Cracking behavior of reinforced concrete beams strengthened with CFRP anchorage system under cyclic and monotonic loading

Engineering Structures 207 (2020) 110222

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Cracking behavior of reinforced concrete beams strengthened with CFRP anchorage system under cyclic and monotonic loading

T

Yonglai Zhenga, Yujue Zhoua, Yubao Zhoua, , Tanbo Pana, Qin Zhanga, Don Liub ⁎

a b

Department of Hydraulic Engineering, Civil Engineering College, Tongji University, China Department of Engineering Mechanics, Louisiana Tech University, United States

ARTICLE INFO

ABSTRACT

Keywords: CFRP Anchors Cyclic loading Beams Cracks Fractal dimension Ultrasonic detection

This paper presents the details of an experimental and analytical study that addresses the influence of carbon fiber-reinforced polymer (CFRP) anchors on the bearing capacity and fatigue behavior of reinforced concrete beams strengthened by CFRP strips. The experimental set comprised seven beams from which four beams strengthened by CFRP strips and anchors of four different lengths were first subjected to cyclic loading, and subsequently loaded until failure under monotonic loading. The remaining three beams were designed to establish the baseline response. The residual bearing capacity, damage degree, cracking behavior and ultrasonic inspection were analyzed. The results showed that the length of CFRP anchors significantly influenced the residual bearing capacity and failure modes of the specimens. A deep anchoring depth may result in a brittle failure of the specimen at the mid-stage of cyclic loading. In addition, based on the good correlation between residual bearing capacity and the fractal dimension of surface cracks of the beams, a novel damage index was proposed. The results also demonstrated that fractal dimension analysis together with ultrasonic inspection could be exploited to assess damage levels when mechanical testing is not available.

1. Introduction Fiber-reinforced polymer (FRP) strengthening is a widely used technology for the rehabilitation and repair of various reinforced concrete (RC) structures [1–4]. There have been many contributions in the area of flexural strengthening of reinforced concrete members subjected to monotonic loading [5–17]. On average, FRP fabrics are prone to premature debonding in a generally brittle manner, and a CFRP sheet is exhausted at a low ratio of its tensile strength when the specimen fails because of premature debonding of the CFRP ends [18], which is a severe limitation to this strengthening method. With the aim of preventing premature debonding, the novel CFRP anchor is a potential solution, behaving in a similar manner to traditional chemical anchors and steel mechanical fasteners and involving a notable increase in capacity [19,20]. CFRP anchors, also referred to as CFRP dowels, have been proposed as an effective means to resist axial forces (pullout), although some studies have relied on a complex force transfer that includes axial, shear, and bending resistance [21–25]. The main advantages of this anchorage system are its high strength-to-weight ratio, noncorroding characteristics and ease of construction. Earlier studies by Rasheed et al. [6] have noted the efficacy of this system in resisting the premature debonding of FRP sheets, more than ten years later, the ⁎

parameters affecting the performance of FRP anchors are still being studied [16]. To date, numerous studies regarding RC structures strengthened with CFRPs and CFRP anchors under monotonic loading have been widely published [26–31]. Recent studies in Chalioris et al. [32] have used CFRP ropes as the only transverse shear reinforcement of RC beams. But research on these structures subjected to cyclic loading are still limited [18,33–36]. Commonly, most engineering materials subjected to cyclic loading over many thousands of cycles exhibit lower residual strength than their monotonic static strength. RC members externally strengthened with CFRP sheets, subjected to cyclic loading, also show lower fatigue strength than their monotonic static strength [18], depending on the rate of loading, the number of cycles and CFRP installation parameters. There have been different design guidelines [37–41] suggesting that the CFRP stress should be limited to avoid fatigue failures of the CFRP strengthened RC members, as shown in Table 1. To adapt an externally bonded CFRP strengthening and CFRP anchoring system for real RC structures subjected to low-cycle cyclic loading such as wheel load and berthing force, the influence of loading cycle numbers, RC members characteristics and CFRP anchor installation parameters must be investigated. This paper focuses on assessing the feasibility of a CFRP anchorage system under cyclic loading.

Corresponding author. E-mail address: [email protected] (Y. Zhou).

https://doi.org/10.1016/j.engstruct.2020.110222 Received 27 March 2019; Received in revised form 5 December 2019; Accepted 11 January 2020 0141-0296/ © 2020 Elsevier Ltd. All rights reserved.

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Table 1 [18]. Stress limits in bonded fiber-reinforced plastic (FRP) subjected to cyclic loading. Guidelines

Carbon fiber-reinforced plastic

Glass fiber-reinforced plastic

Aramid fiber-reinforced plastic

ACI 440.2R-17 (ACI 2008)

0.55f fu

0.20f fu

0.30f fu

Technical report 55 (concrete society 2004)

0.80f fu

0.30f fu

0.70f fu

Concrete engineering series 41 (JSCE 2001)

0.84f fu

Fib bulletin 14 (fib task group 9.3 2001) CNR-D 200/2013 (CNR 2013)

– 0.50f fu

Note: ffu–ultimate strength of fiber-reinforced plastic.

Moreover, it aims to provide a fundamental understanding of the strengthening effects of anchor installation geometrical parameters on load transferring mechanism and establish a quick method to evaluate the damage level of beams strengthened by CFRP strips and anchors under cyclic loading.

3.2. Construction and installation of CFRP anchor Several detailed instructions of FRP anchor manufacture and assembly are contained in Llauradó and Zhang [20,43]. The method of CFRP anchor manufacturing used in this study is reported herein. Seven rectangular portions of unidirectional carbon fiber sheets 25 mm in width and 65 mm to 95 mm in 10-mm interval length were cut in advance (which meant that a 50-mm long rolled carbon fiber was retained after insertion of all anchors into the concrete), following the impregnation of the shaft region. According to Llauradó [20], the hardened length must not exceed 2/3 of the embedment length to avoid affecting the bending region; therefore, epoxy was applied to an end portion extending 10 mm across the whole width of the sheet for the formation of the hardened shaft. The epoxy resin used in this study is the HM-120CP Carbon Fiber Plate Adhesive (HORSE Co. Ltd). Because the applied epoxy resin increased the surface tension, the preimpregnated ends of anchors must be trimmed to the required lengths after hardening to obtain the specified anchor fans and dowel lengths as shown in Fig. 1. Several hours prior to installation of the CFRP anchor, four 8-mm diameter holes were drilled into the bottom faces of the beams; pressurized air and a vacuum were used to remove loose concrete particles and dust left on the drilled holes [20], and then the area of concrete to be strengthened with a CFRP laminate was prepared by removing the top few millimeters of concrete with a grinder [43]. Holes were then filled approximately halfway with epoxy prior to anchor injection, and the laminate was then pasted onto the strengthened area using the wet lay-up technique. Next, the anchor dowel was inserted into the hole. It should be noted that in the process of anchor insertion, the anchor dowel was slipped over the locally parted CFRP sheet to avoid cutting the fiber off. Finally, the holes were filled until the epoxy resin was level with the CFRP sheets, and the free ends of the anchors were fanned out and epoxied onto the sheets by the same epoxy to form the integrated CFRP anchoring system. The construction and installation process of the CFRP anchor is shown in Fig. 3.

2. Research significance and objectives CFRP laminates in structure strengthening applications were limited because of the lack of an efficient anchoring system. CFRP anchors have been proven feasible in effectively resisting premature failure under static loading. To be accepted for engineering practices, the performance of the anchor system under cyclic loading must be investigated. This study evaluated the fatigue performance of the CFRP anchors embedded in the RC beams that were strengthened by CFRP laminates at various anchoring depths. The study was conducted to satisfy two main objectives: (a) investigating the behaviors of the CFRP anchor system under cyclic loading and (b) establishing empirical relationships between the fractal dimensions of cracks, the average ultrasonic velocity and the integral mechanical degradation properties of anchored beams strengthened by CFRP laminates and anchors. 3. Methodology and experimental program 3.1. Details of specimens A total of 7 RC beam specimens with and without anchors were tested under three-point bending loading. Fig. 1 shows the details of the beams, while Fig. 2 shows the test set-up. The beams were nominally 120 mm wide by 150 mm deep by 400 mm long and reinforced by two 12-mm diameter deformed bars and 8-mm diameter plain stirrups spaced at 80 mm. A concrete cover of 20-mm thick was used around the stirrups. The same types of carbon fiber sheets were used for the construction of both the CFRP anchors and laminates. The carbon fiber sheets used in this study were nominally 0.11-mm thick per layer. The CFRP laminates of 100-mm width used herein were made from two layers of carbon fiber sheets in a wet lay-up manner. The supported area of the beams was created by prebonding thick steel blocks 30 mm in length at both ends of the bottoms. The specimens were divided into two series and are described in detail in Table 2. The control series contained two unstrengthened beams (S-0, F-0) and one beam that was only strengthened with CFRP laminates (SH-0). The control series were designed to establish the baseline response. The influence of anchoring depth (lanc ) and the robustness of CFRP anchors were investigated in the anchored series. The anchors were positioned in the near-end area of the specimens to achieve the maximum utilization of the CFRP anchors strength. The lengths (lanc ) of the anchors varied from 15 mm to 45 mm in 10 mm intervals, as shown in Fig. 1. The RC beams were balanced-reinforced with the area of flexural reinforcements of 226 mm2 . Although the shear ratio of the seven beam specimens is equal to 1.33, the little differences between flexural and shear capacity combined with the dispersion of concrete could highlight the influence of CFRP strengthening on the failure mode of beams [42].

3.3. Test set-up, loading and instrumentation The bending test program selected was a common working condition in wharf engineering at the Port of Shanghai, China. The influence of repeated ship-berthing impact on the wharf structures was studied. The loads were provided by an HTS 300 kN SANEA250 electrohydraulic servo actuator, which was restrained in a steel reaction frame (Fig. 2). Beam F-0 in the control series was tested under monotonic quasi-static loading in advance to determine the amplitude of the subsequent cyclic load, as shown in Fig. 4(a). The remaining six specimens (specimen S-0, SH-0, SH-15, SH-25, SH-35 and SH-45) shared the same loading scheme, as shown in Fig. 4(b). They were initially tested under cyclic loading followed by destructive monotonic quasistatic loading tests to determine their residual bending capacity. In all cases, each beam specimen was finally tested to failure under monotonic quasi-static loading. To be specific, in the cyclic loading test, the six beam specimens were first preloaded monotonically up to the required load level (equal to half of F-0′s ultimate load capacity, corresponding to a loading of 2

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Fig. 1. Details of specimens.

64.8 kN ) at a load rate of approximately 2 kN/s [16]. Then, repeated loading in the form of a sinusoidal curve (cyclic loading) was applied for 5000 cycles with a frequency of 1 Hz and a constant amplitude, as shown in Fig. 4(b). The number of cycles (5000 cycles) and the loading rate (1 Hz) were selected to simulate the typical repeated ship berthing impact during the design reference period of the typical wharf

structures of Shanghai Port [44]. The applied cyclic loading could be described as follows:

f (t ) = 32.4

(sin2 t + 1)

(1)

where f (t ) is the cyclic loading applied in the test (kN ); t is the test time (s). 3

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Table 2 Details of the test scheme. Series

Control series Anchored series

Specimen ID

F-0 S-0 SH-0 SH-15 SH-25 SH-35 SH-45

Bonded laminate1

Anchor details

Loading2

Y/N

lanc (mm)

F/S

N N Y Y Y Y Y

– – 03 15 25 35 45

S S&F S&F S&F S&F S&F S&F

1

Y/N = strengthened with CFRP/not strengthened. F/S = cyclic loading/monotonic static loading. 3 lanc = 0 means that specimen SH-0 was only strengthened by CFRP laminates and not strengthened by anchors. 2

and a total of 24 measuring points were selected for each specimen, as shown in Fig. 5. Two inspection tests were conducted for each specimen both before and after the cyclic loading test. The first inspection test was conducted before cyclic loading for all specimens. Then, the results of the second inspection obtained after the cyclic loading and before the final monotonic quasi-static loading were compared with those of the first inspection to ascertain the highlighted defects due to fatigue.

Fig. 1. (continued)

The generic layout of monitoring instrumentations, including the laser displacement sensor (denoted as LD) and the 50-mm (denotes as SG-1) and 3-mm (denoted as SG-2) electric resistance strain gauges, are shown in Fig. 1. SG-1 and SG-2 were located at the mid-span of the beam bottoms and reinforcing steel bars, respectively. Subsequently, the strains of concretes and steel bars were obtained by calculating the average values of SG 1–1, SG 1–2 and SG 2–1, SG 2–2, respectively. LD1 monitored the in-plane vertical displacement in the mid-span of the beam bottoms, and LD-2 was used to monitor the out-of-plane movements of the beams (the values of out-of-plane displacements in this study were mostly less than 0.5-mm and hence should be neglected, according to [21,45]). The beam specimens were inspected using a ZBL U-5100 system operating at a frequency of 1 MHz (Fig. 5). The ultrasonic test system consisted of a pair of transducers (a pulse generator and a receiver) and a high-speed data-acquisition system. The transducers were arranged on both sides of the specimens with a contact medium of water-soluble grease

3.4. Material properties All RC beams and six 150-mm cubic samples used to determine the compressive strength of concrete were poured in one batch from commercially sourced concrete whose composition is outlined in Table 3. The specimens were demolded after 48 h of casting and then water cured for 28 days before simulated marine environment exposure. The 28-day cube compressive strength of the concrete was on average 34 ± 1.7 MPa. The deformed reinforcements in all specimens were 12mm nominal diameter steels with a yield strength of 335 MPa and an ultimate strength of 445 MPa. The 8-mm diameter plain bars used for stirrups had a yield strength of 240 MPa and an ultimate strength of 380 MPa. The CFRP sheet used in the construction of the CFRP anchor and laminates had a modulus of elasticity of 65 GPa, ultimate tensile strength of 3,000 MPa and an elongation of 2.1% at breakage. The material properties of reinforcements and CFRPs were taken from our previous laboratory tests.

Fig. 2. The cyclic loading test set-up. 4

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(a) manufacturing procedure of CFRP anchor

Beam bottom epoxy

Holes

Step.2 Holes were filled halfway with epoxy and the sheet was pasted

Step.1 8 mm diameter holes were drilled

Step.3 Inserting CFRP anchors

(b) procedure of applying CFRP anchorage system Fig. 3. The process of construction and installation of CFRP anchor.

Fig. 4. Loading schemes.

5

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Fig. 5. Ultrasonic examination set-up. Table 3 Concrete mix constituents. Specific weight (kg/ m3) Concrete grade

Density (kg/m3)

Fine aggregate/aggregate

Water/ cement ratio

Cement

Fine aggregate

Coarse aggregate

C40

2374

0.45

0.6

383.3

792.3

968.4

Notes. River sand was used as the fine aggregate and crushed granite stone with a maximum size of 10 mm was used as the coarse aggregate.

Fig. 6. Strain response of all specimens. 6

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Fig. 7. Typical failure modes of CFRP anchorage system.

Fig. 8. Cycle numbers at initiation of incompatible deformation and cover cracking.

4. Experimental results and discussion 4.1. Strain response The incoordinate deformation between steel and concrete developed with the accumulation of fatigue damage induced by cyclic loading, as shown in Fig. 6. The strains of concrete and reinforcement were obtained by calculating the average values of strain gauges SG 1–1, SG 1–2 and SG 2–1, SG 2–2, respectively. A typical three-stage characteristic could be distinguished, namely, stage I-III, which indicate the cooperation between the anchorage system and RC beam, a partial failure of the anchorage system and a total failure of the anchorage system, respectively. Points c1 and c2 are the numbers of cycles at the boundary of stage I, II and II, III, respectively. To be specific, the value of c1 is the cycle numbers at initiation of incompatible deformation between steel and concrete, which also implies the cooperative working duration between the CRFP

Fig. 9. Schematic of cracks recording procedure.

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Fig. 10. Cracking pattern of specimens.

Fig. 11. Diagram of box-counting method for calculating the fractal dimension (r is the box size).

anchorage system and RC beams. The value of c2 is the cycle numbers at cover cracking and the tensile failure of SG1-1 and/or SG1-2, which reveals the life spans of the CRFP anchorage system. The three typical failure modes of the CFRP anchorage system are shown in Fig. 7 for each specimen. The deformations of specimen SH-0 were similar to those of the unstrengthened specimen S-0, entering stage III quickly at the beginning of cyclic loading (Fig. 6(a) and (b)). This could be attributed to the premature debonding of CFRP laminates (Fig. 7(a)) that occurred in specimen SH-0 without the restriction of anchors. The CFRP anchors were pulled out (Fig. 7(b)) in specimens SH15 and SH25 at approximately 2000 and 3000 cycles, respectively. Correspondingly, the curves of specimen SH-15 and specimen SH-25 exhibited all three stages, each having a various duration (Fig. 6(c) and (d)). Stage III and I disappeared in strains of specimen SH-35 and specimen SH-45 (Fig. 6(e) and (f)), respectively, corresponding to observations in the cyclic loading tests that the anchorage system in

specimen SH-35 performed well in the whole test process, while fiber rupture (Fig. 7(c)) occurred in the middle span of the strengthened CFRP laminates of specimen SH-45 at approxiamately1500 cycles. The results of the cycle times at point c1 and c2 of each specimen are included in Fig. 8. Both the values of c1 and c2 increased first but then dropped as the anchoring depth increased, and the maximum values were achieved by specimen SH-35. Therefore, it is clear that the 35-mm depth anchor is considerably more effective in both strengthening cooperation between the CRFP anchorage system and the RC beam and extending the working life span of the CRFP anchorage system. 4.2. Fractal dimension analysis of surface cracks 4.2.1. Cracking patterns The geometric morphology of the cracks that had been marked during the cyclic loading tests were mapped into different colors to 8

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Fig. 12. Plots of lgN(r ) versus lg(r) for all specimens.

distinguish the recorded time, as shown in Fig. 9. Visual cracks of two specimens in the control series (S-0 and SH-0) were first observed at the midspan of the bottom face, and then a long diagonal crack that displayed a 45° angle appeared on the side face of the beams (Fig. 10(a) and (b)). In the anchored series, the cracking pattern of specimen SH-15 was analogous to those of specimens in the control series, as shown in Fig. 10(c). As the embedment depths increased, the cracking patterns changed dramatically. Specimen SH-25 started cracking on both side faces of the beam, followed by cracking in the bottom of the midspan (Fig. 10(d)). For specimen SH-35, smaller diagonal cracks initiated during 1500–2000 cycles, which was much later than that of specimen SH-25. It should be noted that no crack appeared in the bottom of the midspan of specimen SH-35 throughout

the entire cycle loading test (Fig. 10(e)). Cracks of specimen SH-45 originated on both sides as early as 500–1000 cycle numbers, distributing along the axes of the four predrilled holes (Fig. 10(f)). 4.2.2. Fractal dimension Fractal dimension (FD) was used as a geometric parameter to characterize the irregularity of the cracking maps [46,47]. A boxcounting method that counted the number of boxes containing cracks N (r) as a function of box size r (m) was applied to estimate the fractal dimension of cracks on the surface of specimens (Fig. 11). The fractal dimension (FD) is defined by Eq. (2):

9

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fractal dimension analysis, a damage index (D) could be defined by Eq. (4):

FDi 1 2 FDf

D=

(4)

where FDi is the fractal dimension computed at i times the load cycle, and FDf is the fractal dimension at the initiation of visual cracks. Therefore, D varies between 0 and 1 and represents the difference between the current status of crack patterns and the baseline status FDf . 4.3. Mechanical property test 4.3.1. Failure modes and residual bearing capacity of beams This section provides a summary of the overall behavior of the beam specimens in the final monotonic static bearing capacity tests, in terms of failure mode, load-deflection behavior and ultimate bearing capacity. The cracking patterns at failure of all the tested beams are illustrated in Fig. 14. For the unstrengthened specimen (S-0), the specimen only strengthened with CFRP laminates (SH-0) and the specimen strengthened with 15 mm anchors (SH-15), similar crack patterns and failure modes were observed (Fig. 14(a) and (c)). The flexural cracks around the mid-span that had already formed during the cyclic loading propagated as the load increased, and signs of vertical cracking around the mid-span were evident. Subsequently, the already formed diagonal cracks began to widen significantly and propagate closer to the loading point and supports. During the propagation of the flexure-shear cracks, crushing of the concrete cover occurred on the top surface and near the loading points. For the specimen strengthened with 25 mm anchors (SH-25) and 35 mm anchors (SH-35), the rate of propagation and formation of flexural cracks around the mid-span significantly decreased, and no flexural cracks were observed in specimen SH-35. Only some of the already formed diagonal cracks continued to slowly propagate (Fig. 14(d) and (e)). The failure mode of specimen SH-45 was quite different. The vertical cracks that formed in the cyclic load began to widen and propagate quickly along the drilled holes as the load increased, causing severe damage of concrete on the left side (Fig. 14(f)). What’s more, no prior warning of collapse was evident, with failure occurring in a sudden, brittle manner. Fig. 15 shows the load-deflection curves in the final monotonic static bearing capacity tests for all specimens. It is evident that the specimen strengthened with 15 mm anchors (SH-15) and 45 mm anchors (SH-45) had limited improvement in ultimate loads compared with those of the unstrengthened specimen (SH-0), and the specimen only strengthened with the CFRP laminate, as is shown in Fig. 15(b) and (e). The ultimate loads of SH-25 and SH-35 approached 132.6 KN and 139.7 KN, respectively, with corresponding increase rates of 60.3% and 69.0% in comparison with the unstrengthened specimen S-0. The ultimate load values of both SH-25 and SH-35 even exceeded that of specimen F-0 that suffered no fatigue damage (Fig. 15(c) and (d)). The drop of load occurred at the middle of the curve of specimen SH45 (Fig. 15(e)) at the very moment of the concrete cracking along the drilled holes. As discussed above (Fig. 7(c)), SH-45 suffered a partial rupture of CFRP laminates at approximately 1500 cycles under cyclic loading. However, this partial premature rupture of the CFRP laminates

Fig. 13. Fractal dimension (FD) versus cycle numbers.

FD =

lim r

0

log10N(r ) (2)

log10 (r)

In an actual application, FD is estimated by fitting a linear curve to the plot of log10N(r ) versus log10 (r) , which can be expressed as Eq. (3):

lgN(r ) =

(3)

FDlg(r) + C

In Eq. (3), C is a constant. The slope of the least-squares fit line is taken as an estimate of the fractal dimension (FD) [48]. Fig. 12 shows the plots of lgN(r ) versus lg(r) of specimens with various embedment depths at different cycle numbers. For a particular cycle, the cracks of the specimens remained constant. According to the box-counting method, a linear relationship would be established between the number of boxes containing cracks N(r) and box size r (m) in the limit sense. Theoretically, the slope of this linear relationship is exactly the values FD. In an actual application, FD is estimated by fitting a linear relationship to the plot of log10N(r ) versus log10 (r). The FDs grow in value as the cycle numbers are increased. Fig. 13 illustrates the evolution of the fractal dimensions versus cycle numbers. Two stages (the growth stage and the plateau stage) can be observed in the curves: the FD increases linearly in the growth stage and then reaches a plateau. The comparison among the specimens shows that the FD values decrease first and then rise as the embedment depths increase, and the minimum is achieved by SH-35. Table 4 shows the maximum slope segments of the FD evolution curves. In this segment, the fractal dimension increases sharply within a short time. It should be noted that the duration of the maximum slope segment is consistent with the features of the strain response. The aforementioned values of c1 and c2 are mostly located in the ranges of the maximum slope segments in the FD curves. Therefore, the values of maximum slope that vary between 2.1–5.9 × 10−4 per cycle have the potential to warn of failure of the CFRP anchorage system in practical applications even if no severe cracks were observed. 4.2.3. A novel damage index (D) To estimate the damage level of the specimens using the results of

Table 4 Correspondence between feature points of strain and the maximum slope segment of FD. Specimen identification

S-0

SH-0

SH-15

SH-25

SH-35

SH-45

Cycle times at c1 Cycle times at c2 Range of maximum slope portion

0 4 500–1000 1000 5.86

516 516 1000–1500

1013 1742 1000–2000

1117 2874 1500–2500

3566 > 5000 3500–4000

0 702 0–1000

3.65

3.02

2.14

2.17

4.14

Maximum slope (10−4/cycle) cycle)

10

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Fig. 14. Failure mode of beam specimens.

did not lead to a full loss of bearing capacity for SH45. In fact, in the final monotonic loading test, the partially-damaged CFRP strengthening system could still share a load after the concrete damage occurred along the drilled holes, resulting a rerise of load. The loss rate of ultimate load P max (compared with specimen F-0) determined the damage level of the beams due to fatigue, which can be expressed by Eq. (5): Pmax

=

Pmax . Fo Pmax × 100% Pmax . Fo

“severe”, and the damage degree was correspondingly divided into three levels: I, II, and III, according to values of loss rates of ultimate load ( P max ): when the values of P max are less than 0, which means that the ultimate bearing capacity of beam specimen is even higher than that of the control specimen F0 with no fatigue damage, the damage level is defined as “I”. The damage level is defined as “II” and “III” when the values of P max are in the range of 0–35 and above 35 (%), respectively. Table 6 summarizes P max , D and FD for all specimens. As shown in Fig. 16, the evolution of P max was consistent with that of D. The loss rates of ultimate load ( P max ) could assess the strength loss with an accepted error. Therefore, D can be exploited to judge the damage condition of beams strengthened by CFRP strips and anchors under cyclic loading through visual inspection of crack patterns in cases where mechanical testing is not available.

(5)

where Pmax is the ultimate bearing capacity and Pmax. Fo is the ultimate bearing capacity of the control specimen F-0. The stiffness degradation rate K can be expressed by Eq. (6): K

=

K .F 0 K × 100% K .F 0

(6)

4.4. Ultrasonic test

where K is the secant stiffness and K.F0 is the secant stiffness of the control specimen F-0. The results of the ultimate load (Pmax ), loss rate of ultimate load ( P max ), secant stiffness (K) and stiffness degradation rate ( K ) as well as the CFRP failure modes of each specimen are summarized in Table 5.

4.4.1. Results of the ultrasonic test Fig. 17 shows the time-amplitude response of typical ultrasound signals before and after cyclic loading. The IOE point is the initiation of excitation where the pulser sends the synchronization pulse and the FAS is the first arrival point where the ultrasound first reaches the receiver [49]. As shown in the figure, the signal strength obviously decreased and the ultrasonic waveforms became more irregular after cyclic loading.

4.3.2. Correlation between strength loss correlated with damage index (D) Damage levels could be classified as “weak”, “moderate” or 11

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Fig. 15. Load-deflection responses of specimens.

The mean results and scatters of amplitude of the first echo peak and the wave velocity of specimens in the first supersonic inspection (before the cyclic loading test) are summarized in Table 7, including the standard deviation (SD), coefficient of variation (CV) and 95% confidence interval (CI) of each beam. The scatter of the ultrasonic wave velocity data that were preprocessed by confidence interval technique have been significantly reduced. Therefore, those data could be reliably used to evaluate damage condition of beam specimens. The 95% confidence intervals (CI) of the undamaged specimens in the first inspection (Table 7) are used as a criterion. Only the obtained values of certain measurement points after

cyclic loading, which are out of the ranges of the 95% confidence intervals (CI) of the undamaged specimen, are defined as “damage point”. Table 8 shows the numbers of “damage point” (Np ), mean results and scatters of amplitude of the first echo peak and the wave velocity of each specimen that were obtained after cyclic loading test. For specimens strengthened with the anchors of moderate depths (SH-15, SH-25 and SH-35), smaller scatters characteristic of ultrasonic features including CV and SD can be observed. The possible reason is that the CFRP anchor system can effectively resist the fracture extension inside the concrete beam through enhancing the cooperation between the CFRP laminates and the beams. By contrast, for the unstrengthened 12

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Table 5 Mechanical property test results. Specimen identification

Pmax (KN)

F-0 S-0 SH-0 SH-15 SH-25 SH-35 SH-45

129.6 82.7 97.6 107.7 132.6 139.7 77.0

P max (%)

– 36.2 24.7 16.9 −2.3 −7.8 40.6

K × 106 (N/m) 37.0 16.2 20.8 20.9 30.8 36.3 11.2

K (%)

– 56.2 43.8 43.5 16.8 1.9 70.0

Failure mode of CFRP – – Debonding Pull out Pull out Debonding* Fiber rupture

Notes. The failure mode of CFRP labeled with “*” denotes that the failure occurred in the final monotonic static bearing capacity test and those without “*” denote that the failure of CFRP occurred in cyclic loading. Table 6 Categories of damage degree defined by the values of the damage index, D, and fractal dimension, FD. Specimen

Pmax (KN)

S-0 SH-0 SH-15 SH-25 SH-35 SH-45

82.7 97.6 107.7 132.6 139.7 77.0

P max (%)

36.2 24.7 16.9 −2.3 −7.8 40.6

Damage degree

Damage classification

FD

D

Fig.17. Time-amplitude response of specimen S-0 at one of the measure points.

III II II I I III

Severe Moderate Moderate Weak Weak Severe

1.461 1.448 1.427 1.39 1.133 1.462

0.47 0.45 0.43 0.39 0.13 0.73

in Table 7 and 8). 4.4.2. Validation of the proposed damage index (D) based on ultrasonic inspection analysis The ultrasonic wave velocities have much lower scatters and thus are selected as an index of damaged level for CFRP beams. To reduce the impact of random error, only the reduction of wave velocity of “damaged points” is taken into consideration, and the average reduction of wave velocity ( v¯ ) of specimen can be expressed by Eq. (7): Np

v¯ =

j=1

vj Nt

=

Np· v¯p Nt

= k· v¯p

(7)

In Eq. (7), Np is the number of “damaged points”, vj is the reduction of wave velocity at the No. j “damaged point”, Nt is the amount of the measurement points, v¯p is the average reduction of wave velocity of “damaged points”, andk is the coefficient of the damaged area, which Np is defined as k = N . t The coefficient of the damaged area (k ) indicates the size of the damaged areas in specimens and the average reduction of “damaged points” ( v¯p ) implies the damage level of the damaged area. Hence, an average reduction of wave velocity ( v¯ ) that contains both k and v¯p has the potential to show the damaged levels of the specimens. Table 9 shows the good correspondence between the average reduction of wave velocity ( v¯ ) and the proposed damage index (D), verifying the rationality of the proposed damage index (D). Fig. 16. Relationship between

P max

4.4.3. Regression analysis between v¯ and Pmax Analysis above shows that the damage condition of the CFRP strengthened beams has a significant effect on both the ultrasonic wave velocity and the residual bearing capacity, and the relation between them can be used to predict the bearing capacity by means of the supersonic non-destructive detection, which has very high application value in the engineering practice. A best-fit relationship between the average reduction of wave velocity, v¯ , and ultimate bearing capacity, Pmax , for different fatigue damaged degrees is shown in Fig. 19(a) The exponential best-fit trend line representing the obtained data could be expressed in mathematical form as follow:

and D within the studied range.

specimen (S-0) and the specimen with the deepest anchoring depth (SH45), much greater scatters in these statistical parameters could be observed, which could be attributed to the rapid development of cracks resulting from the lack of the restriction of the CFRP laminates. Fig. 18 shows the comparisons of the ultrasonic response before and after the cyclic loading, complemented with an analysis of standard deviation (SD) error bars. After the cyclic loading, the values of both the wave velocity and amplitude of the first echo peak show a decreasing trend, and their scatter degrees increased. The comparison among the specimens demonstrates that declines of the two parameters decreased first then increased with the increase of embedment depths, and specimen SH-35 exhibited the least decline and lowest scatter. Additionally, the scatter was much lower for wave velocity both before and after the cyclic loading, in comparison with that of the amplitude of the first echo peak (which could also be concluded from the CV values

Pmax = 89.17·exp(

v¯/0.524) + 67.940. 11 < v¯ < 1.23(Km/s)

(8)

For the convenience of application, the v¯ and Pmax are transformed into the dimensionless forms: v¯ and Pmax , respectively, which are expressed by Eqs. (9) and (10): Pmax

13

=

Pmax pmax. F 0

(9)

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Table 7 Results of ultrasonic features before cyclic loading. Specimen identification

Wave velocity (Km/s)

Amplitude of the first echo peak (dB)

Average (Km/s)

SD (Km/s)

CV (Km/s)

CI (Km/s)

Average (dB)

SD (dB)

CV (dB)

CI (dB)

S-0 SH-0 SH-15 SH-25 SH-35 SH-45

3.95 3.97 4.00 4.01 3.95 3.71

0.13 0.10 0.09 0.08 0.11 0.23

0.03 0.03 0.02 0.02 0.03 0.06

(3.89, (3.93, (3.96, (3.98, (3.90, (3.61,

65.1 69.4 67.2 68.2 65.0 53.4

6.88 5.90 7.04 5.72 6.11 9.80

0.11 0.09 0.10 0.08 0.09 0.18

(62.1, (66.9, (64.2, (65.7, (62.4, (49.2,

4.01) 4.01) 4.04) 4.04) 4.00) 3.81)

68.1) 71.9) 70.2) 70.7) 67.6) 57.6)

Table 8 Results of ultrasonic features after cyclic loading. Specimen

S-0

SH-0

SH-15

SH-25

SH-35

SH-45

Wave velocity (Km/s)

Amplitude of the first echo peak (dB)

Range (Km/s)

Np

Mean (Km/s)

2.70–3.00 3.00–3.30 3.30–3.50 3.50–3.89 Total 2.80–3.10 3.10–3.30 3.30–3.60 3.60–3.93 Total 2.80–3.10 3.10–3.30 3.30–3.60 3.60–3.96 Total 3.20–3.50 3.50–3.60 3.60–3.70 3.70–3.98 Total 3.40–3.60 3.60–3.70 3.70–3.80 3.80–3.90 Total 2.30–2.60 2.60–2.80 2.80–3.30 3.30–3.90 Total

13 5 2 3 23 6 7 4 3 20 4 6 4 3 17 1 3 3 4 11 2 3 2 2 9 8 10 4 2 24

2.79 3.08 3.41 3.64 3.02 2.86 3.34 3.51 3.60 3.27 2.92 3.32 3.69 3.81 3.40 3.25 3.52 3.61 3.85 3.64 3.41 3.62 3.77 3.82 3.65 2.35 2.71 3.10 3.49 2.72

SD (Km/s)

CV (Km/s)

0.31

0.10

0.28

0.09

0.32

0.09

0.19

0.05

0.15

0.04

0.34

0.13

Range (dB)

Np

Mean (dB)

30.0–35.0 35.0–40.0 40.0–55.0 55.0–62.1 Total 30.0–35.0 35.0–40.0 40.0–55.0 55.0–66.9 Total 30.0–40.0 40.0–55.0 55.0–60.0 60.0–64.2 Total 35.0–40.0 40.0–50.0 50.0–60.0 60.0–65.7 Total 45.0–50.0 50.0–55.0 55.0–60.0 60.0–62.4 Total 30.0–35.0 35.0–40.0 40.0–55.0 55.0–62.1 Total

11 5 3 4 23 5 7 7 1 20 3 8 5 1 17 1 5 3 2 11 1 1 1 5 8 8 7 5 2 22

33.9 35.8 52.9 61.2 41.5 33.2 38.4 54.6 65.2 44.1 31.3 42.6 56.6 62.6 45.9 37.4 42.2 55.6 65.2 49.6 42.5 52.9 57.7 60.9 57.2 33.0 35.4 54.6 56.3 40.8

Fig. 18. Error bars: features of ultrasonic inspection before and after the cyclic loading.

14

SD (dB)

CV (dB)

10.90

0.26

10.10

0.23

9.63

0.21

9.62

0.19

6.16

0.11

9.82

0.24

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Table 9 Average reduction of wave velocity ( v¯ ) and the proposed damage index (D). Specimen ID

S-0

SH-0

SH-15

SH-25

SH-35

SH-45

D v¯ D/ v¯

0.47 0.89 0.53

0.45 0.58 0.78

0.43 0.43 1.00

0.39 0.17 2.29

0.13 0.11 1.18

0.75 0.99 0.78

Fig. 19. Exponential plots between the average reduction of wave velocity and ultimate bearing capacity.

v¯

=

v¯ v¯b

failure of the CFRP anchorage system. 3. A proposed damage index (D) derived from the FD was found to be consistent with the loss rate of the ultimate load ( Pmax ) and thus can be used to estimate the damage degree due to fatigue. The ultrasonic wave velocity was selected as the index of the damaged levels for CFRP beams and used for the validation of the proposed damage index (D). The average reduction of supersonic wave velocity after cyclic loading is consistent with bearing capacity and the values of D, according to which, the accuracy of D is verified. 4. The performance of beams under both monotonic and cyclic loading is improved first and then deteriorated with increasing anchoring depth. (In this study, the bearing capacity of the 35 mm anchored beam was approximately 43.1%, 29.7%, 5.4% and 81% higher than those in the unanchored, 15, 25 and 45 mm depth anchored specimens, respectively). It is evident that an anchoring depth of CFRP anchors that is too deep could damage the integrity of the RC component itself. In such cases, the gain of bearing capacity from strengthening would be counteracted. Therefore, an anchoring depth of 1.75 times the cover is recommended for CFRP strengthened beams under cyclic loading.

(10)

where Pmax. F 0 is the bearing capacity of the specimen F-0 and v¯b is the average wave velocity detected before the cyclic loading. Thus, another graph relating dimensionless forms of average reduction of wave velocity, v¯ , and ultimate bearing capacity, Pmax , is shown in Fig. 19(b). The exponential best-fit trend line of the dimensionless forms is expressed in mathematical form by Eq. (11): P max

= 0.688·exp

(

) + 0.542

v¯ /0.131

0.028 <

v¯

< 0.308

(11)

5. Conclusions In this study, the performance of reinforced concrete beams strengthened by CFRP strips and anchors under cyclic loading was studied. The following conclusions can be drawn. 1. Three typical failure modes of the CFRP anchorage system, namely, debonding, pull out and fiber rupture, were observed during the cyclic loading. The depths of CFRP anchors have a significant influence on the failure modes of the CFRP anchorage system. Premature debonding occurred in specimen SH-0, which was only strengthened by the CFRP laminate. CFRP anchors were pulled out in the specimens strengthened by 15 mm and 25 mm anchors (SH-15 and SH-25). Fiber rupture occurred at the middle span of the strengthened CFRP laminate of the specimen strengthened by 45 mm anchors (SH-45), while no visual damage was observed in the specimen strengthened by 35 mm anchors (SH-35) during the entire cyclic loading test. 2. Fractal analysis together with supersonic nondestructive detection were demonstrated to have the potential to assess the damage to RC beams when a mechanical test is not available. The ranges of the maximum slope segments in the curves of fractal dimension (FD) of cracks versus cycle numbers were associated with the time to failure of the CFRP anchorage system. Therefore, the FD that grow in value as the cycle numbers increase can be a parameter not only to identify the cracking patterns of specimens but also to warn of

Credit Authorship Contribution Statement Yonglai Zheng: Resources, Project administration, Funding acquisition. Yujue Zhou: Conceptualization, Methodology, Software, Formal analysis, Investigation, Writing - original draft, Writing - review & editing, Data curation. Yubao Zhou: Conceptualization, Methodology, Software, Formal analysis, Investigation, Writing - original draft, Writing - review & editing, Validation. Tanbo Pan: Investigation. Qin Zhang: Resources. Don Liu: Writing - review & editing, Supervision. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. 15

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Acknowledgements

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