# Flexural Strengthening and Rehabilitation of Reinforced Concrete Beam Using BFRP Composites: Finite Element Approach

Authors: Asaad M. H. Kadhim; Hesham A. Numan; Mustafa Özakça
Journal: Advances in Civil Engineering
 (2019)

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## Abstract

Basalt fiber-reinforced polymer (BFRP) is adopted widely in recent years in many countries to rehabilitate or strengthen structural elements such as reinforced concrete (RC) beams because it is cheap and it has stellar mechanical performance. By activating the finite element (FE) simulation, the present research submits an extensive study on the strengthening and rehabilitation of damaged full-scale RC beams due to corrosions in the main reinforcement caused by BFRP sheets. Different parameters were taken into consideration such as corrosion grade, BFRP wrapping schemes, and the number of layers. The flexural performance of the models that build up as the control model and the damaged and the repaired methodologies by BFRP that are adopted and tested by others under the effects of four-point static loadings were also underwent examination. The full interaction at BFRP-concrete interface and the full bonding between sheets presupposed were investigated for all models. The numerical analysis findings were compared with the experimental measurements and found to be in good agreement. The current numerical analysis proved that the ultimate load rised by 14.8% in spite of 20% corrosion in the flexural steel rebar under eight layers of BFRP composite and bottom wrapping mode. In addition, under all strategies of wrapping schemes, the findings also indicated that the deflection ductility index noticeably reduced for RC beams with BFRP composites compared to the control beam. Finally, all the results of midspan deflection, crack patterns, and strain response of the composite system were analysed and discussed briefly.


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## Body

## 1. Introduction

Since the cost of rehabilitation for RC beams is roughly less than that of rebuilding them, the engineers therefore used different practical strategies to retrofit the existing RC beams with poor structural features. One of the most widespread strategies employed is fiber-reinforced polymer (FRP) family, for example, glass FRP (GFRP), carbon FRP (CFRP), and basalt FRP (BFRP). The FRP family has some advantages such as light weight, low cost, ease in fixing, superior thermomechanical properties, and high resistance to corrosion as compared to other families [1]. GFRP that is used in RC beams as confined materials can minimize the amount of cracks and also increase the flexural capacity of beams [2]. A developed three-dimensional (3D) FE model is used with the near-surface-mounted strategy of strengthened slabs and with the CFRP reinforcement to raise the performance of ductility which has been carried out by Rezazadeh et al. [3]. Garyfalia et al. [4] studied the strength capacity of reinforced concrete beams that corroded rebars by reviewing the analytical and experimental approaches that focused within this limit, then proposed a model to predict the flexural capacity of the beams at yield load, and verified the model by comparing the results with the available experimental data that showed closeness.Ma et al. [5] proposed a model for computing the stiffness of corroded beams after fatigue using flexural stiffness computation. This model mainly comprises the influences both of corrosion-induced cracking and fatigue. Elghazy et al. [6] performed 3D FE modelling of corrosion-damaged RC beams strengthened in flexure with externally bonded composites. They used three parameters in the investigation which are corrosion levels, type of composite, and the number of composite layers. Good agreement was achieved between the analytical and experimental outcomes; therefore, they confirmed that the FE models were able to emulate the nonlinear demeanor of the strengthened beams. Ye et al. [7] studied the shear performance of corroded reinforced concrete beams in which the numerical results indicated that FRP strengthening as the wrapping or U-shaped bonding of FRP sheets was effective to improve the shear strength of RC beams.The results of the study accomplished by Huang et al. [8] pointed out the influence of strengthening RC by BFRP is insignificant on precracks of concrete. The GFRP that is used in the RC beams as confined materials can minimize the amount of cracks and also increase the flexural capacity of beams [9]. Fiore et al. [10] pointed out that the load capacity of the structural member increased based on the mechanical properties of BFRP. According to the experimental work accomplished by Duic et al. [11] and Chen et al. [12], the effective method to increase the flexural strength of RC beams is by bounding the RC beams with external BFRP sheets. Garyfalia et al. [13] investigated the effectiveness of patch repair and FRP-bonded laminates to retrofit reinforced concrete beams with corrosion damage and concluded from experimental test data that the shear strengthening improved the bond performance.The main conclusions by Shen et al. [14] were the RC box beam repaired by BFRP worked to confine the development crack of concrete, besides the increased stiffness and the natural frequency of the repaired beam at the rate of 16.6% and 8.0% as compared with the beam without repair, respectively. Due to the mechanical properties of the BFRP, the experiential findings proved that the RC beam strengthened by BFRP behaved as linear up to failure based on the study conducted by Pawłowski and Szumigała [15].The mechanical properties of the BFRP indicated that they have durable, high-temperature resistance as introduced by Sim et al. [16]. Furthermore, at elevated temperature, Lu et al. [17] observed that the pultruded GFRP plates and glass fiber rovings and the basalt-fiber roving and BFRP plates showed much better mechanical tensile properties and temperature resistance.Under seismic loading, Jiang et al. [18] pointed out that the repaired RC columns by using BFRP restored the flexural capacity more than the original columns. Ibrahim et al. [19] performed the experimental test on concrete columns reinforced by steel basalt-fiber composite bars, and the test results showed that the failures of all four columns were flexural. Cascardi et al. [20] studied three full-reversible FRP-confinement innovative techniques of heritage masonry columns. Minafò et al. [21] explored the compressive behaviour of eccentrically loaded slender masonry columns confined by FRP and found that the effects of confinement vanished in case of length greater than 20. Rousakis [22] observed the reinforced concrete columns that were reinforced by nonbonded composite ropes subjected to seismic loadings that focused on the damage buildup and control at member level that may prevent the collapse.Under repeated loading, Attari et al. [23] studied the cost-effectiveness of twin stratum carbon-glass FRP fabric as a strengthening arrangement of RC structures. According to long-term cyclic loadings, Zhao et al. [24] observed that the presence of BFRP resisted more cyclic stresses without fatigue happening. Long-term tests on RC beams that strengthened by BFRP were conducted by Atutis et al. [25]; the results of this study pointed out that the BFRP has resistance to creep. Micelli et al. [26] studied the predamage status of concrete cylinders with 100 mm in diameter and 200 mm in length at the different preloading levels with the existence unidirectional FRP sheets.The failure modes of tested walls strengthened by BFRP sheets were different in a reference wall (without the presence of BFRP sheets) based on the experimental study submitted by Zhou et al. [27]. Daghash and Ozbulut [28] investigated the flexural behaviour of RC beams reinforced with near-surface-mounted BFRP bars. The outcomes of this study indicated that the existence of BFRP bars worked to restore the original beam strength capacity and gave a more ductile behaviour. Garyfalia et al. [29] investigated the behaviour and failure modes of the corroded rebars of reinforced concrete beams with experimental tests indicating that the presence of the FRP-laminated sheet enhanced the strength and behaviour of the corroded beams.Different BFRP ratios were used as the main reinforcement by Tomlinson and Fam [30] to investigate the effects of these ratios on the behaviour and strength capacity of the RC beams. The test results proved that the ultimate and yield loads were increased with the flexural reinforcement ratio. Under static and dynamic loadings, the test results of mechanical properties of BFRP showed that the dynamic strength of BFRP was around twice than that under static loading based on the investigation submitted by Chen et al. [31].After exposing the pullout specimens to accelerated conditioning environments and under direct tensile load, Altalmas et al. [32] observed that the GFRP bars showed lower adhesion and bond strengths to concrete than the BFRP bars. Dong et al. [33] investigated the bond durability of BFRP bars, and steel-fiber-reinforced composite bars under the effects of the ocean environment for a long-term period. In the damaged cylinder strengthened by BFRP, Ma et al. [34] observed that the initial elastic modulus and the ultimate compressive strength of the BFRP-confined concrete tended to minimize with an increase in the level of the predamage.Al-Saidy and Al-Jabri [35] noticed that the effect of replacing the damaged concrete cover of corroded beams by using CFRP worked to increase the yield and ultimate load capacities of damaged beams. Besides that, the U-shaped strips had a similar effect on the ultimate capacity and ductility as replacing the concrete cover because it was successful in preventing debonding failure. The test results of the study introduced by Choi et al. [36] confirmed that the strengthened T-beams prestressed by CFRP (near-surface-mounted technique) worked to enhance both the serviceability performance and the ultimate load-carrying capacity as compared with the unstrengthened beam. Minafò et al. [37] analysed the stress-strain behaviour as a literature review of masonry confined by FRP and compared the analysis results with available experimental data. Monaco et al. [38] analysed masonry panels strengthened by FRP using finite elements method and suggested simplified analytical formulations and compared the analysis results with experimental data from literatures.


## 2. Aim and Significance of Research

The main aim of this article is to assess and emulate influences of green substance (BFRP sheets) on a performance of corroded RC beams when subjected to four-point static loadings. To achieve this aim, a series of numerical analyzes were performed by using the commercial FE package ANSYS [39].Based on the literature survey of this study, besides a thorough deep seeking, to the best of the published researches that accomplished by the authors, really scarce studies simulated the influence of the hybrid action BFRP composite on the demeanour and trend of RC beams using FE approach. Therefore, it has become necessary to fill this hiatus of researches through activating FE simulation in ANSYS package [39] to solve this issue. Hence, eight full-scale beam models are submitted and simulated in this research. On the contrary, the present study gives us an opportunity to visualize about the actual structural performance of RC beams that are strengthened and rehabilitated by external BFRP layers without restoring to the experimental tests that always need more time and somewhat costly.


## 3. Finite Element Approach

In the current study, the numerical analyses are conducted based on the FE approach by using commercial ANSYS software [39] to simulate all arrangement patterns of BFRP in the RC beam models. Different elements are accurately selected from this program to emulate the behaviour of strengthening and rehabilitation of corroded RC beams by BFRP layers. The main elected elements are SOLID65, LINK180, SOLID185, and SHELL181. SOLID65 is activated to represent the concrete component because this element is capable of emulating both cracking in tension and crushing in compression; this element has eight nodes, and at each node, it has three degrees of freedom (DOFs). Due to the discussion of the uniaxial tension-compression situation in LINK180, this element is selected to emulate the demeanor, both main and stirrups reinforcements in all models. LINK180 is composed of two nodes with three DOF at each node. On the contrary, SOLID185 is applied to simulate the supports and the plates under the applied loads. SOLID185 has stress stiffening, plasticity, large deflection, and large strain susceptibilities, and it contained eight nodes with three DOFs. To emulate the BFRP layers, SHELL181 is activated because it is suitable for analysing thin to moderately thick shell components. SHELL181 is composed of four nodes, and at each node, it has six DOFs.The relationship connection between the reinforcements (main and stirrups) with concrete is the perfect interaction, besides the concrete nodes at the interaction with the same nodes of reinforcements. The connection between BFRP and concrete interface is under the full degree of interaction though embodiment of the coating epoxy layer is more than enough at the interface zone (rigid regions and kinematic constraints) so that no slip and strain slip occur between them and to complete the bonding achieved between BFRP layers. The concrete was modelled as a homogeneous and isotropic material. On the contrary, the assumed plane sections remain plane after deformation and that matched with consideration of the Bernoulli–Euler hypothesis. The stress-strain for reinforcements is elastic-full plastic, and for BFRP, it is of linear relationship. Full interactions were found between main and secondary reinforcements with surrounding concrete and no interactions between reinforcements and BFRP.The tolerance (convergence) of the solution found using the Newton–Raphson iterative method was 5%, while it was considered infinite with displacement control. The applied load was divided into substeps, and the model mesh was selected to reduce solution time and obtain an accurate solution, in which the maximum substeps is 150, substeps 100, and minimum substeps 1, and the number of steps for convergence occurred within this limits is shown in Table1. Loadings, boundary condition, RC beam configuration, distribution of BFRP layers, and mechanical properties of the components of the composite system were all adopted from the study of Duic et al. [11] to verify the validity of the outcomes of the current study.Table 1
Number of steps for each model.
Model
B1
B2
B3
B4
B5
B6
B7
B8
Number of steps for convergence
13
13
15
16
13
14
16
13


## 4. Mechanical Properties of Materials

According to the mechanical properties for each of the concrete, reinforcements with no hardening, and BFRP reported by Duic et al. [11], these properties were adopted in the current study as the required inputs in the ANSYS package [39]. Table 2 shows the mechanical properties of all components present in the technical sheet of BFRP from suppliers.Table 2
Mechanical properties of the composite system.
Properties
Concrete
Reinforcement
BFRP
Compressive strength (MPa)
37
430
—
Splitting tensile strength (MPa)
3.62
—
—
Modulus of rupture (MPa)
4.11
—
—
Modulus of elasticity (MPa)
28600
200000
20400
Poisson’s ratio
0.15
0.30
0.30
Tensile strength (MPa)
—
420
1684
Thickness (mm)
—
—
0.33


## 5. Configuration of Finite Element Models

The current model of beam was built with dimensions 275 × 500 × 3200 mm with simply supported boundary conditions as illustrated in Figure1. The main reinforcements at the bottom face were 5ϕ10 and 5ϕ15 mm, while at the top face, it was 2ϕ10 mm, and the stirrups were ϕ10 at 250 mm center to center. Each rebar of 10 mm in diameter has 100 mm2, while 15 mm has 200 mm2, as calculated by Duic et al. [11], the cross-sectional area so that the reinforcement ratios were 0.41 and 0.83%, respectively.Figure 1
Beam configuration and cross section [11].Two techniques were introduced for BFRP wrapping of RC beams that are midspan and bottom. The midspan technique contained A and B schemes, while the bottom technique composed of C and D schemes. The scheme A is composed of one layer with 100 mm width and 400 mm height of wrapping, while scheme B contained three or eight layers of BFRP composite with a full width of the cross section. On the contrary, scheme C contained three layers of BFRP wrapping with a height of 150 mm and length of 2600 mm, while scheme D contained eight layers of BFRP composite with a full width of cross section and length of 2600 mm. The locations and dimensions of all schemes are illustrated clearly in Figure2 in which the direction of the fibers is horizontal (i.e., along the beam axis). The direction of fibers in all scheme cases is along the beam axis except A that is parallel to the stirrups that is shown in Figure 2. Table 3 lists the models with descriptions in detail for each model. Twenty percent of the total cross-sectional area on the tension steel in the lower three bars was taken away to simulate the corrosion.Figure 2
Wrapping techniques and sections: (a) midspan scheme, (b) bottom scheme, and (c) sections and (d) directions of BFRP along the beam axis for A, B, C, and D [11].Table 3
Model descriptions.
Model mark
Main reinforcement ratio at tension zone (%)
Number of BFRP layers
Status
Schemes
B1
0.41
—
Control
—
B2
0.83
—
Control
—
B3
0.41
3
Strengthened
Midspan
B4
0.83
3
Strengthened
Midspan
B5∗
0.41
8
Strengthened
Midspan
B6∗
0.83
8
Strengthened
Bottom
B7
0.66
0
Loss of 20% of main reinforcement area
—
B8
0.66
8
Strengthened and loss of 20% of main reinforcement area
Bottom
∗Innovative model.As described in Table3, models B1 and B2 were employed as control beams; and the percentages of main reinforcement ratio of these models were 0.41 and 0.83%, respectively. Both the models B3 and B4 represented the RC beam strengthened using the midspan wrapping technique, and different percentages of ratios of main reinforcement were used for each model, while B5 and B6 represented the RC beams strengthened using the midspan and bottom wrapping techniques, respectively, and also different percentages of ratios of main reinforcement were employed for each model. On the contrary, both B7 and B8 models have the same percentage of main reinforcement ratio, that is, 0.66, but the B7 model is built with a loss of 20% of the main reinforcement area in the tension zone without any wrapping technique, while B8 is modelled with strengthening using the bottom wrapping technique and a lose of 20% of main reinforcement area in the tension zone. Figure 3 illustrates the 3D view of the RC beam, mesh density, elevation of the reinforcement, and 3D of the reinforcement’s configuration, while Figure 4 represents the models B3, B4, and B5 and the BFRP strips, and Figure 5 shows the models B6 and B8 and the BFRP strips. The closed and open shear cracks coefficients for concrete assumed as 0.7 and 0.2 respectively that were adopted to complete the requirements input for concrete in ANSYS.Figure 3
3D view of the (a) RC beam model and (b) mesh model and (c) 3D configuration of reinforcements.
(a)
(b)
(c)Figure 4
(a) Models B3, B4, and B5 using the midspan wrapping technique and (b) the BFRP strips.
(a)
(b)Figure 5
(a) Models B6 and B8 using the bottom wrapping technique and (b) the BFRP strips.
(a)
(b)


## 6. Comparison of Experimental and Numerical Results

Table4 and bar charts in Figures 6 and 7 illustrate the comparison of the yield and maximum deflections gathered from the experimental study [11] and the present numerical analysis (the deflections at yield load that is the load which caused the first crack at the yield loadings within 40% of the ultimate load and the maximum deflection that occurred at the ultimate applied load). Three principle statistical concepts were carried out to investigate the degree of agreement between the experimental and the numerical results. The first one was the arithmetic mean which is a result of the division the summation of observations by the number of observations. The second concept was the standard deviation, and it refers to the square root of the arithmetic mean of the squares of deviations of observations from their mean value. The third concept was the variance which is the square of standard deviation. If the first concept achieved unity, smaller values of the standard deviations and variance obtained would signify that the degree of agreement between the experimental and the numerical outcomes is excellent.Table 4
Comparison of experimental and current FE approach (the yield and maximum deflections).
Model mark
Deflection (mm) (experimental)
Loadings (experimental)-numerical (kN)
Deflection (mm) (numerical)
Yield
Ultimate
Yield
Ultimate
Yield
Ultimate
B1
6.80
61.80
(165)-165
(247)-247
6.63
61.80
B2
10.70
40.20
(265)-265
(397)-397
11.27
40.72
B3
7.50
40.10
(209)-215
(313)-313
7.18
40.00
B4
13.10
39.40
(324)-318
(487)-487
12.67
39.61
B5
NA
NA
NA -293
NA-375
6.26
22.54
B6
NA
NA
NA-335
NA-425
8.97
17.94
B7
10.50
50.00
(241)-251
(362)-362
10.67
50.40
B8
9.70
22.90
(301)- 321
(452)-452
9.66
22.67
NA: not applicable.Figure 6
The experimental and numerical yield deflection vs. model.Figure 7
The experimental and numerical maximum deflection vs. model.To validate yield and maximum deflection of findings that obtained from the current FE analysis, these findings were compared with those gathered from experimental measurements [11]. Figure 6 depicts the comparison between numerical and experimental deflections at the yield stage of loading, while Figure 7 illustrates the comparison of numerical and experimental deflections at the maximum stage of loading. From the outcomes in Figures 6 and 7, the computed arithmetic mean values of yield and maximum deflections were 0.9941 and 1.003, respectively. Moreover, the calculated standard deviations at the yield and maximum deflections were 0.0327 and 0.0178, respectively, while the calculated variance ranged from 0.001 to 0.0003 of yield and maximum deflections. From the results of statistical concepts, it can be said that the FE results matched well with the experimental ones. Hence, the present FE simulation proved the ability to effectively analyse the structural response of the RC beams under externally strengthening or rehabilitating them by BFRP sheets.


## 7. Results of Analysis and Discussions

### 7.1. Load-Deflection Performance

Figure8 shows the behaviour and trend of load-deflection curves at midspan for all proposed models. This figure represents the midspan deflections for each model due to the incremental loadings up to the ultimate load. In all models, the slope behaviour of the load-deflection started from zero up to the elastic limit (inflection point) is the same but has different values. These slopes represent the stiffness of the beam that becomes less in the case of lower strength loading capacity. In the case of less main reinforcement, the load strength capacity of the model became less as compared with that of the model having a higher main reinforcement ratio. The inflection point represents the load producing cracks and the behaviour of the model transformed from linear to nonlinear. Therefore, the change in load strength capacity and the slope became less because the stiffness of the beam became less up to failure. The experimental beams from the experimental test [11] are drawn separately and are compared with the models B1, B2, B3, B4, B7, and B8 in Figures 8(d) to 8(i), and they showed a closeness in behaviour and the results with some divergence. Table 5 lists the comparisons between the test results as deflection at yield and maximum for all models with that of the experimental test [11]. The mean values of deflections at yield and maximum are rounded to unity which means very close results between the experimental and numerical analysis. The standard deviations and variance were also very small which means that all points are rounded near the mean values. Figures 8(b) and 8(c) represent the comparisons between experimental and numerical analysis results that are drawn with line 45°. All results were near the line so that the numerical results can show closeness with experimental and conservatives.Figure 8
(a) Load-deflection performances at the midspan for all models. Deflection comparisons between experimental and numerical analysis at the (b) yield stage and (c) maximum stage. Load-deflection compression for models (d) B1, (e) B2, (f) B3, (g) B4, (h) B7, and (i) B8.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)Table 5
Statistical comparison of experimental and current FE approach (the yield and maximum deflections).
Model mark
Deflection (mm) (experimental)
Deflection (mm) (numerical)
Ratio (numerical/experimental)
Yield
Ultimate
Yield
Ultimate
Yield
Ultimate
B1
6.80
61.80
6.63
61.80
0.975
1.000
B2
10.70
40.20
11.27
40.72
1.053
1.013
B3
7.50
40.10
7.18
40.00
0.957
0.997
B4
13.10
39.40
12.67
39.61
0.967
1.005
B5
NA
NA
6.26
22.54
NA
NA
B6
NA
NA
8.97
17.94
NA
NA
B7
10.50
50.00
10.67
50.40
1.020
1.008
B8
9.70
22.90
9.66
22.67
0.996
0.989
Mean
0.994
1.002
Standard deviation
0.035
0.008
Variance
0.001
0.0001As shown in Figure8(a), the maximum percentage was different at the failure load occurred between B8 and B1 models and was 57.14%, while the maximum difference of displacements at the failure took place between B1 and B6 models and was 43.54 mm. The outcomes of Figure 8 proved that the stiffness of strengthening or rehabilitating models by BFRP layers was more than that of two control models. In this figure, the numerical result of deflection at the yield and maximum stage for all models was compared with that gathered from the experimental study. Additionally, the full behaviour of some models is drawn to compare with experimental results. In spite of losing 20% of flexural steel rebar in the B8 model, it is noticed that the tendency curve of the B6 model was similar to the tendency curve of the B8 model to a great extent. Moreover, the percentage difference between these models at the failure load did not exceed 3.39%. This is because of using the same wrapping technique and the number of BFRP layers on these models.The yield load and the load corresponding to the deflection are equal to the two criteria such as L/360 and L/180, where L is the center to center span of the simply supported beam so that the deflection criteria at midspan are equal to 8.33 and 16.66 mm. The second criterion adopted by some researchers was the yield load which is Pu/1.5, in which Pu is the maximum sustained load that adopted here. The 3D views of yield and maximum deflections for all beam models shown in Figures9–16 represent the full performance of the analysis results by ANSYS for whole models with all deflection values along the span of the beam models. Figures 9–16 represent the whole performance of the models under the effects of yield and at maximum load stage that has been converted to the curve shown in Figure 8 that reads the results at the node that gave maximum deflection (at the center of bottom face for each model).Figure 9
3D views of deflections in the B1 model at (a) the yield load stage and (b) the maximum load stage.
(a)
(b)Figure 10
3D views of deflections in the B2 model at (a) the yield load stage and (b) the maximum load stage.
(a)
(b)Figure 11
3D views of deflections in the B3 model at (a) the yield load stage and (b) the maximum load stage.
(a)
(b)Figure 12
3D views of deflections in the B4 model at (a) the yield load stage and (b) the maximum load stage.
(a)
(b)Figure 13
3D views of deflections in the B5 model at (a) the yield load stage and (b) the maximum load stage.
(a)
(b)Figure 14
3D views of deflections in the B6 model at (a) the yield load stage and (b) the maximum load stage.
(a)
(b)Figure 15
3D views of deflections in the B7 model at (a) the yield load stage and (b) the maximum load stage.
(a)
(b)Figure 16
3D views of deflections in the B8 model at (a) the yield load stage and (b) the maximum load stage.
(a)
(b)


### 7.2. Ductility

The deflection ductility index for each model is listed in Table6, and the ratio between the midspan deflections at ultimate load to the midspan deflection at yield load was calculated. From Table 6, it is clear that the maximum deflection ductility index was 9.15 and took place at control beam B1 model when the percentage main reinforcement ratio at the tension zone was 0.41. Table 6 lists the comparisons between numerical analysis and experimental data from test for ductility, and they showed closeness.Table 6
Ductility index.
Model mark
Deflection (mm) (numerical)
Ductility index (numerical)
Ductility index (experimental) [11]
Ratio of ductility index (numerical/experimental)
Yield
Ultimate
B1
6.63
61.80
9.32
9.10
1.02
B2
11.27
40.72
3.61
3.80
0.95
B3
7.18
40.00
5.57
5.30
1.05
B4
12.67
39.61
3.13
3.00
1.04
B5
6.26
22.54
3.61
NA
NA
B6
8.97
17.94
2.00
NA
NA
B7
10.67
50.40
4.72
4.80
0.98
B8
9.66
22.67
2.35
2.80
0.84
Mean
0.98
Standard deviation
0.078
Variance
0.006Another important note recorded on the results in Table6 is that the peak percentage of reduction in the deflection ductility index was determined when the model transferred from B1 to B6 and was about 78%. On the contrary, the minimal percentage of reduction in the deflection ductility index was registered between B2 and B4 models and was 15.63%. These reasonable results were because of the presence of BFRP sheets. The absolute differences of deflection values at the ultimate loading stage were somewhat huge compared to the absolute differences of deflections at the yield loading stage, as clearly depicted in Figure 8. The increase of BFRP sheets number in the RC beam was inversely affected by the value of the deflection ductility index as clearly depicted when compared to the values at B3 model with B5 model (the same percentage reinforcement ratio and wrapping strength technique). A similar behaviour of the deflection ductility index was also diagnosed by Rezazadeh et al. [3], Attari et al. [23], and Choi et al. [36], who used GFRP-CFRP hybrid fabrics, CFRP, and GFRP for the rehabilitation of samples. Duic et al. [11] and Attari et al. [23] also diagnosed that all strengthened specimens showed less ductility than did the control samples. From these considerations, it is possible to say that all the models implemented in the ANSYS program [39] of the present work are capable of effectively simulating the actual trend of such members under a different strategy of BFRP composites.


### 7.3. Crack Moment, Resisting Moment, and Ultimate Moment

For all proposed models, Table7 illustrates the values of load at ultimate load in [11], besides the applied load, yield load, crack moment, resisting moment (internal moments rely on the plastic analysis of the beam), and ultimate moment from the current numerical analysis. From this table, it is clear that the maximum value of crack moment was recorded on the B8 model and was 45.82 kN m. The maximum crack moment was decreased by about 5.70%, 5.43%, 5.15%, and 5.65% when the analysis transformed from model B8 to control beams, models B3 and B4, models B5 and B6, and model B7, respectively. This is because there are eight layers of BFRP in the model B8 that contributed to increasing the moment of inertia for the model; besides these layers worked to restrict the tension zone.Table 7
Load stages, crack moment, resisting moment, and ultimate moment.
Model mark
P ultimate [11] (kN)
P applied ANSYS (kN)
P yield ANSYS (kN)
Crack moment (kN·m)
Resisting moment (kN·m)
Ultimate moment (kN·m)
B1
247
247
165
43.21
90.24
123.50
B2
397
397
265
43.21
177.29
195.00
B3
313
313
215
43.33
114.71
156.50
B4
397
397
318
43.33
201.45
243.50
B5
380
380
375
43.46
157.32
175.00
B6
435
435
425
43.46
239.79
200.00
B7
362
362
251
43.23
143.54
181.00
B8
452
452
321
45.82
204.87
226.00Another finding that is worthy to be mentioned can be shown in Table6 which is the peak resisting moment registered on the B6 model and was 239.79 kN m, whereas the ultimate moment was recorded at the B4 model and was 243.50 kN m. These outcomes demonstrated that the flexural capacity of RC beams noticeably increased under the externally strengthened RC by BFRP sheets.


### 7.4. Strain Response

Figures17–19 show the load strain at the top fiber of concrete beam models longitudinally to check out if there is exceeding in the values on the concrete strain or not. The strain in the concrete of models B2, B4, B5, B6, and B8 increased because the amount of reinforcement in the tension zone is more. The maximum strain at the compression zone based on American Concrete Institute (ACI-318-2016) [40] is 0.003 at the top fiber of the concrete beam. All strain values in the case of control models were within the range. The slope of load strain of the composite systems was more than the control models because the modulus of elasticity for these systems was greater than the modulus of elasticity of concrete. Hence, these systems have more strength and less deflection compared to control models.Figure 17
Load strain in concrete performances for models B1, B2, B3, and B5.Figure 18
Load strain in concrete performances for models B1, B2, B4, and B6.Figure 19
Load strain in concrete performances for models B1, B2, B7, and B8.


### 7.5. Pattern of Crack and Mode of Failure

Figure20 shows the crack patterns and the failure modes at the end of the test for all models. From this figure, it can be clearly noticed that the number of cracks was larger at the control beam model (B1) than did those other models. This is because B1 has the lowest reinforcement ratio and is without any strengthening technique. As expected, the crack spacing and the number of cracks in the B3 model were largely similar to those of B7 model (strengthened by the lowest number of BFRP layer model and the corroded model). In general, two modes of failure were diagnosed for all proposed models during the loading stages, and they are flexural tension exhibiting firstly resulting from yielding of steel rebar and when approaching to the final stage of loading, the flexural compression failure appeared.Figure 20
(a) Crack patterns and the failure modes at the end of test for all models, (b) crack patterns for B1 from experimental test [11], and (c) cracks patterns for B2 from experimental test [11].
(a)
(b)
(c)


## 7.1. Load-Deflection Performance

Figure8 shows the behaviour and trend of load-deflection curves at midspan for all proposed models. This figure represents the midspan deflections for each model due to the incremental loadings up to the ultimate load. In all models, the slope behaviour of the load-deflection started from zero up to the elastic limit (inflection point) is the same but has different values. These slopes represent the stiffness of the beam that becomes less in the case of lower strength loading capacity. In the case of less main reinforcement, the load strength capacity of the model became less as compared with that of the model having a higher main reinforcement ratio. The inflection point represents the load producing cracks and the behaviour of the model transformed from linear to nonlinear. Therefore, the change in load strength capacity and the slope became less because the stiffness of the beam became less up to failure. The experimental beams from the experimental test [11] are drawn separately and are compared with the models B1, B2, B3, B4, B7, and B8 in Figures 8(d) to 8(i), and they showed a closeness in behaviour and the results with some divergence. Table 5 lists the comparisons between the test results as deflection at yield and maximum for all models with that of the experimental test [11]. The mean values of deflections at yield and maximum are rounded to unity which means very close results between the experimental and numerical analysis. The standard deviations and variance were also very small which means that all points are rounded near the mean values. Figures 8(b) and 8(c) represent the comparisons between experimental and numerical analysis results that are drawn with line 45°. All results were near the line so that the numerical results can show closeness with experimental and conservatives.Figure 8
(a) Load-deflection performances at the midspan for all models. Deflection comparisons between experimental and numerical analysis at the (b) yield stage and (c) maximum stage. Load-deflection compression for models (d) B1, (e) B2, (f) B3, (g) B4, (h) B7, and (i) B8.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)Table 5
Statistical comparison of experimental and current FE approach (the yield and maximum deflections).
Model mark
Deflection (mm) (experimental)
Deflection (mm) (numerical)
Ratio (numerical/experimental)
Yield
Ultimate
Yield
Ultimate
Yield
Ultimate
B1
6.80
61.80
6.63
61.80
0.975
1.000
B2
10.70
40.20
11.27
40.72
1.053
1.013
B3
7.50
40.10
7.18
40.00
0.957
0.997
B4
13.10
39.40
12.67
39.61
0.967
1.005
B5
NA
NA
6.26
22.54
NA
NA
B6
NA
NA
8.97
17.94
NA
NA
B7
10.50
50.00
10.67
50.40
1.020
1.008
B8
9.70
22.90
9.66
22.67
0.996
0.989
Mean
0.994
1.002
Standard deviation
0.035
0.008
Variance
0.001
0.0001As shown in Figure8(a), the maximum percentage was different at the failure load occurred between B8 and B1 models and was 57.14%, while the maximum difference of displacements at the failure took place between B1 and B6 models and was 43.54 mm. The outcomes of Figure 8 proved that the stiffness of strengthening or rehabilitating models by BFRP layers was more than that of two control models. In this figure, the numerical result of deflection at the yield and maximum stage for all models was compared with that gathered from the experimental study. Additionally, the full behaviour of some models is drawn to compare with experimental results. In spite of losing 20% of flexural steel rebar in the B8 model, it is noticed that the tendency curve of the B6 model was similar to the tendency curve of the B8 model to a great extent. Moreover, the percentage difference between these models at the failure load did not exceed 3.39%. This is because of using the same wrapping technique and the number of BFRP layers on these models.The yield load and the load corresponding to the deflection are equal to the two criteria such as L/360 and L/180, where L is the center to center span of the simply supported beam so that the deflection criteria at midspan are equal to 8.33 and 16.66 mm. The second criterion adopted by some researchers was the yield load which is Pu/1.5, in which Pu is the maximum sustained load that adopted here. The 3D views of yield and maximum deflections for all beam models shown in Figures9–16 represent the full performance of the analysis results by ANSYS for whole models with all deflection values along the span of the beam models. Figures 9–16 represent the whole performance of the models under the effects of yield and at maximum load stage that has been converted to the curve shown in Figure 8 that reads the results at the node that gave maximum deflection (at the center of bottom face for each model).Figure 9
3D views of deflections in the B1 model at (a) the yield load stage and (b) the maximum load stage.
(a)
(b)Figure 10
3D views of deflections in the B2 model at (a) the yield load stage and (b) the maximum load stage.
(a)
(b)Figure 11
3D views of deflections in the B3 model at (a) the yield load stage and (b) the maximum load stage.
(a)
(b)Figure 12
3D views of deflections in the B4 model at (a) the yield load stage and (b) the maximum load stage.
(a)
(b)Figure 13
3D views of deflections in the B5 model at (a) the yield load stage and (b) the maximum load stage.
(a)
(b)Figure 14
3D views of deflections in the B6 model at (a) the yield load stage and (b) the maximum load stage.
(a)
(b)Figure 15
3D views of deflections in the B7 model at (a) the yield load stage and (b) the maximum load stage.
(a)
(b)Figure 16
3D views of deflections in the B8 model at (a) the yield load stage and (b) the maximum load stage.
(a)
(b)


## 7.2. Ductility

The deflection ductility index for each model is listed in Table6, and the ratio between the midspan deflections at ultimate load to the midspan deflection at yield load was calculated. From Table 6, it is clear that the maximum deflection ductility index was 9.15 and took place at control beam B1 model when the percentage main reinforcement ratio at the tension zone was 0.41. Table 6 lists the comparisons between numerical analysis and experimental data from test for ductility, and they showed closeness.Table 6
Ductility index.
Model mark
Deflection (mm) (numerical)
Ductility index (numerical)
Ductility index (experimental) [11]
Ratio of ductility index (numerical/experimental)
Yield
Ultimate
B1
6.63
61.80
9.32
9.10
1.02
B2
11.27
40.72
3.61
3.80
0.95
B3
7.18
40.00
5.57
5.30
1.05
B4
12.67
39.61
3.13
3.00
1.04
B5
6.26
22.54
3.61
NA
NA
B6
8.97
17.94
2.00
NA
NA
B7
10.67
50.40
4.72
4.80
0.98
B8
9.66
22.67
2.35
2.80
0.84
Mean
0.98
Standard deviation
0.078
Variance
0.006Another important note recorded on the results in Table6 is that the peak percentage of reduction in the deflection ductility index was determined when the model transferred from B1 to B6 and was about 78%. On the contrary, the minimal percentage of reduction in the deflection ductility index was registered between B2 and B4 models and was 15.63%. These reasonable results were because of the presence of BFRP sheets. The absolute differences of deflection values at the ultimate loading stage were somewhat huge compared to the absolute differences of deflections at the yield loading stage, as clearly depicted in Figure 8. The increase of BFRP sheets number in the RC beam was inversely affected by the value of the deflection ductility index as clearly depicted when compared to the values at B3 model with B5 model (the same percentage reinforcement ratio and wrapping strength technique). A similar behaviour of the deflection ductility index was also diagnosed by Rezazadeh et al. [3], Attari et al. [23], and Choi et al. [36], who used GFRP-CFRP hybrid fabrics, CFRP, and GFRP for the rehabilitation of samples. Duic et al. [11] and Attari et al. [23] also diagnosed that all strengthened specimens showed less ductility than did the control samples. From these considerations, it is possible to say that all the models implemented in the ANSYS program [39] of the present work are capable of effectively simulating the actual trend of such members under a different strategy of BFRP composites.


## 7.3. Crack Moment, Resisting Moment, and Ultimate Moment

For all proposed models, Table7 illustrates the values of load at ultimate load in [11], besides the applied load, yield load, crack moment, resisting moment (internal moments rely on the plastic analysis of the beam), and ultimate moment from the current numerical analysis. From this table, it is clear that the maximum value of crack moment was recorded on the B8 model and was 45.82 kN m. The maximum crack moment was decreased by about 5.70%, 5.43%, 5.15%, and 5.65% when the analysis transformed from model B8 to control beams, models B3 and B4, models B5 and B6, and model B7, respectively. This is because there are eight layers of BFRP in the model B8 that contributed to increasing the moment of inertia for the model; besides these layers worked to restrict the tension zone.Table 7
Load stages, crack moment, resisting moment, and ultimate moment.
Model mark
P ultimate [11] (kN)
P applied ANSYS (kN)
P yield ANSYS (kN)
Crack moment (kN·m)
Resisting moment (kN·m)
Ultimate moment (kN·m)
B1
247
247
165
43.21
90.24
123.50
B2
397
397
265
43.21
177.29
195.00
B3
313
313
215
43.33
114.71
156.50
B4
397
397
318
43.33
201.45
243.50
B5
380
380
375
43.46
157.32
175.00
B6
435
435
425
43.46
239.79
200.00
B7
362
362
251
43.23
143.54
181.00
B8
452
452
321
45.82
204.87
226.00Another finding that is worthy to be mentioned can be shown in Table6 which is the peak resisting moment registered on the B6 model and was 239.79 kN m, whereas the ultimate moment was recorded at the B4 model and was 243.50 kN m. These outcomes demonstrated that the flexural capacity of RC beams noticeably increased under the externally strengthened RC by BFRP sheets.


## 7.4. Strain Response

Figures17–19 show the load strain at the top fiber of concrete beam models longitudinally to check out if there is exceeding in the values on the concrete strain or not. The strain in the concrete of models B2, B4, B5, B6, and B8 increased because the amount of reinforcement in the tension zone is more. The maximum strain at the compression zone based on American Concrete Institute (ACI-318-2016) [40] is 0.003 at the top fiber of the concrete beam. All strain values in the case of control models were within the range. The slope of load strain of the composite systems was more than the control models because the modulus of elasticity for these systems was greater than the modulus of elasticity of concrete. Hence, these systems have more strength and less deflection compared to control models.Figure 17
Load strain in concrete performances for models B1, B2, B3, and B5.Figure 18
Load strain in concrete performances for models B1, B2, B4, and B6.Figure 19
Load strain in concrete performances for models B1, B2, B7, and B8.


## 7.5. Pattern of Crack and Mode of Failure

Figure20 shows the crack patterns and the failure modes at the end of the test for all models. From this figure, it can be clearly noticed that the number of cracks was larger at the control beam model (B1) than did those other models. This is because B1 has the lowest reinforcement ratio and is without any strengthening technique. As expected, the crack spacing and the number of cracks in the B3 model were largely similar to those of B7 model (strengthened by the lowest number of BFRP layer model and the corroded model). In general, two modes of failure were diagnosed for all proposed models during the loading stages, and they are flexural tension exhibiting firstly resulting from yielding of steel rebar and when approaching to the final stage of loading, the flexural compression failure appeared.Figure 20
(a) Crack patterns and the failure modes at the end of test for all models, (b) crack patterns for B1 from experimental test [11], and (c) cracks patterns for B2 from experimental test [11].
(a)
(b)
(c)


## 8. Conclusions

BFRP is considered as a green material and has illustrated to be a promising material for developing the infrastructure sustainability in RC members. In this paper, eight 3D FEs of strengthening and rehabilitating full-scale RC beams using BFRP strips were built under the theory of full-composite action and entire bonding between these strips as layers and the full interaction with concrete. Based on the analysis results for the proposed models, the main conclusions can be drawn as follows:(i)
The arithmetic mean values of percentage of deflections at yield and ultimate comparisons between numerical and experimental test results ratios were rounded to unity, besides that the standard deviations and variances for these ratios were small enough. From these results of statistical basis, it can be deduced that the outcomes of the present analyses were very close and matched with the experimental ones.(ii)
A closer look at the findings of the load capacity for all models found that the ultimate load was at the model B8, where the ultimate load increased by 14.8% when transferred between the B2 and B8 models in spite of the corrosion of the main reinforcement at the tension zone which was 20% in B8 compared to that in B2. Furthermore, the difference in the percentage reinforcement ratio did not exceed 0.25 between the B8 and B1 models; but the B8 model achieved the increase in load capacity of 80% compared to the B1 model. On the contrary, under the strengthened beams with only three layers of BFRP, the yield and ultimate loading was increased by about 39% and 28%, respectively (between B1 and B3 models with the same percentage reinforcement ratio).(iii)
The increase in the load capacity did not exceed 14.47% when transferring from B5 to B6 model; in spite of the B5 model has almost half percentage reinforcement ratio with respect to B6 model (these models have the same BFRP layer’s number). Therefore, it is concluded that the midspan wrapping technique was more effective as compared to the bottom technique of wrapping as regards to the presented models. On the other hand, BFRP composites made the yield load becomes larger so that the stiffness of the composite model becomes higher. In addition, there was an enhancing in elastic deformation in presence of BFRP sheets.(iv)
Under the same percentage reinforcement ratio, an increasing number of BFRP layers (approached to eight layers) decreased deflection ductility index by about 46%, which took place between B2 and B6 models. The peak decreasing in the deflection ductility index was recorded between B1 and B6 models and was approximately 78%. However, based on prestigious studies that presented in the literature survey of this research, it was determined that the deflection ductility decreased in the RC beams with different strategies of strengthening them by FRP family. Hence, the current study gives us a better vision about the real structural response of such members.(v)
Presence of BFRP makes the slope of the load strain more than the control models do which indicate that the equivalent composite modulus of elasticity is more than the modulus of elasticity of concrete.(vi)
Generally, there were no remarkable differences in the crack patterns of all proposed models. Two modes of failure were experienced of all suggested models. These models firstly exhibited a flexural tension failure, while at the ultimate load, the final failure mode was a flexural compression. However, no debonding failure was determined in all composite models, and the result can apply the perfect interaction between concrete and BFRP interfaces. On the contrary, in general, the first crack delayed in appearing under different schemes of BFRP layers as compared that under to control beams. This means there is an enhancement in tensile resistance of composite models.(vii)
The numerical analysis results were compared with the experimental test results for the deflections at yield and ultimate stages, ductility index, ultimate load, and strain as listed in tables, and as shown in figures above, the statistical comparisons show closeness with little divergence in behaviour but remain the same at yield and ultimate stages.(viii)
Statistical analysis was adopted to check out the mean values ratio of numerical and experimental results for deflection at yield and ultimate stages, and the magnitude of ductility index indicates that the mean values were rounded to unity with small values of standard deviations and variances.(ix)
The presence of the BFRP to restrengthen corroded reinforced concrete beam models indicated that it can be adapted to increase the load capacity and restore the losses in capacity due to reinforcement corrosions.(x)
Finite elements simulations gave results that agree with the experimentally tested beams; therefore, it can be adopted to check out the remaining strength of beams and prevent any deficient or failure occurs.The current study provides the opportunity to develop insight for future studies such as simulating the effects of dynamic loading on the composite system, the orientation of fibers and other arrangements of wrapping by BFRP, and the degree of composite interaction, besides thermal effects (environmental and fire conditions) with existence of BFRP composites on RC beams. Moreover, the current strategy of simulating interaction and bonding of RC beams with BFRP composites can be used as a starting point for strengthening and rehabilitating the other composite systems by this kind of fiber, such as the RC columns and slab.



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*Source: 4981750-2019-03-04.xml*