Partially corroded reinforced concrete piers under axial compression and cyclic loading: An experimental study

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Partially corroded reinforced concrete piers under axial compression and cyclic loading: An experimental study Haijun Zhoua,b, , Yanan Xua, Yanrong Penga, Xuebing Lianga, Dawang Lia, Feng Xinga ⁎

a b

Guangdong Provincial Key Laboratory of Durability for Marine Civil Engineering, Shenzhen University, Shenzhen 518060, China Institute of Urban Smart Transportation & Safety Maintenance, Shenzhen University, Shenzhen 518060, China

ARTICLE INFO

ABSTRACT

Keywords: Bridge pier Reinforced concrete Marine environment Corrosion Axial compression Cyclic loading

Twelve reinforced concrete (RC) pier specimens were developed and partially corroded to simulate severe corrosion in splash and tidal zones. Six target corrosion levels were applied to rebars and stirrups using an electrochemical accelerated corrosion technique. Axial compression loading and cyclic loading tests were carried out with six specimens per group. The test results showed that mechanical parameters of pier specimens degraded with an increase in corrosion. The ultimate load, ductility factor, energy dissipation decreased by 29.96%, 9.26%, 67.44% for axial compression specimen with 15.82% rebar mass loss compared to those of intact specimen; for cyclic loading specimens, they decreased by 10.69%, 21.47%, 57.46% with 15.71% rebar mass loss, respectively. Comparative analysis showed that the difference for the degradation level of dimensionless parameters was not obvious between axial compression loading and cyclic loading tests. Findings also showed that for severely corroded specimens, the plastic hinge zone transferred from the bottom of RC piers to the splash and tidal zones. Although the extent of the degradation of the results between the published paper and this test shows significant variations; degradation of dimensionless energy dissipation was always the most serious one.

1. Introduction

[22] studied the mechanical behaviors of corroded axial compression columns using finite element analysis. Ou et al. [23] presented a new seismic evaluation methodology for corroded RC bridges, which considered the effect of mechanical property degradation of reinforcements, degradation of core concrete and bonding strength, etc. Li et al. [24] examined the effects of rebar corrosion on the mechanical behaviors of an RC column via a cyclic loading test and found that the ultimate load and energy dissipation of a specimen with 18.45% rebar mass loss declined by 21.85% and 40.50%, respectively. Guo et al. [19] and Vu et al. [25] conducted a cyclic loading test to study the effects of rebar and stirrup corrosion on the mechanical behaviors of an RC column. Guo et al. found that the ultimate load of a specimen with 15.24% rebar mass loss and 30.19% stirrup mass loss degraded by 24.92%. Vu et al. discovered that the ultimate load and energy dissipation of a specimen with 6.8% rebar mass loss and 26.1% stirrup mass loss declined by 23.1% and 63.5%, respectively. The above test results show that the degraded mechanical behaviors of column specimens with rebar and stirrup corrosion were more serious than that of specimens with rebar corrosion under cyclic loading. Stirrup corrosion is often more serious than that of rebars due to a smaller diameter and thinner cover thickness [19,25,26]. Some researchers [27,28] have carried out experiments to study the effects of

Corrosion of reinforcements due to chloride ion penetration and accumulation is a primary deterioration mechanism of reinforced concrete (RC) structures in the marine environment [1]. Reinforcement corrosion in concrete structures may lead to reduction of the effective cross-sectional area and degradation of the mechanical behaviors of reinforcements [2–5], loss of bonding between reinforcements and concrete [6–11], and cracking and spalling of the concrete cover [2,12–13]. These phenomena eventually result in degraded mechanical behaviors of corroded RC structures [14–18]. Corrosion of RC piers is often non-uniform along the elevation of bridge piers in the marine environment. The corrosion at splash and tidal zones of piers is always more severe than other parts due to the combined factors of higher surface chloride concentration, oxygen abundance, and dry–wet cycles [5,19–20]. Severe corrosion in splash and tidal zones degrades the mechanical behaviors of RC piers. Some studies have addressed the degradation of mechanical behaviors of corroded RC piers. Campion et al. [21] proposed a theoretical model of the axial compressive bearing capacity of corroded RC columns, which considered the effects of concrete cracking and spalling, mechanical property degradation of reinforcements, rebar buckling, etc. Li et al. ⁎

Corresponding author at: College of Civil Engineering, Shenzhen University, Nanhai Road 3688, Nanshan District, Shenzhen, Guangdong Province 518060, China. E-mail addresses: [email protected] (H. Zhou), [email protected] (D. Li), [email protected] (F. Xing).

https://doi.org/10.1016/j.engstruct.2019.109880 Received 7 April 2019; Received in revised form 29 September 2019; Accepted 31 October 2019 0141-0296/ © 2019 Elsevier Ltd. All rights reserved.

Please cite this article as: Haijun Zhou, et al., Engineering Structures, https://doi.org/10.1016/j.engstruct.2019.109880

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stirrup corrosion on the mechanical behaviors of RC specimens. Experimental studies of stirrup-confined concrete specimens by Vu et al. [27] indicated that the stress–strain curve of confined concrete was significantly affected by stirrup corrosion. Li et al. [28] conducted a cyclic loading test on eight corroded stirrup-confined concrete specimens and found that degradation in the ultimate load, stiffness, ductility factor, and energy dissipation capacity of specimens increased with an increase in corrosion. These studies demonstrated that stirrup corrosion greatly influences the degradation of mechanical behaviors of RC specimens. However, most experimental studies have examined a corroded rebar and stirrup without controlling for the corrosion difference between them; others only examined a corroded rebar. Moreover, these studies were conducted under axial compression or cyclic loading separately. Therefore, simultaneous tests of axial compression loading and cyclic loading are needed to further study the mechanical property degradation of partially corroded RC columns and the degradation difference in both tests. In this paper, 12 RC bridge pier specimens were partially corroded to simulate severe corrosion in splash and tidal zones via an electrochemical accelerated corrosion technique. The actual stirrup corrosion condition was more serious than that of rebar and was considered by designing a target stirrup corrosion level that was 2.5% higher than that of the rebar to highlight the effects of stirrup corrosion on the performance degradation of RC piers in the marine environment, which was based on the findings that the corrosion level of stirrups was slightly higher than that of rebars in a demolished bridge and an over 20-year building structure [5,29]. Axial compression loading and cyclic loading tests were carried out with six specimens per group. The corrosion crack opening, mass loss of reinforcements, axial load–displacement curves, and hysteresis curves of RC piers with different degrees of corrosion were obtained.

respectively. The difference between the two groups of specimens was the shape of the top cross-section, which was circular for axial loading specimen and square for cyclic loading specimen. The top cross-section of cyclic loading specimen was designed to be square to fit for the lateral loading. The diameter of the concrete pier was 300 mm, and the height above the fixing beam was 1350 mm. The cross-section of the fixing beam was 800 × 410 mm with a height of 300 mm. Six rebars with diameters of 14 mm and 14 stirrups with diameters of 8 mm were used for each pier model. The stirrup spacing was 100 mm, and the thickness of the concrete cover was 30 mm. The tested yield strength and ultimate strength of the rebar was 404.97 MPa and 548.6 MPa, respectively. The tested yield strength and ultimate strength of the stirrup was 391.05 MPa and 576.78 MPa, respectively. Fig. 1(c) and (d) show photographs of the reinforcement cage and the specimen after concrete casting, respectively. The rebar and stirrup were corroded separately, electrical tape wrapping and epoxy resin coating were used to insulate between the rebar and stirrup as shown in Fig. 1(c). Fig. 1(d) shows that the RC pier and fixing beam of the specimen were cast in PVC pipe with a diameter of 300 mm and a wooden mold, respectively. 2.2. Concrete mix design The concrete mix was designed to have a compression strength of about 30 MPa with a w/c ratio of 0.47, which is widely used for bridge substructures in mainland China. The concrete mix per cubic meter was 175.43 kg water, 287.59 kg ordinary Portland cement (P.O.42.5R), 816.75 kg sand, and 1130.23 kg stone. Concrete cubes with dimensions of 150 × 150 × 150 mm3 were cast for the compression test, and the 28-d average compression strength was 42.22 MPa. 2.3. Artificial corrosion

2. Test setup

The corrosion zone of pier specimens was based on a severely corroded bridge in the coastal city of Shenzhen at a section height of 170–770 mm as shown in Fig. 2(a). Table 1 lists the target corrosion levels of the rebar as 0, 2.5%, 5%, 10%, 15%, and 20%, respectively. The 20% rebar corrosion level was based on the detailed detection data of the demolition bridge in the coastal city of Shenzhen [5]; which showed that when the corrosion level was higher than 20%, the concrete cover would be spalling. Li et al. [24], Yang et al. [30] and Meda et al. [31] also studied the seismic behavior of corroded RC column by designing a maximum target corrosion level of 20%. In addition, considering that stirrup corrosion is more serious than that of the rebar in practical engineering, the target corrosion level of the stirrup was 2.5% higher than that of the rebar in this study. As indicated in Fig. 2(b), pier specimens were partially corroded to simulate severe corrosion in splash and tidal zones by using an electrochemical accelerated corrosion technique that involves passing a direct current through the specimen to accelerate the oxidation process in this experiment. Electrochemical accelerated corrosion was carried out in the dry–wet cycle; rebars were electrified for 5 days, stirrups were electrified for 4 days, and the pier model was dried for 1 day as one cycle. The current density was set as 300 μA/cm2, smaller than 500 μA/cm2 as the maximum current density for electrochemical accelerated corrosion in concrete [12]. The corrosion duration of bridge pier specimens with different corrosion levels can be calculated using Faraday’s law:

2.1. Test specimens Twelve RC bridge pier model specimens were created based on the bridge pier with diameter of 1000 mm and concrete cover of more than 50 mm of an old bridge in the coastal city of Shenzhen [5]. The specimens were divided into two groups according to the different loading schemes, as shown in Table 1, which were used for the axial compression loading test and cyclic loading test, respectively. Each specimen was labeled as “A(C)-TCL”, where “A” denotes axial compression loading, “C” denotes cyclic loading, and “TCL” is a percentage representing the target corrosion level. Fig. 1(a) and (b) present the dimensions and reinforcement layout of the axial compression loading and cyclic loading specimens, Table 1 Test specimens and corrosion cracks. Specimen no.

Target corrosion level (%, rebar)

Target corrosion level (%, stirrup)

Total crack length (mm)

Maximum crack width (mm)

A-0 A-2.5 A-5* A-10 A-15 A-20 C-0 C-2.5 C-5* C-10 C-15 C-20

0 2.5 5 10 15 20 0 2.5 5 10 15 20

0 5 7.5 12.5 17.5 22.5 0 5 7.5 12.5 17.5 22.5

– 171.0 344.6 582.4 698.5 796.7 – 159.4 89.8 566.2 682.5 746.4

– 0.22 0.25 0.28 0.42 0.60 – 0.18 0.24 0.27 0.46 0.63

T=

mt × 2 × F I × 55.847

(1)

where T is the corrosion duration; mt is the target mass loss, calculated by the product of the target corrosion level and reinforcement mass before corrosion; F is the Faraday constant; and I is the average current intensity. As shown in Fig. 2(a), accelerated partial corrosion of pier specimens was conducted by wrapping copper mesh, water-retaining sponge, and plastic film successively on the surface of the corrosion

A-5* specimen was damaged during the loading process and regarded as invalid when analyzing the results of mechanical behaviors. C-5* specimen was the final cast specimen and exhibited poorer mechanical behaviors during the test. 2

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(a) Axial compression (unit: mm)

(b) Cyclic loading (unit: mm)

(c) Reinforcement cage

(d) Concrete casting Fig. 1. Test specimen.

zone. The rebar and stirrup were connected to the anode, and copper mesh was linked with the cathode, respectively. A sponge soaked in 5% NaCl solution was used to keep the surface of each pier specimen wet during the accelerated corrosion process. A 5% NaCl solution of 2 × 10−3 m3 was added to moisten the sponge on each specimen every 2 h to maintain a stable current density, as shown in Fig. 2(b). Moreover, each specimen needed to be wetted 72 h before the start of each electrification to ensure that chloride permeated into the reinforcement surface.

were 2500 kN and 2000 kN, respectively; the displacement range was ± 400 mm. For the axial compression loading test, specimens were first centered and levelled, and then a 50 kN vertical load was applied in the preloading process to ensure all devices worked properly. Fig. 3(b) and (c) displays the schematic diagram and photo of axial compression loading test setup, respectively. As shown in Fig. 3(b), four annular strain gauges were affixed to the upper, middle, and lower position of the RC bridge pier for a total of 12 strain gauges. Three vertical displacement gauges were uniformly installed around the concrete pier. Fig. 3(c) shows that the load was applied to the top of the column head along the axis of the column, and loading was controlled by displacement at a loading speed of 0.3 mm/min. The axial load, annular strain and axial displacement of pier specimens were recorded. The cyclic loading test was combined cyclic lateral displacement loading and constant axial force loading, the axial load ratio of each specimen was 0.17 with an axial force of 399.8 kN to simulate the weight (girder, pavement, railing, etc.) loaded on the bridge pier. It should be

2.4. Loading and measuring instrumentation The corroded RC bridge pier specimen was loaded by a multifunctional structural test system (WAW-J12000J) in the structural laboratory of Shenzhen University as displayed in Fig. 3(a). The maximum vertical compression and pulling force were 12,000 kN and 5000 kN, respectively; the displacement range is ± 300 mm for this loading instrument. The maximum lateral pushing and pulling force 3

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Results show that cracks on the pier specimen surface gradually formed a network and then spread throughout the corrosion zone with an increase in corrosion. The stirrup corrosion also had an important effect on the cracking of the concrete cover given the formation of many transverse cracks along the stirrups. In this experiment, the concrete cover crack opening length and width were measured using a ruler and width gauge, respectively. Table 1 lists the total crack length and maximum crack width of corroded pier specimens, indicating that the total crack length and maximum crack width expanded with an increase in corrosion. Many narrow and long cracks appeared at the initial corrosion stage. The length of corrosion cracks clearly increased when the rebar corrosion mass loss was lower than about 8%. Crack width increased clearly when the rebar corrosion mass loss exceeded roughly 8%.

(a) Schematic diagram (unit: mm)

3.2. Mass loss of reinforcements To obtain the mass loss of the reinforcements, each specimen was broken after the loading test. Six rebar fragments with a length 600 mm and six stirrups in the corroded zone were removed. Then, corroded reinforcements were cleaned using 12% diluted hydrochloric acid solution to remove the corrosion products before being dried for weighing. The mass loss of reinforcement was calculated using Eq. (2):

=

m0

mr m0

× 100%

(2)

where is the mass loss ratio of reinforcements, m 0 is the mass of reinforcements before corrosion, and mr is the mass of reinforcements after removing the corroded products. The mass loss ratio of each corroded reinforcements are listed in Table 2. The reinforcement specimen was labeled as A(C)-TCL-R(S); “A(C)” and “TCL” were defined in Section 2.1, whereas “R” represents rebar and “S” represents stirrup. As shown in Table 2, Er and Es represent the efficiency of rebar and stirrup corrosion, respectively:

(b) Photograph Fig. 2. Electrochemical accelerated corrosion.

noted that the disadvantage situation with a higher axial load ratio was considered in this test as the typical range of axial load on bridge column is around 0.10. Fig. 3(d) and (e) show the schematic diagram and photo of cyclic loading test setup, respectively. As shown in Fig. 3(d), loading to the right was positive whereas the reverse was negative. Fig. 3(e) illustrates that the axial load was applied to the top of the column head along the axis of the column; the lateral load was applied to the side of the column head and perpendicular to the axis of the column in the cyclic loading test. The lateral displacement loading history is displayed in Fig. 3(f), where the initial displacement value was set as Δ = 2 mm and then incremented by 2Δ for each displacement level. Each displacement level was repeated three times until failure; specimen failure occurred when the post-ultimate load of the concrete pier under positive and negative loading declined to 85% of the ultimate load. The NDI Optotrak Certus 3D Motion Capture System was used to measure the pier’s horizontal displacement at different heights in this experiment; the schematic diagram is shown in Fig. 3(h). Fourteen markers were uniformly installed along the height direction on the left and right sides of the pier specimens, respectively, as shown in Fig. 3(d). The horizontal displacement of the pier model at different heights was accurately recorded by capturing markers’ positions in real time during the loading process.

Er =

r m r t

× 100%

Es =

s m s t

× 100%

(3) (4)

where mr and tr denote the mean value of the six-rebar mass loss ratio and target corrosion level of the rebars, respectively; ms and ts are the mean value of six stirrups’ mass loss ratio and the target corrosion level of stirrups, respectively. The listed Er and Es indicate that the corrosion level of reinforcements in this test was close to the target corrosion level. Moreover, Es was larger than Er for the corroded reinforcement specimens, indicating that stirrup corrosion was more serious than that of rebars in this test, aligning well with results of the field survey and the test design. 3.3. Axial compression loading test 3.3.1. Axial load–displacement curves The axial load–displacement curves of RC bridge pier specimens subjected to axial compression tests at different corrosion levels are shown in Fig. 5. The axial load–displacement curve of each pier specimen was substantially affected by reinforcement corrosion. The ultimate load, stiffness, ductility, and energy dissipation of each pier specimen showed a tendency to increase slightly at first followed by a reduction with an increase in corrosion. The reason for the increase of performance of A-2.5 specimen might be due to the fact that reinforcement corrosion products would fill the voids between reinforcement and the surrounding concrete pore at the initial corrosion stage, which not only increases the compactness [28], but also enhances the friction and decreases the slip between reinforcement and concrete [8–11]. As the reduction of reinforcement

3. Test results 3.1. Corrosion crack opening Fig. 4(a) and (b) show that reddish-brown corrosion products appeared on the pier specimen surface after corrosion of C-10 and C-20 specimens, respectively. Most corrosion products were distributed around corrosion cracks. In particular, C-20 specimens exhibited corrosion products nearly covering the entire corrosion zone. Fig. 4(c) and (d) present the crack patterns of C-10 and C-20 specimens, respectively. 4

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(b) Schematic diagram of axial loading setup

(a) Multi-functional structural test system

(c) Preloading (A-0)

(d) Schematic diagram of cyclic loading setup

Lateral Displacement (mm)

20

10

Until failure 0

-10

-20

(e) Preloading (C-20)

0

2

4

6

8

10

12

Cycle number

14

16

18

(f) Cyclic loading

Fig. 3. Loading and measuring system.

area is very slight, finally the slight corrosion may improve the mechanical performance. Certainly, the dispersion of concrete material or casting quality might also introducing such kind of difference, further investigation and test are still needed to confirm this phenomenon.

With the increase of reinforcement corrosion level, the area of reinforcement was reduced significantly; the accumulation of corrosion products at the interface between reinforcement and concrete will not only damage the bonding between the reinforcement and concrete, but 5

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2100

A-0 A-2.5 A-10 A-15 A-20

1800

Axial load (kN)

1500 1200 900 600 300 0

0

2

4

Axial displacement (mm)

6

Fig. 5. Axial load–displacement curves.

(h) NDI Optotrak Certus 3D Motion Capture System

also cause cracking and spalling of concrete cover. The serious damage caused by corrosion of reinforcement will lead to the significant degradation of mechanical behaviors of RC specimens.

Fig. 3. (continued)

(a) Photograph (C-10)

(b) Photograph (C-20)

(c) Crack pattern (C-10)

(d) Crack pattern (C-20)

Fig. 4. Corrosion-induced cracks.

3.3.2. Ultimate loads The ultimate load results of RC bridge pier specimens for the axial compression test are shown in Table 3. The ultimate load of the A-2.5 specimen was 6.74% larger than that of the intact specimen as stated above. However, the ultimate loads of pier specimens began to decrease with a further increase in corrosion duo to the excessive accumulation of corrosion products at the interface between reinforcements and concrete leading to crack damage of concrete. The ultimate loads of the A-10, A-15, and A-20 specimens declined by 12.16%, 17.09%, and 29.96%, respectively, compared with the intact specimen. It can be concluded that the ultimate load of pier specimen reduced sharply with the increase of corrosion, especially for the A-15 and A-20 specimen; the decrement was about two times of the corrosion mass loss.

Table 2 Mass loss of corroded reinforcements. Reinforcement no. A-0-R A-2.5-R A-5-R A-10-R A-15-R A-20-R C-0-R C-2.5-R C-5-R C-10-R C-15-R C-20-R

r m (%)

0.11 2.14 4.29 8.31 12.38 15.82 0.09 2.06 4.19 8.18 12.42 15.71

Er (%)

Reinforcement no.

– 0.86 0.86 0.84 0.83 0.79 – 0.82 0.84 0.82 0.83 0.79

A-0-S A-5-S A-7.5-S A-12.5-S A-17.5-S A-22.5-S C-0-S C-5-S C-7.5-S C-12.5-S C-17.5-S C-22.5-S

s m (%)

0.13 4.58 6.94 11.45 15.33 20.54 0.08 4.42 7.10 11.32 15.48 20.41

Es (%) – 0.92 0.93 0.92 0.88 0.91 – 0.88 0.95 0.91 0.88 0.91

3.3.3. Initial stiffness The slope of the fitting curve was defined as the initial stiffness of the RC bridge pier specimens, fitted by a 0–20% ultimate load 6

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it also presents certain degree of variability with the increase of corrosion level, which was similar to that of the initial stiffness parameter. It can be concluded that the ultimate load was degraded more regular than the above two parameters.

Table 3 Test results of axial loading. Specimens

A-0

A-2.5

A-10

A-15

A-20

Ultimate load (kN) Initial stiffness (kN/mm) Ductility factor Energy dissipation (kN·mm)

1870.47 1238.40 1.62 4645.25

1996.60 1631.25 1.65 5114.05

1643.00 1190.50 1.51 4464.31

1550.86 586.59 1.08 2092.86

1312.83 948.54 1.47 1512.60

3.3.5. Energy dissipation Energy dissipation was defined as the area under the axial load–displacement curve up to the ultimate displacement, which can also be regarded as the combination of the above three mechanical parameters. The results of axial compression energy dissipation for RC bridge pier specimens with different degrees of corrosion are shown in Table 3. The energy dissipation of the A-2.5 specimen was 10.09% larger than that of the intact specimen, whereas the energy dissipations of the A-10, A-15, and A-20 specimens were 3.90%, 54.95%, and 67.44% lower than that of the intact specimen, respectively. It can be concluded that energy dissipation of the severely corroded pier specimen was degraded significantly: less than 50% of energy dissipation was left for the A-15 and A-20 specimen.

ascending segment of the axial force–displacement curve. Table 3 presents the initial stiffness values of axial compression pier specimens at different corrosion levels. The initial stiffness value of the A-2.5 pier specimen increased about 31.72%, which may be due to combined effects of slight corrosion of reinforcement and/or the dispersion of concrete material and casting quality. The initial stiffness values of the A-10, A-15, and A-20 pier specimens declined by 3.87%, 52.63%, and 23.04%, respectively, compared with the intact specimen. It can be concluded that initial stiffness of pier specimen was also very sensitive to corrosion as ultimate load; however, the initial stiffness value shows greater variability with the increase of corrosion.

3.3.6. Axial stress–hoop strain curves The axial stress–hoop strain curves of RC bridge pier specimens are presented in Fig. 7. The stress–strain curve of pier specimens was substantially affected by reinforcement corrosion. Axial stress was defined as the ratio of the axial load to the cross-sectional area of the specimens. The axial strain of pier specimens adopted the ratio between the mean value of three displacement gauges and the height of each pier specimen. Considering that the corrosion zone was in the middle of the specimens, the mean value of four annular strain gauges in the middle part was adopted as the hoop strain of the pier specimen. As displayed in Fig. 7, the slope of the stress–strain curve of the slightly corroded specimen was greater than that of the intact specimen, indicating that the initial stiffness was improved for the slightly corroded specimen as stated above. The stress–strain curve of severely corroded specimens deviated to the lower left and the lower right with an increase in corrosion, indicating that the stiffness of the specimens was declining. In addition, the axial stress–hoop strain curve of the A-15 specimen exhibited a horizontal segment due to a vertical crack at the location of the strain gauge.

3.3.4. Ductility factor The ductility factor was defined as the ratio of ultimate displacement µ to yield displacement y of the pier specimens:

µ=

µ

(5)

y

where µ is the ultimate displacement corresponding to the 0.85 ultimate load in the descending segment of the axial load–displacement curve. y is the yield displacement calculated by the equivalent energy method [19–20,24,28,30] shown in Fig. 6, determined using Eq. (6):

SOABCE = SOBDCE =

max

+

max

2

y

Fu

(6)

where Fu is the ultimate load, and max is the displacement corresponding to the ultimate load. Test results for the ductility factor of axial compression for corroded RC bridge pier specimens are shown in Table 3, which show similar tendency with the increase of corrosion compared with the above two mechanical parameters. The ductility factor of the slightly corroded specimen was also improved compared with that of the intact specimen, but it degraded to varying degrees with an increase in corrosion level. The ductility factor of the A-2.5 specimen was 1.85% larger than that of the intact specimen. The ductility factors of the A-10, A-15, and A-20 specimens were 6.79%, 33.33%, and 9.26% lower than that of the intact specimen, respectively. The ductility factor of axial compression pier specimen was also obviously affected by reinforcement corrosion;

3.4. Cyclic loading test Hysteresis curves and skeleton curves were obtained from the experiment. The resultant ultimate load, stiffness, ductility factor, and energy dissipation could then be used to evaluate seismic performance of the structure with respect to strength, stiffness, and deformation.

Axial stress (MPa) A-0 A-2.5 A-10 A-15 A-20

35 30 25 20 15 10 5 0 -2500 -2000 -1500 -1000 -500 -6 Axial strain (10 ) Fig. 6. Determination of yield point.

0

500 1000 1500 -6 Hoop strain (10 )

Fig. 7. Axial stress vs. axial strain and hoop strain. 7

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150

150

C-0

100

50

Lateral load (kN)

50

Lateral load (kN)

C-2.5

100

0 -50

-100

0 -50

-100

-150

-150 -40

-20

0

20

Lateral displacement (mm)

40

-40

-20

(a) C-0

150

C-5

Lateral load (kN)

Lateral load (kN)

40

20

40

20

40

C-10

100

50 0 -50

50 0 -50

-100

-100

-150

-150 -40

-20

0

20

Lateral displacement (mm)

40

-40

-20

0

Lateral displacement (mm)

(c) C-5

(d) C-10

150

150

C-15

C-20 100

50

50

Lateral load (kN)

100

Lateral load (kN)

20

(b) C-2.5

150 100

0

Lateral displacement (mm)

0 -50

-100

0 -50

-100

-150

-150 -40

-20

0

20

Lateral displacement (mm)

40

-40

(e) C-15

-20

0

Lateral displacement (mm)

(f) C-20 Fig. 8. Hysteresis curves.

3.4.1. Hysteresis curves The hysteresis curves of the RC bridge pier specimens with different corrosion levels are shown in Fig. 8. At the initial loading stage, hysteresis curves of the pier specimens showed linear development, and the area enclosed by the hysteretic loop was quite small. When the lateral loading

displacement exceeded the yield displacement of pier specimens, the hysteresis curve gradually became non-linear. The C-5 specimen was the final cast specimen, which was abnormal and exhibited poor hysteretic performance during the test, so the data of C-5 was discarded in the following analysis. The C-2.5 and C-10 specimen presented similar hysteretic 8

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25

performance as the C-0 specimen, indicating that the degradation of hysteretic performance of specimen with less than about 8% rebar mass loss ratio was not obvious. However, the hysteretic curves of the C-15 and C-20 specimen showed obvious pinching with the increase of corrosion level, which was mainly caused by the slippage between the concrete and rebar. Fig. 8 also shows the maximum/minimum load, stiffness and energy dissipation of the second and third cycle loading are all decreased compared with the first cycle loading in the same displacement level due to the accumulation of loading damage.

Secant stiffness(kN/mm)

20

15

10

3.4.2. Skeleton curves A skeleton curve is an envelope composed of the positive and negative peak points of the first cycle at each loading displacement level. Fig. 9 displays the skeleton curves of RC bridge pier specimens at varying corrosion levels; the skeleton curves of pier specimens were greatly affected by reinforcement corrosion. It can be found that the skeleton curves were unsymmetrical in positive and negative direction, which may be due to the effects of dispersion of concrete material, casting quality, or the non-uniform corrosion of reinforcements. In addition, the ultimate load, ductility, stiffness, and energy dissipation of severely corroded pier specimens degraded to varying degrees with an increase in corrosion. Among them, the ultimate loads of the C-2.5, C10, C-15, and C-20 specimens respectively degraded by 9.17%, 3.18%, 15.67%, and 10.69% compared with the intact specimen.

Vun1 Sn1

Vun2 Sn2

15

20

25

30

Lateral displacement(mm)

35

40

45

Ductility factor

4.09

Ductility factor

3.26

3.12

3

2.64

2.56

12.42

15.71

2

(7)

1 0

0.09

2.06

8.18 ξs (%)

Fig. 11. Ductility factor vs. mass loss ratio of rebar.

100000

0

90000 80000 70000 60000

st

rd

1 -3 cycles th

th

th

st

10 -12 cycles 19 -21 cycles 73668.99

th

th

4 -6 cycles th

th

nd

th

13 -15 cycles 22 -24 cycles

th

th

7 -9 cycles th

th

th

th

th

th

16 -18 cycles 25 -27 cycles 28 -30 cycles st

62643.46

31 cycles

58272.77 47100.52

50000 40000 30000

26647.69

20000 10000 0

-50

-100

0.09

2.06

8.18

ξs (%)

12.42

15.71

Fig. 12. Energy dissipation vs. mass loss ratio of rebar.

-150 -200 -50

10

4

Energy dissipation(kN·mm)

Lateral load (kN)

50

5

5

C-0 C-2.5 C-10 C-15 C-20

100

0

Fig. 10. Stiffness degradation.

where Vun1 and Vun2 are the maximum and minimum lateral loading force, respectively; Sn1, Sn2 denote the corresponding lateral displacement, respectively; and n represents the nth cycle. Experiment results regarding the secant stiffness curves of RC bridge pier specimens with different degrees of corrosion are shown in Fig. 10. With the exception of the last point, the points on each curve represent the mean value of secant stiffness for the three cycles, whereas the last point represents the secant stiffness of the last cycle. It can be concluded that the secant stiffness of all specimens exhibited a downward trend with an increase in lateral displacement due to the accumulation of loading damage. Moreover, the secant stiffness declined rapidly at the initial loading stage, whereas the downward trend tended to become gentle with an increase in

150

5

0

3.4.3. Stiffness degradation In this study, the stiffness degradation of pier specimens with different degrees of corrosion was studied on the basis of secant stiffness of the positive and negative peak point of the hysteresis curve, calculated using Eq. (7):

Kn =

C-0 C-2.5 C-10 C-15 C-20

-40

-30

-20

-10

0

10

20

Lateral displacement (mm)

30

40

lateral displacement. The slightly corroded specimen has larger stiffness and the severely corroded specimens have smaller stiffness compared with intact specimens under the same lateral displacement. However, the difference was decreasing with an increase in lateral displacement, which might suggest the major damage factors transferring from corrosion damage to loading damage as the displacement increases.

50

Fig. 9. Skeleton curves. 9

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H. Zhou, et al.

1200

1200

C-0 Pull

800 600 400 200 0 -0.0006 -0.0004 -0.0002

0.0000

0.0002

Sectional curvature (1/mm)

0.0004

C-2.5

1000

Push

Depth of section (mm)

Depth of section (mm)

1000

600 400 200 0 -0.0004

0.0006

-0.0002 0.0000 0.0002 Sectional curvature (1/mm)

(a) C-0

1200

C-10

1000

1000

Push

Pull

Depth of section (mm)

Depth of section (mm)

0.0004

(b) C-2.5

1200

800 600 400 200 0 -0.0008

Push

Pull

800

-0.0004

0.0000

0.0004

Pull

Push

800 600 400 200 0 -0.0005

0.0008

Sectional curvature (1/mm)

C-15

0.0000

(c) C-10

0.0005

0.0010

0.0015

Sectional curvature (1/mm)

0.0020

0.0025

(d) C-15

1200

Depth of section (mm)

1000

C-20 Pull

Push

800 600 400 200 0 -0.0002

0.0000

0.0002

Sectional curvature (1/mm)

0.0004

(e) C-20 Fig. 13. Sectional curvature curves.

3.4.4. Ductility factor The calculation method of the ductility factor of RC bridge pier specimens was defined in Section 3.3.4, the skeleton curve was used to calculate the ductility factor of each specimen as shown in Fig. 11. The ductility factor of the C-2.5 specimen was 25.46% higher than that of

the intact specimen, whereas the ductility factor of the C-10, C-15, and C-20 specimens was 4.29%, 19.01%, and 21.47% lower than that of the intact specimens, respectively. It also shows that slight corrosion may improve the ductility behavior of RC bridge pier. The degradation of the ductility factor was not obvious when the mass loss ratio was less than 10

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degradation exerted a substantial effect on the sectional curvature of pier specimens. The sectional curvature at the bottom position of the pier specimens was largest for the C-0, C-2.5, C-10, C-15, and C-20 specimens, suggesting that the plastic hinge zone was at the bottom of the specimens. However, the sectional curvature of the C-15 specimen was largest at 300 mm from the fixing beam under positive loading; see Fig. 13(d). It was found a large-width annular corrosion crack was formed at 300 mm from the fixing beam. The crack propagated continuously during the loading process until positive loading reached the maximum displacement. As a result, the plastic hinge zone was transferred from the bottom to the splash and tidal zones for the C-15 specimen. Upward movement of the plastic hinge zone of the RC bridge pier revealed that its seismic performance clearly changed.

Dimensionless mechanical parameters

1.2 1.0 0.8 0.6

A-DUL A-DDF A-DED

0.4 0.2 0.0

0

C-DUL C-DDF C-DED

5

10

4. Discussion

15

ξs (%)

4.1. Failure modes

Fig. 14. Dimensionless mechanical parameters vs. mass loss ratio of rebar.

Reinforcement corrosion may alter the failure mode of a structure, as has been found by some researchers [8,11,20,26,28]. In this experiment, the failure modes of corroded RC bridge pier specimens changed with an increase in corrosion. For the axial compression loading test, the failure zone transferred from the loading end to the corrosion zone in the severely corroded axial compression specimen. A-20 specimen was subjected to crack development, cover concrete spalling, stirrups fracture, and core concrete crushing in the corrosion zone. For the cyclic loading test, the specimens showed significant bending failure characteristics. For C-0, C-5, and C-10 specimens, the load-induced cracks mainly occurred in the plastic hinge region at pier bottom, which experienced elastic, elastic-plastic, and failure stages. Finally the above specimens were failed with cracking and spalling of cover concrete, crushing of core concrete in the bottom of the pier. C-15 and C-20 specimens were subjected to crack development in corrosion zone and bottom of pier, and finally a new plastic hinge occurs in the corrosion area for the C-15 specimen. The variability of corroded RC bridge pier specimens exceeded that of intact specimen due to reinforcement corrosion; therefore, additional theoretical research is needed to examine the critical corrosion level of modified failure modes in the RC pier.

about 8%, but the ductility factor degraded obviously with an increase of corrosion level, especially for the C-15 and C-20 specimen. 3.4.5. Energy dissipation The area enclosed by a single hysteresis loop was used to evaluate the energy dissipation of pier specimens. Fig. 12 shows the cumulative energy dissipation results of pier specimens at different corrosion levels. With the exception of the top box, each box is the sum of the energy dissipation of three cycles, and the top box represents the energy dissipation of the last cycle. The cumulative energy dissipation parameter was an important parameter to evaluate the seismic performance of the corroded RC column. The cumulative energy dissipation of pier specimens tended to increase slightly at first and then decline with an increase in corrosion. Cumulative energy dissipation of the C-2.5 specimen increased by 17.60%, whereas that of the C-10, C-15, and C-20 specimens degraded by 6.98%, 24.81%, and 57.46%, respectively, compared with the intact specimen. The cumulative energy dissipation presented similar degradation trend compared with ductility factor, which degraded a little when the mass loss ratio less than about 8%. However, the above mechanical parameters degraded sharply for the C-15 and C-20 specimen. It can be concluded that the mechanical parameters of severely corroded pier specimens may be decreased more than the mass loss ratio of rebar, especially in terms of cumulative energy dissipation.

4.2. Degradation comparison of two loaded groups Fig. 14 presents results of the dimensionless parameters of the RC pier specimens under axial compression and cyclic loading tests to compare the degradation of mechanical parameters between two loaded groups. Dimensionless parameters refer to the ratio of the

3.4.6. Sectional curvature curves The sectional curvature results of RC bridge pier specimens with different corrosion levels are illustrated in Fig. 13. Corrosion Table 4 Test results of cyclic loading. Reference no.

Specimen size (mm)

fc (Mpa)

Current density (μA/cm2)

Axial load ratio

Mass lossof rebar (%)

Mass loss of stirrup(%)

Strength degradation (%)

Ductility degradation (%)

Energy dissipation degradation(%)

Guo et al. [19] Wei et al. [20] Li et al. [24]

600 × 250 × 2500 φ400 × 2600 300 × 300 × 1370

42.9 36.3 50.2

200 300 300–1000

Vu et al. [25]

350 × 350 × 1780

–

500

Ma et al. [26] *

φ260 × 1000

32.4

–

Yang et al. [30] Meda et al. [31] This paper

210 × 210 × 1000

46.4

609

0.1 0.13 0.1 0.3 0.1 0.25 0.15 0.25 0.4 0.18

0–15.24 0–30.71 0–18.45 0–16.32 0–6.8 0–7.5 0–9.5 0–9.7 0–9.3 0–16.8

0–30.19 0–35.96 0 0 0–26.1 0–18.2 – – – 0–9

0–24.92 0–20.41 0–21.85 0–42.7 0–23.1 0–25 – – – 0–20

– 0–38.68 −98.6–0 −69.68–7.44 – – −2.96–0 −15.3–24.53 0–9.11 0–32.1

– 0–41.5 0–73.72 0–71.71 0–63.5 0–61.9 0–8.41 0–55.84 0–52.13 0–50.8

300 × 300 × 1800

20

250

0.22

0–21.5

0

0–23.58

–

–

φ300 × 1350

42.2

300

0.17

0–15.71

0–20.41

0–23.91

−17.19–14.29

0–67.38

* The corrosion mass loss of stirrup is not available in Ref. [26]. 11

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Dimensionless ultimate load

loss and then declined as corrosion increased for the two loaded groups. A slight difference was found for the degradation level of dimensionless parameters between two loaded groups. Degradation of the axial compression pier specimens seemed slightly more severe than that of the cyclic loading pier specimens. However, given the large variation in published test results as discussed below, the difference between them was not obvious.

[19] [20] [24] [25] [30] [31] This paper

1.0

0.9

0.8

4.3. Published degradation of cyclic loading tested specimens 0.7

0.8

Table 4 lists the reported results of cyclic loading tests [19–20,24–26,30,31] and the results of this paper. It can be found that the degradation of energy dissipation was most severe in all mechanical property parameters. Dimensionless parameters of the test results were applied in subsequent analysis due to differences in specimen size, concrete strength, corrosion current density, etc. Fig. 15 shows the relationship between dimensionless parameters and rebar mass loss ratio in the cyclic loading test results of the published papers and this paper, which was based on the data of Table 4. Fig. 15(a) indicates that dimensionless ultimate loads degraded clearly as rebar mass loss increased. The maximum degradation recorded in Ref. [24] indicated that less than 60% of the dimensionless ultimate load was left with a rebar mass loss of 16.32%; for the other tested cases, the degradation ranged between 0 and 25% with a rebar corrosion mass loss between 0 and 30.71%. Fig. 15(b) and (c) show that the dimensionless ductility factor, energy dissipation increased for slightly corroded specimens and then seriously degraded as rebar mass loss increased. Two abnormal data points appear in Fig. 15(b) with a high dimensionless ductility factor and should be ignored. The increase in the dimensionless ductility factor was 25.46% when rebar corrosion mass loss was 2.06%; the maximum degradation of the dimensionless ductility factor was 38.68% at a rebar mass loss ratio of 30.71%. As shown in Fig. 15(c), the dimensionless energy dissipation for some specimens with rebar corrosion mass loss of 6.63–16.32% left only about 30% remaining. Fig. 15 shows the dimensionless ultimate load, ductility factor, and energy dissipation degraded severely for the corroded specimens with large mass loss ratio, although the extent of the degradation of the results between the published paper and this paper shows significant variations. Detailed studies are needed to further quantify the variation in degradation. The degradation of mechanical behaviors in this test is only slightly smaller than that of the other test in the published papers, which indicates that the local corrosion could also significantly degrade the mechanical behaviors of the RC column. Degradation of dimensionless energy dissipation was the most serious one compared with the other two parameters.

0.6

5. Conclusions

0.4

In this paper, axial compression and cyclic loading tests were carried out to study the degradation of partially corroded RC bridge piers. Conclusions are as follows:

0.6 0

5

10

15

20

25

30

35

ξS(%)

(a) Dimensionless ultimate load 2.0

[20] [24] [26] [30] This paper

Dimensionless ductility factor

1.8 1.6 1.4 1.2 1.0 0.8 0.6 0

5

10

15

20

25

30

35

ξS(%)

(b) Dimensionless ductility factor 1.4

[20] [25] [30]

Dimensionless energy dissipation

1.2

[24] [26] This paper

1.0

0.2 0.0

0

5

10

15

20

25

30

(1). The mechanical behaviors of axial compression loaded bridge pier specimens were substantially degraded by reinforcement corrosion. The ultimate load, ductility factor, energy dissipation decreased by 29.96%, 9.26%, 67.44% for axial compression specimen at 15.82% rebar mass loss, respectively, compared with the intact specimen. (2). The hysteresis curve of bridge pier specimens under cyclic loading exhibited an obvious pinching effect with an increase in corrosion. The ultimate load, initial stiffness, ductility factor, and energy dissipation of corroded bridge pier specimen degraded by 10.69%, 21.47%, 57.46% for cyclic loading specimen at 15.71% rebar mass loss, respectively, compared with the intact specimen. (3). Corrosion deterioration exerted a significant effect on the sectional curvature of the RC bridge pier; importantly, the plastic hinge zone

35

ξS(%)

(c) Dimensionless energy dissipation Fig. 15. Dimensionless parameters vs. mass loss ratio of rebar.

parameter values of each specimen to those of the intact specimen, which is also used to define dimensionless parameters in the following section. These parameters were named “A(C)-parameter”; “A(C)” was defined in Section 2.1, and “parameter” represents the “dimensionless ultimate load (DUL)”, “dimensionless ductility factor (DDF)”, and “dimensionless energy dissipation (DED)”, respectively. Fig. 14 shows that most of dimensionless parameters increased at roughly 2% rebar mass 12

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transferred from the bottom of the RC pier to the splash and tidal zones in severely corroded piers. (4). A comparison of two loaded groups revealed similar parameter degradation, although the axial compression pier specimen showed slightly more severe degradation than the cyclic loading pier specimen. Mechanical property parameters of severely corroded pier specimens decreased more than the mass loss ratio of rebar, especially in energy dissipation. These phenomena were similar to other cyclic loading test findings; however, large variation was founded in different reported findings.

Ph.D. Dissertation; Chalmers University of Technology, Gothenburg; 2016. [8] Zhou HJ, Liang XB, Wang ZQ, Zhang XL, Xing F. Bond deterioration of corroded steel in two different concrete mixes. Struct Eng Mech, Int J 2017;63(6):725–34. [9] Zhao Y, Lin H, Wu K, Jin W. Bond behaviour of normal/recycled concrete and corroded steel bars. Constr Build Mater 2013;48:348–59. [10] Zhou HJ, Lu JL, Xv X, Xing F. Effects of stirrup corrosion on bond-slip performance of reinforcing steel in concrete: an experimental study. Constr Build Mater 2015;93:257–66. [11] Zhou HJ, Liang XB, Zhang XL, Lu JL, Xing F, Mei L. Variation and degradation of steel and concrete bond performance with corroded stirrups. Constr Build Mater 2017;138:56–68. [12] Coronelli D, Hanjari KZ, Lundgren K. Severely corroded RC with cover cracking. ASCE J Struct Eng 2013;139(2):221–32. [13] Chen HP, Nepal J. Effect of cover cracking on reliability of corroded reinforced concrete structures. Comp Concrete 2017;20(5):511–9. [14] Wang L, Zhang XH, Zhang JR, Ma Y, Liu YM. Effects of stirrup and inclined bar corrosion on shear behavior of RC beams. Constr Build Mater 2015;98:537–46. [15] Tapan M, Aboutaha RS. Strength evaluation of deteriorated RC bridge columns. ASCE J Bridge Eng 2008;13(3):226–36. [16] Wang XH, Liang FY. Performance of RC columns with partial length corrosion. Nucl Eng Des 2008;238(12):3194–202. [17] Xia J, Jin WL, Li LY. Performance of corroded reinforced concrete columns under the action of eccentric loads, ASCE. J Mater Civ Eng 2015;28(1). [18] Ou YC, Nguyen ND. Influences of location of reinforcement corrosion on seismic performance of corroded reinforced concrete beams. Eng Struct 2016;126:210–23. [19] Guo AX, Li HT, Ba X, Guan XC, Li H. Experimental investigation on the cyclic performance of reinforced concrete piers with chloride-induced corrosion in marine environment. Eng Struct 2015;105:1–11. [20] Yuan W, Guo AX, Li H. Experimental investigation on the cyclic behaviors of corroded coastal bridge piers with transfer of plastic hinge due to non-uniform corrosion. Soil Dyn Earthquake Eng 2017;102:112–23. [21] Campione G, Cannella F, Minafò G. A simple model for the calculation of the axial load-carrying capacity of corroded RC columns. Mater Struct 2016;49(5):1935–45. [22] Li JB, Markeset G, Kioumarsi M. Nonlinear FEM simulation of structural performance of corroded RC columns subjected to axial compression. Nordic Concrete Res 2017;57(2):15–22. [23] Ou YC, Fan HD, Nguyen ND. Long-term seismic performance of reinforced concrete bridges under steel reinforcement corrosion due to chloride attack. Earthquake Eng Struct Dyn 2013;42(14):2113–27. [24] Li DW, Wei R, Xing F, Sui LL, Zhou YW, Wang WY. Influence of Non-uniform corrosion of steels on the seismic behavior of reinforced concrete columns. Constr Build Mater 2018;167:20–32. [25] Vu NS, Li B. Seismic performance assessment of corroded reinforced concrete short columns. ASCE Eng Struct 2018;144(4). [26] Ma Y, Che Y, Gong JX. Behavior of corrosion damaged circular reinforced concrete columns under cyclic loading. Constr Build Mater 2012;29(29):548–56. [27] Vu NS, Yu B, Li B. Stress-strain model for confined concrete with corroded transverse reinforcement. Eng Struct 2017;151:472–87. [28] Li Q, Niu DT, Xiao QH, Guan X, Chen SJ. Experimental study on seismic behaviors of concrete columns confined by corroded stirrups and lateral strength prediction. Constr Build Mater 2018;162:704–13. [29] Ma G, Li H, Hwang HJ. Seismic behavior of low-corroded reinforced concrete short columns in an over 20-year building structure. Soil Dyn Earthquake Eng 2018;106:90–100. [30] Yang SY, Song XB, Jia HX, Chen X, Liu XL. Experimental research on hysteretic behaviors of corroded reinforced concrete columns with different maximum amounts of corrosion of rebar. Constr Build Mater 2016;121:319–27. [31] Meda A, Mostosi S, Rinaldi Z, Riva P. Experimental evaluation of the corrosion influence on the cyclic behaviour of RC columns. Eng Struct 2014;76:112–23.

This paper confirmed the significant degradation of mechanical parameter for the corroded piers; however, it was also found that slight corrosion might improve the performance of the mechanical behaviors. The theoretical analysis and simulation are still needed to explore and confirm the behind mechanisms; the quantification of the variation of the mechanical parameters after corrosion are also urgently needed to assess the residue bearing capacity of existing corroded structures. Declaration of Competing Interest The authors confirm that there are no known conflicts of interest to this work. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted. Acknowledgements The work described in this paper was financially supported by the National Natural Science Foundation of China (grant nos. 51378313 & 51520105012) and the Ministry of Science and Technology of China (no. 2011CB013604), to whom the writers are grateful. References [1] Duan A, Dai JG, Jin WL. Probabilistic approach for durability design of concrete structures in marine environments, ASCE. J Mater Civ Eng 2015;27(2). [2] Tuutti K. Corrosion of steel in concrete. Stockholm, Sweden: Swedish Cement and Concrete Research Institute; 1982. [3] Zhang WP, Song XB, Gu XL, Li SB. Tensile and fatigue behavior of corroded rebars. Constr Build Mater 2012;34(5):409–17. [4] Zhou HJ, Liang XB, Zhou YF, Feng X. Statistical analysis of the tensile behavior of corroded steel bars. Proc. of the 6th International Symposium on Reliability Engineering and Risk Management (6ISRERM). 2018. p. 185–90. [5] H.J. Zhou, S.Y. Chen, Y.F. Zhou, Z.Y. Lin, X.B. Liang, J. Liu, F. Xing, Field test of a reinforced concrete bridge under marine environmental corrosion, Engineering Failure Analysis. (Under Review). [6] Coronelli D, Castel A. Corroded post-tensioned beams with bonded tendons and wire failure. Eng Struct 2009;31(8):1687–97. [7] M. Tahershamsi, Structural effects of reinforcement corrosion in concrete structures,

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