An Experimental Approach to Evaluate the Effect of Reinforcement Corrosion on Flexural Performance of RC Beams

Abstract

The corrosion of reinforcing steel in concrete has been reported as one of the main durability problems of reinforced concrete (RC) structures exposed to chloride, carbonation or both. To investigate the structural performances of RC structures subjected to corrosive exposure, the corrosion of rebars embedded in concrete is accelerated to induce a targeted degree of reinforcement corrosion in a short time duration. Several earlier researchers have attempted to develop a setup to induce the accelerated corrosion of steel bars in concrete structures. However, the induced corrosion has not been simulative of the naturally occurring corrosion of steel in concrete, causing a lack of accuracy in the test results. In this study, an attempt was made to develop a novel approach that could be utilized to induce required degrees of reinforcement corrosion following a natural pattern. To demonstrate the efficacy of the proposed setup and procedure of introducing uniform reinforcement corrosion, RC beam specimens were designed, cast, and corroded to three different corrosion levels. After inducing reinforcement corrosion, the beams were tested under flexural stress, and then the corroded bars were extracted to measure the mass loss due to corrosion. The visual inspection and gravimetric and flexural test results showed the capability of the proposed corrosion setup and procedure to induce the targeted uniform corrosion of steel bars, simulating a real-life scenario and facilitating the evaluation of the effect of reinforcement corrosion on the flexural performances of RC beams with very high accuracy.

1. Introduction

The corrosion of reinforcing steel embedded in concrete is one of the most significant factors influencing the long-term performances of reinforced concrete (RC) structures. When corrosion is initiated, steel bars dissolve into the surrounding area as the passive film is degraded locally. The depassivated regions expand due to an increase in the volume of the corrosion products. When the corrosion products become solid, they have a larger volume than the original volume of the metal, which results in high pressure around the embedded steel bars. As a result, the concrete cover expands, potentially causing cracking, spalling, and delamination of the concrete structure [1,2,3,4,5]. In addition, the corrosion process has multiple interconnected effects, including reduction in the cross-sectional area of the steel bars due to the formation of corrosion products and the degradation of steel-concrete bond. The severity of reinforcement corrosion impacts the performances of RC structures, including adverse effects on flexural strength, ductility, bond behavior, and failure mode. These phenomena compromise the structural integrity of RC structures and may cause them to fail prematurely [6,7,8,9]. Due to the importance of this issue, an enormous amount of research has been carried out to investigate the effects of reinforcement corrosion on the behavior of RC structures.

Reinforcement corrosion is a gradual process in natural conditions that depend on several factors, such as moisture, humidity, oxygen, aggressive conditions, concrete quality, and fiber reinforcement content [10,11]. Under normal exposure conditions, the first corrosion crack on a concrete surface can take several years to be observed, making it difficult to investigate the adverse impact of reinforcement corrosion on the structural performances of RC structures in a short duration of time. Thus, the corrosion process needs to be accelerated to induce a significant degree of reinforcement corrosion in a short time duration [12,13,14]. Several factors affect the process of accelerated reinforcement corrosion, including (i) the degree of the targeted corrosion level; (ii) the duration of the application of impressed current; (iii) aggressive exposure (chloride, wetting–drying cycles, etc.) during accelerated corrosion; (iv) the resistivity of the concrete; and (v) the equipment used to induce corrosion. The impressed current accelerated technique (ICAT) is employed to accelerate reinforcement corrosion in RC structures to complete research experiments in an acceptable time period [15,16,17]. The impressed current method has been widely utilized to investigate the impact of accelerated corrosion on concrete cover cracking, the bond between steel bars and concrete, and the residual load-bearing capacity of RC structural elements [17,18,19,20,21,22,23,24,25,26,27,28]. The ICAT consists of applying a direct current from a DC power supply to a steel bar embedded in a concrete sample, making it an anode and causing a considerable degree of corrosion damage. A counter electrode (cathode; external steel bar, or a steel plate) is connected to the negative terminal of the DC power supply. The impressed current causes corrosion of the reinforcing steel bars, while the counter electrode (cathode) is protected. A sodium chloride solution (NaCl) acts as an electrolyte connecting the anode and cathode. The ICAT provides several advantages in addition to saving money and time. The ability to control the corrosion rate, which usually varies due to changes in resistivity, oxygen content, and temperature, is one advantage over other accelerated corrosion approaches [29].

Accelerated reinforcement corrosion using the ICAT was proved as a suitable method for studying the corrosion process of steel in concrete and its impact on concrete cover damage [17]. There is strong scientific justification for utilizing the impressed current approach to accelerate corrosion in RC structures. It decreases the time of steel depassivation from several years to a few days. It ensures the desired corrosion rate without compromising the reality of the generated corrosion products [30]. The effect of concrete coatings, cladding, sealants, and coatings on reinforcing steel against reinforcement corrosion can be investigated in a relatively short period of time due to the flexibility of the impressed current method [31].

Previous researchers have used current densities typically varying in the range from 100 to 2000 µA/cm² [32,33,34,35,36,37], which is substantially higher than corrosion rates measured in the field for normal environmental conditions [38,39]. In severe environmental conditions, Andrade et al. [40] measured a maximum reinforcement corrosion rate between 100 and 200 µA/cm². Almusallam et al. [18] reported a maximum corrosion current density of 10,400 µA/cm², while minimum corrosion current density was reported by Pedrosa and Andrade [41] to be 5 µA/cm². Maaddawy and Soudki [15] experimentally evaluated the impact of impressed current density on the effect of concrete strain produced by corrosion products. They reported that raising the current density to more than 200 µA/cm² significantly increased the strain response and cover crack width. In addition, they reported that varying the applied current density to achieve different degrees of induced corrosion over the same time period could have unintended consequences that might lead to misinterpretation of the test results [15].

As mentioned earlier, counter electrodes and electrolytes (mostly NaCl solution) are used as parts of the accelerated reinforcement corrosion process, and these two components play important roles in the process of the induction of reinforcement corrosion. Various researchers have used counter electrodes and electrolytes in different ways. Azad et al. [42] developed an accelerated corrosion setup to corrode reinforcing steel bars in large-sized specimens. A stainless-steel plate was used as a counter electrode and a 5% NaCl solution was used as an electrolyte. The same approach was adopted by Al-Saidy et al. [43] to induce the corrosion of reinforcing steel bars, but they replaced the stainless-steel plate with several stainless-steel bars. Xie and Hu [44] coated the bottom surfaces of beam specimens with a copper mesh and then connected the copper mesh to the negative terminal of a DC power source to act as a cathode, while steel bars were connected to the positive terminal of the DC power supply. On the other hand, the counter electrodes and the electrolyte substance can also be placed inside specimens during the concrete casting of the beams. Elghazy et al. [45] cast and corroded several beam specimens using the ICAT by placing stainless-steel tubes inside specimens and adding salted concrete (to act as an electrolyte) over the portion of the specimens to be corroded. Another alternative setup was developed by Yuan et al. [46], where the same concept of placing a stainless-steel bar inside a beam during casting was used without adding salt to the concrete. The beams were placed in a tank containing NaCl solution to act as the electrolyte during the corrosion process. Several specimens were connected in a series to a DC power source to be corroded simultaneously. The number of specimens connected in a series to the DC power source depended mainly on the voltage capacity of the equipment. The researchers combined several sequential specimens in series to induce reinforcement corrosion to the same degree [43,45,47,48,49].

There are other alternative strategies reported in the literature for speeding up steel corrosion in RC structures. The chloride-induced corrosion technique is considered one of the most prevalent degradation mechanisms in RC structures exposed to marine environmental conditions or deicing salt weathering [50,51]. Ha et al. [52] employed a macro-cell corrosion approach with an impressed voltage technique. Husain et al. [53] employed an accelerated AC impedance method to detect the breakdown of passivity and evaluate the effectiveness of steel reinforcement in concrete in a considerably short time. Geng et al. [54] investigated the performance of corrosion inhibitors rapidly by electrically accelerating the diffusion of chloride ions over the surfaces of embedded steel bars in concrete to induce corrosion. Another method for accelerating reinforcement corrosion was developed by Yang et al. [55]. It was based on the electrochemical approach of accelerating chloride ion migration in cement-based materials to evaluate their permeability using an accelerated chloride migration test.

The literature review as presented above indicates that accelerated reinforcement corrosion can be induced in large-sized RC specimens by applying impressed currents of very high intensity [42,46,56], which might cause the non-uniform loss of steel due to corrosion over the surfaces of reinforcing bars. However, the loss of load-carrying capacity for any reinforced concrete structure is calculated based on the assumption of uniform losses in the cross-sectional area and in bonding [57,58,59]. The prediction of the residual load-bearing capacity of corroded structural samples cannot be estimated accurately unless the corrosion of a steel bar is induced uniformly over the entire length of a reinforcing bar. Considering this fact, there is a need for a novel setup and procedure to induce reinforcement corrosion simulating the real-life uniform corrosion of steel bars embedded in concrete. In addition, the method of submerging large-sized beam specimens in big tanks containing chloride solution, which leads to the dissolving of oxidation products [42,60,61,62], can be avoided by using an automated system of cyclic wetting for the whole duration of the corrosion process. In the present work, a novel accelerated corrosion setup and procedure are developed and used to accelerate the corrosion of steel reinforcement bars in concrete beams. RC beam specimens are cast, and reinforcing steel bars are corroded to three levels to represent moderate, severe, and very severe corrosion damage. The corroded beams are tested under flexural stress, and the structural behavior of the tested beams is investigated and compared to an uncorroded beam specimen. Then, the corroded bars are extracted and used to conduct a visual inspection and a gravimetric test to examine the efficiency of the proposed setup to induce uniform reinforcement corrosion to targeted degrees.

2. Experimental Investigation

In this section, firstly, the details of the developed corrosion setup are presented. In order to demonstrate the capability of the developed setup to induce the uniform corrosion of steel in RC beam specimens, an experimental investigation was carried out that included the following: the preparation of RC beams, induction of the corrosion of steel in the RC beams to three different targeted degrees, visual inspection of the corroded RC beams, flexural testing of the corroded RC beams compared with a control RC beam, and a gravimetric test on the corroded reinforcing bars extracted from the beam specimens after completion of the flexural testing.

2.1. Development of Setup for Accelerating Corrosion of Steel Bars in RC Beams

The developed setup for accelerating corrosion consisted of a DC power supplier capable of maintaining sufficient voltage to corrode the steel bars inside the beam specimens so that a targeted impressed current density could be maintained constantly (by adjusting the voltage) for the intended time duration. The positive terminal of the power supply was connected to the steel bars of the specimen (acting as an anode), while the negative terminal was connected to a stainless-steel plate (acting as a cathode). A relatively higher voltage from the DC power supplier was required in the beginning due to higher resistance in the circuit because of the higher resistivity of the concrete and uncorroded bars. At later stages, the voltage requirement to maintain the same intendent constant current density became lowered due to decrease in the resistivity of the concrete due to wetting and decrease in the resistivity of steel bars due to corrosion.

RC beam specimens should be placed upside down so that the main steel bars that needed to be corroded would be closer to the top surface of the beam where the stainless-steel sheet acting as the cathode was placed to apply the impressed current. To enhance the electrical connectivity between the steel bars (anode) and stainless-steel sheet (cathode), wet towels were placed between the stainless-steel sheet and the concrete surface. During the accelerated reinforcement corrosion process, the towels remained wet to allow the OH⁻ ions to pass from the cathode to the anode. Holes were made in the stainless-steel sheet, and nozzles were placed along the sheet to spray 5% NaCl every 3 h to keep the towel wet during corrosion induction without dissolving the oxidation products. Weights should be placed over the stainless-steel sheet to avoid its lifting and ensure electrical connectivity throughout the entire period of the induction of reinforcement corrosion. A schematic drawing showing the proper orientation of the RC beam specimens during corrosion induction, the towel, the stainless-steel sheet with holes, the weights, and the salt solution sprayers used in the proposed accelerated reinforcement corrosion setup is shown in Figure 1.

In order to avoid non-uniform corrosion of the reinforcing bars, an impressed DC current density of 200 µA/cm² was optimally selected for application to the RC beam specimens constantly over the entire duration of the accelerated reinforcement corrosion process. This current density was chosen to represent the intensity of the reinforcement corrosion current in real RC structures. In addition, this current density level was highly recommended by El Maaddawy and Soudki [15] to avoid expected bond loss, which can occur at the steel–concrete interface due to current. A schematic diagram showing the RC beam specimens connected to the proposed setup is shown in Figure 2.

Faraday’s law (Equation (1)) can be used to calculate the time required to achieve a targeted degree of reinforcement corrosion (i.e., targeted mass loss due to corrosion) under the influence of a selected impressed current density:

$$m=\frac{I · t · a}{n · F}$$

(1)

where m is the corrosion mass loss in grams; $n$ is the number of electrons transferred during the corrosion process, which is equal to 2 for steel bars; F is Faraday’s constant = 96,500 C/mol; $I$ is the impressed corrosion current in amperes; t is the duration of the corrosion process in seconds; and $a$ is the atomic mass of iron, which is equal to 55.847 g for steel bars.

The proposed procedure to ensure proper and uniform electrical connectivity between the cathode and anode by keeping a wet towel between them during the entire period of accelerated corrosion without dissolving the oxidation products, as well as the selection of a lower value of impressed current density (close to real-life reinforcement corrosion) so that the accelerated corrosion of steel bars in the RC beam specimens could be naturally simulated, constituted novel efforts made in the present work.

2.2. Details of RC Beam Specimens: Preparation and Casting

Four RC beam specimens were prepared and cast to introduce corrosion of the reinforcing steel. The total length of the beam specimens was 1.6 m, having a rectangular cross-section with a width of 140 mm and a depth of 230 mm. All beams were reinforced with 2 Φ 12 mm deformed bars at the bottom and 2 Φ 10 mm deformed bars at the top of the beam to support the stirrups. Stirrup bars with a diameter of 8 mm were placed along the length of the beam at a spacing of 50 mm. Epoxy-coated bars were used to eliminate the effect of induced current on the top reinforcement bars and the stirrups. The dimensions and reinforcement details of the RC beam specimens are shown in Figure 3. One RC beam specimen without the inducement of reinforcement corrosion was used as a control and named with the notation (U). The other three RC beam specimens were divided into three groups of A, B, and C and were corroded to three targeted corrosion levels of 10, 20, and 30%, respectively.

Before casting the beams, copper wires with a thickness of 2.5 mm were fixed on the ends of the main bars from both sides. The wires were tied firmly to the bars using pliers to reduce any chance of movement or disconnection during the induction of accelerated reinforcement corrosion. The wires were then covered with epoxy to prevent galvanic corrosion, which can occur when two dissimilar metals are connected, such as copper and steel.

A normal concrete mixture made of ASTM C150 [63] Type-1 cement, natural dune sand, crushed limestone, sweet water (at a water/cement ratio of 0.4 by mass), and high-range water reducer (ASTM C494 Type A&F) [64] was used for casting all the RC beam specimens. A mechanical vibrator was used during casting for consolidation of the concrete. The RC beam specimens were cured using steam for 6 h continuously. After that, the specimens were air-cured for 28 days before initiating the accelerated corrosion process.

2.3. Induction of Corrosion of Steel Bars in RC Beam Specimens Using Developed Setup

Three targeted levels of corrosion mass loss were considered, namely, 10% (RC beam specimen A), 20% (RC beam specimen B), and 30% (RC beam specimen C). The RC beam specimens were placed in a tank to induce reinforcement corrosion using the proposed setup and procedure, as shown in Figure 4.

An optimally selected constant current density of 200 µA/cm² was applied through the electrical circuit for 48, 96, and 144 days for the three RC beams of A, B, and C, respectively. The duration of the accelerated corrosion for each of the three beams was calculated using Equation (1) by substituting their targeted degrees of reinforcement corrosion and the density of the impressed current density (i.e., 200 µA/cm²).

2.4. Flexural Testing of the Corroded RC Beam Specimens

In order to examine the effect of the degree of reinforcement corrosion on the flexural strength of the RC beams, they were subjected to flexural testing after being corroded to different targeted degrees. The beams were loaded until failure using a four-point bending configuration, ensuring the failure of the beam specimens under pure bending, as shown in Figure 5. The distance between the two supports of the tested beam specimens was 1400 mm. The beams were loaded maintaining mid-span deflection at a rate of 0.5 mm/min. Two linear variable differential transducers (LVDTs) were placed on the bottom surface of the beam at mid-span to measure the mid-span deflection. The LVDTs and load cell were connected to a 40-channel data-logging system that captured the load versus mid-span deflection data every two seconds.

2.5. Gravimetric Analysis of the Corroded Reinforcing Bars

After conducting flexural testing on the corroded beam specimens, they were broken to extract the corroded reinforcing bars for gravimetric analysis. The corroded bars were extracted carefully to avoid any damage or loss of the steel bars. A jackhammer was used first to remove the concrete cover. Then, an iron hammer was used to gently remove the surrounding concrete from the extracted bars, as shown in Figure 6. As planned during the design and casting of the beam specimens, while the top two bars and shear stirrups were not affected by the induced current during the corrosion process due to epoxy coating, the main two tensile bars were duly corroded, as shown in Figure 7.

After extracting the corroded bars from the broken RC beam specimens, each corroded bar was cut into four equal pieces of 385 mm in length. The gravimetric test was performed on the corroded bars in accordance with ASTM G1 [65] to determine the actual mass loss due to reinforcement corrosion. The solution required to clean the bars was prepared according to ASTM G1 [65]. To prepare the solution, 20 g of antimony trioxide (Sb₂O₃) and 50 g of stannous chloride (SnCl₂) were added to 1000 mL of hydrochloric acid (HCL) with a specific gravity of 1.19. The solution was stirred until the entire amount of salt was dissolved. The weight of the corroded bars was recorded first. Then, the bars were submerged in the solution for 20 min at a temperature of 23 ± 0.5 °C. After that, the bars were taken out carefully from the solution and brushed gently using a stiff, steel brush and cold water. The bars were dried to remove water from the surface of the bars, and then the residual weight was recorded. The bars were then submerged again in the solution for another 20 min, and this procedure was repeated until the residual weight of the bars became almost constant. Figure 8 illustrates an example showing the change in mass of RC beam specimen B.

The mass loss of the corroded bars was calculated using the following equation (Equation (2)):

$$\% mass loss=\frac{W_i-W_f}{W_i}\times 100\%$$

(2)

where $W_i$ is the weight of the bars before corrosion, and $W_f$ is the weight of the bars after removing all the rust.

3. Results and Discussion

3.1. Visual Inspection

After completion of the induction of accelerated reinforcement corrosion in the RC beam specimens, the specimens were visually inspected to record the presence of rust products and cracking on the surfaces of the beams due to reinforcement corrosion. As evident from Figure 9, rust stains and longitudinal cracks were observed on the concrete surfaces of the beams. The corrosion cracks were continuous on the lateral surfaces and soffits of the beams parallel to the corroded steel bars, as shown in Figure 9. The cracks and rust stains occurred through the entire length of the beams, indicating uniform corrosion of the bars. In contrast, no cracks were detected in the compression sides and around the stirrups due to the usage of epoxy-coated bars. The cracks became wider for RC beam specimens corroded to a higher degree due to a relatively higher increase in the volume of the corrosion products. The cracks were measured on all sides of the beams before flexural testing. The maximum and average cracks were 1.2 mm and 0.8 mm wide for beam A, 2.1 mm and 1.2 mm for beam B, and 2.9 mm and 1.5 mm wide for beam C, respectively. The measured crack widths of the corroded beams exceeded the maximum allowable limits required by ACI 318-14 [66] criteria, which limit the maximum crack width to 0.40 mm.

3.2. Gravimetric Test Results

The actual average mass losses of beams A, B, and C were measured to be 9.8, 17.4, and 20.8% against the targeted mass losses of 10, 20, and 30%, respectively. The plots of the gravimetric test results shown in Figure 10 indicated a discrepancy between the actual and theoretical targeted mass losses in the corroded steel bars for the RC beams corroded to cause targeted mass losses of 20 and 30%. There was a negligible discrepancy for the 10% targeted mass loss; however, the discrepancy for the 20% targeted mass loss was significant, followed by a very high discrepancy for the 30% targeted mass loss. This discrepancy between the actual and targeted corrosion mass losses could be attributed to several reasons, such as changes in the demand for electrical energy to commence corrosion, bar composition, concrete resistivity, and the electrical characteristics of minerals in the concrete with increase in the duration of the application of the impressed current [28]. Liu and Weyers [67] reported a decrease in the rust production rate as the corrosion process progressed as the reason behind increase in the discrepancy between the actual and targeted mass losses at higher degrees of reinforcement corrosion. In addition, it is recommended in future research work to test more than one beam specimen for each degree of reinforcement corrosion to eliminate the possibility of human and equipment errors.

A close visual observation of the corroded bars, as shown in Figure 11, indicated the presence of very few corrosion pits, which were randomly dispersed over the surface area of the bars for beams A and B (with targeted mass losses of 10 and 20%, respectively). However, more pitting corrosion was observed at some locations of the corroded bars for beam C (with a targeted mass loss of 30%).

From the above discussion on the results of gravimetric testing, it is recommended that the targeted mass loss due to accelerated corrosion should not exceed 20% to avoid the occurrence of pitting corrosion and discrepancies between the targeted and actual mass losses.

3.3. Flexural Behavior of Corroded RC Beams

The control beam specimen (U) and the corroded RC beam specimens (A, B, and C) were failed in a flexural mode similar to the typical failure modes of under-reinforced concrete beams. Several flexural cracks were formed in the middle zones, where the bending moments reached the maximum values, as shown in Figure 12. The tensile reinforcing bars yielded first, followed by concrete crushing at the tops of the beam specimens. Flexural cracks were initiated at loads of 19.5, 17.4, 16.4, and 16.1 kN for beams U, A, B, and C, respectively, indicating a significant decrease in the cracking loads of the corroded beams due to partial damage of the concrete at the tension zone compared to the uncorroded control beam (U). It should also be noted that the developed crack patterns in the corroded and uncorroded RC beams were almost the same, indicating that the ductile mode of failure of the corroded beams did not change significantly due to the reinforcement corrosion of the tensile steel bars.

Plots of the results of flexural testing (i.e., load versus mid-span deflection curves) conducted on the control RC beam (U) and corroded RC beams (A, B, and C) are shown in Figure 13. It can be observed that the yielding and ultimate loads for corroded beams became significantly lowered compared to the control beam. The load–deflection curves of the control and corroded RC beams obtained in this study were compared with those of other studies reported by Azad et al. [42] and Azher [68], as shown in Figure 14a,b. The results of Azher [68] showed a large discrepancy between the flexural behaviors of corroded beams compared to an uncorroded beam, as shown in Figure 14b, which could be attributed to the pitting and non-uniform corrosion induced in their study. On the contrary, in the present study, similar flexural behaviors of both the corroded and uncorroded beams can be seen in Figure 14a, confirming that the proposed setup induced uniform accelerated corrosion of the bars in the beams.

Table 1. Summary of the flexural testing results.

Beam ID	Actual Mass Loss	Average Crack Width	At Cracking		At Steel Yielding		At Ultimate Load
	%	${\mathit{C}}_{\mathit{a}\mathit{v}\mathit{g}} \left(\mathbf{m}\mathbf{m}\right)$	${\mathit{P}}_{\mathit{c}\mathit{r}} \left(\mathbf{k}\mathbf{N}\right)$	${\mathit{\delta }}_{\mathit{c}\mathit{r}} \left(\mathbf{m}\mathbf{m}\right)$	${\mathit{P}}_{\mathit{y}} \left(\mathbf{k}\mathbf{N}\right)$	${\mathit{\delta }}_{\mathit{y}} \left(\mathbf{m}\mathbf{m}\right)$	${\mathit{P}}_{\mathit{u}\mathit{l}\mathit{t}} \left(\mathbf{k}\mathbf{N}\right)$	${\mathit{\delta }}_{\mathit{u}\mathit{l}\mathit{t}} \left(\mathbf{m}\mathbf{m}\right)$
U	0	0	19.5	0.83	75.1	5.5	85.5	14
A	9.8	0.8	17.4	0.72	59.3	4.7	70.7	14.3
B	17.4	1.2	16.4	0.61	48.2	4.1	65.4	14.9
C	20.8	1.5	16.1	0.56	46.5	3.8	62.8	15

summarizes the flexural test results of the beams. Plots of the data presented in Table 1 are shown in Figure 15. It can be observed from the plots shown in Figure 15 that the adverse effects of reinforcement corrosion on the yielding and ultimate load were sharp for beam A with the targeted mass loss of 10%. However, for an increase in the degree of reinforcement corrosion from 10 to 20%, the decreases in the yielding and ultimate loads were lower than those for an increase in the degree of reinforcement corrosion from 0 to 10%. It is worth noting that the reductions in the yielding and ultimate loads were insignificant for an increase in the degree of reinforcement corrosion from 20 to 30%.

The reason behind the insignificant effect of the increase in the degree of reinforcement corrosion from 20 to 30% could be attributed to (i) a very small increase in the actual mass loss and (ii) an insignificant loss in bonding due to reinforcement corrosion when the targeted mass loss increased from 20 to 30%. At 10% mass loss, both the decrease in the cross-sectional areas of the corroded bars and the loss of bonding between the bars and the surrounding concrete affected the yielding and ultimate load. Since the bond was already completely destroyed at 10% mass loss, the reduction in the load-carrying capacities of the corroded beams was only controlled by the loss in the cross-sections of the bars due to corrosion targeted for mass losses beyond 10%. Since the difference in the actual mass losses of beams B and C (17.4% for B and 20.8% for C) was very small, for the reason mentioned earlier, these corroded beams had a very small difference in their load-carrying capacities.

3.4. Ductility of Corroded RC Beams

The ductility of the tested corroded RC beams was determined using the ductility index (µ), which was calculated as the deflection at the maximum load (${\Delta }_u$) divided by the deflection at the yielding load (${\Delta }_y$) [69,70,71,72,73]. In addition, the energy absorption index (Ω) could be estimated by calculating the area under the load–deflection curve up to the maximum point [45,74]. The results of the ductility and energy absorption indices are listed in

Table 2. Results for ductility.

Beam ID	Values of Deflection (mm) at		µ	Nor. µ	Ω (kN.mm)	Nor. Ω
	$\mathbf{Yield} \left({\Delta }_{\mathit{y}}\right)$	$\mathbf{Maximum} \left({\Delta }_{\mathit{u}}\right)$
U	5.5	14	2.55	1.00	938.4	1.00
A	4.7	14.3	3.04	1.20	852.1	0.91
B	4.1	14.9	3.63	1.43	788.4	0.84
C	3.8	15	3.95	1.55	766.5	0.82

.

It was observed that the corroded beams had higher ductility indices than the control RC beam (U). The ductility index showed a significant increase with the increase in the mass loss of the corroded RC beams. Corroded beams A, B, and C showed ductility indices of 3.04, 3.63, and 3.95, representing 120, 143, and 155%, respectively, of that of the control RC beam (U). In contrast, the results showed that the energy absorption index decreased with the increase in the mass loss of the corroded RC beams. This proves that increasing the corrosion degree of the reinforcing bars had a significant effect on lowering the flexural strength and the energy absorption of the beam specimens. Corroded beams A, B, and C showed energy absorption indices of 91, 84, and 82% of that of the control RC beam (U), respectively. The results of the ductility and energy absorption indices of the corroded RC beams are consistent with the findings of Elghazy et al. [45].

4. Analytical Modeling

An analytical mechanistic model was developed to predict the ultimate load-carrying capacities of the corroded RC beam specimens using fundamental knowledge of the structural mechanics and properties of the materials used to cast the RC beams. A model proposed by Du et al. [75] was used to estimate the reduction in the cross-sectional areas and yield stress values of the corroded reinforcing bars, which were used for the analysis of the corroded beams. The material test results used in the analytical modeling of the corroded beams were obtained for steel reinforcement bars and normal concrete as follows: (i) normal concrete was modeled using Whitney’s compressive stress distribution block in accordance with ACI 318 Section 10.2.7, (ii) the steel reinforcement bars were modeled using a bilinear stress–strain curve, and (iii) the upper reinforcing bars were neglected in the analytical calculations.

Figure 16 shows the strain and stress distribution diagrams used for the analytical modeling of the RC beam specimens. The compressive force ($C_c$) and the tensile force ($T_s$) were calculated using Equations (3) and (4):

$$C_c=0.85 f_c^{\prime } {\beta }_c x b_c$$

(3)

$$T_s=A_{st} f_{yc}$$

(4)

where $f_c^{\prime }$ is the compressive strength of the concrete, and ${\beta }_c$ is the reduction factor for the depth of the concrete equivalent to the rectangular stress block.

$${\beta }_c=0.85-0.05 \frac{f_c^{\prime }-28}{7} f_c^{\prime }>28 \mathrm{MPa}$$

(5)

where $x$ is the location of the neutral axis, $d$ is the effective depth of the RC beam,$h_c$ is the original depth of the RC beam,$b_c$ is the original width of the RC beam, $A_{st}$ is the cross-sectional area of the corroded reinforcing bars, and $f_{yc}$ is the yield stress of the corroded reinforcing bars.

Ignoring the loss in bonding between the steel reinforcing bars and the surrounding concrete, the decrease in the ultimate strength of the damaged RC beams due to reinforcement corrosion can be related to reduction in the cross-sectional areas of steel bars [20,60]. It was also reported by Lin and Zhao [76] that the effect of bonding loss could be greatly decreased due to the use of extensive numbers of epoxy-coated, noncorroded stirrups and low impressed current density similar to that used in the current study. Degradation in the cross-sectional area and yield stress of corroded steel bars due to reinforcement corrosion was reported by Du et al. [75]. Reductions in the cross-sectional area and yield strength of corroded bars can be estimated based on the actual mass loss in reinforcing bars using Equations (6) and (7), as proposed by Du et al. [75]:

$$A_{st}=\left(1-0.01 X_p\right) A_s$$

(6)

$$f_{yc}=\left(1-0.005 X_p\right) f_y$$

(7)

where $A_{st}$ is the estimated cross-sectional area of the corroded bars, $f_{yc}$ is the estimated yield stress of the corroded bars, $A_s$ is the cross-sectional area of the original reinforcing bars, $f_y$ is the yield stress of the original reinforcing bars, and $X_p$ is the actual mass loss of the corroded bars.

The tensile force of the corroded steel bars can be calculated using Equation (8):

$$T_s=\left(1-0.01 X_p\right) \left(1-0.005 X_p\right) A_s f_y$$

(8)

Following the force equilibrium equation, the summation of the compression and tensile forces in the cross-section area equals zero. Therefore, the value of x can be calculated using Equation (9):

$$x=\frac{A_{st} f_{yc}}{0.85 f_c^{\prime } {\beta }_c b_c}$$

(9)

The predicted bending moment capacity can be calculated by taking the moment of the compression and tensile forces around the neutral axis, as expressed in Equation (10). The difference between the experimental and analytical values is expressed using Equation (11):

$$M_{predicted}=A_{st} f_{yc} \left(d-x\right)+0.85 f_c^{\prime } {\beta }_c x b_c\left(x-\frac{a_c}{2}\right)$$

(10)

$$Difference (\%)=\frac{P_{analytical}-P_{experimental}}{P_{experimental}}\times 100\%$$

(11)

Table 3. Experimental and analytical values of load-carrying capacities of control and corroded RC beams (using actual mass loss).

Beam ID	${\mathit{P}}_{\mathit{e}\mathit{x}\mathit{p}\mathit{e}\mathit{r}\mathit{i}\mathit{m}\mathit{e}\mathit{n}\mathit{t}\mathit{a}\mathit{l}}$ $\left(\mathbf{k}\mathbf{N}\right)$	${\mathit{P}}_{\mathit{a}\mathit{n}\mathit{a}\mathit{l}\mathit{y}\mathit{t}\mathit{i}\mathit{c}\mathit{a}\mathit{l}}$ $\left(\mathbf{k}\mathbf{N}\right)$	Difference (%)
U	85.5	84.81	−0.80
A	70.7	73.40	3.82
B	65.4	64.95	−0.69
C	62.8	61.29	−2.41

shows the values of the load-carrying capacities of the control and corroded RC beams measured experimentally and predicted using the analytical model. The results of the analytical model showed good matching with the corresponding experimental results, with a minor percentage of error. The maximum difference between the experimental and analytical results was less than 4%. Figure 17 illustrates a strong fit between the experimental and analytical values of the ultimate load-carrying capacities of the tested beam specimens, as indicated by a high R² value of 0.97.

The agreement of the experimental and analytical results of the load-carrying capacities of the RC beam specimens also confirms that the corrosion induced by the developed setup was uniform, simulating a real-life scenario of reinforcement corrosion in RC structures. The excellent agreement between the experimental and analytical results of load carrying capacity using the proposed model was due to the use of the actual mass loss of the corroded steel bars in the analytical calculations. However, if the values of the targeted mass loss (i.e., 10, 20, and 30%) were used in the predicted model instead of the actual mass loss values, the difference between the experimental and analytical results would increase to reach a maximum value of 16.9% in the case of 30% mass loss, as shown in

Table 4. Experimental and analytical values of load-carrying capacities of control and corroded RC beams (using targeted mass loss).

Beam ID	${\mathit{P}}_{\mathit{e}\mathit{x}\mathit{p}\mathit{e}\mathit{r}\mathit{i}\mathit{m}\mathit{e}\mathit{n}\mathit{t}\mathit{a}\mathit{l}}$ $\left(\mathbf{k}\mathbf{N}\right)$	${\mathit{P}}_{\mathit{a}\mathit{n}\mathit{a}\mathit{l}\mathit{y}\mathit{t}\mathit{i}\mathit{c}\mathit{a}\mathit{l}}$ $\left(\mathbf{k}\mathbf{N}\right)$	Difference (%)
U	85.5	84.81	−0.80
A	70.7	73.19	3.52
B	65.4	62.27	−4.79
C	62.8	52.20	−16.9

. Figure 18 shows a higher difference between the experimental and analytical results of the ultimate load-carrying capacities of the tested RC beam specimens using the targeted mass loss values, as indicated by the low R² value of 0.89.

5. Conclusions

In the present paper, novel setup and procedure methods developed to induce the accelerated uniform corrosion of rebars in RC beam specimens were described. Based on the results of the experimental investigation conducted to demonstrate the efficacy of the setup to induce accelerated uniform reinforcement corrosion in RC beam specimens and to simulate a real-life scenario, the following conclusions were drawn:

(1)

The rust stains and cracking observed on the surfaces of RC beam specimens corroded using the developed setup indicated the capability of the setup to induce uniform accelerated corrosion throughout the entire length of the reinforcing bars. This was achievable by adopting the idea of choosing a suitably lower impressed current density of 200 µA/cm² and enhancing the electrical connectivity between the stainless-steel sheet (cathode) and the rebars (anode) using an automated system for spraying NaCl solution frequently as an integral part of the setup. The combination of these two measures helped reduce the chances of pitting corrosion and, therefore, made the proposed setup a novel one.

(2)

The actual mass loss was almost same as the targeted mass loss at 10%, and the difference was marginal at 20%. However, the actual mass loss was much lower at the targeted mass loss of 30%. Furthermore, pitting corrosion was not significant up to a 20% targeted mass loss. Therefore, to avoid non-uniform corrosion (pitting corrosion) and discrepancy between the targeted and actual mass losses, it is strongly recommended that the targeted mass loss through accelerated corrosion should not exceed 20%.

(3)

The experimental and analytical results pertaining to the load-carrying capacities of the RC beams corroded using the proposed setup indicated the utility of the setup in evaluating the effect of reinforcement corrosion on the flexural performances of RC beams with a fair degree of accuracy.