Finite Element Analysis of CFRP- Reinforced Concrete Beams Análisis de elementos finitos de Vigas de Hormigón Armado CFRP

This study concerns with flexural behavior of RC beams strengthened by carbon fiber reinforced polymer (CFRP) using finite element method (FEM). ABAQUS program has been used in this research. The load-deflection relationship, crack pattern, strain in the concrete at mid-span section of the beam and failure modes of all tested beams are studied. After validation of FEM model, parametric studies are presented to assess the effect of the compressive strength of concrete, thickness, and length of CFRP, and the presence of CFRP on stress in steel bars. From the current results, it can be obtained that the flexural capacity of RC beams strengthened with CFRP increased by 6.6% for beam strengthed by EBR and to 108.8% for beam strengthed by near surface mounted (NSM) compared to the reference beams. According to parametric studies, it is found that by increasing the compressive strength of concrete from 30 MPa to 70 MPa, the beam capacity increase by 25.6%, while increasing the length of CFRP from 600 mm to 900 mm leads to increase the beam capacity by 12.7%. Increasing thickness of CFRP sheet from 0.11 mm to 0.5 mm leads to an increase in the stiffness and the flexural capacity of the beam by 47.9%. Also, the results of this study approved that the strengthening of RC beams by CFRP laminates using the NSM technique is more efficient than externally bonded reinforcement (EBR) techniques and this is agreed with the experimental results. Finally, it can be concluded that the finite element model provides good accuracy compared to the experimental results and ACI-440 results . se puede obtener información que la capacidad de flexión de las vigas RC reforzadas con CFRP aumentó en un 6.6% para vigas reforzadas por EBR y a 108.8% para vigas reforzadas por montaje cerca de la superficie (NSM) en comparación con las vigas de referencia. Según estudios paramétricos, se encuentra que, al aumentar la resistencia a la compresión del concreto de 30 MPa a 70 MPa, la capacidad de la viga aumenta en un 25.6%, mientras que el aumento de la longitud de CFRP de 600 mm a 900 mm conduce a aumentar la capacidad de la viga en 12,7%. El aumento del grosor de la lámina de CFRP de 0,11 mm a 0,5 mm conduce a un aumento de la rigidez y la capacidad de flexión de la viga en un 47,9%. Además, los resultados de este estudio probaron que el fortalecimiento de las vigas RC por laminados CFRP utilizando la técnica NSM es más eficiente que las técnicas de refuerzo unido externamente (RUE) y esto está de acuerdo con los resultados experimentales, se puede concluir que el modelo de elementos finitos proporciona una gran precisión en comparación con los resultados experimentales y los resultados de ACI-440


Introduction
Reinforced concrete structures usually have to face modification and improvement of their performance throughout their service life. The most contributing factors are modification in their use, new design standards, deterioration because of corrosion in the steel caused by exposure to an aggressive environment and accident events like earthquakes .
The improvement of the performance of RC members throughout their service life can do it by strengthening or retrofitting and repairing of the member. Replacement of the structure might need determinate disadvantages like high prices of materials and labors, a stronger environmental impact and inconvenience because of interruption of the function of the structure. Therefore, it is preferring to repair or rehabilitation of the member. Using CFRP to strengthen RC beams is a common type of strengthening in the field of structural engineering (Obaidat, 2011); (Bodzak, 2019).
The use of CFRP in strengthening RC beams has become an important alternative method and more effective than other methods such as strengthening by steel plate. CFRP has good mechanical properties such as high resistance to the corrosion, very high strength to density ratio, faster installation and reduced maintenance costs (Obaidat et al., 2010); (El Gamal et al., 2019). (Barros et al., 2007); (El Gamal et al., 2019) presented that the strengthening of RC beams by CFRP using near-surface mounted (NSM) and externally bonded reinforcement (EBR) techniques have been increased the loadcarrying capacity of RC beams by up to 114%, approximately, the same conclusion has been adapted by (Attari et al., 2012); (Khalifa, 2016) showed that the strengthening of RC beams by CFRP using NSM method has many advantages compared to the EBR method, such as reducing the risk of debonding, and much better protection from the external sources of damage. He found that the beams strengthened with NSM laminate achieved a higher maximum load than those strengthened with EBR for a similar area of CFRP. (Hong et al., 2011) and (EI-Hacha and Rizkalla, 2004) found that the failure mode of RC beams strengthened by CFRP strips usually occurs due to CFRP strip rupture, accompanied by concrete compression failure. However, 65-75% of strips do not completely fracture. (De Lorenzis et al., 2000) studied the effect of groove size on the structural behavior of CFRP beams. An increasing groove size led to higher bond strength was observed. The maximum load increased by 8% and 24% as the groove size increased from 5/8 in. to 3/4 in. (Hassan and Rizkalla, 2004) found that CFRP strips are better than CFRP rods in the strengthening of RC beams with NSM techniques with the same axial stiffness because the strips give a higher bond strength. (Hassan and Rizkalla, 2003) presented an experimental study to strengthen RC beams with NSM and they showed that the minimum clear spacing between the strips groove must not be less than twice the bar diameter. Also, the minimum edge distance should not be less than four times the bar diameter. ( Lee et al., 2011) showed that the CFRP composite was used as external strengthened and as a cathodic protection (CP) system of steel in concrete elements. (Zaki and Rasheed, 2020) showed that the CFRP sheets used with both anchorage devices significantly increased the flexural capacity beyond that of unanchored and U-wrap anchored specimens. (Almusallam et al., 2018) showed that the ultimate capacity of the RC beams with opening not influenced by the opening in the pure flexural zone if the depth of the top chord was equal or greater than the depth of the concrete stress block. (Ghaedi et al., 2018) found that the CFRP with orthotropic or isotropic properties has no important influence on beam responses like stresses, displacements and damage response under applied loadings. Zhang et al., 2016)

Material properties
The same properties of steel reinforcement and concrete proposed by (Barros et al., 2007) have been used in this study. (Table 1) shows the properties of steel and concrete materials.
Two types of CFRP were used in this study: the first type is CFRP-sheets with 80 mm in width. The second type is CFRP-laminates with 1.4 x 9.6 mm 2 as a cross-sectional area. The properties of two types of CFRP are listed in the (

Finite element analysis
Nonlinear finite element analysis was performed to study the behavior of RC beams. ABAQUS program was used in this study.

Concrete
Plastic damage was performed to represent concrete. The main failure modes of the concrete are tensile cracking and compression failure as shown in (Figure 1) (Hibbit and Sorensen, 2000).
where: f t : tensile strength of concrete, f' c : compressive strength of concrete, E c : elastic modulus, ∈ t : strain in the tension zone, σ t : tensile stress in plastic range, ∈ cst : tensile strain in the plastic range, ∈ c1 : strain at the peak stress, σc: compressive strength of concrete in plastic range.

Steel reinforcement
The steel reinforcement was used as an elastic-plastic material according to CEN, Eurocode, design of steel structures-Part 1-1: General rules and rules for buildings (CEN, 2005). (Figure 2) shows the stress-strain relationship of steel in compression and tension behavior. The modulus of elasticity and the yield stress of steel bars were obtained from the experimental work conducted by (Barros et al, 2007). A Poisson's ratio of 0.3 was used in this study. A perfect bond between concrete and steel was assumed.

CFRP
Generally, two models were used to represent CFRP. Firstly, CFRP was assumed as a linear elastic isotropic until failure. While in another model, CFRP was assumed as a linear elastic orthotropic material. The first model has been used in this study. The CFRP properties as specified by the manufacturer. A Poisson's ratio of 0.3 was used for CFRP. The stress-strain of CFRP is shown in (Figure 3).

CFRP-concrete interface
Two models were utilized to model the interface between CFRP concrete surfaces. A perfect bond was assumed in the first model and a cohesive model was assumed in the second one. (Figure 4) shows the relationship between maximum shear stress (τ max ) and effective opening displacement (δ) in the interface zone between concrete and CFRP by using simple bilinear traction-separation law. The interface is modeled with a small thickness and the initial stiffness K 0 is defined"as shown in (Equation 10)   where: The value of fracture energy (G cr ) was ranged between 300 J/m 2 and 1500 J/m 2 as assumed by others (JCI, 2003) (JCI, 1998). The value of 900 J/m 2 was used in current research.
The damage was assumed to occur firstly when the nominal stress ratios reached the value one, this criterion can be represented by (Equation 13) (Hibbitt and Sorensen, 2000): °σ n = f t =4.4 MPa, and t°s = t°t = 1.5 MPa, used for this study.

Structural modeling using ABAQUS
Generally, each analytical model using the ABAQUS program will be processed in the following steps: 1. Build up the geometry of the structure under a set of elements. (part module, mesh module).
In this study, the part module consists of the concrete beam, CFRP sheet or laminate, and reinforcing steel. While the meshing process based on different factors, such as the geometric specifications. Generally, the meshing process is straightforward. The process consisted of two stages. In the first stage, seeds are assigned to the edge of the components and in the second stage, meshes are assigned to each part. The desired level of accuracy depends on the size of the mesh. The property module contains the input of the nonlinear stress-strain curves of material for each part.

Introduce material information (property module) 4. Assign material properties and section to the members (Property module) 5. Assemble parts to make the complete structure (assembly module, mesh module, and interaction module).
Models usually consist of the components that are assembled to form the final shape. These components are known as part instances. For example, the model in this study consisted of CFRP laminates or sheet concrete, steel rods, and epoxy layers. It is more convenient to model each of these elements separately and then assemble them. This method is considerably helpful for forming complex configurations.

Create steps and select analysis method (step module) 7. Introduce boundary conditions and load (load module)
In this study, simply supported beams subjected to four-point load have been modeled. (Figure 6).

Beam designation
Type of strengthening CFRP type

Load-deflection curve
The control beams S1-R, S2-R, and S3-R failed at loads of 36.9, 47.84 and 67.94 kN respectively. While, the strengthened beams S1-EXT-LAM, S2-EXT-LAM, S3-EXT-LAM, S1-NSM, S2-NSM, S3-NSM, S1-EXT-M, S2-EXT-M, and S3-EXT-M were failed at loads of 39. 34, 77.33, 80.17, 77.05, 86.12, 86.31, 43.72, 84.38 and 89.76 KN respectively, It should be noted that the load-carrying capacities of strengthed beams: S1-EXT-LAM, S2-EXT-LAM, S3-EXT-LAM, S1-NSM, S2-NSM, S3-NSM, S1-EXT-M, S2-EXT-M, and S3-EXT-M have been increased by 6.6%, 61.6%, 18%, 108.8, 79.96%, 26%, 18.4%, 76.3%, 32.1% respectively when compared with the load-carrying capacity of control beam(S1-R). The maximum gun in the strength was obtained when the RC beam strengthed by NSM, (Table 4) also, shows the percentage of increase for all beams. Also, the results showed that when increasing  the amount of CFRP by 50% the load-carrying capacity increased only by 3.6%, this is very clear when comparing the load-carrying capacity of the beam S3-EXT-LAM with the beam S2-EXT-LAM. This means that the increase at a certain limit of the amount of CFRP may be led to a slight increase in the maximum load. The load-midspan deflection curves for the control and strengthened beams are shown in (Figure 7). It is clear from this figure there is a good agreement between the experimental and FE results. (Table 4)

Modes of Failure
The control beams failed by yielding of main reinforcement. The flexural cracks formed followed a typical flexure crack. The first visible crack was observed in the flexural region. New cracks started to form when the load was increasing as shown in (Figure 8). Beams (S1-EXT-LAM, S2-EXT-LAM, and S3-EXT-LAM) failed by debonding of CFRP strip. The debonding was followed by the crushing of concrete. The debonding started from end-span due to the intermedi¬ate crack mechanism typically after yielding of primary steel reinforce¬ment when the flexural cracks widen as shown in (Figure 9). In beam S1-NSM, the failure occurred after yielding of steel reinforcement and CFRP strips rupture, this fail¬ure usually takes place in lightly reinforced and lightly strengthened sections while beams S2-NSM and S3-NSM failed by yielding of main reinforcement and then concrete cover separation has occurred as shown in (Figure 10). This failure starts at the CFRP curtailment because of stress concentration at the plate or sheet. Once cracking starts at an angle and then changes to a horizontal crack parallel to steel bar at the level of major steel because the stirrups reinforcement work to hold the inclined crack. The fracture of the CFRP sheet in two pieces has occurred in beam S1-EXT-M, the flexural strength of the beam dropped gradually while beams S2-EXT-M and S3-EXT-M failed by concrete cover separation as shown in (Figure 11). The failure mode of beam S2-EXT-M is different from the experimental failure mode. Numerically the beam (S2-EXT-M) failed by concrete cover separation while experimentally the failure was by rupture of CFRP. Also, the failure mode of S1-NSM is different from experimental failure. Numerically the beam failed by rupture of CFRP while experimentally the beam failed by yielding of the longitudinal reinforcement and then concrete cover separation has occurred.      (30 MPa,40 MPa,52.2 MPa,60 MPa,and 70 MPa) were considered to assess the effect of f' c on the behavior of CFRP-RC beams. (Figure 12) shows the effect of fc' on the behavior of EBR and NSM beams. It seems that the maximum load and stiffness increased with increases in the compressive strength while the maximum deflection decreased with increases in the compressive strength for concrete. (Figure 13) explains the relationship between compressive strength and maximum load. Mode of failure changed from rupture of CFRP stirp to delamination of the concrete cover in near-surface mount techniques at f' c =30 MPa,while,in other beams,no change in the mode of failure has occurred.

Effect of length of CFRP laminate
The efficiency of the strengthening RC beam by CFRP depends on the length of the CFRP laminate. Three different values of length of CFRP laminate (L=900, L=750, and L=600) mm have been used to study the effect of the length on the behavior of RC beams strengthened with CFRP. (Figure 14) shows that the stiffness of all beams at a load equal to 20 KN is almost the same, after that the strengthened beam with a length of CFRP equal to 900 mm is more stiffness than the beam with length equal to 600 mm. This may be attributed to the beam strengthened with length equal to 900 mm of CFRP laminate have a sufficient length outside the region of the maximum moment and it is more efficient in the critical zone. The debonding failure has been occurred in all beams due to high shear stress at the end of the CFRP laminate. However, the properties of the epoxy are important concerning the debonding failure. Also, from this figure can be seen that the maximum load of beam strengthened with a length of CFRP 900 mm higher than a load of beams with a length of 600 mm and 750 mm as shown in (Figure 15). Finally, it can be observed that the length of CFRP has an important effect on the stiffness as well as on the strength of RC beams.

Effect of thickness of CFRP sheet
Three beams (S1-EXT-M, S2-EXT-M, and S3-EXT-M) have been used as a case study to investigate the effect of CFRP sheet thickness on the behavior of CFRP-RC beams. Two values of thickness were used (0.5 and 0.111 mm). (Figure 16) shows that the increase of thickness of the CFRP sheet leads to an increase in the stiffness and max load of the beams due to increasing the cross-section of CFRP. Also, (Figure 17) shows the relationship between the max load and the thickness of the CFRP sheet.

The effect of the presence of CFRP on steel bar stresses
In this study, four beams (S2-EXT-M, S2-NSM, S2-EXT-LAM, and S2-R) have been used to investigate the effect of the presence of CFRP on steel bar stresses. (Figure 18) shows that the load at yield point of steel reinforcement in S2-R, 72.5,74.3 and 78.1 respectively. This indicated that the presence of CFRP has an effect on the applied load at the yielding of steel regardless of the type of strengthening. This means that the CFRP has a contribution to carrying the applied load.

The strain distribution through the depth of control and strengthened beams
The finite element model with an effective depth of 300 mm was developed to show the strain distribution through the depth of the beams. (Figure 19) shows the strain distribution of beams ( S2-R, S2-NSM, S2-EXT-LAM, and S2-EXT-M ), it is clear that the beams with CFRP sheet or laminate have more strain in compression and tension zone than the control beam (S2-R).

Appraisal of the ACI-440
The ultimate load of externally bonded reinforcement (EBR) beams can be calculated by  and (Equation 15) as follow: Where: