Study on Axial Compression Performance of Corroded Reinforced Concrete Columns Strengthened by Concrete Canvas and Carbon Fiber Reinforced Plastic under Secondary Corrosion

Abstract

To investigate the effects of concrete canvas (CC) and carbon fiber reinforced plastic (CFRP) reinforcement on the mechanical properties of corroded reinforced concrete columns (compressive strength, flexure strength, strength of extension, and so on), 42 columns in four groups were designed and axial compression experiments were carried out. For the corroded reinforced concrete columns reinforced with CC and CFRP, the effects of initial corrosion rate (5%, 10%), secondary corrosion time (15 d, 30 d), number of CC layers (0, 1), and number of CFRP layers (1, 2, 3) on the failure morphology, load carrying capacity, and ductility of concrete columns were analyzed. The test results show that the properties of the single layer CC confined specimens are improved to a certain extent, and the ductility properties are enhanced. The properties of the CC–CFRP composite constrained specimens are greatly improved, the plastic deformation ability is enhanced, and the typical ductile damage characteristics are shown. The corrosion inhibition of CC for specimens with a theoretical corrosion rate lower than 20% showed an increasing trend, and the corrosion inhibition rate ranged from 23.0% to 31.2%. CC and CFRP restrain the concrete jointly, hindering the expansion inside the concrete, and the peak strain of the joint restraint specimen itself changes greatly, while the overall peak strain of the corrosion specimen is very small under the action of the joint steel bar. Finally, according to the existing peak stress–strain model and the experimental data in this paper, a peak stress–strain model suitable for corroded reinforced concrete columns is established. The established calculation model has a high accuracy, which provides a certain theoretical basis for subsequent research.

1. Introduction

Reinforced concrete structures are one of the most common structural forms in the field of modern construction engineering and are widely used in bridges, buildings, and infrastructures. However, with the passage of time and the constant influence of environmental factors, reinforced concrete structures often suffer from corrosion and aging problems, which seriously affect the load-bearing capacity and service life of the structure. specially in environments that are humid, highly saline or affected by chemical corrosion, and reinforced concrete structures are more prone to corrosion. Therefore, how to effectively reinforce and repair corroded reinforced concrete structures has become an important problem to be solved. Traditional reinforcement methods include the use of steel plates, encapsulated reinforced concrete or grouting, etc. These methods often have some limitations, such as the increase in weight after reinforcement, construction difficulties, and damage to the original structure. Therefore, it is important to find more effective structural reinforcement methods to improve the load-bearing capacity and extend the service life of the structure.

To address the above issues, literature [1] and literature [2] proposed the use of carbon fiber fabric for winding reinforcement on the surface of concrete columns, and the results show that, for ordinary concrete columns, the presence of hoops under axial pressure will produce a good restraining effect on the concrete in the core region, which plays a key role in improving the load-bearing capacity of the members. Research on the type of hoop reinforcement for axial compression columns has gradually increased. Literature [3] proposed the use of high strength hoops. Literature [4] compared the restraining effect of carbon fiber hoop restraint with ordinary hoops. Literature [5] proposed basalt fiber hoop composite restraint, while literature [6] proposed a composite mesh hoop. Additionally, literature [7,8,9,10] conducted a lot of research starting from the form of hoops. It can be seen that the restraining performance of non-traditional hoops on concrete columns has received more and more attention in research. From the point of view of enhancing the restraining effect of hoops and solving the problem of easy carbonization and corrosion of steel reinforcement, carbon fiber cloth has the advantages of involving small pollution, being light weight and high strength, featuring good fatigue resistance, convenient construction, and corrosion resistance, which can replace or partially replace ordinary steel reinforcement to play its characteristics. Literature [11,12,13,14] conducted a large number of experimental studies on carbon fiber composites, including using carbon fiber composite tendons configured in beams to study the stress properties, and also winding carbon fiber cloth on the surface of columns to study the stress properties under eccentric loading. For short concrete columns subjected to axial compression loading, carbon fiber tape restraint was proposed to restrain the vertical reinforcement, i.e., by wrapping the vertical reinforcement with carbon fiber tape along the circumference, the tensile properties of the fibers can be fully utilized while simplifying the anchorage measures of the fibers.

Concrete canvas (CC) and carbon fiber composite (CFRP), as two kinds of reinforcing materials widely used in the field of structural reinforcement nowadays, have good mechanical and durability properties. CFRPs have the advantages of high strength, light weight and corrosion resistance, which play a good bearing capacity and seismic performance in the reinforcement of concrete structures. In the reinforcement process, the carbon fiber cloth is bonded to the concrete through the combination of the adhesive, and then through curing to achieve a common force. Therefore, by studying the axial compressive properties of CC and CFRP reinforced corroded reinforced concrete columns, it can provide an effective engineering practice guide for reinforcing and repairing the existing corroded reinforced concrete structures, as well as providing technical support and theoretical basis for the development and advancement of the field of structural reinforcement. Literature [15] investigated the composition, construction and performance aspects of concrete canvas (CC), optimized the proportion of cementitious materials within the CC, investigated the impact resistance, abrasion resistance, fire resistance and corrosion resistance of CC, and analyzed the structural characteristics of the tent using the finite element method. The results show that CC is characterized by high strength, corrosion resistance and durability, being easy to be mold, having a reasonable structure, and its mass-producability. Literature [16] investigated the tensile properties of CC and the compression characteristics of PVC-covered concrete canvas composite pipe restrained concrete, analyzing the mechanical properties. The results showed that the transverse tensile strength of CC was larger than the longitudinal tensile strength, while the tensile properties of CC were largely affected by the external fabric substrate. The composite tube restraining concrete could significantly improve the strength and toughness of concrete, and with the increase in the number of layers of carbon fiber fabric, the composite tube’s improvement of the strength of the concrete columns showed a decreasing trend. In conclusion, after the introduction of concrete canvas, the mechanical properties of concrete can be improved due to its good abrasion and corrosion resistance.

Zhong et al. [17] conducted uniaxial compression tests on high-temperature damaged concrete cylinders confined by CFRP, which showed that CFRP restraint improved the strength and ductility of concrete with different damage degrees. Through electrochemical accelerated corrosion and axial compression tests, Shan [18] showed that the peak bearing capacity and peak strain of the corroded reinforced concrete cylinders strengthened by CFRPs were improved to varying degrees, and the lower the peak bearing capacity of the constrained cylinder, the better the CFRP constraint effect. It is found that CFRP can improve the elastic modulus and peak bearing capacity of damaged concrete-filled steel tubes, and the increase in peak bearing capacity decreases with the increase in slenderness ratio.

Based on the respective reinforcement restraining performance characteristics of carbon fiber composite (CFRP) and concrete canvas (CC) materials, this study attempts to combine the two materials for reinforcement restraining of concrete and to explore the possibility of improving the performance of concrete members through this combined reinforcement restraining treatment. To this end, this paper explores the use of combined CC and CFRP reinforcement restraint to improve the load carrying capacity and ductility of concrete columns, as well as to improve the corrosion and corrosion resistance properties of concrete structures under attack from acidic and alkaline media and salt solutions, with a view to providing a reference for studies related to the reinforcement of corroded reinforced concrete columns.

2. Materials and Experiments

2.1. Materials

In this study, C40 strength grade concrete was selected by using P·O 42.5 grade ordinary silicate cement, the coarse aggregate was gravel (with a maximum particle size not exceeding 31.5 mm), fine aggregate was medium sand with a fineness modulus of 2.7, and the concrete mix ratio is shown in

Table 1. Concrete mix ratio.

Substrate Strength	Water-Cement Ratio	Water (kg/m3)	Gravel (kg/m3)	Sand (kg/m3)	Cement (kg/m3)
C40	0.48	185	1244	586	385

. CFRPs are produced by Carbon Engineering and Technology Research Institute Co. Ltd. (Jinan, China), the longitudinal reinforcement is a C10HRB400 grade steel bar, and the hoop reinforcement is a B6HPB300 grade steel bar. The selected carbon fiber impregnation adhesive is matched with carbon fiber cloth, and there are two kinds of adhesives, A and B. These two kinds of adhesives are mixed and stirred according to the ratio of A:B = 2:1 when used. The compressive strength test results of concrete at different ages are shown in

Table 2. Compressive strengths of concrete cubes at different curing ages.

Strength Grade	Age
	3 d	7 d	28 d
C40	34.08	36.20	42.60

, and the parameters of concrete canvas, carbon fiber reinforced plastic and carbon fiber impregnated adhesive are shown in

Table 3. Parameters of concrete canvas.

CC Type	Compressive Strength (MPa)	Flexural Strength (MPa)	Weight Capacity (kg/m3)
Concrete canvas	30.10	2.77	1250

,

Table 4. Parameters of CFRP.

Type	Tensile Strength (MPa)	Modulus of Elasticity (MPa)	Elongation at Break (%)	Calculated Thickness (mm)	Unit Mass (g/m2)	Bending Strength (MPa)	Interlaminar Shear Strength (MPa)
CFS-I-300	3520	2.68 × 105	1.77	0.167	296	813	51.9

and

Table 5. Parameters of carbon fiber impregnated adhesive.

Tensile Strength (MPa)	Modulus of Elasticity (MPa)	Elongation at Break (%)	Compressive Strength (MPa)	Bending Strength (MPa)	Non-Volatile Matter Content (%)
55.1	2.71 × 103	2.41	81.7	86.7	99.4

, respectively.

2.2. Specimen Preparation

In this paper, the axial compression tests of corroded reinforced concrete columns reinforced with a combination of CC and CFRP were carried out at different initial corrosion rates, secondary corrosion durations and numbers of CFRP wrapping layers. The specimens used in the tests were cylindrical, with dimensions of diameter D × height H = 150 mm × 300 mm, and the preparation process is shown in Figure 1. As an important strengthening material, the special performance and advantages of CC and CFRP in strengthening concrete structures should be fully analyzed and summarized by comparison with other types of materials. For example, CFRP has higher mechanical properties and better fatigue resistance, corrosion resistance, and creep resistance than other FRPs. The following research cases can be further reviewed to emphasize the performances and advantages. The specimens were subjected to accelerated electrochemical corrosion to simulate the corrosion damage of reinforced concrete in a western saline environment (sodium chloride brine), and the initial corrosion rates were controlled at 5% and 10%, respectively.

In the natural environment, the corrosion rate of the steel bar is slow, and the actual corrosion situation cannot be monitored. Therefore, this paper adopts the method of electrochemical corrosion to simulate the corrosion of the steel bar in the natural environment. This method is convenient to operate and easy to monitor. According to Faraday’s law, the chemical change in the electrodes in a battery is proportional to the amount of electricity passing through the electrodes. Therefore, when determining the surface current density, the mass corrosion rate of the steel bar can be controlled by controlling the energizing time. Faraday’s law is stated as follows:

$$\Delta m=\frac{MIt}{FZ}$$

(1)

where m is the mass loss of steel bar corrosion in g; M is the molar mass of iron and M = 56 g/mol; I is the strength of energized corrosion current A; t is the power-on time in s; Z is the chemical valence state of the reaction electrode, and the first reaction generates bivalent iron ion, so Z is +2; and F is the Faraday constant, equal to 96,500 C/mol, which is 26.801 Ah/mol.

The mass loss due to the corrosion of steel bars caused by electricity is shown in the following formula:

$$\Delta m=\frac{1}{4}\pi D^{2}L\gamma {\eta }_{\rho }$$

(2)

where D is the diameter of the steel bar in mm; L is the total length of the corroded steel bar in mm; ${\eta }_{\rho }$ is the steel density, equal to 7.86 × 10⁻³ g/mm³; and p is the mass corrosion rate of steel bar.

From the above, two formulas can be obtained:

$$t=\frac{\pi D^{2}L\gamma {\eta }_{\rho }ZF}{4MI}=\frac{0.0059D^{2}L\gamma {\eta }_{\rho }}{I}$$

(3)

The wrapping method is whole package, and the number of wrapping layers is divided into 3 layers. In order to reflect the anti-corrosion performance of CC more intuitively, a concrete column without CC wrapping was set up, and the specific parameters of the specimens are shown in

Table 6. Parameters of individual specimens.

Specimen Name	Initial Corrosion Rate (%)	Secondary Corrosion Time (d)	Number of CC Layers	Number of CFRP Layers	Concrete Strength
C00-0-0	0	0	0	0	C40
C515-0-0	5	15	0	0	C40
C515-1-0	5	15	1	0	C40
C515-1-1	5	15	1	1	C40
C515-1-2	5	15	1	2	C40
C530-1-3	5	30	1	3	C40
C530-0-0	5	30	0	0	C40
C530-1-0	5	30	1	0	C40
C530-1-1	5	30	1	1	C40
C530-1-2	5	30	1	2	C40
C530-1-3	5	30	1	3	C40
C1015-0-0	10	15	0	0	C40
C1015-1-0	10	15	1	0	C40
C1015-1-1	10	15	1	1	C40
C1015-1-2	10	15	1	2	C40
C1015-1-3	10	15	1	3	C40
C1030-0-0	10	30	0	0	C40
C1030-1-0	10	30	1	0	C40
C1030-1-1	10	30	1	1	C40
C1030-1-2	10	30	1	2	C40
C1030-1-3	10	30	1	3	C40

Note: The subscripts 0, 5, and 10 indicate different corrosion rates; the second number is the secondary corrosion time; and the third and fourth numbers are the numbers of layers of CC and CFRPs, respectively; e.g., specimen “C5-15-1-2” represents a corroded reinforced concrete column with an initial corrosion rate of 5%, a secondary corrosion time of 15 d, and a wrapping of one layer of CC and two layers of CFRPs.

.

2.3. Test Methodology

The tests were carried out in a 5000 kN hydraulic testing machine in the Structural Laboratory of the School of Civil Engineering, and the loading device is shown in Figure 2. The test load was measured and controlled by the transducer installed on the top of the specimen, and the loading process referred to GB/T50152-2012 [19]. In order to eliminate the influence of external factors on the loading process, the position of the specimen was adjusted to the center position before loading the specimen, and then the specimen was preloaded. All specimens were tested in axial compression, the specimens were first formally loaded by the loading control method at a loading rate of 25 kN/min, and then loaded by the displacement control method at a displacement growth rate of about 0.0025 mm/min after the peak load was reached, until the specimens were damaged.

2.4. AE Test

During the loading process, the AE signals were acquired and stored using a DISP series all-digital AE workstation manufactured by Physical Acoustics Inc. in the U.S. The threshold was set to 40 dB. Additionally, to avoid the influence of environmental noise, the threshold was set to 40 dB, the sampling frequency was set to 1 MHz, and the software set the preamplifier gain to 40 dB, which was consistent with the preamplifier. The coordinate position and schematic diagram of the AE probe are shown in Figure 3. AE tests were conducted on five sets of specimens, i.e., C5-15-0-0, C5-15-1-0, C5-15-1-1, C5-15-1-2 and C5-15-1-3. By analyzing the test results of the specimens and utilizing the AE theory, the effects of the number of CFRP wrapping layers and the number of CC layers on the concrete confinement were determined. The AE localization tests were performed using the localization diagrams used in the literature [20], as shown in

Table 7. List of sensor deployment.

Sensors Number	2	3	4	5	6	7
Coordinates	(−75, 30, 0)	(0, 30, −75)	(75, 270, 0)	(−75, 270, 0)	(0, 270, 75)	(75, 50, 0)

Note: The diameter of the specimen is 75 mm for single confined by CFRP and 95 mm for combined CC and CFRP confined.

.

3. Results and Discussion

3.1. Failure Patterns

The damage process of different specimens under axial compressive loading was recorded, and the failure modes of the specimens are shown in Figure 4. For the unconfined specimens, there was no obvious phenomenon in the specimens at the beginning of loading. With the increase in loading, the tiny cracks in the specimen began to expand and become wider rapidly, the concrete fragments on the side of the specimen were dislodged, and the specimen lost bearing capacity and underwent brittle damage. For the single-layer CC restrained specimens, it was observed that the fracture at the CC joints was concave, and the energy released when the CC fractured was vigorous, resulting in the shattering of some CCs. Adhered fragments were observed at the fractured CC joints, indicating that the CC was adhered well to the concrete and that the damage process of the specimen was slow, implying that it belonged to ductile damage. For the combined CC and CFRP restrained specimens, as the number of CFRP layers increased, the sound emitted when the CFRPs broke became more intense, the damage became more severe, and the plasticity of the specimen developed fuller. The reason for this is, that for core concrete, the more the number of CFRP layers, the more pronounced the constraint to the core concrete, the fuller the plastic development of the concrete, and the more severe the damage, with more layers of CFRPs.

3.2. Corrosion Resistance Analysis of CC

The mechanism of rebar corrosion in chloride salt environment is mainly due to the competitive adsorption of Cl^- destroying the passivation film on the surface of the rebar and forming a corrosion cell, which generates corrosion currents, causes pitting of the rebar, rapidly expanding and leading to further damage of the specimen [20]. Under normal circumstances, passivation film can stably protect steel bars from corrosion; however, when concrete undergoes a carbonation reaction, if there is a trace amount of carbonate solution in the concrete soil, it will cause corrosion reaction of the steel bars in the concrete. In practical engineering projects, due to the exposure of reinforced concrete structures to corrosive environments, trace amounts of carbonate solution in the concrete will gradually reduce the pH value inside the concrete as time goes on. When the passivation film comes into contact with the acidic medium inside the concrete, it indicates that the passivation film begins to break and the steel bars begin to rust. In this paper, the mass of the rebar was weighed and recorded before loading, and then the marked rebar was descaled and weighed again after loading was completed to derive the difference in mass before and after corrosion, so as to determine the change in corrosion rate [21,22,23,24,25].

The corrosion results are shown in

Table 8. Comparison of the theoretical and actual rust rates.

Specimen	Rebar Number	Original Weight (g)	Weight after Corrosion (g)	Theoretical Corrosion Rate	Actual Corrosion Rate	Average Value	Standard Deviation
C5-0-0-0	1	314	241	5%	7.48%	6.84%	0.0032
	2	311	233		8.40%		0.0078
	3	304	230		5.21%		0.00815
	4	306	223		6.27%		0.00285
C5-15-0-0	5	309	230	10%	11.5%	11.29%	0.001
	6	308	230		13.85%		0.01275
	7	309	221		9.26%		0.0102
	8	308	198		10.58%		0.0036
C5-15-1-0	9	313	226	10%	11.59%		0.01455
	10	312	214		8.69%	8.67%	5 × 10−5
	11	306	218		6.54%		0.0107
	12	305	221		7.88%		0.004
C5-30-0-0	13	306	232	15%	16.88%	17.11%	0.0012
	14	307	228		17.52%		0.002
	15	309	232		17.65%		0.00265
	16	310	228		16.42%		0.0035
C5-30-1-0	17	309	213	15%	11.66%	12.60%	0.0047
	18	306	208		12.84%		0.0012
	19	307	211		13.63%		0.00515
	20	310	219		12.28%		0.0016
C10-0-0-0	21	312	196	10%	11.88%	12.06%	0.0009
	22	316	230		12.85%		0.00395
	23	309	229		8.56%		0.0175
	24	311	217		14.95%		0.01445
C10-15-0-0	25	310	228	15%	17.52%	17.88%	0.00185
	26	309	215		17.72%		0.00085
	27	307	203		18.08%		0.00095
	28	311	210		18.23%		0.0017
C10-15-1-0	29	309	215	15%	12.62%	12.53%	0.00045
	30	308	225		11.34%		0.00595
	31	311	207		13.55%		0.0051
	32	308	207		12.62%		0.00045
C10-30-0-0	33	310	230	20%	22.56%	23.63%	0.00535
	34	306	212		23.67%		0.0002
	35	308	213		24.52%		0.00445
	36	308	230		23.77%		0.0007
C10-30-1-0	37	311	205	20%	18.69%	17.53%	0.00575
	38	309	216		15.65%		0.00945
	39	307	225		17.58%		0.0002
	40	306	196		18.23%		0.00345

, and it can be seen that the corrosion rate of the specimens increases with the increase in the initial corrosion rate. It is found that the difference between the actual corrosion rate and the theoretical corrosion rate increases gradually; this is because when the corrosion rate of the specimen is more than 10%, the corrosion rate of the reinforcement will be accelerated, resulting in the gap between the actual corrosion rate and the theoretical rate of the specimen increasing further with the increase in the corrosion rate. The corrosion inhibition ability of CC on a specimen with a theoretical corrosion rate lower than 20% shows an increasing trend, and its corrosion inhibition rate is 23.0~31.2%, which indicates that CC has a good corrosion inhibition ability [26]. However, for the specimens with a theoretical corrosion rate higher than 20%, the corrosion inhibition rate showed a decreasing trend, and the corrosion rate was 25.8% due to the corrosion of the specimens being too severe, meaning the corrosion inhibition ability of CC was not enough to resist the competitive adsorption of a large amount of Cl^-. In addition, the corrosion of reinforcing bars in the concrete specimens to be tested is shown in Figure 5.

In summary, it can be concluded that the corrosion inhibition ability of CC on concrete specimens with a theoretical corrosion rate within the range of 20% has been greatly enhanced, while the enhancement of the corrosion inhibition ability on specimens with a corrosion rate of more than 20% has been gradually weakened. Therefore, CC can have a good corrosion inhibition effect on specimens with a corrosion rate in the range of 20%, but the effect on specimens with a corrosion rate more than 20% is gradually weakened.

3.3. Analysis of AE Characteristic Parameters

Many researchers have studied the acoustic emission properties of concrete specimens subjected to uniaxial compressive loading, trying to use acoustic emission technology to analyze and explain the formation and propagation process of cracks in concrete specimens for the purpose of explaining the damage mechanism of the concrete specimens under study. However, the concrete specimen parameters (water–cement ratio, strength, age, constraint, etc.) as well as the test conditions, test procedures, test methods and analytical approaches used by the various scholars are different, and thus the results lack comparability [27,28,29,30].

In order to study the evolution of internal damage in concrete specimens tested under uniaxial compression, the mechanical and acoustic emission properties of concrete specimens were correlated and analyzed in this paper, and the test results are shown in Figure 6. According to the general concept of the acoustic emission analysis technique, combined with the damage process of the concrete specimen, the acoustic emission signal changes during the whole process of load loading can be divided into four stages. The initial stage refers to the process when the load device and the concrete specimen are just in contact and there exists a part of the acoustic emission signal output, which is mainly released due to the gradual closure of the microcracks produced by the concrete specimen itself in the process of load increase. At this time, the acoustic emission signal energy is relatively small, but there is still energy accumulation. The acoustic emission signal at this stage coincides with the initial compaction stage of the concrete specimen, which can be found in Figure 6. The energy accumulation rate curve during this process is usually an upward concave curve, i.e., the accumulation rate of the acoustic emission energy becomes smaller and smaller as the load increases, which corresponds to the process of crack reclosure in the concrete specimens. As the load further increases, the slope of the energy accumulation rate curve will gradually increase, which indicates that micro-cracks have appeared in the concrete specimens due to the applied load. As the specimen is subjected to compression for a longer time, the concrete specimen successively enters a relatively stable phase of acoustic emission. Continuing to increase the load, the specimens began to enter a stable linear deformation phase. As the load is increased, the specimen continues to expand and extend under the load and the energy is released, so the acoustic emission count accumulation curve increases steadily with the load. At this point, the energy accumulation curve is close to a straight line, and the starting point of the straight line segment is the so-called “critical point”, which indicates that the concrete specimen starts to show obvious cracks from this point in time, and it is also the critical point of concrete specimen damage under pressure.

Further observation shows that the energy accumulation curve in Figure 6a goes directly into a straight line phase, and the previous study shows that the compressive performance of the unreinforced specimen of this is poor. From Figure 6b, it can be seen that, when the concrete specimen is reinforced with one layer of CC, its compressive capacity is enhanced to withstand 25 pressure units and the compressive time is significantly increased to 120 time units.

In order to discuss the reinforcing effect of CFRPs on concrete specimens, it is necessary to comparatively analyze Figure 6c–e, which correspond to concrete specimens with the same CC reinforcing conditions, with the difference being the different numbers of CFRP reinforcing layers (corresponding to the number of CFRP reinforcing layers of one, two, and three in the three figures, respectively) [31,32,33]. It can be seen that the concrete specimens corresponding to Figure 6c entered the stage of increasing microcracking after 250 time units, whereas the concrete specimens corresponding to Figure 6d,e entered the stage of increasing microcracking after 400 time units. The corresponding concrete specimens appeared before structural damage after 500, 630 and 875 time units, respectively, indicating that the reinforcing effect of CFRPs plays a significant role in the stage between the increased microcracking and structural damage of the concrete specimens, effectively enhancing the concrete specimens to withstand the stresses for a longer period of time. In this stage, the rate of crack expansion in the specimens increased with the further increase in load. Compared to the previous stage, the acoustic emission signals in this stage were significantly enhanced in terms of activity, intensity, and signal density, while the intensity of the acoustic emission energy also increased dramatically, with a large number of high-amplitude signals appearing to form hollow clusters of high-amplitude signals. At the same time, it can be observed that several large cracks appeared on the outer surface of the specimen, indicating that the specimen had been damaged and ruptured, the load-bearing capacity decreased dramatically, the material entered into an unstable state, and structural damage had occurred. It indicates that the combination of CC and CFRPs was used and that the increase in CFRP layers can prolong the duration of this stage under the condition of a certain number of CC layers [34].

3.4. Bearing Capacity Analysis

Based on previous analyses and past literature, it is understood that the relationship between the number of cladding layers and the load carrying capacity is nonlinear. Therefore, in this section, an optimal amount of confinement is found by varying the number of cladding layers of carbon fiber composites (CFRPs) to maximize the load carrying capacity enhancement of the confined specimens, which is very important for the current experimental study of the load carrying capacity of concrete confined specimens. The bearing capacities of the restrained specimens are shown in

Table 9. Bearing capacities of the restrained specimens.

Specimen	Νμ (kN)	Improvement Rate of Bearing Capacity (%)
C5-15-0-0	602.26	-
C5-15-1-1	806.46	33.90%
C5-15-1-2	953.25	58.28%
C5-15-1-3	1010.12	67.72%
C5-30-0-0	535.27	-
C5-30-1-1	703.88	31.01%
C5-30-1-2	813.32	51.95%
C5-30-1-3	866.55	61.89%
C10-15-0-0	512.31	-
C10-15-1-1	693.11	35.29%
C10-15-1-2	790.25	54.25%
C10-15-1-3	873.21	70.45%
C10-30-0-0	430.05	-
C10-30-1-1	581.53	35.22%
C10-30-1-2	657.66	52.93%
C10-30-1-3	713.31	65.87%

, which shows that, for specimens with different initial corrosions and different secondary corrosion durations, the enhancement of the specimens with two layers of CFRP cladding is greater than that of the specimens with one layer of CFRPs, while the enhancement of the specimens with three layers of CFRP cladding is significantly lower than that of the specimens with two layers of CFRPs. This indicates that the enhancement of the load carrying capacity of the specimens gradually decreases after the number of CFRP layers exceeds two, and the specimens can achieve the maximum cost-effective performance at two CFRP layers. Compared to three-layer CFRPs, the number of layers of two-layer CFRPs has a significant effect on improving bearing capacity, and, at the same time, the construction process is simpler and relatively cheaper.

Comparison of the bearing capacities of individual specimens is shown in Figure 7. With the increases in the initial corrosion rate and corrosion time of the specimen, the bearing capacity of the unrestrained specimen sustains a significant and gradual decrease in the peak stress and a gradual increase in the peak strain. The reason for this is that the diameter of the specimen reinforcement becomes smaller after corrosion and expands after the concrete is pressurized, while the ability of the reinforcement to restrain the concrete core of the specimen is significantly reduced. At the same time, due to the corrosion of the reinforcement, cracks of irregular shapes and sizes were produced in the protective layer of the concrete, and then the concrete provided support for the extrusion of the reinforcement, which led to the failure of the specimen in reaching a large strain. The peak stress–strain relationships of the specimens that were jointly reinforced by CC and CFRPs were basically the same as that of the unconfined specimens, but the peak strains were smaller. The reason for this is that, when the specimen is in compression cracking, CC and CFRPs combine to restrain the concrete and impede the expansion within the concrete. Additionally, the peak strain of the jointly restrained specimen itself varies greatly, and the overall peak strain is very small in the corroded specimen under the action of the combined reinforcement.

One of the reasons for the improvement of the specimen bearing capacity is that concrete is a non-uniform material; the presence of CC can avoid direct contact between carbon fibers and concrete, reduce the uneven radial deformation generated by the specimen under pressure, and lead to the phenomenon of localized stress concentration of carbon fibers so that the carbon fibers can give full play to their role. Secondly, CC fiber mesh is filled with fast-hardening cement, which has a certain thickness and stiffness, and thus the carbon fibers are uniformly distributed by CC to restrain the stresses, then transferred to the specimen to ensure that the specimen will not lose its load-bearing capacity due to local damage. Thirdly, in compression, the fast-hardening cement in the CC needs to be crushed first due to the presence of peripheral CFRPs, but the CC itself has a certain circumferential tensile strength, and the restraining effect of the CC on the specimen works before a large range of carbon fibers approach the tearing strain. The presence of CC slows down the uneven deformation of the concrete in the core area, making the radial deformation of the joint constrained specimen more uniform when reacting to the outer layer of CFRPs. The existence of CC causes the outer layer of CFRPs to be changed to uniform, which can fully utilize the tensile deformation capacity of CFRPs and achieve a better reinforcement effect.

In summary, it can be concluded that the load bearing capacity of the specimen is proportional to the number of CFRP layers. As the number of CFRP layers increases, the bearing capacity of the specimen increases, and the proportion of the bearing capacity of the CFRP restrained specimen also increases. However, the bearing capacity of CFRP reinforced specimens decreases with the increase in the number of layers. This is due to the gradual decrease in the percentage of bearing capacity provided by the core concrete. The higher the bearing capacity, and the closer to the CFRP tearing strain, the smaller the increase and the strength of the specimen (this is because the bearing capacity provided by the core concrete gradually decreases). Meanwhile, the peak strain of the specimen increases with the increase in the number of CFRP layers, but the enhancement of specimens with different corrosion rates does not differ much. The main reason is that, during the loading process of the specimens, the concrete is squeezed and undergoes lateral expansion, at which time the CFRPs are subjected to the stresses caused by the compression of the concrete. After the internal CFRPs were torn, the external CFRPs continued to be subjected to the stress until most of the external CFRPs reached the tearing strain, the specimen lost its load-bearing capacity and failed, and thus the peak strain of the specimen was enhanced.

3.5. Stress–Strain Curves

The stress–strain curves of individual specimens at different corrosion rates are shown in Figure 8, and it can be seen that the stress–strain curves of the damaged concrete specimens restrained by CC and CFRPs together basically show three stages: the first stage belongs to the elastic stage and the curve rises smoothly; the second stage belongs to the elastic-plastic stage, which is a transitional stage with rising and falling parts; and the third stage belongs to the strengthening stage. With the increase in the amount of constraint, the slope of the rising part of the specimen gradually increases, and its transverse strain develops slowly. When the ultimate compressive strain of unconfined concrete is reached, the transverse strain of the specimen begins to develop rapidly, and the curve of the specimen shows a certain decline at this time. As CC and CFRPs start to play a role, the curve starts to rise again. The unconstrained specimen is a typical weakly constrained specimen, which is destroyed once the ultimate compressive strain is reached, and the curve decreases immediately after the rising part. The curve of the single-layer CC restrained specimen shows a weakly restrained state. After reaching the ultimate compressive strain, the curve of the specimen has a certain plateau area and shows certain signs of damage, the curve is close to a straight line parallel to the X-axis, and the specimen shows a weakly restrained state. For the combined CC and CFRP restrained specimens, the specimens show a strong restrained state, and the third stage of the curve shows a gradual increase in slope with the increase in the number of CFRP layers, while the strong restrained state is more obvious. This indicates that the restrained state of the specimen improves with the increase in the number of CFRP layers.

4. Peak Stress–Strain Modeling of Corroded Concrete Short Columns

4.1. Model Development

For the concrete reinforcement stress–strain relationship model, many researchers have proposed various expressions. Among them, the monoclinic model was the main one in the early stage, while some researchers used empirical formulas in the middle stage, and then parabolic descriptions of the incremental segment model were established in combination with the intrinsic model until the bilinear model. In this paper, only some of the more typical intrinsic models are listed. Literature [35] modeled the early peak stresses and peak strains of concrete without considering FRP constraints based on a reinforced restrained concrete model:

$$f_{cc}^{\prime }=f_{co}^{\prime }\left[1+4.1\left(\frac{f_l}{2f_{co}^{\prime }}\right)\right]$$

(4)

$${\epsilon }_{\mathrm{cc}}\approx 0.002+0.0005\frac{E_l}{f_{\mathrm{co}}^{\prime }}$$

(5)

where $f_{cc}^{\prime }$ is the strength of concrete partially restrained by the protective layer; $f_{co}^{\prime }$ is the strength of partially confined concrete in the core area; $f_l$ is the yield stress of the reinforcement; and ${\epsilon }_{\mathrm{cc}}$ is CC tear strain.

In the literature [36], based on the empirical equations, effective constraint coefficients were obtained by regression analysis of the test data, and thus the peak stresses and peak strains of constrained concrete were modeled as follows:

$$f_{cc}^{\prime }=2.1f_{co}^{\prime }\left(\frac{f_l^{0.87}}{f_{co}^{\prime }}\right)$$

(6)

$${\epsilon }_{\mathrm{cc}}^{\prime }={\epsilon }_{co}+0.01\left(\frac{f_l}{f_{co}^{\prime }}\right)$$

(7)

In the literature [37,38], by combining the experimental data and the intrinsic model of concrete with the parabolic incremental segments in the literature [39], the following models for the peak stress and peak strain of constrained concrete were proposed:

$$\frac{f_{cc}^{\prime }}{f_{co}^{\prime }}=1+3.845\left(\frac{f_l^{\prime }}{f_{co}^{\prime }}\right)$$

(8)

$$\frac{{\epsilon }_{cc}}{{\epsilon }_{co}}=1+10.6{\left(\frac{f_{cc}^{\prime }}{f_{co}^{\prime }}\right)}^{0.373}\left(f_{co}^{\prime }=30 \mathrm{MPa}\right)$$

(9)

$$\frac{{\epsilon }_{cc}}{{\epsilon }_{co}}=1+10.6{\left(\frac{f_{cc}^{\prime }}{f_{co}^{\prime }}\right)}^{0.525}\left(f_{co}^{\prime }=50 \mathrm{MPa}\right)$$

(10)

Literatures [40,41] promoted a new peak stress–strain model for FRP-constrained concrete based on previous research, which focuses on the effect of FRP strain on the axial strain of concrete. The linear expression of the modulus of elasticity of the unconfined concrete was used as the initial slope, and the second linear part was used as the linear segment, and the strength of the unconfined concrete was used as the intersection of the line segment and the stress axis. In this paper, the modeling analysis is carried out and the peak stress model and peak strain model of CFRP restrained concrete columns are obtained with the following equations:

$$\frac{f_{cc}^{\prime }}{f_{co}^{\prime }}=1+2\frac{f_1}{f_{co}^{\prime }}$$

(11)

$$\frac{{\epsilon }_{\mathit{cc}}}{{\epsilon }_{co}}=2+15\frac{f_l}{f_{co}^{\prime }}$$

(12)

In order to determine the peak stress and peak strain models for corroded reinforced concrete short columns reinforced with CC and CFRPs, the computational models from the existing literature were compared with the peak stresses and strains from the present tests. An error analysis was then carried out, and the results are presented in

Table 10. Calculated values and errors for peak stress models.

Specimen		C5-15-1-1	C5-15-1-2	C5-30-1-1	C5-30-1-2	C10-15-1-1	C10-15-1-2	C10-30-1-1	C10-30-1-2
Test results		45.66	53.97	39.85	46.04	39.24	44.74	34.67	39.63
Fardis et al. [42].	fp (MPa)	38.98	58.55	43.98	55.97	49.58	52.48	48.28	54.57
	Error (%)	14.63	7.80	10.36	21.57	26.35	17.30	39.25	37.69
Karbhari et al. [43].	fp (MPa)	57.08	41.28	52.36	40.53	33.52	60.29	39.85	46.28
	Error (%)	25.01	23.35	31.39	11.97	14.58	34.75	14.94	16.78
Miyauchi [44]	fp (MPa)	34.35	35.43	30.57	30.95	29.19	29.46	24.57	24.80
	Error (%)	24.77	34.35	23.29	32.77	25.61	34.15	29.13	37.42
Teng et al. [45].	fp (MPa)	39.55	47.86	34.19	50.16	33.28	37.54	27.53	33.56
	Error (%)	6.11	11.30	14.20	9.91	15.18	16.09	2.05	6.07

. The Teng model is established by summarizing a large number of previous experiments, and its model has been verified by a large amount of data and is more reliable. It can also be concluded from Table 10 that the values calculated by the Teng model are smaller, the overall safety factor is higher, and the average error rate is smaller, which is more in line with the actual situation.

4.2. Model Computational Analysis

The test data of the experiment are shown in

Table 11. Bearing capacity test results of individual specimens.

Specimen	fcc/MPa	εcu	fcc/fco	εcc/εco
C5-15-0-0	34.09	2895.55	-	-
C5-15-1-1	45.66	6856.23	1.34	2.37
C5-15-1-1-2	40.93	6635.21	1.43	2.29
C5-15-1-2	53.97	8472.36	1.58	2.92
C5-15-1-2-2	46.31	8569.36	1.59	2.96
C5-15-1-3	57.19	9110.09	1.68	3.14
C5-15-1-3-2	46.22	9305.11	1.72	3.21
C5-30-0-0	30.30	2635.41	-	-
C5-30-1-1	39.85	5862.82	1.31	2.22
C5-30-1-1-2	38.66	5639.35	1.27	2.14
C5-30-1-2	46.04	7158.38	1.52	2.72
C5-30-1-2-2	47.75	7295.37	1.57	2.77
C5-30-1-3	51.09	7826.37	1.69	2.97
C5-30-1-3-2	53.78	8031.62	1.77	3.05
C10-15-0-0	29.00	2112.36	-	-
C10-15-1-1	39.24	4351.23	1.35	2.06
C10-15-1-1-2	41.08	4628.86	1.42	2.19
C10-15-1-2	44.74	4924.53	1.54	2.33
C10-15-1-2-2	45.36	4850.57	1.56	2.29
C10-15-1-3	49.43	4815.69	1.70	2.28
C10-15-1-3-2	50.02	5052.31	1.72	2.39
C10-30-0-0	24.34	1686.39	-	-
C10-30-1-1	34.67	3675.27	1.42	2.18
C10-30-1-1-2	33.39	3423.36	1.37	2.03
C10-30-1-2	39.63	4015.36	1.63	2.38
C10-30-1-2-2	37.56	3856.23	1.54	2.29
C10-30-1-3	44.29	4594.67	1.82	2.72
C10-30-1-3-2	43.99	4298.69	1.81	2.55

. According to the test data in Table 11, the Teng model was fitted to the specimens with different initial corrosion rates, k₁ = 1.33 and R² = 0.98 for the specimens with an initial corrosion rate of 5%. For the specimens with an initial corrosion rate of 10%, k₁ = 1.15 and R² = 0.98, the peak stress fitting results are shown in Figure 9, and the error ranges are shown in Figure 10.

Up to this point, a model for calculating the peak stresses of the short columns of corroded reinforced concrete with a combination of CC and CFRP constraints was derived. The peak stress calculation models for initial corrosion rates of 5% and 10% are shown in Equations (13) and (14), respectively.

$$\frac{f_{cc,2}}{f_{co}}=1+2.25\frac{f_{lc}}{f_{co}}$$

(13)

$$\frac{f_{cc,2}}{f_{co}}=1+4.15\frac{f_{lc}}{f_{co}}$$

(14)

where $f_k$ is the yield stress of the reinforcement.

Based on the fitting results [46], the model for calculating the peak strain of the combined restrained corroded reinforced concrete columns was obtained with the model shown in Equations (15)–(17). The peak strain fitting results are shown in Figure 11, and the error ranges are shown in Figure 12.

$$\frac{{\epsilon }_{cc}}{{\epsilon }_{co}}=1+k_2\frac{f_{lc}}{f_{co}}$$

(15)

$$\frac{{\epsilon }_{cc}}{{\epsilon }_{co}}=1+7.02\frac{f_{lc}}{f_{co}}$$

(16)

$$\frac{{\epsilon }_{cc}}{{\epsilon }_{co}}=1+9.2\frac{f_{lc}}{f_{cc}}$$

(17)

where $k_2$ is the constraint validity coefficient.

Based on the original model of Lam and Teng [47], the stress–strain principal model for combined CC and CFRP restrained corroded reinforced concrete columns is developed as follows:

$${\sigma }_{cc}=\{\begin{array}{ccc}{E}_c{\epsilon }_c& 0\le {\epsilon }_c\le {\epsilon }_1& \\ A{\epsilon }_c^2+B{\epsilon }_c+C& {\epsilon }_1\le {\epsilon }_c\le {\epsilon }_t& \\ E{\epsilon }_c+f_0& {\epsilon }_1\le {\epsilon }_c\le {\epsilon }_{cc}& \end{array}$$

(18)

$${\epsilon }_t=\frac{E_c+E_2}{E_c-E_2}{\epsilon }_1+\frac{2\left(f_0-f_{co}^{\prime }\right)}{E_c-E_2}$$

(19)

$${\epsilon }_1=\frac{f_{co}^{\prime }}{E_c}$$

(20)

where $f_{co}^{\prime }$ is the strength of partially confined concrete in the core area; $f_0$ is the yield stress of the reinforcement; and ${\epsilon }_{cc}$ is CC tear strain.

By combining Equations (15)~(20), it can be concluded that:

$$A=\frac{E_c-E_2}{2\left({\epsilon }_1-{\epsilon }_t\right)}$$

(21)

$$B=E_c-2a{\epsilon }_1$$

(22)

$$C=f_{co}^{\prime }-A{\epsilon }_1^2-B{\epsilon }_1$$

(23)

$$E_2=\frac{f_{cc}^{\prime }-f_0}{{\epsilon }_{cc}}$$

(24)

$$E_c=4733\sqrt{f_{co}^{\prime }}$$

(25)

According to the test results, the fitting curves of individual specimens are shown in Figure 13, and the parameter values of the specimens at different corrosion rates are shown in

Table 12. Fitting parameters for individual specimens.

Specimen	A	B	C
C5-15-1-1	1.83	−0.01	50.77
C5-15-1-2	1.11	−0.007	54.27
C5-15-1-3	3.31	−0.01	55.23
C5-30-1-1	1.78	−0.009	43.90
C5-30-1-2	8.31	−0.005	48.22
C5-30-1-3	4.02	−0.01	49.03
C10-15-1-1	1.87	−0.009	45.81
C10-15-1-2	1.28	−0.007	49.06
C10-15-1-3	1.83	−0.008	50.11
C10-30-1-1	1.51	−0.006	37.06
C10-30-1-2	8.57	−0.02	46.73
C10-30-1-3	2.32	−0.002	47.41

.

From Figure 13, it can be seen that the constitutive model proposed in this paper for the corroded reinforced concrete columns with CC and CFRP co-constrained has high accuracy and can well characterize its axial compressive mechanical properties.

5. Conclusions

• From the damage forms of the specimens, the unconfined reinforced concrete columns showed brittle damage with no obvious signs of damage. The bearing capacity of the reinforced concrete columns reinforced by single-layer CC was improved, but the increased bearing capacity was low. At the same time, the specimens showed ductile damage at the time of damage, and when the reinforced concrete columns with both CC and CFRP constrained together were damaged, the damage process of the CFRPs was slower and the specimens exhibited ductility. As the number of CFRP layers increases, the damage process of CFRP becomes slower and slower, the sound of damage becomes louder, the energy released by the damage is larger, and the concrete in the core area is completely crushed.
• The actual corrosion rates of the CC-restrained specimens are smaller than those of the unrestrained specimens, and they are also smaller than their theoretical corrosion rates, which indicates that the CC has a stronger ability to inhibit corrosion. For specimens with a theoretical corrosion rate of 20% or less, the corrosion inhibition ability of CC increases with the rising of the initial corrosion rate and the secondary corrosion length of the longitudinal bars. For specimens with a theoretical corrosion rate greater than 20%, the corrosion inhibition ability of CC on specimens decreases.
• The stress–strain curves of the concrete columns reinforced by CC and CFRPs and normal concrete columns both have rising and falling parts. However, the curves of concrete columns restrained by CC and CFRPs together show a pattern of first rise, then a small decrease and then rise. In this paper, an axial compression principal model applicable to the corroded reinforced concrete columns with CC and CFRPs jointly restrained is developed, which has high accuracy and can better describe the axial compression mechanical properties of corroded reinforced concrete columns.