified as follows [29]:

Lp ¼ 0:08Lc þ 0:022f yl dl þ

 0:72 2r Lpc bc

ð12Þ

where r is radius of chamfer corner and Lpc is plastic length that allows for the FRP confinement effect and can be written as follows [30]:

Lpc ¼ 3:028kf

when 0 6 kf < 0:1

Lpc ¼ ð0:51  2:30kf þ 2:28k2f ÞLc

when 0:1 6 kf < 0:5

ð13Þ ð14Þ

where kf is confinement ratio, defined by:

kf ¼

fl f co

ð15Þ

where f co is compression strength of unconfined concrete and f l is confining pressure provided by FRP and can be calculated as follows [31]:

fl ¼

2f frp tfrp bc

ð16Þ

where f frp and t frp are tensile strength and thickness of FRP, respectively. Base on Eq. (12), the plastic hinge length of the FRPstrengthened column tested here was 236 mm. Then,

Cr ¼ 3:012  1013 J mm2:3 can be obtained through Eq. (7), and it should be noted that the average value EAE end;r obtained from sensors 1 and 2 was used here to calculate Cr . Then, a concise but reliable damage index for practical FRP-strengthened columns with the same shape as the column tested here can be expressed as follows:

DAE ¼

EAE p 3:012  1013 V 0:77 p

ð17Þ

Both Eqs. (6) and (17) present the damage index based on AE energy, while a simple and more accessible V p is used in Eq. (17) instead of EAE end , which is hard to obtain in practical application. In fact, the fractal theory based damage index expressed in Eq. (17) can also be used in the damage evaluation of unstrengthened RC columns, provided that Cr and V p can be obtained for unstrengthened

G. Ma, H. Li / Construction and Building Materials 144 (2017) 86–98

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Table 3 Damage level classifications for FRP-strengthened RC columns based on AE damage index. Damage levels

Damage index

Slight Minor Moderate Severe Collapse

DAE < 0:1 0:1 6 DAE < 0:25 0:25 6 DAE < 0:4 0:4 6 DAE < 1:0 DAE P 1:0

columns. Based on the damage classification criterion for RC structures proposed by Park et al. [23], the damage levels of FRPstrengthened columns can be determined quantitatively based on the value of damage index, as shown in Table 3. The damage index DAE can be obtained through Eq. (17) utilizing AE monitoring data. For the FRP-strengthened column tested here, the variations of the fractal theory based damage index during the cyclic test are shown in Fig. 18, where the trend of the damage index is identical to that of the AE energy shown in Fig. 17(a), and hence the trend of AE energy is not given here. In Stage 1 and Stage 2, the damage level of the strengthened column was slight (with a damage index of 0.012). In Stage 3, the minor, moderate and severe damage levels occurred in sequence. Hence, it can be concluded that the majority of the damage was accumulated in Stage 3 for the FRP-strengthened column. It should be noted that the damage levels determined from DAE (as shown in Fig. 18) were a little different from those determined qualitatively from the distribution of AE hits (as shown in Table 2). For the unstrengthened RC columns, the damage evaluation process is similar to that of FRP-strengthened columns and is omitted here for conciseness. Because concrete cracks are covered by FRP sheets and no FRP breakage occurs for FRP-strengthened RC columns subjected to earthquake striking, in-situ observation is unable to determine the damage states of those columns. Therefore, the fractal theory based damage index can be quite useful to assess the damage levels of FRP-strengthened RC columns in practical engineering. In the present study, AE parameters such as AE hits, AE amplitude, and AE energy, were used to analyze the crack process of the column specimens. Hence, the results were unaffected by geometry boundary conditions, material heterogeneity, propagation path, and sensor characteristics. Although only two column specimens (the FRP-strengthened and unstrengthened columns) were tested and studied, the AE analysis results can be reliable. In practical engineering applications, the damage levels of an FRP-strengthened column can be determined from the distribution of AE hits qualitatively but rapidly, then a more accurate damage level can be determined after DAE is calculated.

Fig. 18. Variations of the damage index of the FRP-strengthened column during the cyclic test.

Furthermore, the distribution of AE amplitudes exhibited an obvious relationship with the peak displacements of the strengthened RC column under cyclic loading. (2) The b-value method was a convenient way to reveal the crack magnitude of the FRP-strengthened RC column. The crack magnitude was small at the early loading stage and relative large b-values were obtained. Then, b-values reduced obviously because the crack magnitude became larger due to the increasement of the control displacement. (3) The AE energy and hysteretic energy of the FRPstrengthened column under cyclic loading showed a good correlation with each other. The fractal theory based damage index was effective to determine the damage levels of the FRP-strengthened column and can be used in the damage assessment of FRP-strengthened columns in practical engineering.

Acknowledgements This research was sponsored by the National Natural Science Foundation of China (Grant No. 51408211), the Natural Science Foundation of Hunan Province, China (Grant No. 2015JJ3032), the State Scholarship Fund of China Scholarship Council (File No. 201606135057), the Open Fund of Hunan Province Engineering Laboratory of Bridge Structure (Changsha University of Science & Technology, Grant No. 14KD02), and the Fundamental Research Funds for the Central Universities through the Project of Young Teacher Growth of Hunan University (Grant No. 531107040799). References

7. Conclusions In this paper, AE techniques were utilized to study the crack process of the plastic hinge regions of FRP-strengthened RC columns. AE parameter analysis and b-value analysis were carried out in depth. Finally, a fractal theory based damage index was proposed to assess the damage levels of FRP-strengthened columns. The primary conclusions are summarized as follows: (1) AE hits analysis was effective in revealing the characteristics of the concrete crack process for both the FRP-strengthened and unstrengthened RC columns, although the concrete at the plastic region was covered by FRP for the strengthened column. Based on the distribution of AE hits, the damage process of FRP-strengthened RC columns can be divided into four different damage levels qualitatively: intact, slight damage, moderate damage, and severe damage.

[1] J.G. Teng, J.F. Chen, S.T. Smith, L. Lam, RP Strengthened RC Structures, Wiley, London, 2002. [2] S.S. Pendhari, T. Kant, Y.M. Desai, Application of polymer composites in civil construction: a general review, Compos. Struct. 84 (2) (2008) 114–124. [3] C.U. Grosse, M. Ohtsu, Acoustic Emission Testing: Basics for Research— Applications in Civil Engineering, Springer, New York, 2008. [4] A. Mirmiran, S. Philip, Comparison of acoustic emission activity in steelreinforced and FRP-reinforced concrete beams, Constr. Build. Mater. 14 (6–7) (2000) 299–310. [5] H.D. Yun, W.C. Choi, S.Y. Seo, Acoustic emission activities and damage evaluation of reinforced concrete beams strengthened with CFRP sheets, NDT&E Int. 43 (7) (2010) 615–628. [6] C.U. Grosse, H.W. Reinhardt, F. Finck, Signal-based acoustic emission techniques in civil engineering, J. Mater. Civ. Eng. 15 (3) (2003) 274–279. [7] B. Gutenberg, C.F. Richter, Earthquake magnitude, intensity, energy, and acceleration, Bull. Seismol. Soc. Am. 32 (3) (1942) 163–191. [8] C.H. Scholz, The frequency-magnitude relation of microfracturing in rock and its relation to earthquakes, Bull. Seismol. Soc. Am. 58 (1) (1968) 399–415. [9] P.R. Sammonds, P.G. Meredith, S.A.F. Murrel, I.G. Main, Modelling the damage evolution in rock containing pore fluid by acoustic emission, in: Proc., Eurock’94, Balkema, Rotterdam, The Netherlands.

98

G. Ma, H. Li / Construction and Building Materials 144 (2017) 86–98

[10] T. Shiotani, M. Ohtsu, K. Ikeda, Detection and evaluation of AE waves due to rock deformation, Constr. Build. Mater. 15 (5–6) (2001) 235–246. [11] M.V.M.S. Rao, K.J.P. Lakshmi, Analysis of b-value and improved b-value of acoustic emissions accompanying rock fracture, Curr. Sci. India 89 (9) (2005) 1577–1582. [12] S. Colombo, I.G. Main, M.C. Forde, Assessing damage of reinforced concrete beam using ‘b-value’ analysis of acoustic emission signals, J. Mater. Civ. Eng. 15 (3) (2003) 280–286. [13] G. Ma, H. Li, Z.D. Duan, Repair effects and acoustic emission technique-based fracture evaluation for predamaged concrete columns confined with fiberreinforced polymers, J. Compos. Constr. 16 (6) (2012) 626–639. [14] D.G. Aggelis, S. Verbruggen, E. Tsangouri, T. Tysmans, D. Van Hemelrijck, Characterization of mechanical performance of concrete beams with external reinforcement by acoustic emission and digital image correlation, Constr. Build. Mater. 47 (2013) 1037–1045. [15] N. Alver, H.M. Tanarslan, Ö.Y. Sülün, E. Ercan, M. Karcılı, E. Selman, K. Ohno, Effect of CFRP-spacing on fracture mechanism of CFRP-strengthened reinforced concrete beam identified by AE-SiGMA, Constr. Build. Mater. 67 (2014) 146–156. [16] F. Seible, M.J. Priestley, G.A. Hegemier, D. Innamorato, Seismic retrofit of RC columns with continuous carbon fiber jackets, J. Compos. Constr. 1 (2) (1997) 52–62. [17] J.K. Wight, J.G. MacGregor, Reinforced Concrete: Mechanics and Design, sixth ed., Pearson Education, 2011. [18] Code of China, Specification of Testing Methods for Earthquake Resistant Building (JGJ101-96), Publishing House of Building Industry in China, Beijing, 1996 (in Chinese). [19] S. Yuyama, T. Okamoto, M. Shigeishi, M. Ohtsu, Quantitative evaluation and visualization of cracking process in reinforced concrete by a moment tensor analysis of acoustic emission, Mater. Eval. 53 (6) (1995) 751–756.

[20] A. Mirmiran, M. Shahawy, H.E. Echary, Acoustic emission monitoring of hybrid FRP-concrete columns, J. Eng. Mech. 125 (8) (1999) 899–905. [21] R. Gutkin, C.J. Green, S. Vangrattanachai, S.T. Pinho, P. Robinson, P.T. Curtis, On acoustic emission for failure investigation in CFRP: pattern recognition and peak frequency analyses, Mech. Syst. Signal. Process. 25 (4) (2011) 1393–1407. [22] S. Degala, P. Rizzo, K. Ramanathan, K.A. Harries, Acoustic emission monitoring of CFRP reinforced concrete slabs, Constr. Build. Mater. 23 (5) (2009) 2016– 2026. [23] Y.J. Park, A.H.S. Ang, Y.K. Wen, Damage-limiting aseismic design of buildings, Earthquake Spectra 3 (1) (1987) 1–26. [24] T. Shiotani, K. Fujii, T. Aoki, K. Amou, Evaluation of progressive failure using AE sources and improved b-value on slope model tests, Prog. Acoust. Emission 7 (7) (1994) 529–534. [25] A. Carpinteri, N. Pugno, A fractal comminution approach to evaluate the drilling energy dissipation, Int. J. Numer. Anal. Methods 26 (5) (2002) 499– 513. [26] A. Carpinteri, N. Pugno, A multifractal comminution approach for drilling scaling laws, Powder Technol. 131 (1) (2003) 93–98. [27] A. Carpinteri, G. Lacidogna, N. Pugno, Structural damage diagnosis and lifetime assessment by acoustic emission monitoring, Eng. Fract. Mech. 74 (1–2) (2007) 273–289. [28] M.J.N. Priestley, F. Seible, G.M. Calvi, Seismic Design and Retrofit of Bridges, John Wiley & Sons, New York, USA, 1996. [29] C. Jiang, Y.F. Wu, G. Wu, Plastic hinge length of FRP-confined square RC columns, J. Compos. Constr. 18 (4) (2014) 04014003. [30] D.S. Gu, Y.F. Wu, G. Wu, Z.S. Wu, Plastic hinge analysis of FRP confined circular concrete columns, Constr. Build. Mater. 27 (1) (2012) 223–233. [31] Y.F. Wu, L.M. Wang, Unified strength model for square and circular concrete columns confined by external jacket, J. Struct. Eng. 135 (3) (2009) 253–261.