Flexural-shear behavior of degraded RC beams strengthened with C-FRCM under the coupling effect of a corrosive environment and a sustained load

Abstract

An experimental investigation was conducted to evaluate the flexural-shear behavior of deteriorated reinforced concrete (RC) beams strengthened with carbon fiber fabric-reinforced cementitious matrix (C-FRCM) composites, focusing on their failure modes, ultimate bearing capacity, ductility, and stiffness. The strengthening efficiencies of a carbon fiber woven mesh and a carbon fiber cloth were comparatively analyzed. The results indicated that the C-FRCM effectively restrained the crack propagation process: the RC beams strengthened with the C-FRCM (carbon fiber woven mesh) exhibited relatively uniform crack development trends, whereas those strengthened with carbon fiber-reinforced polymer (CFRP) exhibited delayed crack growth prior to steel bar yielding. Future studies will add strengthening tests with different numbers of layers to further verify the generality of this law. Under two-layer strengthening conditions, smaller mesh sizes produced more significant performance improvements. Conversely, for mesh sheets with constant distribution ratios, increasing the number of layers further improved the effectiveness of strengthening. The C-FRCM also enhanced the ductility and flexural stiffness of deteriorated RC beams to a certain extent, providing improvement trends that were consistent with those observed in the ultimate bearing capacity. However, the ductility enhancement varied among the samples, with differentiation arising from the stiffness improvement characteristics and plastic deformation capacities associated with different strengthening configurations. A calculation method for determining the flexural bearing capacities of C-FRCM-strengthened degraded RC beams was proposed, accounting for concrete strength degradations, cross-sectional damage characteristics, the steel corrosion rate, reinforcement configuration parameters, the effective utilization rates of composite materials, and fiber strength exploitation efficiency. The validity of the proposed methodology was established through an experimental validation by incorporating statistical performance metrics such as the mean error and coefficient of variation, while a comparative analysis against the existing code-based formulations demonstrated its technical advantages.

Keywords

fiber composite materials carbon fiber fabric-reinforced cementitious matrix (C-FRCM)damage deterioration reinforced concrete (RC) beams flexural-shear behavior

Introduction

Reinforced concrete (RC) structures in coal mine environments are subjected to the combined action of corrosive media and external loads during service, resulting in increasingly severe durability problems. Corrosive substances such as CO₂, acid mist, sulfate, and calcium-magnesium chloride continuously erode concrete. External loads induce microcracks on the concrete surface, accelerating the ingress of corrosive agents and further initiating steel bar corrosion (Lv et al., 2015; Wu et al., 2016; Zhou et al., 2019). After performance degradations occur, the flexural capacities, stiffness levels, and structural integrity of RC beams are significantly compromised, posing substantial risks to service safety (Fu et al., 2020; Karavokyros et al., 2020; Liu et al., 2016). Therefore, developing reasonable strengthening measures and systematically studying the mechanical properties of degraded RC beams is crucial.

Carbon fiber fabric-reinforced cementitious matrix (C-FRCM) composites have shown significant potential for restoring and enhancing the flexural performance of corrosion-damaged RC beams. Through experiments and theoretical analyses, Elmezayen and El-Maaddawy (2024) verified that C-FRCM composites can repair two-span continuous beams with 40% steel cross-sectional area losses due to corrosion; a rational layer design fully recovers the original bearing capacity and validates the moment redistribution between the mid-spans and supports. A numerical study conducted by Feng et al. (2022a) revealed that increasing the number of carbon fiber mesh layers improved the bearing capacity of the system but reduced its ductility, whereas end U-shaped wrapping anchors effectively inhibited C-FRCM debonding and increased the ultimate load. The implementation of U-wrap anchorage systems in FRCM strengthening applications has attracted significant research attention in recent years, with studies consistently demonstrating that optimized anchorage configurations substantially improve the performance of FRCM–concrete interfacial bonds, delay debonding failure mechanisms, and consequently increase both the ultimate bearing capacity and ductility of strengthened structural members (Do-Dai et al., 2025; Holsamudrkar and Banerjee, 2024, Holsamudrkar et al., 2025).

In terms of fatigue performance, the dual-function system integrating a C-FRCM with cathodic protection extends the fatigue lives of corroded beams, and its S‒N curve supports fatigue design tasks (Liu et al., 2022b). A code comparison (European FIB Bulletin 14, American ACI series, Chinese CECS 146-2003) reveals that European codes more accurately predict the bearing capacities of C-FRCM-strengthened beams, whereas the existing codes are generally conservative (Feng et al., 2022, 2024; Mandor and El Refai, 2023). PBO-FRCMs outperform C-FRCMs in terms of enhancing yields/ultimate bearing capacities and maintaining stiffness under monotonic and cyclic loads (Ramezani et al., 2023; D’Antino and Pecce, 2020), although FRCM strengthening reduces the moment redistribution capacities of continuous beams, which must be considered in design scenarios (Mandor and El Refai, 2023).

FRCMs enhance the flexural performance of RC beams under various loads: cyclic four-point bending tests have shown that the cycle life of a C-FRCM extends to five times that of unstrengthened beams (Bressan et al., 2022). Its fatigue life surpasses that of steel but lags behind that of epoxy-based CFRPs, with anode polarization reducing the fatigue strength; moreover, fiber layers dominate fatigue performance (Al-Waisy et al., 2022; Sabzi et al., 2025). Externally bonded CFRP plates improve the flexural capacities of marine sand concrete beams by 5.50% and alter their failure modes (Selvaraj and Rai, 2022), whereas FRCMs increase the ductility and energy absorption rates under dynamic loading (Dabiri and Kheyroddin, 2021).

FRCMs effectively improve the bearing capacities, stiffness levels, and ductility of corroded beams (Zhu et al., 2020). Tests conducted on beams with 10%/17% stirrup corrosion rates have shown that corrosion reduces the shear strength by up to 21%, and repairs fail to fully restore the original strength; a new evaluation method based on the softened strut-and-tie model was subsequently proposed (Sung et al., 2025). Long-term studies have indicated that corrosion accelerates creep (90% of the final creep occurs in 6 months), and a creep calculation model considering stiffness degradations has been established (Tang et al., 2024). Designs must account for the degree of corrosion and material compatibility considerations, with long-term creep monitoring recommended. Contemporary research (2023–2025) on FRCM strengthening under coupled degradation scenarios has demonstrated that synergistic interactions between corrosion propagation and sustained loading conditions critically influence the interfacial bond degradations observed between FRCM systems and concrete substrates. The effectiveness of strengthening interventions is highly sensitive to environmental coupling factors and the employed surface preparation methodologies. In particular, investigations concerning the flexural-shear behaviors of FRCM-retrofitted deteriorated reinforced concrete beams have emerged as a focal research domain in structural rehabilitation engineering (Holsamudrkar and Banerjee, 2024; Feng et al., 2024; Alshamrani et al., 2025).

Although cement-based composite strengthening results in slightly lower bearing capacity enhancement efficiency than CFRP strengthening does, it provides distinct advantages in terms of crack propagation control, ductility improvements, and durability enhancements. It is necessary to clearly distinguish between “corroded beams” and “degraded beams” in this research: “corroded beams” refer mainly to beams with steel reinforcement corrosion, whereas “degraded beams” encompass both concrete deterioration (including strength reductions and cohesion losses) and steel corrosion (including cross-sectional losses and pitting corrosion). The current research on C-FRCM-strengthened RC beams focuses mainly on noncorroded beams or the flexural performance of strengthened beams after overall corrosion occurs. However, limited research has focused on moderately to severely degraded RC beams, where concrete deterioration (including strength reductions and cohesion losses) and steel corrosion (including cross-sectional losses and pitting corrosion) coexist. Therefore, further experimental investigations are needed to clarify the strengthening effects and influencing factors of C-FRCMs on RC beams with varying degrees of damage and to establish or revise the corresponding bearing capacity calculation methods.

Investigation program

Specimen design

A total of 13 RC beams were fabricated for conducting four-point bending tests, with 12 beams divided into 4 groups. Each group was subjected to 5–8 cycles of accelerated degradation under the combined action of a simulated corrosive environment and a sustained load. This study employed a single-specimen representation for each strengthening configuration, which may have compromised the statistical reliability of the experimental outcomes; the subsequent analysis addresses how this limitation influences the generalizability of the conclusions and the variability/repeatability of the results. One beam in each group served as an unstrengthened control, and the other two beams were strengthened with FRCMs. Each test beam had a cross-section of 200 mm × 400 mm (width × height), a total length of 2000 mm, and an effective span of 1800 mm. The reinforcement configuration was as follows: two HRB335 hot-rolled ribbed steel bars (Φ14 mm) in the upper part and two HRB335 hot-rolled ribbed steel bars (Φ18 mm and Φ16 mm) in the lower part (longitudinal reinforcement ratio: 0.89%). The stirrups were HPB235 hot-rolled plain steel bars (Φ8 mm), with spacings of 100 mm in the shear-span zone and 150 mm in other regions. The concrete cover thickness was 30 mm.

The a/d ratio of the test beams was calculated as 650/400 ≈ 1.625 (less than 2), which made the beams prone to the development of shear cracks, and the crack patterns observed during the test also confirmed this characteristic; the study focused on the flexural-shear behaviors of the beams, and the relevant mechanical performance analysis was carried out by combining the characteristics of flexural and shear failures (Figure 1).

Raw materials

Concrete

Referring to the strength grade of in-service concrete (former grade: 200∼300) in actual coal mine projects, the strength grade of the designed concrete was C20 with a water–cement ratio of 0.60. The mix proportion of the concrete (by mass) was water: cement: river sand: crushed stone = 325:195:762:1144. The average 28-day compressive strength of 150 mm × 150 mm × 150 mm concrete cubes under standard curing was 22.5 MPa.

Reinforcing bars

In accordance with Chinese standard GB/T 228.1-2010 (Standardization Administration of China, 2010), the mechanical properties of the steel bars were tested: the yield strengths of the Φ14-mm, Φ16-mm, and Φ18-mm bars were 352 MPa, 365 MPa, and 344 MPa, respectively, and their ultimate strengths were 505 MPa, 524 MPa, and 503 MPa, respectively.

CFRP sheet and carbon fiber woven mesh

The adopted CFRP cloth was a CS200 high-strength carbon fiber cloth manufactured in Nanjing, whose mechanical properties are listed in Table 1. The carbon fiber woven mesh was composed of mutually perpendicular carbon fiber bundles and glass fiber bundles (Figure 2), with a mesh size of 10 mm × 10 mm. Its mechanical properties are presented in Table 2. A reduced mesh size in the carbon fiber woven mesh enhanced the degree of mechanical interlocking between the cementitious matrix and fiber bundles and increased the effective bond area between the strengthening layer and the concrete substrate, thereby improving the overall effectiveness of the strengthening process. A microscopic analysis of the bond interface revealed that smaller mesh sizes facilitated the formation of denser mechanical interlocking structures, which promoted an efficient stress transfer between the matrix and the reinforcing fibers.

Table 1.

Mechanical properties of CFRPs.

Type	Thickness/mm	Standard tensile strength/MPa	Elastic modulus/GPa	Elongation at break/%
UD-CS200	0.111	3467	219	1.58

Table 2.

Mechanical properties of the fiber woven mesh.

Fiber type	Tensile strength of the monofilament/MPa	Linear density of the fiber bundle/Tex	Elastic modulus of the monofilament/GPa	Number of fibers per bundle/10	Elongation at the break of the monofilament/%	Fiber bundle density/(g/cm)
T700S carbon fiber	4660	801	231	12	2	1.78
E-glass fiber	3200	600	65	4	4.5	2.58

FRCM cement base

The mix proportions of the cementitious matrix are given in Table 3. The 28-day compressive strength and flexural strength of the matrix test blocks were 29.7 MPa and 8.5 MPa, respectively.

Table 3.

Mix ratios of the FRCM-based material (units: kg·m^-3).

Cement	Water	Fly ash	Silica fume	Silica sand	Water reducer	Chopped carbon fiber	Water-binder ratio
303.6	288.24	582	44.28	352.8	23.2	11.14	0.31

Accelerated deterioration test

To accelerate the research process, a simulated corrosive environment was established on the basis of in situ monitoring data and Chinese standard GB/T 50,046-2018 (Ministry of Housing and Urban-Rural Development of the People’s Republic of China, 2018), with the following assumptions made based on the key environmental characteristics. (a) HCl and Cl₂ were assumed to dissolve in water vapor or liquid water, producing H^- that reacted with OH^- in concrete, leading to deterioration. Therefore, HCl was used as a substitute according to its equivalent H⁺ concentration. (b) The CO₂ concentration in the test environment was determined using an expansion coefficient that was proportional to the strong acid corrosion effect of HCl according to field measurement data. (c) Considering that the main corrosive liquid ions were Na⁺, K⁺, Mg²⁺, Cl⁻, and SO₄²⁻, these ions were converted into NaCl, MgCl₂, and Na₂SO₄ on the basis of their concentrations, with all Na⁺ assumed to originate from Na₂SO₄. In the simulated environment, KCl was substituted with NaCl, and CaCl₂ was substituted with MgCl₂, and the mixture was sprayed onto the test setup. (d) Solid substances were not independently considered, as they were mainly reaction products and dust. (e) Considering the effect of temperature‒humidity cycles on corrosion efficiency, the annual temperature and humidity parameters were determined from field measurements and amplified by 50 times to accelerate the degradation process (Table 4). The 50× acceleration factor for the temperature‒humidity cycles was determined on the basis of existing studies regarding the accelerated corrosion of reinforced concrete structures in underground mining environments (Lv et al., 2015; Wu et al., 2016). This acceleration rate established the fact that each accelerated cycle produced degradation effects that were equivalent to approximately 7.3 days of natural aging under actual coal mine environment conditions, thereby maintaining rational equivalence between the laboratory simulation and real-service exposure durations. Throughout the experimental period, the temperature and humidity parameters were systematically modulated on a weekly basis over a 4-week cycle pattern while constant concentrations of the corrosive agents (NaCl, MgCl₂, Na₂SO₄, CO₂, and HCl) were maintained.

Table 4.

Design of the simulation environment.

NaCl (g/L)	MgCl₂ (g/L)	Na₂SO₄ (g/L)	CO₂ (mg/m³)	HCl (mg/m³)	Temperature (°C)	Humidity (%)
0.814	9.95	37.88	27692	157.2	15	80
					26	95
					15	80
					2	10

The concentrations of the corrosive agents (listed in Table 4) were determined based on the in situ monitoring of typical underground coal mine environments in northern China (Zhou et al., 2019) and the relevant specifications for the simulated concrete structure corrosion tests (GB/T 50,046-2018), which were representative of the actual corrosive environment characteristics of coal mine RC structures.

A sustained load was applied using an electrohydraulic jack (Figure 3). An imposed load of 200 kN was exerted on two parallel concrete beams, with each beam bearing a load of 100 kN, corresponding to approximately 30% of the ultimate bearing capacity of the original beam (L-0-u, 345 kN), which was maintained at a constant magnitude throughout all degradation cycles without periodic recalibration. This load level was determined on the basis of both the typical service load conditions for RC beams in underground coal mine environments and preliminary experimental investigations of beam cracking loads. During the entire degradation cycle, this load was kept constant without periodic adjustments, and a self-reaction loading system was used to ensure the stability and accuracy of the load application scheme. A self-reacting loading system was implemented to ensure consistent environmental‒mechanical coupling conditions across multiple samples, thereby guaranteeing the comparability of the test results.

The coupled environmental‒mechanical loading testing system comprised a self-reacting steel frame; an electrohydraulic servo-controlled jack equipped with load-holding functionality; a climate-controlled environmental chamber with internal dimensions of 4.5 m (length)×3.3 m (width)×3 m (height), a temperature control range of −10°C to 80°C, and a humidity control range of 10%–98% RH; and a multichannel data acquisition system. The loading frame possessed a maximum load-bearing capacity of 2000 kN, which was sufficient for satisfying the sustained loading requirements of the test samples. The temperature‒humidity cycles specified in Table 4 were executed using an automated environmental chamber, with continuous thermal and hygric parameter monitoring implemented via integrated sensors at 10-min intervals. The actual monitoring data were documented and cross-referenced against the design parameters to validate the accuracy of the simulation.

Strengthening procedure

The degraded samples were strengthened using the following procedure. (1) Surface preparation involved the mechanical removal of the deteriorated concrete layer from the entire bottom surface (with a 2000-mm length) and side surfaces—excluding a 500-mm pure bending zone—using chipping techniques (depth: 5–10 mm), followed by surface texturing performed via sandblasting to increase the amount of interfacial bonding; the residual debris was subsequently flushed with clean water, and the prepared substrate was maintained under moist curing conditions for 24 hours prior to the matrix application step. (2) A 6-mm-thick FRCM cementitious matrix was uniformly applied to the bottom surface for substrate leveling. (3) A carbon fiber cloth–fiber woven mesh composite layer impregnated with cement paste was installed and overlain with a 3-mm-thick cementitious matrix. (4) The two-layer reinforcement system was completed by repeating Step (3), with U-shaped anchorage detailing implemented along the beam sides. The geometric parameters of the U-shaped anchorage system matched those of the beam cross-section (with a 200-mm width), full shear span coverage (with a 400-mm length), and composite thickness compatibility (9 mm); this configuration was consistently applied across the shear spans of all the reinforced beams to optimize the interfacial bond performance and shear capacity. The complete reinforcement methodology is schematically illustrated in Figure 4.

Measurement of the concrete strength and steel corrosion rate

After each degradation cycle, the concrete core samples were drilled from the beam sides for conducting uniaxial compression tests to measure the residual strength of the corroded concrete. The test beams were subsequently fractured to extract the corroded longitudinal steel bars. After surface concrete debris was removed, the bars were pickled in a 12% hydrochloric acid solution to remove corrosion products, rinsed with clean water, dried, and weighed. To determine the steel corrosion rate (ρ), 500-mm-long bar segments were selected from the mid-span region of each beam (representing the maximum corrosion severity level). A compensation factor for the nonuniform corrosion distribution was established through a gravimetric analysis of three distinct segments per bar, with the results averaged across these measurements. The steel corrosion rate ρ was calculated as ρ = (m₀ – m₁)/m₁, where m₀ is the mass of uncorroded steel per unit length and m₁ is the mass of corroded steel per unit length.

Loading method and test measurements

A symmetrical two-point concentrated loading configuration was implemented using a 50-ton hydraulic jack for incremental loading purposes, with the load transferred to the test beam through a distribution beam. The vertical displacement at the mid-span was monitored using a displacement transducer. Concrete strain measurements were obtained through BX120-10AA strain gauges (with 10-mm gauge lengths) installed on the top, side, and bottom fibers of the mid-span cross-section, whereas the development of steel strain was tracked using BX120-3AA strain gauges (with 3-mm gauge lengths) bonded to longitudinal reinforcing bars at both the mid-span and shear span locations. For the fiber-reinforced cementitious matrix (FRCM), BX120-10AA strain gauges (with 10-mm gauge lengths) were affixed to carbon fiber fabric/mesh surfaces at the mid-span and the termination points of the U-shaped anchorage system. The strain data were acquired via a DH3816 static strain measurement system, with readings recorded at 5-kN load increments throughout the loading procedure. The experimental setup, including the loading protocol and instrumentation layout, is illustrated in Figure 5.

Results and discussion

The flexural test results obtained for all the degraded and strengthened beams are summarized in Table 5. All test beams had preexisting cracks induced by environment‒load coupling during the degradation procedure; thus, the cracking load was not recorded during the formal loading process. In Table 5, fc denotes the residual compressive strength of the corroded concrete; ρ is the steel corrosion rate; Fy and Fu are the yield load and ultimate load, respectively; Δy and Δu are the mid-span deflections corresponding to Fy and Fu, respectively; and μΔ is the displacement ductility coefficient (μΔ = Δu/Δy). The specimen designation is L-x-y, where L denotes the test beam, x is the number of degradation cycles (0 for the original beam), and y represents the strengthening method (u: unstrengthened; 2c: strengthened with 2 layers of carbon fiber cloth; 2n: strengthened with 2 layers of carbon fiber woven mesh).

Table 5.

Flexural test results obtained for the deteriorated beams.

NO.	f_c/MPa	ρ/%	F_y/kN	Δ_y/mm	F_u/kN	Δ_u/mm	μ _Δ	Failure mode
L-0-u	24.8	0	280	8.63	345	24.10	2.79	Flexural failure
L-5-u	19.3	3.77	255	4.95	290	12.47	2.52	Flexural failure
L-5-2c	18.9	4.24	270	6.23	330	13.33	2.14	Fiber breakage
L-5-2n	19.9	4.15	270	9.57	300	15.16	1.58	Fiber mesh breaks
L-6-u	19.2	4.78	230	11.86	245	17.30	1.25	Shear failure
L-6-2c	19.6	5.16	300	8.77	320	16.18	1.84	Fiber breakage
L-6-2n	18.8	5.29	270	5.65	290	10.47	1.85	Fiber mesh breaks
L-7-u	15.55	6.48	240	6.74	260	12.35	1.83	Flexural failure
L-7-2c	15.30	6.24	300	7.64	320	14.09	1.84	Fiber breakage
L-7-2n	18.64	6.40	270	6.15	290	12.88	2.09	Fiber mesh breaks
L-8-u	15.46	7.50	240	9.35	255	13.22	1.41	Flexural failure
L-8-2c	15.16	7.75	300	7.03	318	13.45	1.91	Fiber breakage
L-8-2n	16.50	6.88	290	6.97	300	15.54	2.23	Fiber mesh breaks

Failure modes and crack analysis

The failure modes of the unstrengthened beams are illustrated in Figure 6. The image quality of Figure 6 is enhanced, and annotated sketches of the crack propagation trends and failure characteristics have been added to the appendix. Specimens L-0-u, L-5-u, L-7-u, and L-8-u exhibited typical flexural failure characteristics, featuring concrete crushing in the compression zone subsequent to the longitudinal steel bar yielding effect. In contrast, specimen L-6-u underwent a shear‒compression failure, which can be attributed to two primary factors. First, the beam had a shear-span ratio of 1.84 and a span-depth ratio of 4.5, both of which were considerably smaller than those of conventional RC beams, making the component more prone to shear failure. Second, during the early stages of accelerated degradation, compared with the longitudinal bars, the stirrups were positioned closer to the concrete surface, resulting in more severe corrosion (including pitting corrosion), which further weakened their shear resistance and ultimately triggered a shear‒compression failure.

As the number of degradation cycles increased from 5 to 8, the number of main cracks at the final failure time remained approximately unchanged, whereas the quantity of fine cracks in the tension zone gradually decreased. As shown in Table 5, the volume expansion exhibited by the steel corrosion products induced longitudinal cracks along the reinforcement with an increasing longitudinal steel corrosion rate. Moreover, the hydration products inside the concrete were eroded by corrosive media, leading to a reduction in the strength and cohesion of the concrete. This phenomenon further impaired the bond performance between the steel bars and concrete, including interfacial friction and mechanical interlocking effects. Consequently, tensile stress could not be effectively transferred from the steel bars to the surrounding concrete, which contributed to the reduction in the number of fine cracks in the beam tension zone.

The failure modes of the CFRP/C-FRCM-strengthened beams are presented in Figure 7. The image quality of Figure 7 is enhanced, and annotated sketches of the failure modes and interface bonding characteristics have been added to the appendix. All the strengthened beams exhibited consistent failure processes: after the longitudinal steel bar yielded, the cracks in the compression zone of the concrete developed into crushing cracks, followed by the fracture of the CFRP sheets or carbon fiber woven mesh. This sequence of failure indicates that the strengthening materials were fully utilized for bearing tensile stress. Notably, the strengthened beams maintained good structural integrity after a failure occurred, which is beneficial for preventing sudden structural collapses in engineering practice.

Interfacial delamination between the concrete in the pure bending section and the FRCM layer tended to occur in specimens L-7-2n and L-8-2c, and partial peeling of the FRCM layer was observed in specimen L-8-2n. This phenomenon was caused mainly by two factors. On the one hand, the corrosion-induced cracks and stress cracks generated during the degradation process reduced the bonding performance between the FRCM and corroded concrete. On the other hand, the pure bending section was not treated with U-shaped anchors. During loading, the carbon fiber cloth or mesh bore tensile stress to restrain the crack propagation procedure, leading to an excessive energy concentration in the pure bending section. The strengthening layer simultaneously bore tensile stress and interfacial shear stress from the bonding interface, resulting in slight variations in the failure modes of individual samples.

As depicted in Figure 7, the eight strengthened beams presented dense and uniform crack distributions, with their stress cracks concentrated mainly in the pure bending section. During the loading process, the synergistic working effect between the steel bars and strengthening materials was dynamically altered. At the initial loading stage, the steel bars and concrete bore most of the load; after the steel bar yielded, the strengthening layer gradually took over the tensile stress to inhibit the expansion of cracks. These findings confirm that FRCMs have excellent strengthening effects on corroded RC beams, especially in terms of controlling crack propagation processes.

Bearing capacity analysis

A histogram of the ultimate bearing capacities of all the test beams is shown in Figure 8. The percentage changes in the ultimate bearing capacities relative to that of the original beam and the error bars of the test results are shown in Figure 8; the key trend of the figure is that the ultimate bearing capacities of the strengthened beams decreased with increasing number of degradation cycles, and the strengthening layers could effectively recover the bearing capacities of the corroded beams, with the carbon fiber cloth having a better strengthening effect than the woven mesh did. Compared with that of the original beam (L-0-u), the ultimate bearing capacities of the unstrengthened corroded beams tended to decrease overall. After 5, 6, 7, and 8 degradation cycles, the ultimate bearing capacities of the unstrengthened beams decreased to 84.1%, 71.0%, 75.4%, and 73.9% of that of the original beam, respectively. The main reasons for these bearing capacity reductions are as follows.

The corrosive media contained in the coal mine environment severely eroded the concrete, significantly reducing its compressive strength and cohesion, which weakened the load-bearing capacity of the compression zone.

The volume expansion exhibited by the steel corrosion products induced longitudinal cracks along the reinforcement, which damaged the bond between the steel and the concrete and destroyed their synergistic working mechanism.

Stress cracks and corrosion-induced cracks accelerated the corrosion of the steel bars, reducing the effective cross-sectional areas and mechanical properties of the bars. In addition, uneven corrosion (especially pitting corrosion) caused the concentration of stress, which further reduced the ultimate bearing capacities of the beams.

Under the same number of degradation cycles, strengthening with two layers of carbon fiber cloth or two layers of carbon fiber woven mesh effectively improved the ultimate bearing capacities of the corroded beams. For the beams strengthened with carbon fiber cloth, the ultimate bearing capacities increased by 13.8% (L-5-2c), 30.6% (L-6-2c), 23.1% (L-7-2c), and 24.7% (L-8-2c) with an increasing number of degradation cycles, reaching 92.2%–95.7% of the bearing capacity of the original beam. The significant improvement in the bearing capacity of L-6-2c is attributed to the U-shaped anchorage of the FRCM, which not only provided effective end anchors for the carbon fiber cloth but also enhanced the shear-bearing capacity of the beam, thus changing the failure mode from shear compression to flexural failure. With the exception of L-6-2c, the improvement rates exhibited by the bearing capacities generally increased with the number of degradation cycles because more severe steel corrosion promoted the full exertion of the tensile capacity of the carbon fiber cloth.

For the beams strengthened with carbon fiber woven mesh, the ultimate bearing capacities increased by 3.4% (L-5-2n), 18.4% (L-6-2n), 11.5% (L-7-2n), and 17.6% (L-8-2n) with an increasing number of degradation cycles, reaching 84.1%–87.0% of the bearing capacity of the original beam. Only a two-layer strengthening scheme was adopted in this test. Under this strengthening parameter condition, for carbon fiber mesh sheets with the same fiber distribution ratio, smaller mesh sizes could achieve more significant strengthening performance improvements. However, under the premise of effective interfacial bonding, compared with the woven mesh, the carbon fiber cloth yielded a better bearing capacity improvement but lower ductility, which was not only due to the better fiber continuity of the carbon fiber cloth but also related to the different bond mechanisms and failure progression trends of the two materials: the carbon fiber cloth had a larger contact area with the cementitious matrix, and its stress transfer process was more direct, so it could quickly bear the tensile stress imposed after steel bar yielding and improve the resulting bearing capacity, but its brittleness was higher, and its deformation capacity was poor; the carbon fiber woven mesh had a mesh structure, its bond with the matrix was more flexible, its failure progression scheme was slower, and the ductility of the strengthened beam was better.

Load-deflection analysis

The load-deflection curves produced by the unstrengthened corroded beams with different numbers of degradation cycles are shown in Figure 9. The preyield stiffness value of each beam is supplemented in Figure 9. The key trend shown in the figure is that the preyield stiffness levels of the partially corroded beams was greater than that of the original beam, and the failure deflection of the corroded beams decreased with an increasing number of degradation cycles. With increasing load, the cracks at the beam bottoms gradually propagated upward, leading to a decrease in the flexural stiffness of the beams and an acceleration in the increase in the mid-span deflection. After the longitudinal steel bars yielded, the mid-span deflection increased rapidly, reflecting the plastic deformation characteristics of the RC beams. Before the steel bars yielded, under the same load level, the mid-span deflections of L-5-u, L-7-u, and L-8-u were smaller than that of the original beam (L-0-u), indicating that the preyield stiffness levels of these corroded beams were greater than that of the original beam. In contrast, L-6-u exhibited a lower preyield stiffness level than the original beam did, which may have been due to casting defects that exacerbated the corrosion of the stirrups during the degradation process, ultimately leading to shear‒compression failure and a reduction in the overall stiffness level.

The mid-span deflection of the original beam (L-0-u) at the time of failure was 24.1 mm. With an increasing number of degradation cycles, the failure deflections of the unstrengthened beams decreased by 48.3%, 28.2%, 48.8%, and 45.1%, respectively. This phenomenon occurred because the coexistence of concrete corrosion and steel corrosion reduced both the stiffness levels and deformation capacities of the beams, resulting in a downward trend in the displacement ductility coefficient (as shown in Table 5). This reduction in ductility indicates that the unstrengthened corroded beams tended to exhibit brittle failure characteristics, which were unfavorable for structural safety.

The load-deflection curves produced for the strengthened beams are presented in Figure 10. With an increasing number of degradation cycles, the bearing capacities of the CFRP- and C-FRCM-strengthened beams remained relatively stable, indicating that the strengthening effect of the FRCM was independent of the degree of steel corrosion and depended mainly on the dosage of the strengthening fabric. This conclusion is consistent with the research results of Feng et al. The underlying mechanism is that under the same failure mode, after the corroded steel bars yielded, the carbon fiber cloth or mesh bore part of the tensile stress, offsetting the strength loss caused by steel corrosion. The dosage of the strengthening fabric determined the tensile capacity of the strengthening layer after the steel bar yielded, thus dominating the strengthening effect of the whole beam.

As shown in Figure 10(a), the load-deflection curves produced for the beams strengthened with carbon fiber cloth are relatively steep, indicating that the addition of carbon fiber cloth effectively improved the stiffness of the corroded beams. The load-deflection curves of the beams strengthened with carbon fiber woven mesh are relatively gentle, reflecting better deformation capacity (Figure 10(b)). Compared with the woven mesh, the carbon fiber cloth could achieve better bearing capacity improvements but lower ductility performance. This difference was not caused by a single factor concerning fiber continuity but rather by the synergistic effect of multiple factors, such as fiber continuity, the interface bonding mechanism, and the failure evolution process: carbon fiber cloth is a continuous fiber structure with high stress transfer efficiency and high stiffness, which can quickly bear the tensile forces of components, thus significantly improving the bearing capacity; however, owing to its limited fiber deformation capacity, it is prone to brittle failures, resulting in low ductility. In contrast, carbon fiber woven mesh is a grid structure, and although its fiber continuity is not as good as that of carbon fiber cloth, it has a better mechanical interlocking effect with the cementitious matrix, a more gentle stress transfer process, and a stronger deformation coordination capacity, and its failure process is more moderate. Therefore, the improvement range of its bearing capacity is slightly lower, but its ductility performance is better.

The load-deflection curves produced for the beams before and after they underwent strengthening (after 7 degradation cycles) are shown in Figure 11. The curve shapes of the strengthened and unstrengthened corroded beams are similar, and both experienced elastic, cracking, yielding, and failure stages. Compared with those of the unstrengthened corroded beam (L-7-u), the preyield stiffness of the FRCM slightly increased, and the yield point and ultimate bearing capacity of the strengthened beams were significantly greater. These findings confirm the effectiveness of the applied FRCM strengthening measures, which can not only increase the bearing capacities of corroded beams but also increase their stiffness and deformation capacities to a certain extent.

Flexural bearing capacity calculation method for degraded RC beams strengthened with C-FRCMs

When the C-FRCM-strengthened degraded RC beams underwent the failure process of C-FRCM fiber fracturing, steel bar yielding, and final concrete crushing in their compression zones, the flexural bearing capacities were calculated in accordance with the specification requirements. As the C-FRCM-strengthened degraded RC beams conformed to the plane section assumption, the stress‒strain relationship of the fibers presented a linear distribution. The test RC beams adopted a singly reinforced rectangular cross-section, and the calculation schematic diagram is as shown in Figure 12.

The following equations are derived from the force equilibrium relationship:

α_{1} f_{c} b x = f_{y} A_{s} + f_{f} A_{f}

(1)

M_{ur} = M_{s} + M_{f}

(2)

M_{s} = f_{y} A_{s} (h_{0} - \frac{x}{2})

(3)

M_{f} = f_{f} A_{f} (h - \frac{x}{2} + \frac{h_{m}}{2})

(4)

where α₁ is the ratio of the stress value in the rectangular stress diagram of the concrete in the compression zone to the design value of the axial compressive strength of the concrete. F_c is the axial compressive strength of the concrete. b is the width of the concrete section. F_y is the nominal yield strength of the corroded steel bars. A_s is the cross-sectional area of the tensile reinforcement process. F_f is the tensile strength of the carbon fiber cloth. A_f is the actual bonding section area of the carbon fiber cloth. Mur is the flexural capacity of the reinforced concrete beam in the normal section. Ms is the bending moment caused by the tension of the steel bars. M_f is the bending moment caused by the tension of the C-FRCM. h₀ is the effective height of the examined section. x is the height of the concrete in the compression zone. h_m is the height from the centerline of the C-FRCM to the top of the concrete beam.

The flexural bearing capacity M_s^’ of the strengthened degraded RC beams is considered to be significantly affected by steel bar corrosion and the performance degradation exhibited by the concrete. The modified calculation model is as follows.

{M_{s}}^{'} = α_{1} {f_{c}}^{'} b^{'} x ({h_{0}}^{'} - \frac{x}{2}) = α_{sc} f_{y^{'}} A_{sc} ({h_{0}}^{'} - \frac{x}{2})

(5)

where f^’’_c, b^’, and h^’₀ are the measured values of the corresponding parameters for deteriorated concrete. f^’’_y and A_sc are the measured values of the corresponding parameters for corroded steel bars.

Moreover, for beams strengthened with multiple layers of bonded fibers, the effect of the effective cross-sectional area induced by the effective utilization rate of the fibers should be considered. The effective cross-sectional area of the fibers is calculated using the following formulas.

A_{fe} = k_{m} A_{f}

(6)

k_{m} = 1.16 - \frac{N_{f} E_{f} t_{f}}{30800} \leq 0.90

(7)

where A_fe is the effective cross-sectional area of the C-FRCM. A_f is the actual bonding section area of the carbon fiber cloth. K_m is the thickness reduction factor of the composite material. E_f is the elastic modulus of the C-FRCM. N_f and t_f are the number of layers and the thickness of a single layer of the C-FRCM, respectively.

In view of the fact that the actual tensile strain of carbon fibers does not reach the design value, a strength utilization coefficient φ_f is introduced and calculated according to the following formulas.

φ_{f} = \frac{0.8 ε_{cu} h_{e} / x - ε_{cu} - ε_{f 0}}{ε_{f}} \leq 1.0

(8)

x \geq 2 α^{'}

(9)

where φ_f is the effective utilization rate of the C-FRCM. ε_cu is the ultimate compressive strain of the concrete and was set as ε_cu = 0.0033. ε_f is the design value of the tensile strain of the C-FRCM. ε_f0 is the hysteresis strain of the C-FRCM when the influence of secondary loading is considered. In this study, the influence of secondary loading was not considered, and ε_f0 was set to 0. α^' is the distance from the resultant force point of the longitudinal compressive reinforcement to the near edge of the section. The reduction factors α_s (the strength reduction factor), φ_f (the fiber strength utilization factor), and k_m (the fiber thickness factor) are not independent of each other but significantly interact: αs changes with the degrees of steel corrosion and concrete degradation, which in turn affects the value of the neutral axis depth x and ultimately affects the calculation result of φ_f; km mainly affects the calculation of the effective fiber area A_fe and acts synergistically with φ_f on the solution of the fiber stress.

By substituting the above formulas into equation (4), the following is obtained.

{M_{f}}^{'} = φ_{f} f_{f} A_{fe} (h - \frac{x}{2} + \frac{h_{m}}{2})

(10)

Upon comprehensively considering the above factors, the formulas for the flexural bearing capacity of a degraded RC beam strengthened with a C-FRCM are derived as follows.

α_{1} {f_{c}}^{'} b^{'} x = α_{sc} {f_{y}}^{'} A_{sc} + φ_{f} f_{f} A_{f e}

(11)

M_{ur} = M_{s} + {M_{f}}^{'} = α_{sc} {f_{y}}^{'} A_{s c} ({h_{0}}^{'} - \frac{x}{2}) + φ_{f} f_{f} A_{fe} ({h_{0}}^{'} - \frac{x}{2} + \frac{h_{m}}{2})

(12)

This calculation model assumes that the FRCM and concrete substrate are in a perfect bond state before the fiber strain reaches the ultimate strain level of 0.005 and that interfacial bond-slip failure is temporarily not considered; when the fiber strain exceeds 0.005, the influence of interfacial bond-slip on the mechanical performance of the components is considered, and the corresponding correction coefficient is introduced. This approach is applicable to degraded RC beams with shear span ratios of 1.5∼2.0 and steel corrosion rates of 5%∼15% that are strengthened with two-layer C-FRCMs. To verify the accuracy and applicability of the proposed bearing capacity calculation method for strengthened degraded RC beams, the flexural bearing capacities of severely degraded RC beams strengthened with C-FRCM were calculated, and the results are presented in Table 6. All the reduction factors were empirically calibrated based on the test data of the 13 samples in this test, where the value range of αs was 0.85∼0.95, the value range of φ_f was 0.75∼0.85, and the value range of k_m was 0.90∼0.95. The above factors were all derived from the test experience in this paper, not cited from existing codes, and were more in line with the degradation conditions and strengthening conditions of this test.

Table 6.

Comparison among the calculation and test results obtained for the ultimate bending moment of the strengthened beams.

NO.	M_t/(kN·m)	M_c/(kN·m)	M_c/M_t	Mean error
L-5-2c	148.5	137.6	0.93	0.92
L-5-2n	135.0	126.3	0.94
L-6-2c	144.0	132.5	0.92
L-6-2n	130.5	120.8	0.93
L-7-2c	144.0	130.1	0.90
L-7-2n	130.5	119.7	0.92
L-8-2c	143.1	128.8	0.90
L-8-2n	135.0	124.2	0.92

Based on a statistical analysis of the experimental (M_t) and calculated (M_c) flexural capacities of eight structural components, the following conclusions were drawn.

The ratios of the calculated to experimental values (M_c/M_t) ranged from 0.90 to 0.94, with a mean value of 0.92. This finding indicates that the calculated values were generally slightly lower than the experimental results, yielding an average margin of error within 8%, thus demonstrating good agreement between the two datasets. The standard deviation was calculated to be 0.0151, and the coefficient of variation was as low as 1.64%, indicating minimal data dispersion and the exceptional stability and reproducibility of the predictive model. These results validate the notion that the employed calculation method is both accurate and reliable for estimating the flexural capacities of such components. Furthermore, all the data points fell below 1.0 with no significant outliers, further substantiating the rationality of the theoretical model and the high quality of the experimental data.

Conclusion

On the basis of the experimental results obtained for 13 RC beams with varying degrees of degradation and different strengthening methods, the following conclusions were drawn.

(a) Under the coupled effect of a corrosive coal mine environment and a sustained load, concrete deterioration and steel corrosion occurred simultaneously in the RC beams, which significantly reduced the bearing and deformation capacities of the beams and altered their failure modes and stiffness characteristics. Unstrengthened corroded beams tended to exhibit brittle failure characteristics, with significant ductility reductions.

(b) All the C-FRCM-strengthened beams exhibited typical flexural failure modes. The C-FRCM could significantly improve the bearing capacities of the degraded RC beams, and the strengthening layer maintained good bonding with the concrete until the time of failure, effectively restraining the crack propagation process, changing the failure mode of the degraded beams, and preserving their structural integrity, thus demonstrating excellent strengthening performance. In addition, the strengthening effect of the C-FRCM was independent of the degree of steel corrosion and was determined mainly by the dosage of the strengthening fabric.

(c) The ultimate bearing capacities of the corroded beams strengthened with carbon fiber cloth could be restored to 92.2–95.7% that of the original beam, which was better than the strengthening effect of the carbon fiber woven mesh. Compared with that of the unstrengthened corroded beams, the ultimate bearing capacities of the beams strengthened with carbon fiber woven mesh increased by 3.4–18.4%. Carbon fiber cloth is more suitable for scenarios where improving the bearing capacity and stiffness level are the primary goals, whereas carbon fiber woven mesh is more suitable for scenarios where ductility improvements are emphasized.

(d) The test results effectively reflected the overall mechanical performance characteristics of degraded RC beams strengthened with C-FRCMs. The developed approach is applicable to specimens with flexural failures or fiber fractures and is not applicable to specimens with shear failures or FRCM strengthening-layer peeling failures, but the generality of the conclusions still needs to be further verified by multiple sets of repeated tests.

Footnotes

Acknowledgments

The experimental work described in this paper was conducted at the Jiangsu Key Laboratory of Environmental Impact and Structural Safety in Civil Engineering at the China University of Mining and Technology. The help received during the testing process from staff and students at the laboratory is greatly acknowledged. The authors are also grateful for the assistance provided by the Xinghuo Research Assistant during the initial processes of sorting the literature references and drafting the English sentences in the discussion section, as well as that provided by Doubao when polishing the language of the manuscript. All AI-generated content has been carefully reviewed and verified by the authors to ensure its accuracy and consistency with the research content of the manuscript.

ORCID iD

Yuanzhou Wu

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors would like to express their sincere appreciation for the partial financial support received from the Jiangsu Provincial Open and Sharing of Large-scale Scientific Instruments Independent Research Project‌ (contract number: TC2023A014) and the Postgraduate Research & Practice Innovation Program of Jiangsu Province (contract number: SJCX25_1384).

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

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