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Numerical investigation on the influences of different factors on the seismic performance of TRC-strengthened RC columns
Journal of Building Engineering 30 (2020) 101245
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Journal of Building Engineering
Numerical investigation on the influences of different factors on the seismic performance of TRC-strengthened RC columns Yao Li a, b, Shiping Yin a, b, *, Junyan Dai b, Ming Liu b a b
State Key Laboratory for Geomechanics & Deep Underground Engineering, China University of Mining and Technology, Xuzhou, 221116, China Jiangsu Key Laboratory of Environmental Impact and Structural Safety in Engineering, China University of Mining and Technology, Xuzhou, 221116, China
ARTICLE INFO
ABSTRACT
Keywords: Textile-reinforced concrete (TRC) Reinforced concrete (RC) column Axial compression ratio Shear span ratio Concrete strength grade Seismic performance
To investigate the influences of different factors on the seismic performance of textile-reinforced concrete (TRC)-strengthened reinforced concrete (RC) columns, a numerical model for TRC-strengthened RC columns was established with the finite element software ABAQUS, and the numerical simulation results were analyzed. The numerical results of the TRC-strengthened RC columns were in good agreement with the experimental results. The TRC could effectively restrain the core concrete of the strengthened columns, limit the development of cracks, increase the peak load of the specimens, delay the stiffness degradation of the specimens after yielding, and improve the seismic deformation capacity of the strengthened columns. The bearing capacity and stiffness degradation rate of the strengthened columns increased with increasing axial compression ratio, but the displacement ductility coefficient and energy dissipation capacity exhibited the opposite trend. As the shear span ratio increased, the ductility, deformation capacity and cumulative energy dissipation capacity of the strengthened columns increased, but the bearing capacity of the columns decreased. The TRC could delay the stiffness degradation of the strengthened columns with a large axial compression ratio and a small shear span. The bearing capacity of the strengthened column increased as the strength grade of the core concrete increased. When the strength grade of the core concrete of the strengthened column reached C40, the displacement ductility coefficient of the strengthened column was the largest. However, when the strength grade of the concrete continued to increase, the displacement ductility coefficient and the cumulative energy dissipation capacity of the strengthened column either did not change significantly or even slightly decreased.
1. Introduction Reinforced concrete (RC) is widely used in the field of structural engineering. However, due to the influence of the design, construction defects and external environment, as the service life increases, the safety, reliability and durability of an RC structure will be weakened to a certain extent, thereby affecting the normal use of the structure. In RC buildings, columns are very important load-bearing components. If columns are damaged in an earthquake, whole buildings may collapse, which would cause casualties and economic losses. Therefore, it is of great theoretical importance and engineering value to strengthen existing RC columns and investigate the seismic performance of strengthened columns.
The traditional reinforcement methods for RC columns mainly include increasing the section, the external steel clad method, and the external prestressing method. However, these methods have shortcomings, such as increasing the structural weight, being susceptible to rusting and changing the structural appearance. In recent years, with the development of composite materials, fiber-reinforced polymers (FRPs) have been used not only for reinforcement and restoration of existing structures but also for the development of new structures. Several scholars have also conducted relevant numerical investigations [1–4]. Parvin and Granata [1] used ANSYS—a finite element analysis program-to study the application of FRP materials in strengthening beam-column joints. Lakshmi et al. [2] studied three types of beam-column joints through finite element simulation to explore a reasonable finite element numerical model for beam-column
* Corresponding author. State Key Laboratory for Geomechanics & Deep Underground Engineering, China University of Mining and Technology, Xuzhou, 221116, China. E-mail address: [email protected] (S. Yin).
https://doi.org/10.1016/j.jobe.2020.101245 Received 6 August 2019; Received in revised form 20 December 2019; Accepted 1 February 2020 Available online 4 February 2020 2352-7102/© 2020 Elsevier Ltd. All rights reserved.
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joints. Mahini et al. [3] proposed a model for strengthening beamcolumn joints with FRP plates, in which the model uses nonlinear connection elements to evaluate the seismic performance of the joints. Niroomandi et al. [4] modified the joint stiffness of FRP-strengthened specimens through nonlinear finite element analysis and introduced this modified joint stiffness into the overall frame for seismic evaluation. Besides, Sheikh et al. [5,6] found that with the axial compression ratio increases, the efficiency of improving the seismic performance of FRP-constrained columns decreases, and the constraint efficiency was higher in cylinders than that in square ones. Feng et al. [7] also studied the influence of concrete strength. Their result showed that with increasing of concrete strength, the failure mode could be altered. Although FRP sheets are widely used as an effective reinforcement method, FRP sheets typically use epoxy resin as a binder; thus, FRP sheets have poor compatibility with concrete, and their vapor permeability is not suitable for use in wet environments [8]. Moreover, it is difficult to examine and assess the internal status after FRP sheets strengthening. Therefore, scholars have introduced the concept of reinforcement fibers that combine textile fibers with inorganic substrates (such as cement-based mortar) [9]. Based on this concept, many scholars have proposed a variety of reinforcement systems with little difference, such as textile-reinforced concrete (TRC) [10,11], textile-reinforced mortar (TRM) [9,12] basalt-reinforced mortar (BRM) [13] and fabric-reinforced cementitious matrix (FRCM) [14]. TRC has a substrate suitable for wet environments, TRC does not contain moisture that would cause freeze-thaw cycling, and TRC does not possess other factors that may cause damage [11,15]. In addition, cracks that form in the matrix usually appear on the reinforcement layer, which is convenient for visual inspection [15]. As an alternative to FRP reinforcement, many scholars have conducted preliminary studies on the seismic behavior of RC structures strengthened by TRC [12,16–21]. Bournas et al. [12] performed experiments to study the seismic performance of strengthened RC columns with insufficient bearing capacity. Their results showed that TRM can greatly improve the deformation capacity and energy dissipation capacity of columns by delaying the yield of the rebars in the plastic hinge zone and reducing the bond slip of lap rebars. Bournas and Triantafillou [16] analyzed the yield change in TRM-strengthened RC columns under earthquake action. Their research showed that when the steel bar reached the buckling state, the strengthened column can redistribute the load due to the constraint of TRM, and part of the load is borne by the core concrete. Moreover, as the number of TRM reinforcement layers increases, the deformation capacity of the strengthened column increases. The effects of textile layer, lap length, stirrup ratio and axial compression ratio on the seismic behavior of TRC-strengthened RC columns were studied in literature [17]. The results showed that the textile layers and axial compression ratio have significant effect on the seismic performance of RC columns. Yin et al. [18] studied the seismic performance of strengthened RC columns after corrosion, and their results showed that TRC reinforcement can effectively improve the seismic capability of RC columns under corrosion environments. Another literature study [19] investigated the seismic performance of TRC-strengthened RC columns in a chloride corrosion environment. The test results in this study showed that TRC could delay the corrosion rate of steel bars and improve the seismic performance of a strengthened column in a corrosion environment. Al-Salloum et al. [20] conducted quasistatic tests on beam-column joints strengthened by TRM, and their results showed that TRM reinforcement can significantly improve the ultimate bearing capacity, deformation capacity, ductility and energy dissipation capacity of the joints. As the number of reinforcement layers increased, the bearing capacity and ductility of the joints increased. Alhadded et al. [21] also studied beam-column joints strengthened by TRM and analyzed the load-displacement characteristics, ultimate load and crack develop-
ment model of beam-column joints. Their results showed that TRMreinforced specimens can better limit the development of cracks. Several scholars have investigated the effect of TRC reinforcement on the seismic performance of RC components, and some progress has been made in the research. However, the current research has mainly involved experimental research, and few studies have adopted numerical analysis methods. Therefore, this paper established a TRCstrengthened column model with ABAQUS to further study the seismic performance of TRC-strengthened RC columns. By comparing the stress and strain of moire patterns, hysteresis curves, and skeleton curves and the ductility and energy dissipation ability of the TRCstrengthened columns, the influence of the axial compression ratio, shear span ratio and concrete strength grade on the seismic performance of strengthened columns was discussed. 2. Numerical model 2.1. Overall design of the test program In this paper, specimens from the literature [17] were selected as the research objects for numerical calculation. The column section size is 300 mm × 300 mm, the column height is 940 mm, and the overall height of the specimen is 1740 mm. The diameter of the longitudinal bars in the specimens is 14 mm, the diameter of the stirrup bars is 8 mm, and the spacing is 100 mm. The specific geometric dimensions and reinforcing bars of the specimens are shown in Fig. 1. The basic parameters of the specimens are shown in Table 1. Besides, according to the results in literature [17] and considering the application cost, all the reinforcement layers in the numerical models were selected as two layers. 2.2. Establishment of a numerical model In this paper, the damage plasticity model in ABAQUS is used to simulate the irreversible damage that occurs during concrete crushing. The uniaxial compressive stress-strain relationship of concrete adopts the model proposed by Hognestad et al. [22], and the uniaxial tensile stress-strain relationship of concrete adopts the model proposed by Jiang et al. [23]. The reinforcement constitutive model is considered to be an ideal elastic-plastic model, and the binary stress-strain model is selected according to the code for the design of concrete structures [24,25]. In addition, the TRC is divided into fiber braided mesh and fine-grained concrete to simulate the performance of TRC materials. Warp and weft fiber bundles of textiles are assumed to be ideal linear elastic materials; hence, when the fiber bundles reach their ultimate strength, the fiber bundles are determined to be broken. The constitu-
Fig. 1. Specimen size and reinforcement details. 2
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reinforcement and fiber bundles. The mesh size in models was chosen as 30 mm by considering the accuracy of the calculation results and efficiency of the calculation software. In addition, though the bondslip has effect on the results, as a preliminary exploration, the reinforcements were embedded into the concrete ignoring the bond-slip.
Table 1
Configuration of the specimens. Serial number
Strength grade of concrete
Axial compression ratio
Stirrup spacing
Shear span ratio
Reinforcement layer
C0
C40
0.3
3.8
0
C1
C40
0.3
3.8
2
C2
C40
0.2
3.8
2
C3
C40
0.4
3.8
2
C4
C40
0.5
3.8
2
C5
C40
0.3
2
2
C6
C40
0.3
5.6
2
C7
C30
0.4
3.8
2
C8
C50
0.4
3.8
2
C9
C60
0.4
100 (0.34%) 100 (0.34%) 100 (0.34%) 100 (0.34%) 100 (0.34%) 100 (0.34%) 100 (0.34%) 100 (0.34%) 100 (0.34%) 100 (0.34%)
3.8
2
2.3. Verification of the finite element model of TRC-strengthened RC columns In this paper, finite element analysis of specimens with axial compression ratios of 0.15 and 0.25 from the literature [17] is carried out, and the numerical results and experimental results are compared and analyzed to verify the rationality and accuracy of the established model and the finite element analysis results. Figs. 2 and 3 show that both the numerical and experimental hysteresis curves are spindle shaped, and the overall trends of the curves coincide well. The downward trend when calculating the skeleton curve in the later stage reflects the degradation behavior of strength and stiffness of the reinforced columns during the later stage of loading. In addition, the error of calculating the characteristic points of the skeleton curve is acceptable. Besides, in the numerical model, the type of constraint between the fine-grained concrete and existing concrete was tie so that the fine-grained concrete may contribute to the initial stiffness in the numerical analysis. However, the fine-grained concrete did not work until the core concrete had a larger volume strain in the physical experiment. Different loading system may affect the stiffness. The loading procedure in the physical experiment was jointly controlled by the stresses and displacements and controlled by displacements in the numerical analysis. Therefore, the initial stiffness of numerically simulated model to be higher. Due to the failure to
tive relation of concrete is adopted when fine-grained concrete is assumed to be concrete material. During the process of establishing the numerical model, the degrees of freedom in all directions at the bottom of the strengthened columns were constrained and the allowable displacement of the columns bottom in the horizontal direction was set to zero. The element type of concrete was C3D8R, and the T3D2 was adopted for the
Fig. 2. Hysteresis curves with different axial compression ratios of TRC-strengthened RC columns. (a) Axial compression ratios with 0.25. (b) Axial compression ratios with 0.15.
Fig. 3. Skeleton curves with different axial compression ratios of TRC-strengthened RC columns. (a) Axial compression ratios with 0.25. (b) Axial compression ratios with 0.15. 3
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consider the overall stiffness attenuation caused by bond slip between the reinforcement and the concrete during the loading process, the peak load obtained by the finite element simulation is overestimated. Moreover, because of the asymmetry of specimen loading and the dispersion of the materials, the skeleton curves and hysteresis curves of the specimen are asymmetric, so there are some differences between the numerical calculation results and the experimental results, especially for that in the negative direction of Figs. 2 and 3.
column, followed by the middle, and the upper color change is less obvious. The damage moire patterns of concrete (Fig. 6) show that the damage degree of the concrete is basically consistent with the change law of plastic strain, which indicates that the cracks generated on the surface of the columns were further developed, and the section along the column body is gradually penetrated. Most of the cracks were generated in the plastic hinge area. When the columns reached the failure point, the number of cracks on the surface of the column increased. For the unstrengthened columns, the accumulated damage degree of the concrete was larger at the root, which indicated that the concrete was crushed in a large area. This finding is consistent with the failure mode of the column with the same conditions in the experiment (shown in Fig. 7(a)). For the strengthened columns, the woven fiber mesh is partially broken, and the loading process ended with the bearing capacity of each test piece dropping to 85% of the peak load. All of the failure patterns of columns were primarily bending failure. A comparison of Figs. 4 to Fig. 7 shows that for the unstrengthened column C0, the damage of the column accumulated gradually at the root, the concrete then cracked in the tension zone, and then the cracks developed along the horizontal level. Finally, the concrete was crushed at the root. This result was consistent with the failure process of column Z0 during the experiment, which indicates that the unreinforced column model established in this paper can accurately reflect the failure process and failure modes exhibited by a column during an actual experiment. For the strengthened column C1, according to Figs. 4 to 6, the failure process was similar to that of column C0. Because the TRC layers had a certain bending rigidity, the TRC layers and the reinforcement bore the horizontal load together. Therefore, the plastic strain of the concrete was slightly smaller than that of the unstrengthened column when column C1 failed. This finding indicates that column C1 may be able to withstand a certain load. According to column Z1, due to the restraint of the TRC, the core concrete did not crush in a large area, which indicates that the TRC improved the compressive strength of concrete to some extent. For column C5, because the shear span ratio is small, the column had a high rigidity, and the appearance of the crack was late. Figs. 4 through 6 show that the side concrete stress level and damage degree of the column were large, which easily caused the shear failure of the column. With the rapid increase in the bearing capacity, the damage degree of the concrete in the column increased significantly. In addition, there was little difference in the concrete damage degree when the column reached the yield point and failure point (Fig. 6(c)). However, because of the confinement of
3. Analysis of the seismic behavior of TRC-strengthened RC columns 3.1. Results of the numerical analysis 2.
The numerical analysis results of the specimens are shown in Table
3.2. Failure process and failure pattern analysis The concrete damage plasticity model in ABAQUS cannot directly describe the process of crack development and failure of the specimens, and the specimens exhibited similar failure processes. Therefore, three typical columns were selected with the maximum value of principal plastic strain, the equivalent plastic strain of concrete and the damage of concrete to describe the failure process and failure pattern at the yield point and failure point. In addition, to further illustrate the accuracy of the model in describing the failure process of columns, the corresponding three columns in the previous experiment were selected for verification. Note that because the rationality and accuracy of the model results have been verified with relevant test results, the results of the three columns selected from the previous experiment in this section are not analyzed hereafter. In the early stage of loading, as the loading displacement increases, the horizontal load of the specimen increases, and the tensile stress gradually exceeds the tensile strength of the concrete. Moreover, because of the increase in the damage degree, the cracks first form in the concrete and gradually develop along the normal direction of the tensile stress in the plastic hinge area. Figs. 4 and 5 show that as the loading displacement continues to increase, the concrete plastic strain of the specimen exhibits a gradual change from the bottom to the top, wherein the lower part of the color changes along the Table 2
Numerical analysis results of the specimens. Serial number
C0 C1 C2 C3 C4 C5 C6 C7 C8 C9
Yield
Peak
Failure
Ductility factor
Cumulative energy dissipation
Py/kN
Δy/mm
Pm/kN
Δm/mm
Pu/kN
Δu/mm
average
E/kN·mm
104.59 −102.47 110.75 −110.51 86.50 −87.10 129.44 −129.50 146.42 −145.34 239.87 −248.16 68.61 −69.53 123.48 −126.75 142.94 −135.68 145.21 −145.10
7.09 −6.34 6.05 −6.05 4.93 −4.90 6.77 −6.65 8.00 −7.90 4.00 −4.00 8.30 −8.27 8.81 −7.59 7.16 −6.27 6.76 −5.94
112.85 −110.82 121.80 −123.80 94.35 −94.74 145.50 −146.17 165.61 −166.03 239.87 −248.16 79.54 −79.85 134.35 −134.89 153.50 −151.21 159.70 −162.28
8.00 −8.00 12.00 −12.00 16.00 −16.00 16.00 −16.00 16.00 −16.00 4.00 −4.00 16.00 −16.00 16.00 −16.00 8.00 −8.00 16.00 −16.00
95.92 −94.20 103.53 −105.23 80.20 −80.53 123.68 −124.24 140.77 −141.12 203.89 −210.94 67.61 −67.87 114.19 −114.66 130.48 −128.53 135.75 −137.94
31.55 −27.10 42.52 −41.17 52.00 −52.00 37.51 −33.70 30.26 −29.01 14.05 −12.98 55.46 −55.37 32.58 −29.44 31.54 −35.51 31.47 −31.76
4.36
26072.56
6.91
46881.53
10.58
79246.04
5.30
38825.12
3.73
26009.21
3.38
23151.90
6.69
45778.19
3.79
24231.65
5.03
34664.35
5.00
30299.39
4
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Fig. 4. Moire patterns of maximum principal plastic strains at different stages in specimens. (a) Specimen C0. (b) Specimen C1. (c) Specimen C5.
Fig. 5. Moire patterns of equivalent plastic strains at different stages in specimens. (a) Specimen C0. (b) Specimen C1. (c) Specimen C5.
the TRC, the failure mode of the column was still bending failure when the column failed, which is basically consistent with the failure of column Z2 (Fig. 7(c)). This finding indicates that the TRC improved the failure mode of the column with a small shear span. Therefore, the results suggest that the model established in this paper has a certain rationality and accuracy and can accurately reflect the failure process and failure mode of each specimen in the loading process.
3.3.1. Effect of the TRC reinforcement on the RC columns The hysteresis curves of the unstrengthened column C0 and the strengthened column C1 are shown in Fig. 8 (a) and (b), respectively. The hysteresis curve of the strengthened column C1 is plumper than that of the unstrengthened column C0, and the number of hysteresis loops in the former was significantly higher when the columns failed. In addition, as shown in Table 2, the cumulative energy consumption of C1 is 46881.53 kN mm, which is 79.81% higher than that of C0. This shows that the energy consumption capacity of the strengthened RC column improved. The reason for this increased energy consumption capacity may be that TRC has a good restraining effect on the core concrete, which makes the strength and stiffness of the columns degrade slowly, experience more displacement deformation and dissi-
3.3. Analysis of the hysteresis curves and energy dissipation capacity under different factors The load-displacement hysteresis curves of each column are shown in Fig. 8. 5
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Journal of Building Engineering 30 (2020) 101245
Fig. 6. Damage moire patterns of concrete at different stages in specimens. (a) Specimen C0. (b) Specimen C1. (c) Specimen C5.
Fig. 7. Failure modes of specimens. (a) Un-strengthened Z0. (b) Strengthened with two layer Z1. (c) Strengthened with two layer Z2.
pate more seismic energy. However, for the unstrengthened columns, according to Fig. 4 and Fig. 5, the cracks developed rapidly after the cracking of the columns, and the concrete was crushed, which caused the columns to fail prematurely, resulting in a low energy consumption capacity.
loops, there is little difference in the pinching degree among the columns. Table 2 shows that when the axial compression ratio increased, the cumulative value of energy consumption of all specimens were 40.84%, 59.16% and 67.18% less than that of specimen C2. This trend occurs because under a larger axial compression, the reinforcements yield prematurely in the compression zone, longitudinal cracks form in the column, and the bearing capacity of the columns decreases quickly, which results in poor energy consumption performance.
3.3.2. Effect of the axial compression ratio on the RC columns For columns C2, C1, C3 and C4, as the axial compression ratio increases, the number of hysteresis loops decreases. The pinch phenomenon appeared in the columns, but there was little difference among all columns because the pinch phenomenon is caused by stiffness degradation, and the degree of pinch is related to the crack width and the accumulation of concrete compressive plastic deformation (residual deformation). Fig. 6 and Fig. 7 show that for the columns with smaller axial compression ratios, the concrete strain and the crack width is larger on the tension side than on the compression side. For columns with large axial compression ratios, the axial force could restrain the development of cracks to some extent. Moreover, there is larger lateral expansion in the concrete of columns with a larger axial compression ratio, and the TRC is “activated” so that TRC could confine the concrete and better limit the development of horizontal cracks in the concrete, delay the damage of the concrete, and accelerate crack closure. The crack development in the middle crack is also faster. Therefore, except for the difference in the number of hysteresis
3.3.3. Influence of the shear span ratio on the RC columns Fig. 8(b), (f) and (g) shows that the number of hysteresis loops of specimen C5 is small, and the bearing capacity rapidly decreases with as the horizontal displacement increases after reaching the peak load. Column C5 failed after five cycles, and the ultimate displacement was small. However, the failure mode of column C5 was bending failure, which indicates that TRC could improve the failure mode of columns with a small shear span ratio. As the shear span ratio increases, the number of hysteresis loops of specimens C1 and C6 increases. Moreover, there is an obvious "platform" segment in specimen C6, and the bearing capacity decreases slowly. The ultimate displacement of specimen C6 before failure can reach 55 mm, indicating that the specimens with a large shear span ratio have good ductility and deformation capacity. In addition, according to the results in Table 2, the cumulative 6
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Journal of Building Engineering 30 (2020) 101245
Fig. 8. Hysteresis curves of specimens in different factors. (a) Specimen C0. (b) Specimen C1. (c) Specimen C2. (d) Specimen C3. (e) Specimen C4. (f) Specimen C5. (g) Specimen C6. (h) Specimen C7. (i) Specimen C8. (j) Specimen C9.
energy consumption value of columns C1 and C6 was 102.49% and 97.73% greater than that of C5, respectively, which indicates that although the bearing capacity of the columns with large shear span test pieces is poor, such columns have better energy consumption performance.
number of hysteresis loops greatly increases. When the core concrete strength grade continues to increase, the number of hysteresis loops of the columns changes little (shown in Fig. 8(d), (h), (i), and (j)). In addition, Table 2 shows that the cumulative energy consumption of columns C3, C8, and C9 are 60.22%, 43.05% and 25.04% greater than that of C7, respectively. The reason for this behavior may be that for specimen C3, the compressive strength of the concrete is higher, and the concrete is in a three-way compression state due to the constraint of the TRC, which improved the deformability of the column. There-
3.3.4. Effect of the concrete strength grade on the RC columns For columns with different concrete strength grades, as the strength of the core concrete increases to a strength grade of C40, the 7
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fore, the column could undergo more cycles so that the number of hysteresis loops is much greater and the cumulative energy consumption is relatively larger. Moreover, with the continuous increase in the concrete strength grade, the ultimate compressive strain of the concrete in the specimens reduces further, and the deformation capacity decreases. However, because of the restraining effect of TRC, the deformation ability of specimens C8 and C9 decreases little. Based on Table 2, the ultimate displacements of columns C3, C8 and C9 have little difference, which indicates that the TRC has a good restraining effect on the columns and can improve the deformation ability of the columns with a higher concrete strength grade.
bearing capacity of the specimen increases with increasing axial compression ratio. This behavior is because the restraining effect of the TRC is passive, the transverse expansion deformation of the concrete increases with the larger compressive pressure, and the lateral restraint forces provided by the TRC increase. The strength and ultimate strain of the concrete are improved, and the bearing capacity of the columns is significantly improved. 3.4.3. Effect of the shear span ratio on the TRC-strengthened columns During the initial stage of loading, the stiffness and peak load of C5 are significantly larger than those of C1 and C6. Table 2 shows that the yield load of C5 is 120.57% and 253.29% greater than that of C1 and C6, respectively, and the peak load of C5 is 98.71% and 206.19% greater than that of C1 and C6, respectively. When the bearing capacity reached the peak load, the stiffness of specimen C5 deteriorated significantly, and the bearing capacity decreased rapidly. However, because of the constraint of the TRC, specimen C5 did not exhibit brittle failure; the failure mode was mainly bending failure. As the shear span ratio increased, the ductility and deformation capacity of the specimens improved, although the bearing capacity of the specimens decreased. In addition, the TRC could improve the failure modes of the columns with smaller shear span ratios and avoid shear failure.
3.4. Skeleton curve analysis The skeleton curves of each column are shown in Fig. 9. 3.4.1. Effect of the TRC reinforcement on the RC columns The skeleton curves of the columns before and after reinforcement are shown in Fig. 9(a). The curves show that before and after the column yields, all of the columns are linearly elastic. The curve of the strengthened column is basically coincident with that of the unreinforced column. Table 2 shows that the yield loads of all columns are similar, which means that the TRC does not play a role in the elastic phase. However, as the horizontal load and displacement increase, the concrete expands and causes lateral deformation so that the TRC is activated. Although the thickness of the TRC reinforcement layer is small, the stiffness of the strengthened column is increased to some extent, so that the rigidity of the TRC-strengthened column is slightly larger than that of the unstrengthened column. Fig. 9(a) and Table 2 show that the peak load of C1 is 11.80% greater than that of C0, and the ultimate displacement of the test piece during damage is also significantly larger than that of C0. This finding indicates that TRC can improve the bearing capacity and deformation capacity of the strengthened columns.
3.4.4. Effect of the concrete strength grade on the TRC-strengthened columns Fig. 9(d) shows that during the initial stage of loading, the stiffness of the strengthened columns gradually increases with increasing concrete strength grade. When the bearing capacity reaches the peak load, the peak loads of C3, C8 and C9 are 8.33%, 13.17% and 19.59% greater than that of column C7, respectively. These findings indicate that as the concrete strength grade increases, the peak load and ultimate load of the specimen gradually increase. This behavior occurs because the compressive strength increase as the concrete strength grade increases, and the TRC contributes to the flexural stiffness of the columns. However, after the peak load was reached, the bearing capacity of C8 and C9 with higher concrete strength grades decreased faster than that of column C3, which indicates that the TRC has a greater restraining effect on the specimens with lower concrete strength grades.
3.4.2. Effect of the axial compression ratio on the RC columns Fig. 9(b) and Table 2 show that the yield loads of columns C1, C3 and C4 are 27.91%, 50.00% and 69.77% greater than that of C2, respectively, and the peak loads are 28.72%, 54.26% and 75.53% greater than that of C2, respectively. These findings show that the
Fig. 9. Skeleton curves of specimens in different factors. (a) TRC layers. (b) Axial compression ratio. (c) Shear span ratio. (d) Strength grade of concrete. 8
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tility coefficients of specimens C3, C8 and C9 were 39.84%, 32.72% and 31.93% greater than that of specimen C7, respectively. This phenomenon occurred because after strengthening, the core concrete is in a three-dimensional compressive state and the lateral restraint force is strengthened, which improves the compressive strength of the concrete, delays the failure of the specimens and improves the deformation capacity of the reinforced specimens. In addition, as the concrete strength grade increased, the ductility coefficient of specimen C3 increased the most, and when the concrete strength grade exceeded C40, the ductility coefficient of the specimen decreased. Although the core concrete was confined by the TRC, the concrete with lower strength grade will also be destroyed by concrete crushing due to insufficient compressive strength. Concrete with higher strength grades exhibit brittle characteristics. Although TRC restraint can delay the destruction time to a certain extent, the concrete will still destroy prematurely. Therefore, there may be an applicable range for the concrete strength grade for TRC when strengthening, but this possibility needs to be verified further.
3.5. Ductility analysis The ductility coefficient can quantitatively reflect the ductility of the structures. Thence, the ductility coefficient of the displacement is used to evaluate the ductility of the column. The displacement ductility coefficients is equal to the figure of dividing ultimate displacement by yield displacement. In addition, Park method [26] was used to determine the yield point. The ultimate displacement mainly refers to the displacement corresponding to the load that is the 85% of peak load or the displacement when the specimens failed. 3.5.1. Effect of the TRC reinforcement on the RC columns Table 2 shows that the displacement ductility coefficients of specimens C0 and C1 are 4.36 and 6.91, respectively. The displacement ductility coefficient of C1 is 58.49% greater than that of column C0, and the ultimate displacement of the strengthened column is much larger than that of the unstrengthened column when the columns failed. This finding indicates that the TRC can effectively improve the ductility and deformability of the strengthened columns.
3.6. Stiffness degradation analysis
3.5.2. Effect of the axial compression ratio on the TRC-strengthened columns The displacement ductility coefficients of columns C1, C3 and C4 are 34.69%, 49.91% and 64.74% less than that of column C2, respectively. This behavior occurs because the ultimate compressive strain of the concrete decreases gradually as the axial compression ratio of the columns increases, and the height of the compression zone of the column increases, which results in a decrease in the displacement ductility coefficient of the columns. However, according to Fig. 6 and Fig. 7, the TRC could confine the concrete and limit the development of the horizontal cracks in the concrete, thereby delaying the damage to the concrete. Therefore, the deformation ability of columns with larger axial compression ratios is improved to a certain extent.
The skeleton curves of the columns with different factors are shown in Fig. 10. 3.6.1. Effect of the TRC reinforcement on the RC columns Fig. 10(a) shows that the stiffness degradation curves of specimens C0 and C1 are substantially coincident before the specimen yields, which indicates that the stiffness degradation of each column is basically equivalent before the column yields. However, after the specimen yielded, the rate of stiffness degradation in specimen C0 is significantly higher than that in specimen C1, and the stiffness degradation curve of the reinforced column is also much longer. This behavior shows that the TRC has little effect on the stiffness of the specimens before yielding. However, as the displacement increases after yielding, the TRC has a good restraint effect on the core concrete of the reinforced specimens, which increases the compressive strength of the concrete and slows the deterioration in the stiffness of the specimens. In addition, the TRC delays the failure process of concrete and makes the strengthened column C1 have a larger ultimate displacement than the unstrengthened column C0.
3.5.3. Effect of the shear span ratio on the TRC-strengthened columns The ductility coefficients of C1 and C6 are 104.44% and 97.93% greater than that of specimen C5, respectively. This trend occurs because the initial stiffness of C5 is larger than that of the other specimens and the elastic-plastic deformation of C5 is small, so the bearing capacity quickly reaches the peak load. Although the TRC has a restraining effect on the core concrete, the damage degree of the concrete increased under a large load, and the ultimate compressive strain of the concrete was achieved. The internal concrete was crushed prematurely, causing the column to fail. The ductility of the strengthened column was worse than that of the strengthened columns with a large shear span ratio, indicating that the shear span ratio had a great influence on the ductility of the TRC-strengthened columns and that the shear span ratio is an important factors on the seismic performance for the TRC-strengthened columns. In addition, the ductility coefficient of test piece C6 is slightly lower than that of C1, which is slightly different from the rule presented in the previous experimental results. The analysis shows that except for the errors in the previous experiment and the limitations in accuracy of the model in this paper, the number of specimens in the experiment also has a certain impact. Therefore, a large number of experimental and numerical analyses are needed to further determine the influence of the shear-to-span ratio on the ductility coefficient of TRC-strengthened columns.
3.6.2. Effect of the axial compression ratio on the TRC-strengthened columns The stiffness degradation curves of the specimens with different axial compression ratios are shown in Fig. 10(b). The stiffness degradation rate of each specimen is basically equivalent during the whole loading process. During the later stage of loading, the stiffness degradation rates of the specimens with higher axial compression ratios (C3 and C4) are still slightly higher than those of the specimens with smaller axial compression ratios, and the specimens with high axial compression ratios failed after fewer displacement cycles. After yielding, the stiffness degradation curves of the specimens with lower axial compression ratio (C2 and C1) exhibit a smooth decrease, and the stiffness degradation curves of the reinforced columns are generally longer, which indicates that the deformation capacity and ductility of the reinforced columns decrease with increasing axial compression ratio. However, the stiffness degradation rates of the specimens with higher axial compression ratio do not change significantly, indicating that the TRC has a good restraint effect on the specimens with higher axial compression ratios during the later stage of loading, which could reduce the height of the compression zone of the reinforced specimens to a certain extent and avoid the rapid stiffness degradation of the strengthened columns.
3.5.4. Effect of the concrete strength grade on the TRC-strengthened columns As the strength of the concrete increases, the ultimate compressive strain of the concrete decreases and the deformability decreases, resulting in a decrease in ductility of the RC column. However, in this paper, as the concrete strength grade increased, the displacement duc9
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Fig. 10. Stiffness degradation curves of specimen in different factors. (a) TRC layers. (b) Axial compression ratio. (c) Shear span ratio. (d) Strength grade of concrete.
conclusion needs further verification. In general, the change in core concrete strength grade has little effect on the stiffness degradation rate of strengthened columns.
3.6.3. Effect of the shear span ratio on the TRC-strengthened columns Fig. 10(c) shows that the stiffness degradation of each specimen is faster before and after yielding, and Table 2 shows that specimen C5 reached the peak load immediately after yielding. Therefore, the relative stiffness of specimen C5 is smaller than that of other specimens at the same displacement. This phenomenon occurs because a larger load increases the concrete damage in the specimens increases and the decreases the stiffness of the specimens. In addition, the stiffness degradation rates of specimens C5, C1 and C6 are 0.144, 0.171 and 0.194, respectively, before and after double yield displacement, which indicates that the stiffness degradation rates of the specimens increase as the shear span ratio increases during a period of time after yielding. This phenomenon occurs for the specimens with small shear span ratios because the volume of the concrete expands, and the transverse deformation of specimens increases as the load increases. In contrast to specimens C1 and C6, the TRC was activated prematurely to work in specimen C5, and because of the confinement of the TRC, the stiffness degradation rate of specimen C5 was reduced. However, due to the insufficient restraint of the TRC, specimen C5 failed prematurely. Therefore, the results show that TRC can delay the stiffness degradation rate of the specimens with a small shear span ratio, but a small shear span ratio is still disadvantageous to the strengthened specimens.
4. Conclusions In this paper, the finite element model of a TRC-strengthened RC column was established, and the rationality and accuracy of the model were verified by comparison with the experimental results. Furthermore, the influences of different factors on seismic performance were investigated, and the following conclusions were drawn: (1) The load-displacement hysteresis curve and skeleton curve of the reinforced column obtained by numerical calculation agreed well with the corresponding curves obtained in the previous experiment, which indicated that the model established in the paper had a certain degree of rationality. (2) TRC reinforcement can effectively restrain the core concrete of an RC column, limit the development of cracks, increase the peak load of columns, effectively delay the stiffness degradation of specimens after yielding, and improve the seismic deformation capacity of columns. (3) The bearing capacity of the strengthened column increased with increasing axial compression ratio, but the displacement ductility coefficient and energy dissipation capacity of the reinforced column decreased. (4) As the shear span ratio increased, the ultimate displacement, cumulative energy consumption, ductility, and deformation capacity of the reinforced columns increased, whereas the bearing capacity decreased. In addition, TRC can slow the stiffness degradation rate of small shear span samples to a certain extent after yielding. (5) As the concrete strength grade increased, the peak load of strengthened columns also increased. When the grade of the concrete was within C40, the displacement ductility coefficient and accumulated energy dissipation capacity increased with increasing concrete strength grade. When the concrete strength
3.6.4. Effect of the concrete strength grade on the TRC-strengthened columns Before and after yielding, the stiffness degradation curves of all specimens basically coincide. The stiffness gradually decreases with increasing loading displacement. This trend occurs because there are cumulative damage phenomena after the specimens yield, which cause the stiffness to decrease, and the specimens have elastic-plastic properties after yielding. However, Fig. 10(d) shows that the stiffness degradation rates of the specimens are slightly different in the later stage of loading, and specimens C7 and C8 have longer stiffness degradation curves. The reason may be that for specimens with concrete strength grades between C40 and C50, TRC can play a better role in confinement. However, due to the small amount of data, this 10
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grade reached C40, the displacement ductility coefficient was maximal. However, as the strength grade continued to increase, the changes in the displacement ductility coefficient and accumulated energy dissipation ability were either insignificant or even decreased.
[5] [6] [7]
The study presented herein failed to fully consider the influences of all factors in the establishment of the model used for the numerical analysis, and the number of columns was also small. Whether the conclusions obtained in the paper are universal needs to be verified by a large number of tests and numerical analysis studies in the future.
[8] [9]
Data availability statement
[10]
The datasets used or analyzed during the current study are available from the corresponding author on reasonable request.
[11] [12]
Declaration of competing interest
[13]
We declare that there have not any commercial or associative interests that represent a conflict of interest in connection with this work submitted.
[14] [15]
Acknowledgments
[16]
The authors gratefully acknowledge the financial supported by Outstanding Innovation Scholarship for Doctoral Candidate of CUMT (Grant No. 2019YCBS010). The experimental work described in this paper was conducted at the Jiangsu Key Laboratory of Environmental impact and Structural Safety in Civil Engineering in the China University of Mining and Technology. Help during the testing from staffs and students at the Laboratory are greatly acknowledged.
[17] [18] [19] [20]
Appendix A. Supplementary data
[21]
Supplementary data to this article can be found online at https:// doi.org/10.1016/j.jobe.2020.101245.
[22]
References
[23] [24]
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ordinary RC frames retrofitted at joints by FRP sheets, Eng. Struct. 32 (2010) 2326–2336. S.A. Shamim, G. Yau, Seismic behavior of concrete columns confined with steel and fiber-reinforced polymers, ACI Struct. J. 99 (1) (2002) 72–80. R.D. Iacobucci, S.A. Shamim, O. Bayrak, Retrofit of square concrete columns with carbon fiber-reinforced polymer for seismic resistance, ACI Struct. J. 100 (6) (2003) 785–794. P. Feng, S. Cheng, T. Yu, Seismic performance of hybrid columns of concretefilled square steel tube with FRP-confined concrete core, J. Compos. Construct. 22 (4) (2018) 04018015-1~15. T.C. Triantafillou, C.G. Papanicolaou, P. Zissimopoulos, et al., Concrete confinement with textile-reinforced mortar jackets, ACI Struct. J. 103 (1) (2006) 28–37. L. Koutas, A. Pitytzogia, T.C. Triantafillou, et al., Strengthening of infilled reinforced concrete frames with TRM: study on the development and testing of textile-based anchors, J. Compos. Construct. 18 (3) (2014) A4013015–1~12. J. Hegger, N. Will, O. Bruckermann, Loading-bearing behavior and simulation of textile-reinforced concrete, Mater. Struct. 39 (8) (2006) 765–776. R. Ortlepp, S. Ortlepp, Textile reinforced concrete for strengthening of RC columns: a contribution to resource conservation through the preservation of structures, Construct. Build. Mater. 132 (2017) 150–160. D.A. Bournas, T.C. Triantafillou, K. Zygouris, et al., Textile-reinforced mortar versus FRP jacketing in seismic retrofitting of RC columns with continuous or lapspliced deformed bars, J. Compos. Construct. 13 (5) (2009) 360–371. M.D. Ludovico, A. Prota, G. Manfredi, Structural upgrade using basalt fibers for concrete confinement, J. Compos. Construct. 14 (5) (2010) 541–552. L. Ombres, S. Verre, Structural behaviour of fabric reinforced cementitious matrix (FRCM) strengthened concrete columns under eccentric loading, Compos. Part B 75 (2015) 235–249. R. Azama, K. Soudkib, J.S. Westb, et al., Shear strengthening of RC deep beams with cement-based composites, Eng. Struct. 172 (2018) 929–937. D.A. Bournas, T.C. Triantafillou, Bar buckling in RC columns confined with composite materials, J. Compos. Construct. 15 (3) (2011) 393–403. S.P. Yin, Y. Li, Y. Yang, et al., Influencing factors of seismic performance of RC columns strengthened with textile reinforced concrete, J Zhejiang University (Eng Scie) 51 (5) (2017) 904–913. S.P. Yin, Y. Yang, T. Ye, et al., Experimental research on seismic behavior of reinforced concrete columns strengthened with TRC under corrosion environment, J. Struct. Eng. 143 (5) (2017) 04016231-1~11. Y. Li, S.P. Yin, W.J. Chen, Seismic behavior of corrosion-damaged RC columns strengthened with TRC under a chloride environment, Construct. Build. Mater. 201 (2019) 736–745. Y.A. Al-Salloum, N.A. Siddiqui, H.M. Elsanadedy, et al., Textile-reinforced mortar versus FRP as strengthening material for seismically deficient RC beam-column joints, J. Compos. Construct. 15 (6) (2011) 920–933. M.S. Alhadded, N.A. Siddiqui, A.A. Alsayed, et al., Numerical investigations on the seismic behavior of FRP and TRM upgraded RC exterior beam-column joints, J. Compos. Construct. 16 (3) (2012) 308–321. E. Hognestad, N.W. Hanson, D. McHenry, Concrete stress distribution in ultimate strength design, Proceedings of American Concrete Institute 52 (1955) 455–479. J.J. Jiang, X.Z. Lu, L.P. Ye, Finite Element Analysis of Concrete Structure, Tsinghua University Press, 2005. Gb50010-2015, Code for Design of Concrete Structures, Ministry of Housing and Urban-Rural Development of the People’s of China, Beijing, 2015. D. Liu, H. Huang, J. Zuo, et al., Experimental and numerical study on short eccentric columns strengthened by textile-reinforced concrete under sustaining load, J. Reinforc. Plast. Compos. 36 (23) (2017) 1712–1726. R. Park, T. Paulay, Reinforced Concrete Structures, John Wiley & Sons, New York, 1975.
Contents lists available at ScienceDirect
Journal of Building Engineering
Numerical investigation on the influences of different factors on the seismic performance of TRC-strengthened RC columns Yao Li a, b, Shiping Yin a, b, *, Junyan Dai b, Ming Liu b a b
State Key Laboratory for Geomechanics & Deep Underground Engineering, China University of Mining and Technology, Xuzhou, 221116, China Jiangsu Key Laboratory of Environmental Impact and Structural Safety in Engineering, China University of Mining and Technology, Xuzhou, 221116, China
ARTICLE INFO
ABSTRACT
Keywords: Textile-reinforced concrete (TRC) Reinforced concrete (RC) column Axial compression ratio Shear span ratio Concrete strength grade Seismic performance
To investigate the influences of different factors on the seismic performance of textile-reinforced concrete (TRC)-strengthened reinforced concrete (RC) columns, a numerical model for TRC-strengthened RC columns was established with the finite element software ABAQUS, and the numerical simulation results were analyzed. The numerical results of the TRC-strengthened RC columns were in good agreement with the experimental results. The TRC could effectively restrain the core concrete of the strengthened columns, limit the development of cracks, increase the peak load of the specimens, delay the stiffness degradation of the specimens after yielding, and improve the seismic deformation capacity of the strengthened columns. The bearing capacity and stiffness degradation rate of the strengthened columns increased with increasing axial compression ratio, but the displacement ductility coefficient and energy dissipation capacity exhibited the opposite trend. As the shear span ratio increased, the ductility, deformation capacity and cumulative energy dissipation capacity of the strengthened columns increased, but the bearing capacity of the columns decreased. The TRC could delay the stiffness degradation of the strengthened columns with a large axial compression ratio and a small shear span. The bearing capacity of the strengthened column increased as the strength grade of the core concrete increased. When the strength grade of the core concrete of the strengthened column reached C40, the displacement ductility coefficient of the strengthened column was the largest. However, when the strength grade of the concrete continued to increase, the displacement ductility coefficient and the cumulative energy dissipation capacity of the strengthened column either did not change significantly or even slightly decreased.
1. Introduction Reinforced concrete (RC) is widely used in the field of structural engineering. However, due to the influence of the design, construction defects and external environment, as the service life increases, the safety, reliability and durability of an RC structure will be weakened to a certain extent, thereby affecting the normal use of the structure. In RC buildings, columns are very important load-bearing components. If columns are damaged in an earthquake, whole buildings may collapse, which would cause casualties and economic losses. Therefore, it is of great theoretical importance and engineering value to strengthen existing RC columns and investigate the seismic performance of strengthened columns.
The traditional reinforcement methods for RC columns mainly include increasing the section, the external steel clad method, and the external prestressing method. However, these methods have shortcomings, such as increasing the structural weight, being susceptible to rusting and changing the structural appearance. In recent years, with the development of composite materials, fiber-reinforced polymers (FRPs) have been used not only for reinforcement and restoration of existing structures but also for the development of new structures. Several scholars have also conducted relevant numerical investigations [1–4]. Parvin and Granata [1] used ANSYS—a finite element analysis program-to study the application of FRP materials in strengthening beam-column joints. Lakshmi et al. [2] studied three types of beam-column joints through finite element simulation to explore a reasonable finite element numerical model for beam-column
* Corresponding author. State Key Laboratory for Geomechanics & Deep Underground Engineering, China University of Mining and Technology, Xuzhou, 221116, China. E-mail address: [email protected] (S. Yin).
https://doi.org/10.1016/j.jobe.2020.101245 Received 6 August 2019; Received in revised form 20 December 2019; Accepted 1 February 2020 Available online 4 February 2020 2352-7102/© 2020 Elsevier Ltd. All rights reserved.
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joints. Mahini et al. [3] proposed a model for strengthening beamcolumn joints with FRP plates, in which the model uses nonlinear connection elements to evaluate the seismic performance of the joints. Niroomandi et al. [4] modified the joint stiffness of FRP-strengthened specimens through nonlinear finite element analysis and introduced this modified joint stiffness into the overall frame for seismic evaluation. Besides, Sheikh et al. [5,6] found that with the axial compression ratio increases, the efficiency of improving the seismic performance of FRP-constrained columns decreases, and the constraint efficiency was higher in cylinders than that in square ones. Feng et al. [7] also studied the influence of concrete strength. Their result showed that with increasing of concrete strength, the failure mode could be altered. Although FRP sheets are widely used as an effective reinforcement method, FRP sheets typically use epoxy resin as a binder; thus, FRP sheets have poor compatibility with concrete, and their vapor permeability is not suitable for use in wet environments [8]. Moreover, it is difficult to examine and assess the internal status after FRP sheets strengthening. Therefore, scholars have introduced the concept of reinforcement fibers that combine textile fibers with inorganic substrates (such as cement-based mortar) [9]. Based on this concept, many scholars have proposed a variety of reinforcement systems with little difference, such as textile-reinforced concrete (TRC) [10,11], textile-reinforced mortar (TRM) [9,12] basalt-reinforced mortar (BRM) [13] and fabric-reinforced cementitious matrix (FRCM) [14]. TRC has a substrate suitable for wet environments, TRC does not contain moisture that would cause freeze-thaw cycling, and TRC does not possess other factors that may cause damage [11,15]. In addition, cracks that form in the matrix usually appear on the reinforcement layer, which is convenient for visual inspection [15]. As an alternative to FRP reinforcement, many scholars have conducted preliminary studies on the seismic behavior of RC structures strengthened by TRC [12,16–21]. Bournas et al. [12] performed experiments to study the seismic performance of strengthened RC columns with insufficient bearing capacity. Their results showed that TRM can greatly improve the deformation capacity and energy dissipation capacity of columns by delaying the yield of the rebars in the plastic hinge zone and reducing the bond slip of lap rebars. Bournas and Triantafillou [16] analyzed the yield change in TRM-strengthened RC columns under earthquake action. Their research showed that when the steel bar reached the buckling state, the strengthened column can redistribute the load due to the constraint of TRM, and part of the load is borne by the core concrete. Moreover, as the number of TRM reinforcement layers increases, the deformation capacity of the strengthened column increases. The effects of textile layer, lap length, stirrup ratio and axial compression ratio on the seismic behavior of TRC-strengthened RC columns were studied in literature [17]. The results showed that the textile layers and axial compression ratio have significant effect on the seismic performance of RC columns. Yin et al. [18] studied the seismic performance of strengthened RC columns after corrosion, and their results showed that TRC reinforcement can effectively improve the seismic capability of RC columns under corrosion environments. Another literature study [19] investigated the seismic performance of TRC-strengthened RC columns in a chloride corrosion environment. The test results in this study showed that TRC could delay the corrosion rate of steel bars and improve the seismic performance of a strengthened column in a corrosion environment. Al-Salloum et al. [20] conducted quasistatic tests on beam-column joints strengthened by TRM, and their results showed that TRM reinforcement can significantly improve the ultimate bearing capacity, deformation capacity, ductility and energy dissipation capacity of the joints. As the number of reinforcement layers increased, the bearing capacity and ductility of the joints increased. Alhadded et al. [21] also studied beam-column joints strengthened by TRM and analyzed the load-displacement characteristics, ultimate load and crack develop-
ment model of beam-column joints. Their results showed that TRMreinforced specimens can better limit the development of cracks. Several scholars have investigated the effect of TRC reinforcement on the seismic performance of RC components, and some progress has been made in the research. However, the current research has mainly involved experimental research, and few studies have adopted numerical analysis methods. Therefore, this paper established a TRCstrengthened column model with ABAQUS to further study the seismic performance of TRC-strengthened RC columns. By comparing the stress and strain of moire patterns, hysteresis curves, and skeleton curves and the ductility and energy dissipation ability of the TRCstrengthened columns, the influence of the axial compression ratio, shear span ratio and concrete strength grade on the seismic performance of strengthened columns was discussed. 2. Numerical model 2.1. Overall design of the test program In this paper, specimens from the literature [17] were selected as the research objects for numerical calculation. The column section size is 300 mm × 300 mm, the column height is 940 mm, and the overall height of the specimen is 1740 mm. The diameter of the longitudinal bars in the specimens is 14 mm, the diameter of the stirrup bars is 8 mm, and the spacing is 100 mm. The specific geometric dimensions and reinforcing bars of the specimens are shown in Fig. 1. The basic parameters of the specimens are shown in Table 1. Besides, according to the results in literature [17] and considering the application cost, all the reinforcement layers in the numerical models were selected as two layers. 2.2. Establishment of a numerical model In this paper, the damage plasticity model in ABAQUS is used to simulate the irreversible damage that occurs during concrete crushing. The uniaxial compressive stress-strain relationship of concrete adopts the model proposed by Hognestad et al. [22], and the uniaxial tensile stress-strain relationship of concrete adopts the model proposed by Jiang et al. [23]. The reinforcement constitutive model is considered to be an ideal elastic-plastic model, and the binary stress-strain model is selected according to the code for the design of concrete structures [24,25]. In addition, the TRC is divided into fiber braided mesh and fine-grained concrete to simulate the performance of TRC materials. Warp and weft fiber bundles of textiles are assumed to be ideal linear elastic materials; hence, when the fiber bundles reach their ultimate strength, the fiber bundles are determined to be broken. The constitu-
Fig. 1. Specimen size and reinforcement details. 2
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reinforcement and fiber bundles. The mesh size in models was chosen as 30 mm by considering the accuracy of the calculation results and efficiency of the calculation software. In addition, though the bondslip has effect on the results, as a preliminary exploration, the reinforcements were embedded into the concrete ignoring the bond-slip.
Table 1
Configuration of the specimens. Serial number
Strength grade of concrete
Axial compression ratio
Stirrup spacing
Shear span ratio
Reinforcement layer
C0
C40
0.3
3.8
0
C1
C40
0.3
3.8
2
C2
C40
0.2
3.8
2
C3
C40
0.4
3.8
2
C4
C40
0.5
3.8
2
C5
C40
0.3
2
2
C6
C40
0.3
5.6
2
C7
C30
0.4
3.8
2
C8
C50
0.4
3.8
2
C9
C60
0.4
100 (0.34%) 100 (0.34%) 100 (0.34%) 100 (0.34%) 100 (0.34%) 100 (0.34%) 100 (0.34%) 100 (0.34%) 100 (0.34%) 100 (0.34%)
3.8
2
2.3. Verification of the finite element model of TRC-strengthened RC columns In this paper, finite element analysis of specimens with axial compression ratios of 0.15 and 0.25 from the literature [17] is carried out, and the numerical results and experimental results are compared and analyzed to verify the rationality and accuracy of the established model and the finite element analysis results. Figs. 2 and 3 show that both the numerical and experimental hysteresis curves are spindle shaped, and the overall trends of the curves coincide well. The downward trend when calculating the skeleton curve in the later stage reflects the degradation behavior of strength and stiffness of the reinforced columns during the later stage of loading. In addition, the error of calculating the characteristic points of the skeleton curve is acceptable. Besides, in the numerical model, the type of constraint between the fine-grained concrete and existing concrete was tie so that the fine-grained concrete may contribute to the initial stiffness in the numerical analysis. However, the fine-grained concrete did not work until the core concrete had a larger volume strain in the physical experiment. Different loading system may affect the stiffness. The loading procedure in the physical experiment was jointly controlled by the stresses and displacements and controlled by displacements in the numerical analysis. Therefore, the initial stiffness of numerically simulated model to be higher. Due to the failure to
tive relation of concrete is adopted when fine-grained concrete is assumed to be concrete material. During the process of establishing the numerical model, the degrees of freedom in all directions at the bottom of the strengthened columns were constrained and the allowable displacement of the columns bottom in the horizontal direction was set to zero. The element type of concrete was C3D8R, and the T3D2 was adopted for the
Fig. 2. Hysteresis curves with different axial compression ratios of TRC-strengthened RC columns. (a) Axial compression ratios with 0.25. (b) Axial compression ratios with 0.15.
Fig. 3. Skeleton curves with different axial compression ratios of TRC-strengthened RC columns. (a) Axial compression ratios with 0.25. (b) Axial compression ratios with 0.15. 3
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consider the overall stiffness attenuation caused by bond slip between the reinforcement and the concrete during the loading process, the peak load obtained by the finite element simulation is overestimated. Moreover, because of the asymmetry of specimen loading and the dispersion of the materials, the skeleton curves and hysteresis curves of the specimen are asymmetric, so there are some differences between the numerical calculation results and the experimental results, especially for that in the negative direction of Figs. 2 and 3.
column, followed by the middle, and the upper color change is less obvious. The damage moire patterns of concrete (Fig. 6) show that the damage degree of the concrete is basically consistent with the change law of plastic strain, which indicates that the cracks generated on the surface of the columns were further developed, and the section along the column body is gradually penetrated. Most of the cracks were generated in the plastic hinge area. When the columns reached the failure point, the number of cracks on the surface of the column increased. For the unstrengthened columns, the accumulated damage degree of the concrete was larger at the root, which indicated that the concrete was crushed in a large area. This finding is consistent with the failure mode of the column with the same conditions in the experiment (shown in Fig. 7(a)). For the strengthened columns, the woven fiber mesh is partially broken, and the loading process ended with the bearing capacity of each test piece dropping to 85% of the peak load. All of the failure patterns of columns were primarily bending failure. A comparison of Figs. 4 to Fig. 7 shows that for the unstrengthened column C0, the damage of the column accumulated gradually at the root, the concrete then cracked in the tension zone, and then the cracks developed along the horizontal level. Finally, the concrete was crushed at the root. This result was consistent with the failure process of column Z0 during the experiment, which indicates that the unreinforced column model established in this paper can accurately reflect the failure process and failure modes exhibited by a column during an actual experiment. For the strengthened column C1, according to Figs. 4 to 6, the failure process was similar to that of column C0. Because the TRC layers had a certain bending rigidity, the TRC layers and the reinforcement bore the horizontal load together. Therefore, the plastic strain of the concrete was slightly smaller than that of the unstrengthened column when column C1 failed. This finding indicates that column C1 may be able to withstand a certain load. According to column Z1, due to the restraint of the TRC, the core concrete did not crush in a large area, which indicates that the TRC improved the compressive strength of concrete to some extent. For column C5, because the shear span ratio is small, the column had a high rigidity, and the appearance of the crack was late. Figs. 4 through 6 show that the side concrete stress level and damage degree of the column were large, which easily caused the shear failure of the column. With the rapid increase in the bearing capacity, the damage degree of the concrete in the column increased significantly. In addition, there was little difference in the concrete damage degree when the column reached the yield point and failure point (Fig. 6(c)). However, because of the confinement of
3. Analysis of the seismic behavior of TRC-strengthened RC columns 3.1. Results of the numerical analysis 2.
The numerical analysis results of the specimens are shown in Table
3.2. Failure process and failure pattern analysis The concrete damage plasticity model in ABAQUS cannot directly describe the process of crack development and failure of the specimens, and the specimens exhibited similar failure processes. Therefore, three typical columns were selected with the maximum value of principal plastic strain, the equivalent plastic strain of concrete and the damage of concrete to describe the failure process and failure pattern at the yield point and failure point. In addition, to further illustrate the accuracy of the model in describing the failure process of columns, the corresponding three columns in the previous experiment were selected for verification. Note that because the rationality and accuracy of the model results have been verified with relevant test results, the results of the three columns selected from the previous experiment in this section are not analyzed hereafter. In the early stage of loading, as the loading displacement increases, the horizontal load of the specimen increases, and the tensile stress gradually exceeds the tensile strength of the concrete. Moreover, because of the increase in the damage degree, the cracks first form in the concrete and gradually develop along the normal direction of the tensile stress in the plastic hinge area. Figs. 4 and 5 show that as the loading displacement continues to increase, the concrete plastic strain of the specimen exhibits a gradual change from the bottom to the top, wherein the lower part of the color changes along the Table 2
Numerical analysis results of the specimens. Serial number
C0 C1 C2 C3 C4 C5 C6 C7 C8 C9
Yield
Peak
Failure
Ductility factor
Cumulative energy dissipation
Py/kN
Δy/mm
Pm/kN
Δm/mm
Pu/kN
Δu/mm
average
E/kN·mm
104.59 −102.47 110.75 −110.51 86.50 −87.10 129.44 −129.50 146.42 −145.34 239.87 −248.16 68.61 −69.53 123.48 −126.75 142.94 −135.68 145.21 −145.10
7.09 −6.34 6.05 −6.05 4.93 −4.90 6.77 −6.65 8.00 −7.90 4.00 −4.00 8.30 −8.27 8.81 −7.59 7.16 −6.27 6.76 −5.94
112.85 −110.82 121.80 −123.80 94.35 −94.74 145.50 −146.17 165.61 −166.03 239.87 −248.16 79.54 −79.85 134.35 −134.89 153.50 −151.21 159.70 −162.28
8.00 −8.00 12.00 −12.00 16.00 −16.00 16.00 −16.00 16.00 −16.00 4.00 −4.00 16.00 −16.00 16.00 −16.00 8.00 −8.00 16.00 −16.00
95.92 −94.20 103.53 −105.23 80.20 −80.53 123.68 −124.24 140.77 −141.12 203.89 −210.94 67.61 −67.87 114.19 −114.66 130.48 −128.53 135.75 −137.94
31.55 −27.10 42.52 −41.17 52.00 −52.00 37.51 −33.70 30.26 −29.01 14.05 −12.98 55.46 −55.37 32.58 −29.44 31.54 −35.51 31.47 −31.76
4.36
26072.56
6.91
46881.53
10.58
79246.04
5.30
38825.12
3.73
26009.21
3.38
23151.90
6.69
45778.19
3.79
24231.65
5.03
34664.35
5.00
30299.39
4
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Fig. 4. Moire patterns of maximum principal plastic strains at different stages in specimens. (a) Specimen C0. (b) Specimen C1. (c) Specimen C5.
Fig. 5. Moire patterns of equivalent plastic strains at different stages in specimens. (a) Specimen C0. (b) Specimen C1. (c) Specimen C5.
the TRC, the failure mode of the column was still bending failure when the column failed, which is basically consistent with the failure of column Z2 (Fig. 7(c)). This finding indicates that the TRC improved the failure mode of the column with a small shear span. Therefore, the results suggest that the model established in this paper has a certain rationality and accuracy and can accurately reflect the failure process and failure mode of each specimen in the loading process.
3.3.1. Effect of the TRC reinforcement on the RC columns The hysteresis curves of the unstrengthened column C0 and the strengthened column C1 are shown in Fig. 8 (a) and (b), respectively. The hysteresis curve of the strengthened column C1 is plumper than that of the unstrengthened column C0, and the number of hysteresis loops in the former was significantly higher when the columns failed. In addition, as shown in Table 2, the cumulative energy consumption of C1 is 46881.53 kN mm, which is 79.81% higher than that of C0. This shows that the energy consumption capacity of the strengthened RC column improved. The reason for this increased energy consumption capacity may be that TRC has a good restraining effect on the core concrete, which makes the strength and stiffness of the columns degrade slowly, experience more displacement deformation and dissi-
3.3. Analysis of the hysteresis curves and energy dissipation capacity under different factors The load-displacement hysteresis curves of each column are shown in Fig. 8. 5
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Fig. 6. Damage moire patterns of concrete at different stages in specimens. (a) Specimen C0. (b) Specimen C1. (c) Specimen C5.
Fig. 7. Failure modes of specimens. (a) Un-strengthened Z0. (b) Strengthened with two layer Z1. (c) Strengthened with two layer Z2.
pate more seismic energy. However, for the unstrengthened columns, according to Fig. 4 and Fig. 5, the cracks developed rapidly after the cracking of the columns, and the concrete was crushed, which caused the columns to fail prematurely, resulting in a low energy consumption capacity.
loops, there is little difference in the pinching degree among the columns. Table 2 shows that when the axial compression ratio increased, the cumulative value of energy consumption of all specimens were 40.84%, 59.16% and 67.18% less than that of specimen C2. This trend occurs because under a larger axial compression, the reinforcements yield prematurely in the compression zone, longitudinal cracks form in the column, and the bearing capacity of the columns decreases quickly, which results in poor energy consumption performance.
3.3.2. Effect of the axial compression ratio on the RC columns For columns C2, C1, C3 and C4, as the axial compression ratio increases, the number of hysteresis loops decreases. The pinch phenomenon appeared in the columns, but there was little difference among all columns because the pinch phenomenon is caused by stiffness degradation, and the degree of pinch is related to the crack width and the accumulation of concrete compressive plastic deformation (residual deformation). Fig. 6 and Fig. 7 show that for the columns with smaller axial compression ratios, the concrete strain and the crack width is larger on the tension side than on the compression side. For columns with large axial compression ratios, the axial force could restrain the development of cracks to some extent. Moreover, there is larger lateral expansion in the concrete of columns with a larger axial compression ratio, and the TRC is “activated” so that TRC could confine the concrete and better limit the development of horizontal cracks in the concrete, delay the damage of the concrete, and accelerate crack closure. The crack development in the middle crack is also faster. Therefore, except for the difference in the number of hysteresis
3.3.3. Influence of the shear span ratio on the RC columns Fig. 8(b), (f) and (g) shows that the number of hysteresis loops of specimen C5 is small, and the bearing capacity rapidly decreases with as the horizontal displacement increases after reaching the peak load. Column C5 failed after five cycles, and the ultimate displacement was small. However, the failure mode of column C5 was bending failure, which indicates that TRC could improve the failure mode of columns with a small shear span ratio. As the shear span ratio increases, the number of hysteresis loops of specimens C1 and C6 increases. Moreover, there is an obvious "platform" segment in specimen C6, and the bearing capacity decreases slowly. The ultimate displacement of specimen C6 before failure can reach 55 mm, indicating that the specimens with a large shear span ratio have good ductility and deformation capacity. In addition, according to the results in Table 2, the cumulative 6
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Fig. 8. Hysteresis curves of specimens in different factors. (a) Specimen C0. (b) Specimen C1. (c) Specimen C2. (d) Specimen C3. (e) Specimen C4. (f) Specimen C5. (g) Specimen C6. (h) Specimen C7. (i) Specimen C8. (j) Specimen C9.
energy consumption value of columns C1 and C6 was 102.49% and 97.73% greater than that of C5, respectively, which indicates that although the bearing capacity of the columns with large shear span test pieces is poor, such columns have better energy consumption performance.
number of hysteresis loops greatly increases. When the core concrete strength grade continues to increase, the number of hysteresis loops of the columns changes little (shown in Fig. 8(d), (h), (i), and (j)). In addition, Table 2 shows that the cumulative energy consumption of columns C3, C8, and C9 are 60.22%, 43.05% and 25.04% greater than that of C7, respectively. The reason for this behavior may be that for specimen C3, the compressive strength of the concrete is higher, and the concrete is in a three-way compression state due to the constraint of the TRC, which improved the deformability of the column. There-
3.3.4. Effect of the concrete strength grade on the RC columns For columns with different concrete strength grades, as the strength of the core concrete increases to a strength grade of C40, the 7
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fore, the column could undergo more cycles so that the number of hysteresis loops is much greater and the cumulative energy consumption is relatively larger. Moreover, with the continuous increase in the concrete strength grade, the ultimate compressive strain of the concrete in the specimens reduces further, and the deformation capacity decreases. However, because of the restraining effect of TRC, the deformation ability of specimens C8 and C9 decreases little. Based on Table 2, the ultimate displacements of columns C3, C8 and C9 have little difference, which indicates that the TRC has a good restraining effect on the columns and can improve the deformation ability of the columns with a higher concrete strength grade.
bearing capacity of the specimen increases with increasing axial compression ratio. This behavior is because the restraining effect of the TRC is passive, the transverse expansion deformation of the concrete increases with the larger compressive pressure, and the lateral restraint forces provided by the TRC increase. The strength and ultimate strain of the concrete are improved, and the bearing capacity of the columns is significantly improved. 3.4.3. Effect of the shear span ratio on the TRC-strengthened columns During the initial stage of loading, the stiffness and peak load of C5 are significantly larger than those of C1 and C6. Table 2 shows that the yield load of C5 is 120.57% and 253.29% greater than that of C1 and C6, respectively, and the peak load of C5 is 98.71% and 206.19% greater than that of C1 and C6, respectively. When the bearing capacity reached the peak load, the stiffness of specimen C5 deteriorated significantly, and the bearing capacity decreased rapidly. However, because of the constraint of the TRC, specimen C5 did not exhibit brittle failure; the failure mode was mainly bending failure. As the shear span ratio increased, the ductility and deformation capacity of the specimens improved, although the bearing capacity of the specimens decreased. In addition, the TRC could improve the failure modes of the columns with smaller shear span ratios and avoid shear failure.
3.4. Skeleton curve analysis The skeleton curves of each column are shown in Fig. 9. 3.4.1. Effect of the TRC reinforcement on the RC columns The skeleton curves of the columns before and after reinforcement are shown in Fig. 9(a). The curves show that before and after the column yields, all of the columns are linearly elastic. The curve of the strengthened column is basically coincident with that of the unreinforced column. Table 2 shows that the yield loads of all columns are similar, which means that the TRC does not play a role in the elastic phase. However, as the horizontal load and displacement increase, the concrete expands and causes lateral deformation so that the TRC is activated. Although the thickness of the TRC reinforcement layer is small, the stiffness of the strengthened column is increased to some extent, so that the rigidity of the TRC-strengthened column is slightly larger than that of the unstrengthened column. Fig. 9(a) and Table 2 show that the peak load of C1 is 11.80% greater than that of C0, and the ultimate displacement of the test piece during damage is also significantly larger than that of C0. This finding indicates that TRC can improve the bearing capacity and deformation capacity of the strengthened columns.
3.4.4. Effect of the concrete strength grade on the TRC-strengthened columns Fig. 9(d) shows that during the initial stage of loading, the stiffness of the strengthened columns gradually increases with increasing concrete strength grade. When the bearing capacity reaches the peak load, the peak loads of C3, C8 and C9 are 8.33%, 13.17% and 19.59% greater than that of column C7, respectively. These findings indicate that as the concrete strength grade increases, the peak load and ultimate load of the specimen gradually increase. This behavior occurs because the compressive strength increase as the concrete strength grade increases, and the TRC contributes to the flexural stiffness of the columns. However, after the peak load was reached, the bearing capacity of C8 and C9 with higher concrete strength grades decreased faster than that of column C3, which indicates that the TRC has a greater restraining effect on the specimens with lower concrete strength grades.
3.4.2. Effect of the axial compression ratio on the RC columns Fig. 9(b) and Table 2 show that the yield loads of columns C1, C3 and C4 are 27.91%, 50.00% and 69.77% greater than that of C2, respectively, and the peak loads are 28.72%, 54.26% and 75.53% greater than that of C2, respectively. These findings show that the
Fig. 9. Skeleton curves of specimens in different factors. (a) TRC layers. (b) Axial compression ratio. (c) Shear span ratio. (d) Strength grade of concrete. 8
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tility coefficients of specimens C3, C8 and C9 were 39.84%, 32.72% and 31.93% greater than that of specimen C7, respectively. This phenomenon occurred because after strengthening, the core concrete is in a three-dimensional compressive state and the lateral restraint force is strengthened, which improves the compressive strength of the concrete, delays the failure of the specimens and improves the deformation capacity of the reinforced specimens. In addition, as the concrete strength grade increased, the ductility coefficient of specimen C3 increased the most, and when the concrete strength grade exceeded C40, the ductility coefficient of the specimen decreased. Although the core concrete was confined by the TRC, the concrete with lower strength grade will also be destroyed by concrete crushing due to insufficient compressive strength. Concrete with higher strength grades exhibit brittle characteristics. Although TRC restraint can delay the destruction time to a certain extent, the concrete will still destroy prematurely. Therefore, there may be an applicable range for the concrete strength grade for TRC when strengthening, but this possibility needs to be verified further.
3.5. Ductility analysis The ductility coefficient can quantitatively reflect the ductility of the structures. Thence, the ductility coefficient of the displacement is used to evaluate the ductility of the column. The displacement ductility coefficients is equal to the figure of dividing ultimate displacement by yield displacement. In addition, Park method [26] was used to determine the yield point. The ultimate displacement mainly refers to the displacement corresponding to the load that is the 85% of peak load or the displacement when the specimens failed. 3.5.1. Effect of the TRC reinforcement on the RC columns Table 2 shows that the displacement ductility coefficients of specimens C0 and C1 are 4.36 and 6.91, respectively. The displacement ductility coefficient of C1 is 58.49% greater than that of column C0, and the ultimate displacement of the strengthened column is much larger than that of the unstrengthened column when the columns failed. This finding indicates that the TRC can effectively improve the ductility and deformability of the strengthened columns.
3.6. Stiffness degradation analysis
3.5.2. Effect of the axial compression ratio on the TRC-strengthened columns The displacement ductility coefficients of columns C1, C3 and C4 are 34.69%, 49.91% and 64.74% less than that of column C2, respectively. This behavior occurs because the ultimate compressive strain of the concrete decreases gradually as the axial compression ratio of the columns increases, and the height of the compression zone of the column increases, which results in a decrease in the displacement ductility coefficient of the columns. However, according to Fig. 6 and Fig. 7, the TRC could confine the concrete and limit the development of the horizontal cracks in the concrete, thereby delaying the damage to the concrete. Therefore, the deformation ability of columns with larger axial compression ratios is improved to a certain extent.
The skeleton curves of the columns with different factors are shown in Fig. 10. 3.6.1. Effect of the TRC reinforcement on the RC columns Fig. 10(a) shows that the stiffness degradation curves of specimens C0 and C1 are substantially coincident before the specimen yields, which indicates that the stiffness degradation of each column is basically equivalent before the column yields. However, after the specimen yielded, the rate of stiffness degradation in specimen C0 is significantly higher than that in specimen C1, and the stiffness degradation curve of the reinforced column is also much longer. This behavior shows that the TRC has little effect on the stiffness of the specimens before yielding. However, as the displacement increases after yielding, the TRC has a good restraint effect on the core concrete of the reinforced specimens, which increases the compressive strength of the concrete and slows the deterioration in the stiffness of the specimens. In addition, the TRC delays the failure process of concrete and makes the strengthened column C1 have a larger ultimate displacement than the unstrengthened column C0.
3.5.3. Effect of the shear span ratio on the TRC-strengthened columns The ductility coefficients of C1 and C6 are 104.44% and 97.93% greater than that of specimen C5, respectively. This trend occurs because the initial stiffness of C5 is larger than that of the other specimens and the elastic-plastic deformation of C5 is small, so the bearing capacity quickly reaches the peak load. Although the TRC has a restraining effect on the core concrete, the damage degree of the concrete increased under a large load, and the ultimate compressive strain of the concrete was achieved. The internal concrete was crushed prematurely, causing the column to fail. The ductility of the strengthened column was worse than that of the strengthened columns with a large shear span ratio, indicating that the shear span ratio had a great influence on the ductility of the TRC-strengthened columns and that the shear span ratio is an important factors on the seismic performance for the TRC-strengthened columns. In addition, the ductility coefficient of test piece C6 is slightly lower than that of C1, which is slightly different from the rule presented in the previous experimental results. The analysis shows that except for the errors in the previous experiment and the limitations in accuracy of the model in this paper, the number of specimens in the experiment also has a certain impact. Therefore, a large number of experimental and numerical analyses are needed to further determine the influence of the shear-to-span ratio on the ductility coefficient of TRC-strengthened columns.
3.6.2. Effect of the axial compression ratio on the TRC-strengthened columns The stiffness degradation curves of the specimens with different axial compression ratios are shown in Fig. 10(b). The stiffness degradation rate of each specimen is basically equivalent during the whole loading process. During the later stage of loading, the stiffness degradation rates of the specimens with higher axial compression ratios (C3 and C4) are still slightly higher than those of the specimens with smaller axial compression ratios, and the specimens with high axial compression ratios failed after fewer displacement cycles. After yielding, the stiffness degradation curves of the specimens with lower axial compression ratio (C2 and C1) exhibit a smooth decrease, and the stiffness degradation curves of the reinforced columns are generally longer, which indicates that the deformation capacity and ductility of the reinforced columns decrease with increasing axial compression ratio. However, the stiffness degradation rates of the specimens with higher axial compression ratio do not change significantly, indicating that the TRC has a good restraint effect on the specimens with higher axial compression ratios during the later stage of loading, which could reduce the height of the compression zone of the reinforced specimens to a certain extent and avoid the rapid stiffness degradation of the strengthened columns.
3.5.4. Effect of the concrete strength grade on the TRC-strengthened columns As the strength of the concrete increases, the ultimate compressive strain of the concrete decreases and the deformability decreases, resulting in a decrease in ductility of the RC column. However, in this paper, as the concrete strength grade increased, the displacement duc9
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Fig. 10. Stiffness degradation curves of specimen in different factors. (a) TRC layers. (b) Axial compression ratio. (c) Shear span ratio. (d) Strength grade of concrete.
conclusion needs further verification. In general, the change in core concrete strength grade has little effect on the stiffness degradation rate of strengthened columns.
3.6.3. Effect of the shear span ratio on the TRC-strengthened columns Fig. 10(c) shows that the stiffness degradation of each specimen is faster before and after yielding, and Table 2 shows that specimen C5 reached the peak load immediately after yielding. Therefore, the relative stiffness of specimen C5 is smaller than that of other specimens at the same displacement. This phenomenon occurs because a larger load increases the concrete damage in the specimens increases and the decreases the stiffness of the specimens. In addition, the stiffness degradation rates of specimens C5, C1 and C6 are 0.144, 0.171 and 0.194, respectively, before and after double yield displacement, which indicates that the stiffness degradation rates of the specimens increase as the shear span ratio increases during a period of time after yielding. This phenomenon occurs for the specimens with small shear span ratios because the volume of the concrete expands, and the transverse deformation of specimens increases as the load increases. In contrast to specimens C1 and C6, the TRC was activated prematurely to work in specimen C5, and because of the confinement of the TRC, the stiffness degradation rate of specimen C5 was reduced. However, due to the insufficient restraint of the TRC, specimen C5 failed prematurely. Therefore, the results show that TRC can delay the stiffness degradation rate of the specimens with a small shear span ratio, but a small shear span ratio is still disadvantageous to the strengthened specimens.
4. Conclusions In this paper, the finite element model of a TRC-strengthened RC column was established, and the rationality and accuracy of the model were verified by comparison with the experimental results. Furthermore, the influences of different factors on seismic performance were investigated, and the following conclusions were drawn: (1) The load-displacement hysteresis curve and skeleton curve of the reinforced column obtained by numerical calculation agreed well with the corresponding curves obtained in the previous experiment, which indicated that the model established in the paper had a certain degree of rationality. (2) TRC reinforcement can effectively restrain the core concrete of an RC column, limit the development of cracks, increase the peak load of columns, effectively delay the stiffness degradation of specimens after yielding, and improve the seismic deformation capacity of columns. (3) The bearing capacity of the strengthened column increased with increasing axial compression ratio, but the displacement ductility coefficient and energy dissipation capacity of the reinforced column decreased. (4) As the shear span ratio increased, the ultimate displacement, cumulative energy consumption, ductility, and deformation capacity of the reinforced columns increased, whereas the bearing capacity decreased. In addition, TRC can slow the stiffness degradation rate of small shear span samples to a certain extent after yielding. (5) As the concrete strength grade increased, the peak load of strengthened columns also increased. When the grade of the concrete was within C40, the displacement ductility coefficient and accumulated energy dissipation capacity increased with increasing concrete strength grade. When the concrete strength
3.6.4. Effect of the concrete strength grade on the TRC-strengthened columns Before and after yielding, the stiffness degradation curves of all specimens basically coincide. The stiffness gradually decreases with increasing loading displacement. This trend occurs because there are cumulative damage phenomena after the specimens yield, which cause the stiffness to decrease, and the specimens have elastic-plastic properties after yielding. However, Fig. 10(d) shows that the stiffness degradation rates of the specimens are slightly different in the later stage of loading, and specimens C7 and C8 have longer stiffness degradation curves. The reason may be that for specimens with concrete strength grades between C40 and C50, TRC can play a better role in confinement. However, due to the small amount of data, this 10
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grade reached C40, the displacement ductility coefficient was maximal. However, as the strength grade continued to increase, the changes in the displacement ductility coefficient and accumulated energy dissipation ability were either insignificant or even decreased.
[5] [6] [7]
The study presented herein failed to fully consider the influences of all factors in the establishment of the model used for the numerical analysis, and the number of columns was also small. Whether the conclusions obtained in the paper are universal needs to be verified by a large number of tests and numerical analysis studies in the future.
[8] [9]
Data availability statement
[10]
The datasets used or analyzed during the current study are available from the corresponding author on reasonable request.
[11] [12]
Declaration of competing interest
[13]
We declare that there have not any commercial or associative interests that represent a conflict of interest in connection with this work submitted.
[14] [15]
Acknowledgments
[16]
The authors gratefully acknowledge the financial supported by Outstanding Innovation Scholarship for Doctoral Candidate of CUMT (Grant No. 2019YCBS010). The experimental work described in this paper was conducted at the Jiangsu Key Laboratory of Environmental impact and Structural Safety in Civil Engineering in the China University of Mining and Technology. Help during the testing from staffs and students at the Laboratory are greatly acknowledged.
[17] [18] [19] [20]
Appendix A. Supplementary data
[21]
Supplementary data to this article can be found online at https:// doi.org/10.1016/j.jobe.2020.101245.
[22]
References
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