1. Introduction
Recently, the use of lightweight carbon fiber reinforced composite materials that are nonmetallic has increased for the purpose of repairing and reinforcing concrete structures. “Strengthening a structural member” is a process undertaken when the existing member’s strength is deemed inadequate. Such deficiencies can manifest due to construction errors, such as excessive downward pressure on the steel bars into the cross section during the building process, alterations in the intended capacity, or reductions in capacity caused by human error or environmental factors [
1]. Civil engineering has witnessed the economical and effective implementation of CFRPs for the development and rehabilitation of deteriorating structures. Numerous variables affect the application of CFRPs for the reinforcement of RC members, including fiber type, fiber distribution, fiber orientation, and bond schemes [
2].
Many researchers investigated CFRP reinforcement methods including laminates, bars, or sheets. There are numerous benefits of CFRP composites over conventional materials. The construction industry is progressively adopting these benefits for infrastructure applications—durability, transportability in any length, exceptionally high strength, lightweight, requiring less mechanical fastening, requiring less expensive maintenance, requiring shorter construction periods, minimizing interruptions, having a long service life, and facilitating rapid installation [
3,
4]. Limam et al. [
5], in 2003, provided an experimental investigation and a limit analysis modeled on RC slabs reinforced with CFRP laminate. The findings from the experimental study indicated that externally applying the CFRP plates effectively enhanced the strength of RC slabs. Mosallam and Mosalam [
6], in 2003, examined the ultimate response of reinforced and unreinforced concrete slabs that had been retrofitted and repaired with CFRP laminates, through an experimental and analytical investigation. The carbon fiber/epoxy and E-glass/epoxy composite systems significantly strengthened the repaired areas. Additionally, retrofitting slabs with CFRP systems improved structural integrity. Limam et al. [
7], in 2005, used 2D finite element analysis to quantify the elastic response of simply supported two-way reinforced concrete slabs with CFRP laminates, concentrating on orthotropic composite plates with a central load. Hosseini [
8], in 2016, conducted an experimental program and used computational techniques to evaluate the load-deflection properties of reinforced concrete slabs, highlighting the effects of CFRP percentage, tensile longitudinal bar percentage, and CFRP elasticity modulus. The findings showed that prestressing CFRP laminates with NSM can improve RC slab fracture resistance, serviceability, yield capacity, and ultimate loads. Yılmaz et al. [
9], in 2018, utilized a combination of experimental and numerical methods to examine the impact behavior of two-way RC slabs reinforced with CFRP strips. The findings indicated that reinforcing RC slabs with CFRP strips increased their rigidity and toughness and the maximal acceleration values measured from test specimens correspondingly rose. Akhundzada et al. [
10], in 2019, used unidirectional CFRP laminates to test the efficiency of various strengthening techniques for internal slab-column connections and examined how laminate thickness and anchoring affect strengthening. The findings revealed that strengthening decreased maximum deflection by 50%, increased ultimate load by 25%, increased cracking load, and significantly reduced radial crack length. Mercimek et al. [
11], in 2022, examined RC flat slab efficacy-enhancing methods. The strengthening methods were CFRPs, shear stud, and textile-reinforced mortar (TRM). This study used Abaqus CAE
® to simulate the experiment and compare the results to the actual results. The results showed that TRM was the best out of the three strengthening methods used to improve RC slab performance under punching loads. Türer et al. [
12], in 2023, devised a CFRP strip reinforcing technique to mitigate punching strength loss from two square holes close to the column in two-way RC flat slabs. The specimen’s initial stiffness, load–displacement characteristics, energy dissipation capabilities, maximum load-bearing capacities, and CFRP-enhanced failure patterns were studied at varied opening sizes and positions. For numerical analysis, Abaqus CAE
® was used to model the specimens.
On the other hand, a lot of researchers used the other types of CFRPs (sheet or bar) in strengthening the two-way reinforced concrete slabs. Enochsson et al. [
13], in 2007, examined the structural response of two-way RC slabs reinforced with CFRP sheets, with sawn-up holes, under uniform loads. Both numerical and experimental methods are used to evaluate CFRPs’ ability to absorb excess sectional forces. The results show that externally bonded CFRP sheets may support slabs with openings better than steel-reinforced slabs. Esfahani et al. [
14], in 2009, investigated methods for using CFRP sheets to increase the flat slabs’ resistance against punching shear. The test results underwent comparison with the formulas outlined in both the BS 8110 and ACI 318 Codes. The findings from this investigation align well with outcomes reported by fellow researchers, demonstrating that the addition of CFRP sheets to the slabs’ tension side effectively enhances the slabs’ punching.
Meisami et al. [
15], in 2013, evaluated the potential of FRP rods to enhance shear strength, using an analysis of the punched shear performance of concrete slabs reinforced with epoxy resin and CFRP rods. The experimental findings showed that the selected reinforcement method improved the slabs’ maximum load-bearing capacity and ability to withstand deformation, while also preventing possible brittle failures from vertical point loads. Elsanadedy et al. [
16], in 2015, aimed to illustrate the efficacy of utilizing externally bonded CFRP composites for improving the flexural capacity of RC one-way slabs. The study encompassed both experimental testing and computational analysis, utilizing FE analysis. A comparison was conducted between the experimental and numerical findings, resulting in a satisfactory level of agreement. Behzard, Sharbatdar, and Kheyroddin [
17], in 2015, showcased the efficacy of a novel technology that combines CFRP materials to enhance the flexural strength of existing RC two-way slabs with a thin layer of concrete covering. The test results have shown the feasibility and effectiveness of this technology in enhancing the flexural behavior of reinforced concrete two-way slabs. A 3D nonlinear numerical model was created using the FE approach, to accurately forecast the flexural behavior of the tested slabs. Mahmoud et al. [
18], in 2021, studied the performance of high-strength RC slabs reinforced with CFRP sheets, to enhance their bending strength. The findings from the test were compared together to draw conclusions regarding the extent of CFRP enhancement; the load-carrying capability of the specimens improved after reinforcement using high-strength materials—thin concrete slabs.
The concrete damage plasticity (CDP) model is widely used in structural engineering to assess the behavior of concrete structures under various loads. The CDP model, a continuum-based model, takes into consideration the intricate behavior of concrete, such as cracking, crushing, and plastic deformation. This non-linear model is essential for designing and analyzing buildings that experience significant pressures, as it accurately represents the behavior of concrete after it reaches its peak strength. The CDP model was successfully applied in several situations, including earthquake engineering, blast-resistant building design, and reinforced concrete construction. This discovery might have important implications for the design and construction of reinforced concrete structures, especially in areas prone to earthquakes where ductility is a critical factor [
19]. Various combinations of damage and plasticity were explored by Carol et al. [
20] in 2001, Ibrahim et al. [
21] in 2023, and Rad et al. [
22] in 2023. Gatuingt and Pijaudier-Cabot [
23], in 2002, and Kratzig and Polling [
24], in 2004, utilized isotropic damage in their research, elucidating various combinations of plasticity types. Lubliner et al. [
25], in 1989; Imran and Pantaopoulou [
26], in 2001; and Ananiev and Ozbolt [
27], in 2004, explored theories that describe plasticity in nominal stress space.
This study aims to investigate the impact of varying strengthening ratios on the ultimate load, cracking load, crack width, and deflection. The recent studies did not investigate the behavior of RC two-way slabs with these specific ratios of CFRP. Furthermore, this study demonstrated the need to implement CFRP reinforcement to mitigate the damage to concrete and steel structures using Abaqus CAE®. This research shed light on the performance of CFRP in RC two-way slabs and how its strength might be improved. Engineers and researchers can utilize the findings as a reference for determining the appropriate proportion of reinforcement ratios to employ, to attain certain structural objectives. As well as the fact that this study possesses various distinctive elements that distinguish it as a novel study, it begins by investigating two-way RC slabs experimentally, as well as carrying out an ideal elasto-plastic analysis that focuses on managing concrete damage plasticity using CFRPs and applying a plastic limit load multiplier, with the intention of controlling the plastic deformation of two-way reinforced concrete slabs that have been strengthened with CFRPs. To further our comprehension of how various strengthening ratios affect the behavior of two-way RC slabs, these percentages were derived by testing three specimens; then, their tension and compression behaviors were investigated and compared to the control slab, which did not contain CFRPs. Finally, experimental testing and numerical analysis were utilized in this study for a more thorough evaluation and validation of the findings, which increases the study’s credibility and practicality. It was of the utmost importance to validate numerical models that were derived from the results of laboratory tests, with a particular emphasis on confirming the strengthening ratio. A sequence of simulations that are based on the limitations have been set. As a means of accurately representing the caused damage in the concrete, the numerical model was calibrated by making use of the CDP model. There was an evaluation of the effect of load multipliers on concrete deterioration, using both elastic and plastic analysis. All these parameters were considered and their effects were studied.
Following this introduction,
Section 2 provides a comprehensive explanation of the concrete constitutive model. Then, the experimental work that includes the details of the model and the materials’ properties are present in
Section 3. The test set-up and discussion of the experimental data are presented in
Section 4. Additionally,
Section 5 presents specific information on the numerical model, including the specifics, calibration procedure, and discussion of the numerical findings. Finally, the most significant findings and conclusions are presented in
Section 6.
4. Test Procedure and the Response of Concrete Slabs
The structural performance of the two-way RC slab was monitored at each loading stage, using instrumentation. Data on various parameters including central deflection, fracture widths, initial crack load, and eventual failure load were collected during each loading increment. The testing continued until failure was observed; the maximum burden was recorded. Using a load cell with a capacity of 700 kN, deflection measurements were taken at the center of the bottom tension face of the slab specimens. A dial gauge graduated to 0.01 mm increments was employed for the load measurements.
The specimens undergoing examination were meticulously positioned within the specialized frame apparatus, disregarding their own weight. In the initial phases of the experiment, a load of 5 kN was progressively applied. At zero loading, initial dial gauge readings were obtained. As the applied force progressively escalated by 5 kN at each phase, cracks form on the concrete slabs’ surfaces, documented using a pencil. Concurrently, the initial cracking load was recorded at each load increment, fracture breadth was assessed utilizing steel fillers, and deflection data were gathered via the dial gauge. Following the completion of this procedure, loading continued with the subsequent load step, in accordance with the same protocol. The burden continued to increase until it reached its maximum value, at which juncture it was documented.
Table 4 presents the load of cracking (Pcr), ultimate load (Pu), width of cracks (Wcr) at the ultimate load, and the central deflections (Δv) at the ultimate load. The control slab is designed to undergo flexural failure. For comparative analysis, the following was performed:
The control slab specimens underwent testing without any strengthening technique. Its design aimed for flexural failure. The load was systematically increased and the slab’s behavior was closely monitored. During the initial phase of testing, the slab exhibited elastic behavior until the emergence of the first crack. The first crack became evident in the constant moment region at a load of 120 kN. With continued loading, flexural cracks commenced in the specimens, extending towards the edges, and widening rapidly. At a load of 241 kN, slab G0 experienced flexural failure, marked by a sudden increase in deflection, while the load remained constant.
External CFRP laminates strengthening—in this procedure, CFRP laminate strips were affixed to the underside of the slab using epoxy resin as the adhesive material. The initiation of the initial crack occurred at a load of 190.6 kN for GA, 208.5 kN for GB, and 237.28 kN for GC. At loads of 455 kN, 498 kN, and 564 kN, GA, GB, and GC slabs experienced failure through a punching mode, respectively. Comparing to the control slab G0, there were increases in ultimate loads by 88.7%, 107%, and 134% for slabs GA, GB, and GC, emphasizing the notable influence of augmenting the reinforcement ratio within CFRP laminates. While the load remained constant, there was a rapid increase in deflection. For comparative analysis, the control slab was compared to these three specimens;
Figure 4 illustrates the load deflection behavior for the control slab alongside the GA, GB, and GC, experimentally. Observably, it is apparent that, by increasing the applied load, there is a proportional rise in damage intensity, signifying that the additional load induces supplementary initial stresses in both concrete and steel components. This emphasizes the importance of complementary strain energy in representing plastic damage. Ultimately, the adept management of this factor alleviates instances of plastic damage and failure.
Table 4 reveals that using CFRP laminate in strengthening the concrete slabs enhanced the ultimate load, in contrast to the control slab. Furthermore, slab GC demonstrated the maximum ultimate load and the smallest crack width. The data also indicate that slabs strengthened with CFRP laminates experienced punching failure, while slab GA failed due to debonding. These results underscore the effective capacity of CFRP in enhancing the ultimate load bearing capability of slabs, concurrently reducing the central deflection and the crack width under equivalent loads.
5. Numerical Modeling
FE analysis was employed to replicate the nonlinear response exhibited by two-way RC slabs strengthened with CFRP laminates, as depicted in
Figure 5. The damage plasticity model was adopted in this study, to represent concrete inside the Abaqus CAE
®. The modeling process involved four simply supported two-way RC slabs, derived from the experimental outcomes of one specimen-tested slab as a control slab, without using CFRP, as well as three strengthened concrete slabs with CFRP in different ratios. The concrete slab was modeled using the 8-node solid (C3D8R) element; as for the reinforcement bars, they were depicted as 2-node linear beam elements (T3D2). An embedded region was employed to simulate the bond between concrete and reinforcements. Additionally, the bond between concrete and CFRP was modeled as a surface-to-surface contact, as specified in the Abaqus CAE
® manual. Steel-bearing plates (250 mm × 250 mm × 25 mm) were strategically placed to prevent local failure caused by crushing, utilizing the (C3D8R) 8-node solid element for modeling. Boundary conditions were selected to include a pin support at the first end for rotation and a roller support at the other end for rotation and horizontal movement. Additionally, at the center of the slab a concentrated vertical load was applied to simulate the experimental conditions. To ensure accuracy, a fine mesh was applied, resulting in a total element count for the slabs approximately equal to 21,600 elements. The impact of varying mesh sizes on both numerical precision and computational efficiency was analyzed, revealing that a mesh size of 20 yielded the highest level of accuracy.
For model validation, the slab was compared to a recent study with similar properties and analysis approaches. The validation process involved 3D finite element models, using Abaqus CAE® and the CDP model. Experimental results from four simply supported two-way slabs were used for validation. Concrete material properties were determined through standard cube tests for compressive behavior and split-cylinder tests for tensile behavior, revealing an average compressive strength of f c` = 30 MPa.
Both compressive crushing and tensile cracking are acknowledged as forms of failure mechanisms within the dataset, pertaining to concrete damage plasticity, derived from the tests of the mechanical properties on specimens. The integration of these traits within Abaqus CAE
® facilitates the determination of CDP parameters, ensuring an accurate representation of concrete’s desired damage behavior. Following sensitivity analyses, the CDP plasticity parameters are determined using the information provided in
Table 5. However, it is important to note that these CDP parameters stay consistent throughout the following optimization iterations. In
Figure 5, the numerical model is illustrated.
Figure 6 highlights the congruence in tension damage patterns showcasing a significant reduction in red damaged areas in the flexural portion of the slabs, with the use of CFRP; the Abaqus CAE
® calibrated numerical models exhibited strong agreement with experimental findings, affirming the model’s efficacy in predicting the performance of two-way RC slabs reinforced with CFRPs. The comparable results produced by both experimental and numerical methods are demonstrated in
Figure 7.
Furthermore,
Table 6 illustrates alternative findings, presenting the percentages of tension concrete damage (
%) observed in each case at different loads in specimen GC. The percentages are graphically depicted in
Table 6, with red denoting areas of high damage intensity and blue indicating undamaged regions. Damage intensity rises with increasing load, suggesting that additional stress is introduced into the concrete, steel, and CFRP materials. This highlights the importance of incorporating complementary strain energy to accurately depict plastic damage. Overall, the effective control of this role mitigates plastic damage and failure occurrences.