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Effects of simultaneous fatigue loading and corrosion on the behavior of reinforced beams
Construction and Building Materials 181 (2018) 85–93
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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Effects of simultaneous fatigue loading and corrosion on the behavior of reinforced beams Yiyan Lu, Wenshui Tang, Shan Li ⇑, Mingyong Tang School of Civil Engineering, Wuhan University, Wuhan 430072, China
h i g h l i g h t s Effects of simultaneous fatigue loading and corrosion on RC beams were studied. Different fatigue loads, current and loading frequencies were considered. The inclusion of corrosion significantly decrease the ductility and fatigue life. General and local corrosion simultaneously occurs under corrosion fatigue. The flexural stiffness of RC beams exhibits three-stage characteristic.
a r t i c l e
i n f o
Article history: Received 7 February 2018 Received in revised form 16 May 2018 Accepted 5 June 2018 Available online 15 June 2018 Keywords: Reinforced concrete beams Fatigue loading Corrosion Fatigue life Flexural stiffness
a b s t r a c t This paper investigated experimentally the behavior of reinforced concrete (RC) beams under simultaneous fatigue loading and steel corrosion. Fourteen specimens were manufactured and tested under fourpoint bending fatigue loading, during which reinforcement corrosion was induced by an accelerated method using a 5% NaCl solution combined with a constant impressed current. Four different levels of maximum fatigue loads, namely 50%, 55%, 65% and 75% of ultimate loading capacity with fatigue loading frequencies of 1.5 Hz and 4.5 Hz and corrosion impressed currents of 0.5 A, 1.0 A, 1.5 A and 2.5 A were applied to the beams. Crack patterns, failure modes, fatigue life, reinforcement corrosion, and flexural stiffness were investigated. Test results indicated that the inclusion of corrosion significantly decreased the ductility, fatigue life and flexural stiffness of the RC beams. Greater levels of maximum fatigue loads and impressed current tended to shorten fatigue life. General and local corrosion occurred simultaneously under the joint effects of fatigue loading and corrosion. It was also found that the flexural stiffness of RC beams under coupled fatigue loading and corrosion increased in early loading cycles and then remained approximately stable, followed by a rapid decrease just prior to failure. Ó 2018 Elsevier Ltd. All rights reserved.
1. Introduction Steel reinforcement corrosion is one of the primary problems causing significant damage to reinforced concrete (RC) structures. The corrosion could significantly decrease load-carrying capacity and durability by causing steel cross-sectional area reduction, cracking, spalling of concrete cover, and bond degradation between reinforcing bars and surrounding concrete [1]. Numerous coastal RC structures, which included RC bridges, offshore plats, and mobile drilling structures, were subjected to cyclic loading combined with chloride-induced steel corrosion [2,3]. This is known as coupled corrosion-fatigue, or the corrosion fatigue phenomenon, in which failure occurs prematurely under conditions of simultane⇑ Corresponding author. E-mail address: [email protected] (S. Li). https://doi.org/10.1016/j.conbuildmat.2018.06.028 0950-0618/Ó 2018 Elsevier Ltd. All rights reserved.
ous fatigue loading and corrosion after a smaller number of cycles or at lower stress levels than would have been observed in the absence of a corrosive environment [4]. Over the past decades, extensive studies have been devoted to the separate effects of corrosion or fatigue loading on RC beams, in which load-carrying capacity, including flexural strength [5–8] and shear capacity [9–11], bending stiffness [12,13], corrosioninduced cracks [14–17], bond strength loss [18–22] of corroded RC beams, and fatigue damage model [23,24], fatigue life prediction [25], and fatigue stiffness [26] of uncorroded RC beams, were investigated. These results indicated that corrosion, specifically local and pitting corrosion, had a significant effect on the mechanical performance and service life of RC beams, while pure fatigue loads within an allowable range had no significant influence. In addition to concerns regarding the effects of pure corrosion or fatigue loading, fatigue testing of already-corroded beams was
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conducted by a number of researchers. Sun et al. [27] developed a modified calculation formula for fatigue flexural stiffness as well as a constitutive relationship model for reinforcing bars considering the effects of the corrosion mass loss ratio and the number of fatigue loading cycles. Oyado et al. [28] reported that corrosion could change crack patterns, and the decrease in fatigue strength was proportional to the weight loss of the steel reinforcement. Yi et al. [29] reported that an increase in corrosion caused a decrease in fatigue life. Ma et al. [30] proposed a new method for fatigue life prediction of aging RC structures. With respect to the coupled effects of corrosion and sustained loading, a few experimental studies have been published [31–34]. Test results suggested that steel mass ratios and corrosion-induced crack widths were increased, and the capacity and ductility of beams were significantly under loading [31]. In addition, load levels had a significant effect on the increase in amount of steel corrosion [33]. The above mentioned studies all dealt with either the separate effects of corrosion and fatigue loading, in which corrosion and fatigue loading did not coexist simultaneously in the tests, or the coupled effects of corrosion and sustained loading where loading remained constant during the tests. Only limited studies have been conducted on the coupled effects of corrosion and fatigue loading. Bastidas-Arteaga et al. [35] proposed a new theoretical model based on the coupled corrosion-fatigue phenomena in analytical methods and concluded that coupled corrosion-fatigue had a significant effect on the performance of RC structures and significantly decreased their expected lifespans. Zhang et al. [36] developed a theoretical reliability-based approach for evaluating the damage of the combined effects of pitting corrosion and fatigue loading. W. Ahn at al. [37] conducted a galvanostatic test of fulland half-sized RC beams under static and fatigue loading with different water-cement ratios, and reported that more significant damage of RC beams was induced with fatigue loading and increasing water-cement ratio. However, the studies in [35,36], which were primarily theoretical and based on certain specific hypotheses, including that single pitting corrosion is considered during corrosion fatigue and concrete is a homogenous and isotropic material when using Fick’s second law, might not be consistent with the situations in practice. The study in [37] conducted tests focused on the cracking patterns and ultimate strength bearing capacity of beams. Limited studies have investigated the coupled effects of corrosion and fatigue on the performance of RC beams, specifically for the study of fatigue life, steel corrosion, and flexural stiffness of beams under simultaneous corrosion and fatigue loading. The primary objectives of this study were to experimentally investigate the effects of fatigue loads, corrosion current, and fatigue loading frequency on fatigue life of RC beams; characterize
reinforcement corrosion in terms of mass loss and average corrosion rate; and examine the joint effects of fatigue loading and corrosion on the flexural stiffness of RC beams. The results of the study could provide insights on the joint effects of corrosion and cyclic loading on the behavior of corroded RC beams.
2. Experimental program 2.1. Specimens In this study, fourteen RC beam specimens were prepared and divided into three groups: two specimens subjected to monotonic static loading (Group A), one specimen subjected to cyclic fatigue loading (Group B), and the remaining eleven specimens subjected to simultaneous fatigue loading and corrosion (Group C). The test parameters included: maximum fatigue load: 50%, 55%, 65% and 75% of ultimate loading capacity; impressed corrosion current: 0.5A,1.0A,1.5A and 2.5A; fatigue loading frequency: 1.5 Hz and 4.5 Hz. The 0.5–2.5 A current, which corresponded to a current density of 1327–6635 lA/cm2 was greater than that of the bulk of previous studies, which typically ranged from 200 to 3000 lA/cm2 [38]. The load level of 55–75% was marginally greater than the specified value according to GB50010-2010 [39]. The values selected were aimed at appropriately shortening the time of corrosion fatigue test as the test was both labor-intensive and time-consuming. The inclusion of frequencies from 1.5 to 4.5 Hz was because frequencies in typical engineering structures ranged from 1 to 5 Hz. A summary of the specimens is presented in Table 1. The designations of the specimens were defined as follows: C-4.5-50-1.5, where ‘C’ was the group, ‘4.5’ was the fatigue loading frequency, ‘50’ was the percentage of maximum fatigue load to the ultimate loading capacity, and ‘1.5’ was the level (A) of the impressed corrosion current. All beams were cast as follows: 200 mm deep, 120 mm wide, and 1700 mm long. In addition, a calculated length of 1500 mm and a constant-moment section length of 500 mm were designed for four-point bending loading. Each beam was reinforced with two 12-mm deformed bars in tension, and two 8-mm plain bars in compression. Smooth stirrups with a diameter of 6.5 mm were spaced at 80 mm intervals within the shear span. The dimensions and steel reinforcement arrangement of the beams is shown in Fig. 1. The tensile reinforcement in the constant-moment section was designed to corrode. All other steel including the tensile rein-
Table 1 Details of the specimens. Groups
Specimens
Frequency (Hz)
Fatigue loads
I (A)
Loading scheme
A
A-1 A-2 B-1 C-4.5-50-1.5 C-4.5-55-1.5 C-4.5-65-1.5 C-4.5-75-1.5 C-4.5-55-0.5 C-4.5-55-1.0 C-4.5-55-2.5 C-1.5-55-0.5 C-1.5-55-1.0 C-1.5-55-1.5 C-1.5-55-2.5
– – 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 1.5 1.5 1.5 1.5
– – 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
– – – 1.5 1.5 1.5 1.5 0.5 1.0 2.5 1.5 1.5 1.5 1.5
Monotonic loading
B C
Note: Pu is the ultimate loading capacity of the uncorroded beam.
Pu-0.55 Pu Pu-0.5 Pu Pu-0.55 Pu Pu-0.65 Pu Pu-0.75 Pu Pu-0.55 Pu Pu-0.55 Pu Pu-0.55 Pu Pu-0.55 Pu Pu-0.55 Pu Pu-0.55 Pu Pu-0.55 Pu
Fatigue loading Fatigue loading
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2 8
6.5mm@80mm
500
500 1700
500
Load cell
200
2 12
Spread beam Drillled PVC pipe
120
Sprinklers
Fig. 1. Dimensions and reinforcement arrangement of the beams.
Tensile reinforcing bars
forcements in the shear section, compressive reinforcements and stirrups was coated with epoxy resin to prevent corrosion.
Stainless steel plate Water pump
NaCl electrolyte
Wire
-
2.2. Materials The maximum size of the concrete coarse aggregate was smaller than 15 mm and the apparent density was 2.62 g/mm3. The fine aggregate was natural river sand with a fineness modulus of 2.8 and an apparent density of 2.68 g/mm3. The water cement ratio was 0.5 and the concrete mix ratio was 1:1.71:3.21:0.5 (cement, sand, pebble, and water) by weight. The 28-d compressive strength of the concrete was 32.74 MPa. The mechanical properties of the reinforcing bars were determined, based on standard tensile coupon tests according to Chinese code GB/T 2975-1998 [40], and the yielded strength, tensile ultimate strength, elongation, and elastic modulus of the various types of reinforcement were obtained as presented in Table 2.
DC power supply
+
Fig. 2. Schematic diagram of corrosion fatigue testing system.
2.3. Setup of fatigue loading combined with corrosion The test setup, which allowed the simultaneous application of fatigue loading and corrosion is shown in Fig. 2. A dynamic hydraulic jack and fatigue-testing machine were used for the fatigue testing. A NaCl solution was sprayed through two polyvinyl chloride (PVC) pipes fixed to the sides of the beam by plastic ropes. Sprinklers were placed at 100 mm intervals along the PVC pipes, which were above the tensile reinforcements in the vertical direction to allow the solution to penetrate into the reinforcing bars under the action of gravity. A water pump in a tank filled with 5% NaCl solution was used to pump the solution into the pipes. In addition, a stainless steel plate was attached to the bottom surface of the beam to act as a cathode, sponge material was placed between the plate and beam to retain moisture. The two tensile reinforcing bars served as an anode and a DC power supply provided a constant current for the complete circuit. 2.4. Fatigue and static loading coupled with accelerated corrosion Beams A-1 and A-2 were monotonically loaded to determine their average ultimate loading capacities. Beam B-1 was subjected to cyclic loading without corrosion. All the beams tested under simultaneous fatigue loading and corrosion were first immersed in 5% NaCl solution for three days for the absorption of free chlorides in the solution to prepare for the corrosion of the reinforcements. Before the test, static loads ranging from 0 to 10 kN were pre-applied to ensure good bearing contact and to verify that the data from all measuring channels were correct. When the pump and DC power supply were turned on, the predetermined fatigue
Fig. 3. Picture of corrosion fatigue testing.
load with sinusoidal variation was applied as shown in Fig. 3. As the number of fatigue loading cycles reached pre-defined values, e.g. 10000, 50000, 100000, 20000, 30000, and 400000, the fatigue loading and corrosion process was paused and the beam was monotonically loaded to the corresponding maximum fatigue load under step loading. The deflections were measured by three linear variable displacement transducers (LVDTs) placed at mid-span and the two loading points of the beam. If fatigue failure had not occurred after fatigue loading to two million cycles, a monotonic load was applied until static failure. 2.5. Measurement of reinforcement corrosion Upon completion of the fatigue loading test, two tensile reinforcing bars in the constant-moment section (corrosion section) were removed from the beam and cleaned with an acid solution, rinsed with clean water and dried by a dryer according to JTJ27098 Testing code of concrete for port and waterwog engineering [41]. The residual masses of the reinforcements were measured to determine the mass loss. The mass loss of the reinforcements was calculated by Equation (1):
Table 2 Mechanical properties of reinforcing bars. Reinforcement diameter (mm)
Yield strength (MPa)
Tensile ultimate strength (MPa)
Elongation (%)
Elastic modulus (MPa)
6.5 8 12
274.4 286.6 384.2
356.3 386.4 563.3
25 20 22
1.89 105 2.08 105 1.95 105
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Mass loss ¼
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m mc 100% m
ð1Þ
where m and mc were the mass of reinforcements before and after corrosion, respectively. 3. Experimental results and discussion 3.1. Crack patterns Fig. 4 shows the typical crack patterns of beams. For the beams of Group A, a transverse crack occurred at a load of approximately 15 kN and more primary and secondary cracks formed with increasing load. After the reinforcement yielded, the length and width of the cracks showed a sharp growth followed by the failure of the beam. In beam B-1, the number of transverse cracks remained stable after the first cycle, and the length of cracks was smaller compared to that of the Group A and C beams. With respect to the beams under simultaneous fatigue loading and corrosion, two types of cracks, including corrosion-induced cracks on the side or bottom surface parallel to longitudinal reinforcing bars and transverse flexural cracks, were observed, as can be seen in Fig. 5. The corrosion-induced cracks initiated after a number of fatigue loading cycles and propagated in further cycles. As the two types of cracks crossed, portions of the concrete cover were vulnerable to spall.
Fig. 5. Crack patterns of beams subjected to corrosion fatigue, (a) side and (b) bottom surface.
ing and corrosion as shown in Fig. 6, the beams collapsed instantaneously, marked by the rupture of the tensile reinforcement after a significant increase in the deflection, and the failure was brittle without warning. The rupture of the reinforcement occurred in the location of a relatively wide crack close to the mid-span of the beam because of greater reinforcement stresses at the crack section. In addition, it should be noted that one reinforcing bar ruptured in the beams at a loading frequency of 4.5 Hz while both tensile reinforcing bars ruptured in the 1.5 Hz series test beams at fatigue failure. This was attributed to the lower fatigue loading frequency which contributed to stress redistribution between the two reinforcing bars, which had the same stress level prior to failure. Images of the ruptured section of the corroded reinforcing bars were taken under an electron microscope, and are shown in Fig. 7. It was observed that there was significant corrosion on the reinforcement surface as well as great cross-sectional loss in the rupture section. The rupture was induced by the combined effects of fatigue loading and corrosion, whose shape was irregular, and unlike the relatively flat section of corroded RC beams after fatigue loading [27] or the necking section of reinforcement under static loading with good ductility.
3.2. Failure modes Beams A-1 and A-2 collapsed at an average load of 63 kN in a typical flexural ductile failure mode, in which reinforcing bars in the tensile zone yielded followed by concrete crushing in the compressive zone. Two million fatigue loading cycles failed to destroy beam B-1, and in the subsequent monotonic static loading tests, the beam exhibited a ductile failure mode with an ultimate loading capacity of 60.9 KN, which was 96.7% that of the uncorroded beam. Therefore, fatigue loading had no significant effect on the static performance of RC beams without corrosion. With respect to the failure modes of the beams subjected to simultaneous fatigue load-
(a)
(b)
(c) Fig. 4. The typical crack patterns of (a) Group A, (b) Group B and (c) Group C specimens.
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where 4r and N are stress amplitude of reinforcement and the number of cyclic loading cycles, respectively, and A and B are undetermined constants. The nominal reinforcement stress was calculated using the conversion cross-section method in which the area of reinforcement was transformed into the area of concrete [43]. The nominal fatigue reinforcement stress was then calculated by
rs ¼ aE Icr ¼
Mðh0 xÞ Icr
ð3Þ
1 3 2 bx þ aE As ðh0 xÞ 3
ð4Þ
0sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 2bh0 1A x¼ 1þ b aE As
aE As @
Fig. 6. Failure modes of (a) 4.5 Hz and (b) 1.5 Hz series beams.
3.3. Fatigue life The fatigue life of the beams of Groups B and C are presented in Table 3. Beam B-1, which was subjected to cyclic loading without corrosion, had a fatigue life of greater than two million cycles, which was significantly greater than that of the beams under simultaneous fatigue loading and corrosion. This indicated that corrosion significantly reduced the fatigue life of RC beams. As can be seen in Table 3, the fatigue life significantly decreased with increasing of fatigue load amplitude. The fatigue life of beam C-4.5-50-1.5 with a fatigue load amplitude of 0.4 Pu was 1.142 million cycles, however, it decreased to 0.184 million cycles with a fatigue load amplitude of 0.65 Pu, a decrease of 83.9%. In fatigue life studies, S-N (fatigue stress amplitude versus fatigue life) curves plotted on a double-logarithmic scale would be approximately linear [42], and the following equation was obtained:
lg Dr ¼ A þ B lg N
ð2Þ
ð5Þ
where M is the applied flexural moment, aE is the ratio of the Young’s modulus of steel to that of concrete, Icr is the moment of inertial for a cracked RC beam section, h0 is the effective cross section height, x is the height of compressive zone and As is the area of the tensile reinforcing bars. The fatigue stress amplitude is obtained by
Dr ¼ aE
ðM max M min Þðh0 xÞ Icr
ð6Þ
where Mmax and Mmin are corresponding maximum and minimum flexural moment, respectively. The results of the fatigue stress amplitudes are presented in Table 3. The S-N curves of the beams with different levels of stress amplitude of reinforcement (i.e. beams C-4.5-50-1.5, C-4.5-551.5, C-4.5-65-1.5 and C-4.5-75-1.5) are shown in Fig. 8. It could be seen that there was a good linear correlation between the stress and the number of fatigue loading cycles, which indicated that the S-N curves could be used for fatigue life predictions of RC beams under same corrosive environments. It was important to mention that the validity of this type of empirical correlation is restricted
Fig. 7. Rupture section of reinforcements.
Table 3 Mass loss, fatigue life, stress amplitude and average corrosion rate of the RC beams. Specimens
4r (MPa)
Fatigue life (ten thousand)
Mass loss (%)
Average corrosion rate (%/cycle)
B-1 C-4.5-50-1.5 C-4.5-55-1.5 C-4.5-65-1.5 C-4.5-75-1.5 C-4.5-55-0.5 C-4.5-55-1.0 C-4.5-55-2.5 C-1.5-55-0.5 C-1.5-55-1.0 C-1.5-55-1.5 C-1.5-55-2.5
200 178 200 244 289 200 200 200 200 200 200 200
More than 200 114.2 74.5 35.6 18.4 100.3 101.6 69.2 129.7 122.5 72.5 56.9
0 8.46 7.91 5.44 8.03 4.03 7.35 10.07 8.62 14.54 13.82 18.55
0 0.074 0.106 0.153 0.436 0.040 0.072 0.146 0.066 0.119 0.191 0.326
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corrosion speed which reduced fatigue life. In addition, the decrease in fatigue life with the current ranging from 1.0 to 1.5 A was significantly greater than that with the current varying from 0.5 to 1.0 A and 1.5–2.5A. To better understand this phenomenon, we assumed that, with the current varying from 0.5 to 1.0 A, the corrosion rate increased and reduced the sectional area of the reinforcement and the fatigue life of the beam. As the current increased from 1.0 A to 1.5 A, the local corrosion and pitting corrosion increased, which significantly decreased the fatigue life of the beam. When a current of 2.5 A was applied, the decrease in fatigue life was not evident because of a limited decrease in the sectional area of the reinforcement, because of inadequate moisture and oxygen for faster corrosion rates and heavier local and pitting corrosion. Further, studies and analyses concerning local and pitting corrosion would be required. With respect to the comparison of fatigue life between the 4.5 Hz and 1.5 Hz series beams with the same fatigue loads and level of current, it was observed in Fig. 9 that the life of RC beams with a fatigue loading frequency of 4.5 Hz was shorter than that of beams with a fatigue loading frequency of 1.5 Hz at the current levels of 0.5 A and 1.0 A, while this phenomenon was reversed as current levels of 1.5 A and 2.5 A were applied. In addition, at a smaller fatigue loading frequency, i.e. 4.5 Hz, the change in the fatigue life of RC beams with current was less pronounced. It was concluded that as the smaller fatigue loading frequency was applied, the effect of corrosion on fatigue life was more significant because of longer corrosion periods per cycle.
Fig. 8. S-N curve of the beams.
3.4. Corrosion of reinforcements
Fig. 9. The relationship between fatigue life and current.
to similar material properties and environments, and in order to obtain a general relationship, additional studies were required. Fig. 9 shows the relationship between fatigue life and impressed current. Greater current levels led to shorter fatigue life for both the 4.5 Hz and 1.5 Hz series beams, and the fatigue life of beam C-4.5-55-0.5 was marginally smaller than that of beam C-4.5-55-1.0 because of natural scatter in fatigue phenomena. The reason for this was that the greater current level, which represented a significant corrosive environment, resulted in a greater
Fig. 10 shows the typical corrosion of beams under simultaneous fatigue loading and corrosion. It could be seen that the reinforcement surface was covered with a layer of rust, and uneven corrosion was induced, causing different sectional area losses. Previous studies [33] suggested that local corrosion occurred under natural environment while general corrosion occurred in accelerated corrosion. In this study, both local and general corrosion occurred simultaneously under the effects of fatigue loading and corrosion, indicating that the corrosion pattern was changed by the fatigue loading. The corrosion level of reinforcements was quantitatively assessed in terms of mass loss, as presented in Table 3. It was observed that there was no negative correlation between fatigue life and mass loss which was typically observed in accelerated corrosion tests followed by fatigue loading. The reason for this was that mass loss is time-dependent rather than constant in this study, and the final mass loss was the sum of reinforcement corrosion. The mass loss depended on the level of current density, corrosion duration and corrosion efficiency according to Faraday’s law. In addition, the corrosion duration was the ratio of fatigue loading cycles to frequency and the fatigue life was influenced by fatigue loads and current density as discussed in Section 3.3. In this study, the mass loss was a dependent variable rather than an inde-
Fig. 10. Surface morphology of reinforcement.
Y. Lu et al. / Construction and Building Materials 181 (2018) 85–93
pendent variable. The mass loss varied during the test and could not be determined until the collapse of the beam, which was different from the situation when fatigue loading was applied to already corroded RC beams. Therefore, the mass loss was not suitable for determining the corrosion speed or predicting the fatigue life. As the reinforcement corrosion increased continuously during the test, the average corrosion rate, defined as the mass loss of reinforcement per cycle, was proposed to evaluate the corrosion speed. The results of the average corrosion rate are presented in Table 3. The average corrosion rate increased with increasing maximum fatigue load. It was concluded that this was because the greater the maximum fatigue load, the greater the reinforcement stress level. As a result, wider cracks were induced to provide a better channel for oxygen and moisture, further corroding the steel. It was shown that greater current levels resulted in greater average corrosion rates regardless of the different loading frequencies because the greater current contributed to faster steel corrosion. It was also found that the average corrosion rate of the 1.5 Hz series beams was greater than that of the 4.5 Hz series beams with the same level of current. This was attributed to that longer corrosion periods being applied to the beams per unit time with lower loading frequency (i.e. 1.5 Hz), resulting in a greater mass loss. This appeared to be in conflict with the conclusion that the effect of loading frequency on fatigue life is not evident, as presented in Section 3.3. The reason for this was that the average corrosion rate was not directly proportional to the reduction of sectional area of the reinforcement because of local and pitting corrosion, which significantly affected the fatigue life. Therefore, because of the significant scatter of local and pitting corrosion, the relationship between loading frequency and fatigue life considering the section area loss would have to be investigated in future studies. Besides the effects of fatigue loading and corresponding flexural cracks on corrosion rates, corrosion-induced cracks could accelerate the corrosion process. The cracking process of concrete comprised four stages [44,45]: corrosion initiation, the formation of cracks, crack propagation, and crack coalescence and concrete delamination. When accelerated corrosion through impressed current was applied, the formation of cracks was controlled by a concrete attenuation factor. The attenuation factor, defined as the ability of concrete to absorb expansive stress caused by the corrosion products, was a function of a number of parameters, which included capillary absorption, temperature, and concrete quality which included the water/cement ratio. In this study, because of the high corrosion current compared to that in practice, the generation of oxides was so rapid that the concrete had no opportunity to absorb the expansion stresses, thus decreasing the attenuation factor and causing a sudden cracking. Additionally, the loading frequency of 1.5 Hz prolonged the time of closure and openness of flexural cracks in each cycle, and large amounts of corrosion products were generated to reduce the attenuation factor. Consequently, greater cracks were induced to accelerate the reinforcement corrosion.
Fig. 11. Load-deflection curve of beam C-4.5-55-1.0.
the number of fatigue loading cycles increased, the load-deflection curve exhibited an approximate linear propagation. In addition, the residual deflection gradually increased, as indicated by the interval between the intercepts on the horizontal axis. Fig. 12 shows the evolution of the residual and total deflections of beam C-4.5-55-1.0 at the unloading state and under the maximum fatigue load with the loading cycles. Both the residual and total deflections exhibited three stages: rapid rise, slow growth and sharp increase. However, the rates of increase were not equal, suggesting that the stiffness of the beam varied as the number of fatigue loading cycles increased. Flexural stiffness was regarded as the one of the critical evaluation indices for RC beams. In this study, stiffness was assessed by calculating the secant stiffness by dividing the maximum fatigue load applied by the elastic deflection, namely the difference between the total and residual deflection. Considering the inherent differentiation of each beam, the obtained stiffness values were normalized, by dividing them by their initial stiffness at the first loading. Fig. 13 shows the evolution of normalized stiffness of RC beams with loading cycles. In specimens under combined fatigue loading and corrosion, an increase in normalized stiffness was observed
3.5. Mid-span deflections and stiffness The deflections of RC beams were periodically measured under monotonic static loading after fatigue loading to a certain number of cycles. As the deflection response to loads for all the beams under simultaneous fatigue loading and corrosion were similar, beam C-4.5-55-1.0 was taken as an example and the loaddeflection curve with increasing fatigue loading cycles is shown in Fig. 11. It was observed that the gradient of the curve decreased instantaneously at a load of about 13 kN in the first loading, which indicated a decrease in flexural stiffness because of the occurrence of initial transverse cracks, and the slope then remained stable. As
91
Fig. 12. The residual and total deflections of beam C-4.5-55-1.0.
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during the early cycles followed by the second stage where the normalized stiffness tended to relatively stabilize. Finally, the normalized stiffness exhibited a rapid decrease. This was because the corrosion level increased with increasing loading cycles in this study. Marginal corrosion levels could enhance the bonding between concrete and reinforcements while greater levels of corrosion caused the cracking and debonding of concrete which decreased stiffness [46]. With respect to beam B-1 without corrosion, the normalized stiffness exhibited a rapid decrease in early cycles followed by a gradual drop with increasing loading cycles. As can be shown in Fig. 13(a), the normalized stiffness of beams C-4.5-65-1.5 and C-4.5-75-1.5 did not exhibit the second-stage variation due to limited measurements in their shorter fatigue lives. It was found that the normalized stiffness increased with decreasing maximum fatigue loads. This was primarily ascribed to the greater load resulting in greater reinforcement stress, wider cracks and more rapid fatigue degradation of concrete. Therefore, a smaller effective sectional moment of inertia and the overall smaller elastic modulus of the beam contributed to a lower fatigue flexural stiffness. As can be seen in Fig. 13(b) and (c), at increased levels of impressed current, the normalized stiffness exhibited a greater growth rate in the first stage and faster degradation during the last stage. This was because higher currents produced greater average corrosion rates as discussed in Section 3.4. Therefore, greater stiffness increases were induced in early cycles. However, greater concrete strains and more significant bond damage occurred after the expansive stresses of corrosion products increased to cause concrete cracking. It was also found that there were distinct variations in flexural stiffness increases between the 4.5 Hz and 1.5 Hz series beams with a maximum fatigue load of 55% Pu as shown in Fig. 13(b) and (c), respectively. The maximum normalized stiffness of the 4.5 Hz series beams was smaller than 1.2, while that of 1.5 Hz series beams was greater than 1.35. This phenomenon was noteworthy and it could be inferred that the failure of beams under simultaneous fatigue loading and corrosion was the competitive results between fatigue damage and corrosion deterioration. When the maximum fatigue load was greater (including 0.65 Pu and 0.75 Pu), the behaviour of the beam were more fatigue performance-dependent, including a shorter fatigue life and three-stage feature of stiffness evolution not being observed. When the smaller fatigue loading frequency (i.e. 1.5 Hz) and relatively higher corrosion currents (including all currents used in this study) were included, the beams typically exhibited greater mass and sectional area losses as well as a greater increase in stiffness. As the fatigue loading and accelerated corrosion were time-consuming, the performance of the beams was affected by the selection of influencing parameters, including fatigue load, corrosion current, and fatigue loading frequency. Therefore, smaller loading frequencies and levels of current should be involved in further studies on RC structures under simultaneous fatigue loading and corrosion. 4. Conclusions This paper presented an experimental study on the behavior of RC beams under combined fatigue loading and corrosion, and the following conclusions could be drawn. These conclusions apply for the materials and circumstances of this research. Therefore, they can be extrapolated with the respective precautions.
Fig. 13. The evolution of normalized stiffness of RC beams, (a) different levels of maximum fatigue load, and different current with (b) 4.5 Hz and (c) 1.5 Hz.
1. Corrosion have a significant effect on the fatigue performance of RC beams in terms of crack patterns, ductility, fatigue life and stiffness evolution.
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2. Greater levels of maximum fatigue load and current typically results in a shorter fatigue life. The S-N curve remains valid in a corrosive environment. At a smaller fatigue loading frequency (1.5 Hz), the effect of current on fatigue life is more significant compared to the higher frequency (4.5 Hz). 3. General and local corrosion occurs simultaneously in RC beams under simultaneous fatigue loading and corrosion. Average corrosion rates increases with increasing maximum fatigue load and current, and lower loading frequency. 4. Normalized flexural stiffness of RC beams under coupledcorrosion fatigue exhibits three stages: gradual increase, stabilization and rapid degradation. The stiffness decreases with increasing maximum fatigue load, and greater current results in higher growth rates in the first stage and faster degradation in the final stage. Additionally, the enhancing effect on the stiffness of the 1.5 Hz series RC beams is greater than for the 4.5 Hz series beams. Conflict of interest None. Acknowledgements The research work is funded by National Natural Science Foundation of China (No. 51578428) and Special Project on Technical Innovation of Hubei (No. 2016AAA025), the authors deeply appreciate their financial supports. References [1] C. Fang, K. Lundgren, L. Chen, et al., Corrosion influence on bond in reinforced concrete, Cem. Concr. Res. 34 (11) (2004) 2159–2167. [2] A. Duan, J.G. Dai, W.L. Jin, Probabilistic approach for durability design of concrete structures in marine environments, J. Mater. Civ. Eng. 27 (2) (2011) A4014007. [3] H.L. Wang, J.G. Dai, X.Y. Sun, et al., Characteristics of concrete cracks and their influence on chloride penetration, Constr. Build. Mater. 107 (2016) 216–225. [4] E. Bastidas-Arteaga, P. Bressolette, A. Chateauneuf, et al., Probabilistic lifetime assessment of RC structures under coupled corrosion–fatigue deterioration processes, Struct. Saf. 31 (1) (2009) 84–96. [5] A.K. Azad, S. Ahmad, S.A. Azher, Residual strength of corrosion-damaged reinforced concrete beams, ACI Mater. J. 104 (1) (2007) 40–47. [6] X. Zhang, L. Wang, J. Zhang, et al., Model for flexural strength calculation of corroded RC beams considering bond-slip behavior, J. Eng. Mech. 142 (7) (2016) 04016038. [7] W. Xiaohui, L. Xila, Predicting the flexural capacity of RC beam with partially unbonded steel reinforcement, Comput. Concr. 6 (3) (2009) 235–252. [8] P.S. Mangat, M.S. Elgarf, Flexural strength of concrete beams with corroding reinforcement, ACI Struct. J. 96 (1) (1999) 149–158. [9] X.H. Wang, B. Li, X.H. Gao, et al., Shear behaviour of RC beams with corrosion damaged partial length, Mater. Struct. 45 (3) (2012) 351–379. [10] L. Wang, X. Zhang, J. Zhang, et al., Effects of stirrup and inclined bar corrosion on shear behavior of RC beams, Constr. Build. Mater. 98 (2015) 537–546. [11] D. Zhang, Y. Zhao, W. Jin, et al., Shear strengthening of corroded reinforced concrete columns using pet fiber based composties, Eng. Struct. 153 (2017) 757–765. [12] M. Dekoster, F. Buyle-Bodin, O. Maurel, et al., Modelling of the flexural behaviour of RC beams subjected to localised and uniform corrosion, Eng. Struct. 25 (10) (2003) 1333–1341. [13] J. Zhong, P. Gardoni, D. Rosowsky, Stiffness degradation and time to cracking of cover concrete in reinforced concrete structures subject to corrosion, J. Eng. Mech. 136 (2) (2010) 209–219. [14] C.Q. Li, R.E. Melchers, Analytical model for corrosion-induced crack width in reinforced concrete structures, ACI Mater. J. 103 (4) (2006) 479–487. [15] S.F.U. Ahmed, M. Maalej, H. Mihashi, Cover cracking of reinforced concrete beams due to corrosion of steel, ACI Mater. J. 104 (2) (2007) 153–161.
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Contents lists available at ScienceDirect
Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Effects of simultaneous fatigue loading and corrosion on the behavior of reinforced beams Yiyan Lu, Wenshui Tang, Shan Li ⇑, Mingyong Tang School of Civil Engineering, Wuhan University, Wuhan 430072, China
h i g h l i g h t s Effects of simultaneous fatigue loading and corrosion on RC beams were studied. Different fatigue loads, current and loading frequencies were considered. The inclusion of corrosion significantly decrease the ductility and fatigue life. General and local corrosion simultaneously occurs under corrosion fatigue. The flexural stiffness of RC beams exhibits three-stage characteristic.
a r t i c l e
i n f o
Article history: Received 7 February 2018 Received in revised form 16 May 2018 Accepted 5 June 2018 Available online 15 June 2018 Keywords: Reinforced concrete beams Fatigue loading Corrosion Fatigue life Flexural stiffness
a b s t r a c t This paper investigated experimentally the behavior of reinforced concrete (RC) beams under simultaneous fatigue loading and steel corrosion. Fourteen specimens were manufactured and tested under fourpoint bending fatigue loading, during which reinforcement corrosion was induced by an accelerated method using a 5% NaCl solution combined with a constant impressed current. Four different levels of maximum fatigue loads, namely 50%, 55%, 65% and 75% of ultimate loading capacity with fatigue loading frequencies of 1.5 Hz and 4.5 Hz and corrosion impressed currents of 0.5 A, 1.0 A, 1.5 A and 2.5 A were applied to the beams. Crack patterns, failure modes, fatigue life, reinforcement corrosion, and flexural stiffness were investigated. Test results indicated that the inclusion of corrosion significantly decreased the ductility, fatigue life and flexural stiffness of the RC beams. Greater levels of maximum fatigue loads and impressed current tended to shorten fatigue life. General and local corrosion occurred simultaneously under the joint effects of fatigue loading and corrosion. It was also found that the flexural stiffness of RC beams under coupled fatigue loading and corrosion increased in early loading cycles and then remained approximately stable, followed by a rapid decrease just prior to failure. Ó 2018 Elsevier Ltd. All rights reserved.
1. Introduction Steel reinforcement corrosion is one of the primary problems causing significant damage to reinforced concrete (RC) structures. The corrosion could significantly decrease load-carrying capacity and durability by causing steel cross-sectional area reduction, cracking, spalling of concrete cover, and bond degradation between reinforcing bars and surrounding concrete [1]. Numerous coastal RC structures, which included RC bridges, offshore plats, and mobile drilling structures, were subjected to cyclic loading combined with chloride-induced steel corrosion [2,3]. This is known as coupled corrosion-fatigue, or the corrosion fatigue phenomenon, in which failure occurs prematurely under conditions of simultane⇑ Corresponding author. E-mail address: [email protected] (S. Li). https://doi.org/10.1016/j.conbuildmat.2018.06.028 0950-0618/Ó 2018 Elsevier Ltd. All rights reserved.
ous fatigue loading and corrosion after a smaller number of cycles or at lower stress levels than would have been observed in the absence of a corrosive environment [4]. Over the past decades, extensive studies have been devoted to the separate effects of corrosion or fatigue loading on RC beams, in which load-carrying capacity, including flexural strength [5–8] and shear capacity [9–11], bending stiffness [12,13], corrosioninduced cracks [14–17], bond strength loss [18–22] of corroded RC beams, and fatigue damage model [23,24], fatigue life prediction [25], and fatigue stiffness [26] of uncorroded RC beams, were investigated. These results indicated that corrosion, specifically local and pitting corrosion, had a significant effect on the mechanical performance and service life of RC beams, while pure fatigue loads within an allowable range had no significant influence. In addition to concerns regarding the effects of pure corrosion or fatigue loading, fatigue testing of already-corroded beams was
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conducted by a number of researchers. Sun et al. [27] developed a modified calculation formula for fatigue flexural stiffness as well as a constitutive relationship model for reinforcing bars considering the effects of the corrosion mass loss ratio and the number of fatigue loading cycles. Oyado et al. [28] reported that corrosion could change crack patterns, and the decrease in fatigue strength was proportional to the weight loss of the steel reinforcement. Yi et al. [29] reported that an increase in corrosion caused a decrease in fatigue life. Ma et al. [30] proposed a new method for fatigue life prediction of aging RC structures. With respect to the coupled effects of corrosion and sustained loading, a few experimental studies have been published [31–34]. Test results suggested that steel mass ratios and corrosion-induced crack widths were increased, and the capacity and ductility of beams were significantly under loading [31]. In addition, load levels had a significant effect on the increase in amount of steel corrosion [33]. The above mentioned studies all dealt with either the separate effects of corrosion and fatigue loading, in which corrosion and fatigue loading did not coexist simultaneously in the tests, or the coupled effects of corrosion and sustained loading where loading remained constant during the tests. Only limited studies have been conducted on the coupled effects of corrosion and fatigue loading. Bastidas-Arteaga et al. [35] proposed a new theoretical model based on the coupled corrosion-fatigue phenomena in analytical methods and concluded that coupled corrosion-fatigue had a significant effect on the performance of RC structures and significantly decreased their expected lifespans. Zhang et al. [36] developed a theoretical reliability-based approach for evaluating the damage of the combined effects of pitting corrosion and fatigue loading. W. Ahn at al. [37] conducted a galvanostatic test of fulland half-sized RC beams under static and fatigue loading with different water-cement ratios, and reported that more significant damage of RC beams was induced with fatigue loading and increasing water-cement ratio. However, the studies in [35,36], which were primarily theoretical and based on certain specific hypotheses, including that single pitting corrosion is considered during corrosion fatigue and concrete is a homogenous and isotropic material when using Fick’s second law, might not be consistent with the situations in practice. The study in [37] conducted tests focused on the cracking patterns and ultimate strength bearing capacity of beams. Limited studies have investigated the coupled effects of corrosion and fatigue on the performance of RC beams, specifically for the study of fatigue life, steel corrosion, and flexural stiffness of beams under simultaneous corrosion and fatigue loading. The primary objectives of this study were to experimentally investigate the effects of fatigue loads, corrosion current, and fatigue loading frequency on fatigue life of RC beams; characterize
reinforcement corrosion in terms of mass loss and average corrosion rate; and examine the joint effects of fatigue loading and corrosion on the flexural stiffness of RC beams. The results of the study could provide insights on the joint effects of corrosion and cyclic loading on the behavior of corroded RC beams.
2. Experimental program 2.1. Specimens In this study, fourteen RC beam specimens were prepared and divided into three groups: two specimens subjected to monotonic static loading (Group A), one specimen subjected to cyclic fatigue loading (Group B), and the remaining eleven specimens subjected to simultaneous fatigue loading and corrosion (Group C). The test parameters included: maximum fatigue load: 50%, 55%, 65% and 75% of ultimate loading capacity; impressed corrosion current: 0.5A,1.0A,1.5A and 2.5A; fatigue loading frequency: 1.5 Hz and 4.5 Hz. The 0.5–2.5 A current, which corresponded to a current density of 1327–6635 lA/cm2 was greater than that of the bulk of previous studies, which typically ranged from 200 to 3000 lA/cm2 [38]. The load level of 55–75% was marginally greater than the specified value according to GB50010-2010 [39]. The values selected were aimed at appropriately shortening the time of corrosion fatigue test as the test was both labor-intensive and time-consuming. The inclusion of frequencies from 1.5 to 4.5 Hz was because frequencies in typical engineering structures ranged from 1 to 5 Hz. A summary of the specimens is presented in Table 1. The designations of the specimens were defined as follows: C-4.5-50-1.5, where ‘C’ was the group, ‘4.5’ was the fatigue loading frequency, ‘50’ was the percentage of maximum fatigue load to the ultimate loading capacity, and ‘1.5’ was the level (A) of the impressed corrosion current. All beams were cast as follows: 200 mm deep, 120 mm wide, and 1700 mm long. In addition, a calculated length of 1500 mm and a constant-moment section length of 500 mm were designed for four-point bending loading. Each beam was reinforced with two 12-mm deformed bars in tension, and two 8-mm plain bars in compression. Smooth stirrups with a diameter of 6.5 mm were spaced at 80 mm intervals within the shear span. The dimensions and steel reinforcement arrangement of the beams is shown in Fig. 1. The tensile reinforcement in the constant-moment section was designed to corrode. All other steel including the tensile rein-
Table 1 Details of the specimens. Groups
Specimens
Frequency (Hz)
Fatigue loads
I (A)
Loading scheme
A
A-1 A-2 B-1 C-4.5-50-1.5 C-4.5-55-1.5 C-4.5-65-1.5 C-4.5-75-1.5 C-4.5-55-0.5 C-4.5-55-1.0 C-4.5-55-2.5 C-1.5-55-0.5 C-1.5-55-1.0 C-1.5-55-1.5 C-1.5-55-2.5
– – 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 1.5 1.5 1.5 1.5
– – 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
– – – 1.5 1.5 1.5 1.5 0.5 1.0 2.5 1.5 1.5 1.5 1.5
Monotonic loading
B C
Note: Pu is the ultimate loading capacity of the uncorroded beam.
Pu-0.55 Pu Pu-0.5 Pu Pu-0.55 Pu Pu-0.65 Pu Pu-0.75 Pu Pu-0.55 Pu Pu-0.55 Pu Pu-0.55 Pu Pu-0.55 Pu Pu-0.55 Pu Pu-0.55 Pu Pu-0.55 Pu
Fatigue loading Fatigue loading
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2 8
6.5mm@80mm
500
500 1700
500
Load cell
200
2 12
Spread beam Drillled PVC pipe
120
Sprinklers
Fig. 1. Dimensions and reinforcement arrangement of the beams.
Tensile reinforcing bars
forcements in the shear section, compressive reinforcements and stirrups was coated with epoxy resin to prevent corrosion.
Stainless steel plate Water pump
NaCl electrolyte
Wire
-
2.2. Materials The maximum size of the concrete coarse aggregate was smaller than 15 mm and the apparent density was 2.62 g/mm3. The fine aggregate was natural river sand with a fineness modulus of 2.8 and an apparent density of 2.68 g/mm3. The water cement ratio was 0.5 and the concrete mix ratio was 1:1.71:3.21:0.5 (cement, sand, pebble, and water) by weight. The 28-d compressive strength of the concrete was 32.74 MPa. The mechanical properties of the reinforcing bars were determined, based on standard tensile coupon tests according to Chinese code GB/T 2975-1998 [40], and the yielded strength, tensile ultimate strength, elongation, and elastic modulus of the various types of reinforcement were obtained as presented in Table 2.
DC power supply
+
Fig. 2. Schematic diagram of corrosion fatigue testing system.
2.3. Setup of fatigue loading combined with corrosion The test setup, which allowed the simultaneous application of fatigue loading and corrosion is shown in Fig. 2. A dynamic hydraulic jack and fatigue-testing machine were used for the fatigue testing. A NaCl solution was sprayed through two polyvinyl chloride (PVC) pipes fixed to the sides of the beam by plastic ropes. Sprinklers were placed at 100 mm intervals along the PVC pipes, which were above the tensile reinforcements in the vertical direction to allow the solution to penetrate into the reinforcing bars under the action of gravity. A water pump in a tank filled with 5% NaCl solution was used to pump the solution into the pipes. In addition, a stainless steel plate was attached to the bottom surface of the beam to act as a cathode, sponge material was placed between the plate and beam to retain moisture. The two tensile reinforcing bars served as an anode and a DC power supply provided a constant current for the complete circuit. 2.4. Fatigue and static loading coupled with accelerated corrosion Beams A-1 and A-2 were monotonically loaded to determine their average ultimate loading capacities. Beam B-1 was subjected to cyclic loading without corrosion. All the beams tested under simultaneous fatigue loading and corrosion were first immersed in 5% NaCl solution for three days for the absorption of free chlorides in the solution to prepare for the corrosion of the reinforcements. Before the test, static loads ranging from 0 to 10 kN were pre-applied to ensure good bearing contact and to verify that the data from all measuring channels were correct. When the pump and DC power supply were turned on, the predetermined fatigue
Fig. 3. Picture of corrosion fatigue testing.
load with sinusoidal variation was applied as shown in Fig. 3. As the number of fatigue loading cycles reached pre-defined values, e.g. 10000, 50000, 100000, 20000, 30000, and 400000, the fatigue loading and corrosion process was paused and the beam was monotonically loaded to the corresponding maximum fatigue load under step loading. The deflections were measured by three linear variable displacement transducers (LVDTs) placed at mid-span and the two loading points of the beam. If fatigue failure had not occurred after fatigue loading to two million cycles, a monotonic load was applied until static failure. 2.5. Measurement of reinforcement corrosion Upon completion of the fatigue loading test, two tensile reinforcing bars in the constant-moment section (corrosion section) were removed from the beam and cleaned with an acid solution, rinsed with clean water and dried by a dryer according to JTJ27098 Testing code of concrete for port and waterwog engineering [41]. The residual masses of the reinforcements were measured to determine the mass loss. The mass loss of the reinforcements was calculated by Equation (1):
Table 2 Mechanical properties of reinforcing bars. Reinforcement diameter (mm)
Yield strength (MPa)
Tensile ultimate strength (MPa)
Elongation (%)
Elastic modulus (MPa)
6.5 8 12
274.4 286.6 384.2
356.3 386.4 563.3
25 20 22
1.89 105 2.08 105 1.95 105
88
Mass loss ¼
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m mc 100% m
ð1Þ
where m and mc were the mass of reinforcements before and after corrosion, respectively. 3. Experimental results and discussion 3.1. Crack patterns Fig. 4 shows the typical crack patterns of beams. For the beams of Group A, a transverse crack occurred at a load of approximately 15 kN and more primary and secondary cracks formed with increasing load. After the reinforcement yielded, the length and width of the cracks showed a sharp growth followed by the failure of the beam. In beam B-1, the number of transverse cracks remained stable after the first cycle, and the length of cracks was smaller compared to that of the Group A and C beams. With respect to the beams under simultaneous fatigue loading and corrosion, two types of cracks, including corrosion-induced cracks on the side or bottom surface parallel to longitudinal reinforcing bars and transverse flexural cracks, were observed, as can be seen in Fig. 5. The corrosion-induced cracks initiated after a number of fatigue loading cycles and propagated in further cycles. As the two types of cracks crossed, portions of the concrete cover were vulnerable to spall.
Fig. 5. Crack patterns of beams subjected to corrosion fatigue, (a) side and (b) bottom surface.
ing and corrosion as shown in Fig. 6, the beams collapsed instantaneously, marked by the rupture of the tensile reinforcement after a significant increase in the deflection, and the failure was brittle without warning. The rupture of the reinforcement occurred in the location of a relatively wide crack close to the mid-span of the beam because of greater reinforcement stresses at the crack section. In addition, it should be noted that one reinforcing bar ruptured in the beams at a loading frequency of 4.5 Hz while both tensile reinforcing bars ruptured in the 1.5 Hz series test beams at fatigue failure. This was attributed to the lower fatigue loading frequency which contributed to stress redistribution between the two reinforcing bars, which had the same stress level prior to failure. Images of the ruptured section of the corroded reinforcing bars were taken under an electron microscope, and are shown in Fig. 7. It was observed that there was significant corrosion on the reinforcement surface as well as great cross-sectional loss in the rupture section. The rupture was induced by the combined effects of fatigue loading and corrosion, whose shape was irregular, and unlike the relatively flat section of corroded RC beams after fatigue loading [27] or the necking section of reinforcement under static loading with good ductility.
3.2. Failure modes Beams A-1 and A-2 collapsed at an average load of 63 kN in a typical flexural ductile failure mode, in which reinforcing bars in the tensile zone yielded followed by concrete crushing in the compressive zone. Two million fatigue loading cycles failed to destroy beam B-1, and in the subsequent monotonic static loading tests, the beam exhibited a ductile failure mode with an ultimate loading capacity of 60.9 KN, which was 96.7% that of the uncorroded beam. Therefore, fatigue loading had no significant effect on the static performance of RC beams without corrosion. With respect to the failure modes of the beams subjected to simultaneous fatigue load-
(a)
(b)
(c) Fig. 4. The typical crack patterns of (a) Group A, (b) Group B and (c) Group C specimens.
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where 4r and N are stress amplitude of reinforcement and the number of cyclic loading cycles, respectively, and A and B are undetermined constants. The nominal reinforcement stress was calculated using the conversion cross-section method in which the area of reinforcement was transformed into the area of concrete [43]. The nominal fatigue reinforcement stress was then calculated by
rs ¼ aE Icr ¼
Mðh0 xÞ Icr
ð3Þ
1 3 2 bx þ aE As ðh0 xÞ 3
ð4Þ
0sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 2bh0 1A x¼ 1þ b aE As
aE As @
Fig. 6. Failure modes of (a) 4.5 Hz and (b) 1.5 Hz series beams.
3.3. Fatigue life The fatigue life of the beams of Groups B and C are presented in Table 3. Beam B-1, which was subjected to cyclic loading without corrosion, had a fatigue life of greater than two million cycles, which was significantly greater than that of the beams under simultaneous fatigue loading and corrosion. This indicated that corrosion significantly reduced the fatigue life of RC beams. As can be seen in Table 3, the fatigue life significantly decreased with increasing of fatigue load amplitude. The fatigue life of beam C-4.5-50-1.5 with a fatigue load amplitude of 0.4 Pu was 1.142 million cycles, however, it decreased to 0.184 million cycles with a fatigue load amplitude of 0.65 Pu, a decrease of 83.9%. In fatigue life studies, S-N (fatigue stress amplitude versus fatigue life) curves plotted on a double-logarithmic scale would be approximately linear [42], and the following equation was obtained:
lg Dr ¼ A þ B lg N
ð2Þ
ð5Þ
where M is the applied flexural moment, aE is the ratio of the Young’s modulus of steel to that of concrete, Icr is the moment of inertial for a cracked RC beam section, h0 is the effective cross section height, x is the height of compressive zone and As is the area of the tensile reinforcing bars. The fatigue stress amplitude is obtained by
Dr ¼ aE
ðM max M min Þðh0 xÞ Icr
ð6Þ
where Mmax and Mmin are corresponding maximum and minimum flexural moment, respectively. The results of the fatigue stress amplitudes are presented in Table 3. The S-N curves of the beams with different levels of stress amplitude of reinforcement (i.e. beams C-4.5-50-1.5, C-4.5-551.5, C-4.5-65-1.5 and C-4.5-75-1.5) are shown in Fig. 8. It could be seen that there was a good linear correlation between the stress and the number of fatigue loading cycles, which indicated that the S-N curves could be used for fatigue life predictions of RC beams under same corrosive environments. It was important to mention that the validity of this type of empirical correlation is restricted
Fig. 7. Rupture section of reinforcements.
Table 3 Mass loss, fatigue life, stress amplitude and average corrosion rate of the RC beams. Specimens
4r (MPa)
Fatigue life (ten thousand)
Mass loss (%)
Average corrosion rate (%/cycle)
B-1 C-4.5-50-1.5 C-4.5-55-1.5 C-4.5-65-1.5 C-4.5-75-1.5 C-4.5-55-0.5 C-4.5-55-1.0 C-4.5-55-2.5 C-1.5-55-0.5 C-1.5-55-1.0 C-1.5-55-1.5 C-1.5-55-2.5
200 178 200 244 289 200 200 200 200 200 200 200
More than 200 114.2 74.5 35.6 18.4 100.3 101.6 69.2 129.7 122.5 72.5 56.9
0 8.46 7.91 5.44 8.03 4.03 7.35 10.07 8.62 14.54 13.82 18.55
0 0.074 0.106 0.153 0.436 0.040 0.072 0.146 0.066 0.119 0.191 0.326
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corrosion speed which reduced fatigue life. In addition, the decrease in fatigue life with the current ranging from 1.0 to 1.5 A was significantly greater than that with the current varying from 0.5 to 1.0 A and 1.5–2.5A. To better understand this phenomenon, we assumed that, with the current varying from 0.5 to 1.0 A, the corrosion rate increased and reduced the sectional area of the reinforcement and the fatigue life of the beam. As the current increased from 1.0 A to 1.5 A, the local corrosion and pitting corrosion increased, which significantly decreased the fatigue life of the beam. When a current of 2.5 A was applied, the decrease in fatigue life was not evident because of a limited decrease in the sectional area of the reinforcement, because of inadequate moisture and oxygen for faster corrosion rates and heavier local and pitting corrosion. Further, studies and analyses concerning local and pitting corrosion would be required. With respect to the comparison of fatigue life between the 4.5 Hz and 1.5 Hz series beams with the same fatigue loads and level of current, it was observed in Fig. 9 that the life of RC beams with a fatigue loading frequency of 4.5 Hz was shorter than that of beams with a fatigue loading frequency of 1.5 Hz at the current levels of 0.5 A and 1.0 A, while this phenomenon was reversed as current levels of 1.5 A and 2.5 A were applied. In addition, at a smaller fatigue loading frequency, i.e. 4.5 Hz, the change in the fatigue life of RC beams with current was less pronounced. It was concluded that as the smaller fatigue loading frequency was applied, the effect of corrosion on fatigue life was more significant because of longer corrosion periods per cycle.
Fig. 8. S-N curve of the beams.
3.4. Corrosion of reinforcements
Fig. 9. The relationship between fatigue life and current.
to similar material properties and environments, and in order to obtain a general relationship, additional studies were required. Fig. 9 shows the relationship between fatigue life and impressed current. Greater current levels led to shorter fatigue life for both the 4.5 Hz and 1.5 Hz series beams, and the fatigue life of beam C-4.5-55-0.5 was marginally smaller than that of beam C-4.5-55-1.0 because of natural scatter in fatigue phenomena. The reason for this was that the greater current level, which represented a significant corrosive environment, resulted in a greater
Fig. 10 shows the typical corrosion of beams under simultaneous fatigue loading and corrosion. It could be seen that the reinforcement surface was covered with a layer of rust, and uneven corrosion was induced, causing different sectional area losses. Previous studies [33] suggested that local corrosion occurred under natural environment while general corrosion occurred in accelerated corrosion. In this study, both local and general corrosion occurred simultaneously under the effects of fatigue loading and corrosion, indicating that the corrosion pattern was changed by the fatigue loading. The corrosion level of reinforcements was quantitatively assessed in terms of mass loss, as presented in Table 3. It was observed that there was no negative correlation between fatigue life and mass loss which was typically observed in accelerated corrosion tests followed by fatigue loading. The reason for this was that mass loss is time-dependent rather than constant in this study, and the final mass loss was the sum of reinforcement corrosion. The mass loss depended on the level of current density, corrosion duration and corrosion efficiency according to Faraday’s law. In addition, the corrosion duration was the ratio of fatigue loading cycles to frequency and the fatigue life was influenced by fatigue loads and current density as discussed in Section 3.3. In this study, the mass loss was a dependent variable rather than an inde-
Fig. 10. Surface morphology of reinforcement.
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pendent variable. The mass loss varied during the test and could not be determined until the collapse of the beam, which was different from the situation when fatigue loading was applied to already corroded RC beams. Therefore, the mass loss was not suitable for determining the corrosion speed or predicting the fatigue life. As the reinforcement corrosion increased continuously during the test, the average corrosion rate, defined as the mass loss of reinforcement per cycle, was proposed to evaluate the corrosion speed. The results of the average corrosion rate are presented in Table 3. The average corrosion rate increased with increasing maximum fatigue load. It was concluded that this was because the greater the maximum fatigue load, the greater the reinforcement stress level. As a result, wider cracks were induced to provide a better channel for oxygen and moisture, further corroding the steel. It was shown that greater current levels resulted in greater average corrosion rates regardless of the different loading frequencies because the greater current contributed to faster steel corrosion. It was also found that the average corrosion rate of the 1.5 Hz series beams was greater than that of the 4.5 Hz series beams with the same level of current. This was attributed to that longer corrosion periods being applied to the beams per unit time with lower loading frequency (i.e. 1.5 Hz), resulting in a greater mass loss. This appeared to be in conflict with the conclusion that the effect of loading frequency on fatigue life is not evident, as presented in Section 3.3. The reason for this was that the average corrosion rate was not directly proportional to the reduction of sectional area of the reinforcement because of local and pitting corrosion, which significantly affected the fatigue life. Therefore, because of the significant scatter of local and pitting corrosion, the relationship between loading frequency and fatigue life considering the section area loss would have to be investigated in future studies. Besides the effects of fatigue loading and corresponding flexural cracks on corrosion rates, corrosion-induced cracks could accelerate the corrosion process. The cracking process of concrete comprised four stages [44,45]: corrosion initiation, the formation of cracks, crack propagation, and crack coalescence and concrete delamination. When accelerated corrosion through impressed current was applied, the formation of cracks was controlled by a concrete attenuation factor. The attenuation factor, defined as the ability of concrete to absorb expansive stress caused by the corrosion products, was a function of a number of parameters, which included capillary absorption, temperature, and concrete quality which included the water/cement ratio. In this study, because of the high corrosion current compared to that in practice, the generation of oxides was so rapid that the concrete had no opportunity to absorb the expansion stresses, thus decreasing the attenuation factor and causing a sudden cracking. Additionally, the loading frequency of 1.5 Hz prolonged the time of closure and openness of flexural cracks in each cycle, and large amounts of corrosion products were generated to reduce the attenuation factor. Consequently, greater cracks were induced to accelerate the reinforcement corrosion.
Fig. 11. Load-deflection curve of beam C-4.5-55-1.0.
the number of fatigue loading cycles increased, the load-deflection curve exhibited an approximate linear propagation. In addition, the residual deflection gradually increased, as indicated by the interval between the intercepts on the horizontal axis. Fig. 12 shows the evolution of the residual and total deflections of beam C-4.5-55-1.0 at the unloading state and under the maximum fatigue load with the loading cycles. Both the residual and total deflections exhibited three stages: rapid rise, slow growth and sharp increase. However, the rates of increase were not equal, suggesting that the stiffness of the beam varied as the number of fatigue loading cycles increased. Flexural stiffness was regarded as the one of the critical evaluation indices for RC beams. In this study, stiffness was assessed by calculating the secant stiffness by dividing the maximum fatigue load applied by the elastic deflection, namely the difference between the total and residual deflection. Considering the inherent differentiation of each beam, the obtained stiffness values were normalized, by dividing them by their initial stiffness at the first loading. Fig. 13 shows the evolution of normalized stiffness of RC beams with loading cycles. In specimens under combined fatigue loading and corrosion, an increase in normalized stiffness was observed
3.5. Mid-span deflections and stiffness The deflections of RC beams were periodically measured under monotonic static loading after fatigue loading to a certain number of cycles. As the deflection response to loads for all the beams under simultaneous fatigue loading and corrosion were similar, beam C-4.5-55-1.0 was taken as an example and the loaddeflection curve with increasing fatigue loading cycles is shown in Fig. 11. It was observed that the gradient of the curve decreased instantaneously at a load of about 13 kN in the first loading, which indicated a decrease in flexural stiffness because of the occurrence of initial transverse cracks, and the slope then remained stable. As
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Fig. 12. The residual and total deflections of beam C-4.5-55-1.0.
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during the early cycles followed by the second stage where the normalized stiffness tended to relatively stabilize. Finally, the normalized stiffness exhibited a rapid decrease. This was because the corrosion level increased with increasing loading cycles in this study. Marginal corrosion levels could enhance the bonding between concrete and reinforcements while greater levels of corrosion caused the cracking and debonding of concrete which decreased stiffness [46]. With respect to beam B-1 without corrosion, the normalized stiffness exhibited a rapid decrease in early cycles followed by a gradual drop with increasing loading cycles. As can be shown in Fig. 13(a), the normalized stiffness of beams C-4.5-65-1.5 and C-4.5-75-1.5 did not exhibit the second-stage variation due to limited measurements in their shorter fatigue lives. It was found that the normalized stiffness increased with decreasing maximum fatigue loads. This was primarily ascribed to the greater load resulting in greater reinforcement stress, wider cracks and more rapid fatigue degradation of concrete. Therefore, a smaller effective sectional moment of inertia and the overall smaller elastic modulus of the beam contributed to a lower fatigue flexural stiffness. As can be seen in Fig. 13(b) and (c), at increased levels of impressed current, the normalized stiffness exhibited a greater growth rate in the first stage and faster degradation during the last stage. This was because higher currents produced greater average corrosion rates as discussed in Section 3.4. Therefore, greater stiffness increases were induced in early cycles. However, greater concrete strains and more significant bond damage occurred after the expansive stresses of corrosion products increased to cause concrete cracking. It was also found that there were distinct variations in flexural stiffness increases between the 4.5 Hz and 1.5 Hz series beams with a maximum fatigue load of 55% Pu as shown in Fig. 13(b) and (c), respectively. The maximum normalized stiffness of the 4.5 Hz series beams was smaller than 1.2, while that of 1.5 Hz series beams was greater than 1.35. This phenomenon was noteworthy and it could be inferred that the failure of beams under simultaneous fatigue loading and corrosion was the competitive results between fatigue damage and corrosion deterioration. When the maximum fatigue load was greater (including 0.65 Pu and 0.75 Pu), the behaviour of the beam were more fatigue performance-dependent, including a shorter fatigue life and three-stage feature of stiffness evolution not being observed. When the smaller fatigue loading frequency (i.e. 1.5 Hz) and relatively higher corrosion currents (including all currents used in this study) were included, the beams typically exhibited greater mass and sectional area losses as well as a greater increase in stiffness. As the fatigue loading and accelerated corrosion were time-consuming, the performance of the beams was affected by the selection of influencing parameters, including fatigue load, corrosion current, and fatigue loading frequency. Therefore, smaller loading frequencies and levels of current should be involved in further studies on RC structures under simultaneous fatigue loading and corrosion. 4. Conclusions This paper presented an experimental study on the behavior of RC beams under combined fatigue loading and corrosion, and the following conclusions could be drawn. These conclusions apply for the materials and circumstances of this research. Therefore, they can be extrapolated with the respective precautions.
Fig. 13. The evolution of normalized stiffness of RC beams, (a) different levels of maximum fatigue load, and different current with (b) 4.5 Hz and (c) 1.5 Hz.
1. Corrosion have a significant effect on the fatigue performance of RC beams in terms of crack patterns, ductility, fatigue life and stiffness evolution.
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2. Greater levels of maximum fatigue load and current typically results in a shorter fatigue life. The S-N curve remains valid in a corrosive environment. At a smaller fatigue loading frequency (1.5 Hz), the effect of current on fatigue life is more significant compared to the higher frequency (4.5 Hz). 3. General and local corrosion occurs simultaneously in RC beams under simultaneous fatigue loading and corrosion. Average corrosion rates increases with increasing maximum fatigue load and current, and lower loading frequency. 4. Normalized flexural stiffness of RC beams under coupledcorrosion fatigue exhibits three stages: gradual increase, stabilization and rapid degradation. The stiffness decreases with increasing maximum fatigue load, and greater current results in higher growth rates in the first stage and faster degradation in the final stage. Additionally, the enhancing effect on the stiffness of the 1.5 Hz series RC beams is greater than for the 4.5 Hz series beams. Conflict of interest None. Acknowledgements The research work is funded by National Natural Science Foundation of China (No. 51578428) and Special Project on Technical Innovation of Hubei (No. 2016AAA025), the authors deeply appreciate their financial supports. References [1] C. Fang, K. Lundgren, L. Chen, et al., Corrosion influence on bond in reinforced concrete, Cem. Concr. Res. 34 (11) (2004) 2159–2167. [2] A. Duan, J.G. Dai, W.L. Jin, Probabilistic approach for durability design of concrete structures in marine environments, J. Mater. Civ. Eng. 27 (2) (2011) A4014007. [3] H.L. Wang, J.G. Dai, X.Y. Sun, et al., Characteristics of concrete cracks and their influence on chloride penetration, Constr. Build. Mater. 107 (2016) 216–225. [4] E. Bastidas-Arteaga, P. Bressolette, A. Chateauneuf, et al., Probabilistic lifetime assessment of RC structures under coupled corrosion–fatigue deterioration processes, Struct. Saf. 31 (1) (2009) 84–96. [5] A.K. Azad, S. Ahmad, S.A. Azher, Residual strength of corrosion-damaged reinforced concrete beams, ACI Mater. J. 104 (1) (2007) 40–47. [6] X. Zhang, L. Wang, J. Zhang, et al., Model for flexural strength calculation of corroded RC beams considering bond-slip behavior, J. Eng. Mech. 142 (7) (2016) 04016038. [7] W. Xiaohui, L. Xila, Predicting the flexural capacity of RC beam with partially unbonded steel reinforcement, Comput. Concr. 6 (3) (2009) 235–252. [8] P.S. Mangat, M.S. Elgarf, Flexural strength of concrete beams with corroding reinforcement, ACI Struct. J. 96 (1) (1999) 149–158. [9] X.H. Wang, B. Li, X.H. Gao, et al., Shear behaviour of RC beams with corrosion damaged partial length, Mater. Struct. 45 (3) (2012) 351–379. [10] L. Wang, X. Zhang, J. Zhang, et al., Effects of stirrup and inclined bar corrosion on shear behavior of RC beams, Constr. Build. Mater. 98 (2015) 537–546. [11] D. Zhang, Y. Zhao, W. Jin, et al., Shear strengthening of corroded reinforced concrete columns using pet fiber based composties, Eng. Struct. 153 (2017) 757–765. [12] M. Dekoster, F. Buyle-Bodin, O. Maurel, et al., Modelling of the flexural behaviour of RC beams subjected to localised and uniform corrosion, Eng. Struct. 25 (10) (2003) 1333–1341. [13] J. Zhong, P. Gardoni, D. Rosowsky, Stiffness degradation and time to cracking of cover concrete in reinforced concrete structures subject to corrosion, J. Eng. Mech. 136 (2) (2010) 209–219. [14] C.Q. Li, R.E. Melchers, Analytical model for corrosion-induced crack width in reinforced concrete structures, ACI Mater. J. 103 (4) (2006) 479–487. [15] S.F.U. Ahmed, M. Maalej, H. Mihashi, Cover cracking of reinforced concrete beams due to corrosion of steel, ACI Mater. J. 104 (2) (2007) 153–161.
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