Lateral strength and ductility of reinforced concrete columns strengthened with NSM FRP rebars and FRP jacket
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Abstract
Fiberreinforced polymer (FRP) wrapping of reinforced concrete (RC) columns is an effective way to improve their shear capacity and ductility and prevent buckling in their longitudinal reinforcements. Another strengthening method called the near surface mounted (NSM) reinforcement has been proven effective in improving the flexural strength of RC columns. In this research, the strengthening of RC columns with the combined use of NSM rebars and FRP jacket was studied using a finite element modeling approach. After validating the numerical models with the existing experimental data, a comprehensive parametric study was performed to determine the effect of axial load, implementing the FRP confinement around the base or over the entire height of the column, the number of plies of FRP jacket, the type of jacket fiber, the ratio of NSM reinforcement, and the compressive strength of the concrete on the behavior of the strengthened RC columns. The results show that the optimum number of plies of jacket for reaching a desirable level of ductility can be determined by setting the maximum compressive strain in the confined concrete, \(\varepsilon_{\text{ccu}}\), to 0.008. Increasing the ratio of NSM reinforcement from 0.16% of the total crosssectional area to 1% led to approximately 28% increase in the lateral strength and 50% decrease in the ductility factor.
Keywords
Reinforced concrete column Near surface mounted (NSM) Fiberreinforced polymer (FRP) jacket Flexural strengthening Seismic performanceIntroduction
Fiberreinforced polymer (FRP) wrapping of reinforced concrete (RC) columns can improve their ductility and energy dissipation capacity and prevent buckling in their longitudinal reinforcements. However, FRP wrapping is not much effective against eccentric loads and does not significantly contribute to the flexural strength of RC columns. Hence, alternative methods are needed to increase the flexural strength of these members (ElMaaddawy and ElDieb 2011; Kabir and Mansouri 2008; Yao and Wu 2016). The near surface mounted (NSM) reinforcement is a new method for flexural strengthening of RC columns. This method involves creating a series of grooves in the concrete cover and inserting reinforcing bars or strips inside so as to improve the flexural strength of the column. This method does not require any surface preparation and is faster to implement than other external reinforcement methods (Perrone et al. 2009; Sarafraz and Danesh 2012). The NSM method is also very effective in improving the seismic performance of RC columns against cyclic loads (ElMaaddawy and ElDieb 2011). The drawbacks of this method include the inability to improve the energy dissipation of RC columns and the fact that NSM rebars tend to buckle and get dislodged from concrete cover (Perrone et al. 2009).
To overcome the limitations of FRP wrapping and NSM techniques, researchers have investigated the viability of various combinations of these methods in strengthening the RC columns. Laboratory studies of Bournas and Triantafillou (2009) on the RC columns strengthened with NSM and FRP jacket showed that the combined use of these methods improves the ductility and flexural strength of columns. In another laboratory research, Perrone et al. (2009) studied the behavior of square crosssectional RC columns strengthened with NSM bars and CFRP jacket under constant axial load and cyclic lateral load. This study reported that the use of both methods together led to 67% increase in the bearing capacity of nondamaged columns and 46% increase in that of damaged columns.
ElMaaddawy and ElDieb (2011) investigated the effect of the NSM method and external confinement on the RC columns under axial load and biaxial bending. After developing an analytical model for predicting the capacity, they showed that the confinement system alone cannot effectively improve the flexural strength, but the combined use of NSM and confinement methods improves the loadbearing capacity and the lateral deformation capacity of columns, even under highly eccentric loads. Sarafraz and Danesh (2012) tested seven RC columns strengthened with NSM rebars and FRP jacket under constant compressive axial load and cyclic lateral load. This study found that the use of FRP jacket alone improves the axial strength, shear strength, and stiffness of the member, but not its flexural capacity. It was also reported that the use of NSM rebars increases the lateral loadbearing capacity and flexural strength of RC columns, and the greater the ratio of NSM reinforcement, the greater is the increase in flexural strength. They concluded that the simultaneous use of both methods is the best approach for improving the flexural capacity and ductility of RC columns, as FRP wrapping limits the instability of NSM rebars and prevents cracking in the grout when rebars are subjected to tensile loads. In a research conducted by Moodi et al. (2016), they tested five RC columns strengthened with the NSM method and CFRP confinement system and studied the effect of the size of concrete cover on the loadbearing and energy dissipation results. This study reported that as the size of the concrete cover increased from 20 to 40 mm, the loadbearing capacity and the energy dissipation capacity of NSMstrengthened specimens decreased by 10% and 18%, respectively; but in the specimens strengthened with both methods, these reductions amounted to 25% and 33%, respectively. Fahmy and Wu (2016) studied the strengthening of three RC columns with inadequate lapsplice length by the use of NSM basalt fiberreinforced polymer (BFRP) rebars and BFRP jacket applied to the plastic hinge formation region. They also considered the effect of the texture of the BFRP rebar (smooth/rough) on the results. According to the results of this study, the texture of the FRP rebar has a significant impact on the performance of the strengthened RC columns. They also reported that the specimen strengthened with rough FRP exhibited more ductile behavior with less residual drift. In a study conducted by Jiang et al. (2016), the tests carried out on four circular bridge columns, which had sustained earthquakeinduced damage and then strengthened with BFRP jacket and NSM BRBF rebars, showed that this method is indeed a quick and convenient way to improve the flexural strength, stiffness, and drift capacity of the columns damaged by earthquakes. They also reported that the confinement of the column with BFRP jacket limits the buckling of NSM rebars and increases the ductility of the column. Seifi et al. (2018) studied the behavior of RC columns strengthened with NSM rebars and CFRP jacket through a series of tests conducted on nine specimens. This study found that the specimens strengthened with NSM steel rebars had a higher flexural strength, ductility, and energy dissipation than those strengthened with NSM GFRP rebars. The laboratory tests and modeling conducted by Seifi et al. (2017) also showed that implementing this method of strengthening on vulnerable RC frames allows us to achieve a strong column–weak beam design and prevent the soft story mechanism.
Recent studies on the subject, although still few in numbers, have dominantly demonstrated the desirable performance of RC columns strengthened with the aforementioned methods. However, the actual use of these methods to strengthen RC columns requires further insight into the behavior of the resulting member and the effect of different parameters on its performance. In the present work, the behavior of RC columns strengthened with the aforementioned methods is studied through finite element modeling and analysis. After validating the numerical model with the existing experimental data, a series of parametric analyses are conducted to investigate the effect of axial load, confinement of the column base or the entire column, the number of plies of the FRP jacket, the type of jacket fiber, the ratio of NSM reinforcement, and the compressive strength of the concrete on the behavior of the strengthened RC column. In the course of each analysis, we also provide some suggestions for better strengthening of columns via this method.
Reference experimental data
Modeling of materials
Since specimens are supposed to be made of various materials, each capable of exhibiting distinctive plasticity and damage behavior under lateral load, the use of suitable constitutive models capable of emulating the actual behavior of materials is of particular importance for the accuracy of the results. The constitutive models used in our models are described below.
Concrete
In these relationships, \(\sigma_{\text{nom}}\) and \(\varepsilon_{\text{nom}}\) denote the nominal stress and strain, and \(\sigma\) and \(\varepsilon\) are the true stress and strain values, respectively.
The concrete damaged plasticity model combines the nonassociated multihardening plasticity with scalar (isotropic) damaged elasticity. This model assumes two mechanisms of failure in concrete: tensile cracking and compressive crushing.
In the above equations, \(\tilde{\varepsilon }_{\text{t}}^{\text{ck}}\) is the cracking strain displayed in Fig. 3a and \(\tilde{\varepsilon }_{\text{c}}^{\text{in}}\) is the inelastic strain displayed in Fig. 3b.
Steel
FRP jacket, NSM rebars, and adhesive
Mechanical properties of the composites used in the jacket (Hahn and Tsai 1980)
CFRP  GFRP  

Stress analysis  Failure analysis  Stress analysis  Failure analysis 
\(E_{1} = 181\,{\text{GPa}}\) \(E_{2} = 10.3 \,{\text{GPa}}\) \(\nu_{12} = 0.28\) \(G_{12} = 7.17\,{\text{GPa}}\) \(G_{13} = 7.17\,{\text{GPa}}\) \(G_{23} = 6.30\,{\text{GPa}}\)  \(X_{\text{T}} = 1500\,{\text{MPa}}\) \(X_{\text{C}} = 1500\,{\text{MPa}}\) \(Y_{\text{T}} = 40 \,{\text{MPa}}\) \(Y_{\text{C}} = 246\,{\text{MPa}}\) \(S = 68\,{\text{MPa}}\)  \(E_{1} = 38.6\,{\text{GPa}}\) \(E_{2} = 8.27\,{\text{GPa}}\) \(\nu_{12} = 0.26\) \(G_{12} = 4.14\,{\text{GPa}}\) \(G_{13} = 4.14 \,{\text{GPa}}\) \(G_{23} = 3.10\,{\text{GPa}}\)  \(X_{\text{T}} = 1062\,{\text{MPa}}\) \(X_{\text{C}} = 610\,{\text{MPa}}\) \(Y_{\text{T}} = 31\,{\text{MPa}}\) \(Y_{\text{C}} = 118\,{\text{MPa}}\) \(S = 72\,{\text{MPa}}\) 
Numerical modeling and validation
In emulation of the reference experimental data, a constant axial force of 200 KN was applied to the top of the column, and lateral cyclic displacement was applied to the upper block of the column using the displacementcontrolled approach. The amplitudes of imposed displacements were multiples of 5 mm. Similar to the reference laboratory experiment, the axial load was applied before the lateral displacement, and the bottom block was assumed to be clamped and given no degree of freedom.
The interactions between adhesive and concrete and between concrete and jacket were modeled using the tie constraint. With this constraint, the members remain completely attached together and stay tied and act continuously throughout the analysis. The boundary of concrete with steel reinforcement and with FRP rebars was modeled using the embedded region constraint. Using this constraint, a region of the model will be embedded in another region in a way that they will both have the same degrees of freedom.
Parametric analysis
General specifications of the numerical models
Group no.  Model no.  \(f_{\text{c}}\) (Mpa)  Axial load (kN)  Number of FRP plies  NSM bar diameter (mm)  Jacket fiber  Groove width (mm)  Groove depth (mm)  Jacketing region 

G1  1  24.1  100  2  10  CFRP  18  18  Entire height 
2^{a}  24.1  200  2  10  CFRP  18  18  Entire height  
3  24.1  300  2  10  CFRP  18  18  Entire height  
4  24.1  400  2  10  CFRP  18  18  Entire height  
5  24.1  500  2  10  CFRP  18  18  Entire height  
G2  6  24.1  100  0  10  CFRP  18  18  No jacket 
7^{a}  24.1  200  0  10  CFRP  18  18  No jacket  
8  24.1  300  0  10  CFRP  18  18  No jacket  
9  24.1  400  0  10  CFRP  18  18  No jacket  
10  24.1  500  0  10  CFRP  18  18  No jacket  
G3  11  24.1  100  2  10  CFRP  18  18  Column base 
12  24.1  200  2  10  CFRP  18  18  Column base  
13  24.1  300  2  10  CFRP  18  18  Column base  
14  24.1  400  2  10  CFRP  18  18  Column base  
15  24.1  500  2  10  CFRP  18  18  Column base  
G4  7^{a}  24.1  200  0  10  CFRP  18  18  No jacket 
16  24.1  200  1  10  CFRP  18  18  Entire height  
2^{a}  24.1  200  2  10  CFRP  18  18  Entire height  
17  24.1  200  3  10  CFRP  18  18  Entire height  
18  24.1  200  4  10  CFRP  18  18  Entire height  
19  24.1  200  5  10  CFRP  18  18  Entire height  
G5  20  24.1  200  2  6  CFRP  12  12  Entire height 
2^{a}  24.1  200  2  10  CFRP  18  18  Entire height  
21  24.1  200  2  13  CFRP  24  24  Entire height  
22  24.1  200  2  16  CFRP  30  30  Entire height  
G6  2^{a}  24.1  200  2  10  CFRP  18  18  Entire height 
23  24.1  200  2  10  GFRP  18  18  Entire height  
G7  24  20.0  200  2  10  CFRP  18  18  Entire height 
25  30.0  200  2  10  CFRP  18  18  Entire height  
26  40.0  200  2  10  CFRP  18  18  Entire height  
27  50.0  200  2  10  CFRP  18  18  Entire height 
In groups G1, G2, and G3 of Table 2, the effect of axial load on the columns strengthened with different systems was studied. The models of group G1 were strengthened with NSM rebars and FRP jacket applied to the entire height, the models of group G2 were strengthened only with NSM rebars, and the models of group G3 were strengthened with NSM bars and FRP jacket applied to the lower section of the column up to a height of 40 cm (40% of the overall height). Since numerical results and experimental observations both showed that flexural hinges form at the lower section of the column, in G3 models, the jacket was applied only to this section. In the numerical model, yielding of longitudinal reinforcements was observed in a length of 40 cm at the bottom of the column; Thus, this length is considered as the length of the plastic hinge and is selected for FRP jacketing in the models of group G3. Note that since only the half of the column height (from the base to the moment inflection point) was numerically modeled, the length of the FRP jacket in G3 models is equivalent to 20% of the free height of the prototype column. The models of all three groups were subjected to axial loads of between 100 and 500 kN. Since based on Eq. (13) the pure axial loadbearing capacity of the nonstrengthened column, \(P_{0}\), was approximately 1000 kN, the axial loads applied varied between 10 and 50% of this value.
In the models of group G4, the number of plies of the FRP jacket was changed to investigate the effect of this parameter on the column behavior. The purpose of this investigation was to determine the jacket thickness that results in a desirable degree of ductility in the column. In the models of group G5, we changed the diameter of the NSM rebars to examine the effect of the ratio of NSM reinforcement on the column performance. In these models, the groove size was adjusted such that the ratio of rebar diameter to the groove size would remain almost constant. In the models of group G6, we considered two different materials for the jacket, and in the models of group G7, the compressive strength of the concrete was changed in the range of 20–50 MPa. In all models, every parameter other than the one studied was fixed and set equal to the corresponding values in the experimental data.
Axial load
The axial load is among the most important parameters that influence the behavior of RC columns. An RC column subjected to a combination of axial load and bending moment may experience tensile or compressive failure depending on the magnitude of the applied axial load. Therefore, the effect of this parameter on the behavior of RC columns strengthened with the studied methods requires close examination. The axial load was changed between 10 and 50% of the axial loadbearing capacity of the nonstrengthened column. Figure 8a shows the hysteresis envelope curves of these models under a lateral load.
Figure 9b shows the ductility of the models for different axial load values. As can be seen, the highest ductility values belong to the columns with the FRP jacket applied to the entire height, and the lowest ductility values belong to the columns that have the NSM rebars but lack the jacket. For the latter group of columns, there is a marked decrease in the ductility factor with the increase in the axial load. The same observation can also be made in Fig. 8a for these columns. With the increase in lateral displacement, the columns that are subjected to high axial loads exhibit a significant strength reduction. Increasing the axial load raises the axial loadinduced strain in the concrete, and adding the bending momentinduced strain to this value causes the unconfined concrete to reach the ultimate strain at lower lateral displacement; thus, the unconfined columns with relatively high axial loads experience brittle failure. In contrast, all columns that had a jacket, for the entire height or only in the bottom section, exhibited a relatively ductile behavior. According to these results, it can be concluded that the sole use of NSM rebars is not a good strengthening solution, especially in the cases with high axial loads, and it is better to also add an FRP jacket to improve the column’s ductility. It should also be noted that although fully jacketed models had better ductility than those jacketed at the lower section, the latter specimens were able to maintain an acceptable degree of ductility under increasing axial loads. Therefore, since jacketing the lower section of the column is far more economical and easier than confining its entire height, it can be recommended as the preferable choice for columns under both axial and lateral loads for providing an acceptable level of safely at a lower cost.
Number of plies of the FRP jacket
According to the results discussed in the previous section, the addition of FRP jacket improves the ductility and performance of the column. But the optimum number of plies of the jacket, i.e., the number of plies that can provide desirable ductility improvement at a reasonable cost, needs to be determined. Thus, in G4 models, we changed the number of plies of the jacket from zero (no jacket) to five to investigate the effect of this parameter on the results. Figure 8b shows the hysteresis envelope curves of these models under the lateral load.
In the above equation, \(\varepsilon_{\text{c}}^{'}\) is the maximum unconfined strain corresponding to \(f_{\text{c}}^{'}\) and can be considered equal to 0.002.
Compressive strength and ultimate strain of the concrete confined with different numbers of plies of FRP jacket
Model no.  \(n\)  \(\frac{{A_{\text{e}} }}{{A_{\text{c}} }}\)  \(\varepsilon_{\text{fe}}\)  \(f_{\text{l}} \left({\text{MPa}} \right)\)  \(f_{\text{cc}}^{'} \left({\text{MPa}} \right)\)  \(\varepsilon_{\text{ccu}}\) 

16  1  0.567  0.009  2.05  24.63  0.0056 
2  2  0.567  0.009  4.09  28.27  0.0082 
17  3  0.567  0.009  6.14  31.05  0.0109 
18  4  0.567  0.009  8.18  31.79  0.0135 
19  5  0.567  0.009  10.23  32.30  0.0161 
In general, the purpose of the jacket is to improve the ductility of the column. As shown in Fig. 11b, jacketing the column and increasing the number of plies of jacket to two will improve the ductility, but further increase in the number of plies of jacket results in no significant increase in the ductility of the column. In other words, two layers of the jacket are as much effective in providing confinement as are more layers. In practice, using more layers just reduces the stress in the jacket, while the total confining force may remain the same; thus, it does not provide better confinement for the column. According to Table 3, in the model with two layers of jacket, the maximum compressive strain in the confined concrete (\(\varepsilon_{\text{ccu}}\)) is about 0.008, and in the models with a greater number of layers, \(\varepsilon_{\text{ccu}}\) is larger than this value. Concrete with \(\varepsilon_{\text{ccu}}\) values of more than 0.008 is expected to undergo excessive cracking and damage and lose its integrity. However, although Eq. (21) gives a \(\varepsilon_{\text{ccu}}\) value of greater than 0.008, the ductility has remained unchanged. Hence, it can be concluded that to achieve a desirable level of ductility with the least number of plies of jacket, we must determine the number of plies that results in \(\varepsilon_{\text{ccu}}\) of Eq. (21) becoming equal to 0.008.
Ratio of NSM reinforcement
In the models of group G5, we changed the diameter of the NSM rebars embedded on both sides of the confined RC column to investigate the effect of the ratio of NSM reinforcement on the column performance. It should be noted that the groove size was also adjusted such that the ratio of rebar diameter to the groove size would remain almost constant, but other specifications of the models remained as in the corresponding laboratory data. The diameters to be considered for the FRP reinforcement were chosen according to the specifications of commercially available products. As shown in Table 2, the diameters considered for the NSM rebars were 6.4, 10, 13 and 16 mm, which corresponded to NSM reinforcement being 0.16, 0.39, 0.66, and 1.00% of the total crosssectional area of the column, respectively. Figure 8c shows the hysteresis envelope curves of these models under the lateral load.
Changing the ratio of NSM reinforcement also changes the ductility factor. As shown in Fig. 12b, increasing the NSM reinforcement ratio resulted in lower ductility factors. In the experiments carried out by Sarafraz and Danesh (2012) too, increasing the ratio of NSM reinforcement led to reduced ductility. Also, in a study conducted by Ding et al. (2013) on eight RC columns strengthened with BFRP NSM rebars combined with BFRP jacket, as the diameter of rebars decreased, ductility and energy dissipation increased. According to the aforementioned results, the choice of diameter of NSM reinforcement is one of the most important decisions in regard to this method.
It should be noted that based on the results of the previous sections, applying FRP jackets can improve the ductility of the member. Thus, decreasing the ductility factor by using NSM reinforcement can be compensated by using FRP jackets. This is one of the advantages of the combined use of NSM FRP rebars and FRP jackets for seismic retrofitting of columns.
Type of jacket fiber
To investigate the effect of the type of jacket fiber on the behavior of RC columns, we used the G6 models developed with two types of fiber, CFRP and GFRP, to make a comparison in this respect. The mechanical properties considered for the GFRP fibers are presented in Table 1. Figure 8d shows the hysteresis envelope curves of the columns with these types of FRP jacket.
Compressive strength of concrete
In the models of group G7, the compressive strength of concrete was changed from 20 to 50 MPa to investigate the resulting effects on the performance of the RC column under axial and lateral loads. Other specifications of the models remained unchanged and were set equal to the corresponding values in the laboratory experiments. The hysteresis envelope curves of these models under the lateral load are plotted in Fig. 8e.
These results also show that as the compressive strength of the concrete increased, the damage in the member decreased. This is natural because of the ability of highstrength concrete to endure greater compressive stresses. In all cases, the damage initiated at the bottom of the column and then spread upward as the displacement increased. Also, assuming higher compressive strength values for the concrete resulted in the production of greater stresses in the FRP jacket. This is because as the compressive strength of the concrete increases, the model exhibits a greater lateral strength, which results in greater bending moment and thus greater bending momentinduced compressive stress in the model, which, given the tendency of the concrete to expand under compressive stresses, leads to the formation of greater tensile stress in the jacket. Increasing the compressive strength of concrete also increased the level of stress in the adhesive and NSM rebars.
Conclusion

In all three studied strengthening methods, the lateral strength had an inverse relationship with the axial load. As we increased the axial load from 10 to 50% of the axial load capacity of the nonstrengthened column, the lateral strengths of the columns strengthened with NSM rebars and complete jacket, the columns strengthened with NSM rebars alone, and the columns strengthened with NSM rebars and jacket applied to the lower section of the column decreased by 14.5%, 11.5%, and 8%, respectively.

In the columns strengthened only with NSM rebars, increasing the axial load resulted in a marked decrease in ductility; but all columns that had a jacket, for the entire height or only in the bottom section, exhibited a relatively ductile behavior. Hence, it can be concluded that the use of NSM rebars alone is not a good strengthening approach, especially under high axial loads, and it is recommended to also apply an FRP jacket to improve the ductility of the column.

The column strengthened with NSM rebars and jacket applied at the base of the column exhibited acceptable seismic behavior. The maximum lateral strength of these specimens was very close to that of the columns strengthened with NSM rebars and jacket applied to the entire column. Compared to the unconfined columns, the jacketed columns also showed a smaller ductility reduction with the increase in the axial load. Thus, with the economic aspect of discussion taken into consideration, it is recommended to implement the jacket at two ends of the column instead of the entire column.

Increasing the number of plies of jacket increased the ductility of the column, but after exceeding a certain number of layers, the impact on the ductility became negligible. In other words, there is an optimum number of layers, by which a good degree of concrete confinement can be provided at reasonable cost. In this case, using more layers will not be as much effective because of the expansion of damage and cracking in the concrete. The optimum number of layers is the one that results in the maximum compressive strain in the confined concrete (\(\varepsilon_{\text{ccu}} )\) becoming equal to 0.008.

Increasing the ratio of NSM reinforcement from 0.16% of the total crosssectional area to 1% led to approximately 28% increase in the lateral strength and 50% decrease in the ductility factor.

CFRP and GFRP jacketed models had very similar hysteresis characteristics. Thus, considering the lower price of glass fibers than carbon fibers, it is more reasonable to use the jacket made of glass fibers to increase the ductility of the column.

Increasing the compressive strength of the concrete from 20 to 50 MPa resulted in approximately 37% increase in the lateral strength and 50% decrease in the ductility of the model. The results also showed that when using this strengthening approach, a suitable ductility can be achieved with concrete compressive strength values of less than 30 MPa.
Notes
Compliance with ethical standards
Conflict of interest
The authors declare that they have no conflict of interest.
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