권민수
(Min Su Kwon)
1iD
자바드모르타자비 세예드
(Mortazavi Seyed Javad)
2iD
허종완
(Jong Wan Hu)
3†iD
-
인천대학교 건설환경공학과 대학원생
(Graduate Student, Department of Civil Engineering, Incheon National University, Incheon
22012, Rep. of Korea)
-
인천대학교 도시환경공학부 연구원
(Researcher, Department of Civil and Environmental Engineering, Incheon National University,
Incheon 22012, Rep. of Korea)
-
인천대학교 도시환경공학부 교수
(Professor, Department of Civil and Environmental Engineering, Incheon National University,
Incheon 22012, Rep. of Korea)
Copyright © Korea Concrete Institute(KCI)
키워드
CFRP, 콘크리트 구조물, 유한요소법
Key words
CFRP, concrete structure, finite element method
1. Introduction
In reinforced concrete structures where steel rebars are used to reinforce the concrete,
corrosion of rebars is very common, which causes deterioration and reduction of the
lifetime of concrete structures. Although solutions have been provided to reduce this
problem, it is still one of the biggest challenges of reinforced concrete structures.
One of the solutions offered to solve the problem of corrosion of rebars is to replace
steel material with stainless steel or fiber-reinforced polymer (FRP) materials in
the manufacture of rebars. In addition to reinforcing concrete, FRP materials are
also widely used in repairing damaged concrete structures (Chin and Shafiq 2012). At present, three types of rebar with FRP materials are used in concrete structures,
glass fiber- einforced polymer (GFRP) rebars, basalt fiber-reinforced polymer (BFRP),
and carbon fiber-reinforced polymer (CFRP) (Zhao et al. 2019). As well as corrosion resistance, FRP rebars can have much higher tensile strength
than steel.
Also, The FRP is lighter than steel and non-magnetic. As a result, FRP rebars are
widely used in bridges, offshore structures, nuclear reactor structures, airport pavements,
underground structures, hospital MRI room structures, etc. (Ouria et al. 2016; Parvin and Wang 2002; Aljazaeri et al. 2020; Erfan et al. 2021; Choi et al. 2022; Shill et al. 2022; Cao et al. 2023).
In general, FRP rebars have elastic and brittle behavior (Yoo and Choo 2022). So, unlike steel rebars, if the stress in FRP rebars exceeds the ultimate strength,
the rebar will suddenly break without plastic deformation (Jawdhari and Harik 2018; Kim and Cheon 2022; Kim et al. 2022). So, the behavior of reinforced concrete structures with FRP rebars will be different
from steel reinforced concrete structures. Also, their design criteria are different
(Zhang et al. 2020). Therefore, a detailed investigation of the behavior of these structures is necessary.
Several experimental studies have been conducted on reinforced concrete structures
with FRP bars, and from their results, computational models with good accuracy have
been developed to simulate the behavior of these structures. Accordingly, many researchers
have modeled FRP-reinforced concrete structures using the finite element method (FEM)
and compared the results with the experimental results (Fiedler et al. 2001; Ibrahim and Salman 2009; Jawdhari and Harik 2018; Peng et al. 2018; Higuchi et al. 2020). These results have confirmed the accuracy of the FEM in the modeling and analysis
of these structures.
In this research, the behavior of beams, columns, shear walls, two-way slabs, and
the connection of beams columns of reinforced concrete with CFRP rebars has been investigated
using the FEM. One sample of each of these members has been modeled in FEM structural
analysis software and analyzed under specified load and boundary conditions, and the
results have been presented.
2. Model Description
2.1 Materials
The concrete used in this research has 48 MPa compressive strength and 4 MPa tensile
strength. Its specific weight, elastic modulus, and Poisson’s ratio are considered
equal to 2,350 Kg/ m3, 36,267 MPa, and 0.2, respectively. CFRP rebars with 2,500 MPa ultimate strength,
modulus of elasticity equal to 150 GPa, and 0.25 Poisson’s ratio are used as reinforcement
rebars.
2.2 Column model
A cantilever column with 1.5 m length and a circular cross-section is considered.
An axial compressive load is applied to the upper face of the column. Eight #4 CFRP
bars with 6.35×10-3 m diameter and 1.29×10-4 m2 net area are embedded in this column (Fig. 1).
2.3 Beam model
The studied beam is a simply supported beam with a rectangular cross-section, which
is subjected to a linear gravity load in the middle of the beam. This beam is shown
in Fig. 2 In this beam, three CFRP bars, each with 5.0×10-2 m diameter, are placed as tensile bars throughout the length of the beam.
2.4 Shear wall model
The investigated shear wall has a length of 1.2 m, a thickness of 0.2 m and a height
of 3 m, which is reinforced with two layers of CFRP rebar mesh with 1.0×10-2 m diameter. This wall is fixed at the lower face and is under lateral load at the
upper face as presented in Fig. 3.
2.5 Two-way slab
To study the behavior of reinforced concrete slab with CFRP rebar, a two-way slab
has been selected. One layer of CFRP rebar mesh with 6.0×10-3 m diameter is embedded in this slab according to Fig. 4. This slab has simple support in the lower perimeter of the slab and a distributed
gravity load is applied to the upper face of the slab.
Fig. 4 Two-way slab model
2.6 Beam-column connection
Fig. 5 shows the studied beam-column connection. The beam of this connection is 0.25 m width,
0.4 m height, and 1.75 m length, and the cross section of the column connected to
it is 0.25×0.40 m. Three CFRP rebars are installed at the top and bottom of the beam
and eight rebars are in the column. Each rebar has 8×10-3 m in diameter. Also, the free end of the beam is under gravity load, and both ends
of the column are fixed about the transition degree of freedom.
Fig. 5 Beam-column connection model
3. Finite Element Modeling
Abaqus software has been used for modeling and analyzing the studied models (Simulia 2017). In the modeling process, first, the model geometry is defined using the part module.
In the next step, the mechanical properties of the materials are defined in the property
module. The concrete damage plasticity (CDP) model has been used to define the nonlinear
behavior of concrete (Szczecina and Winnicki 2015). The parameters used in the definition of this model in the Abaqus software are shown
in Table 1.
In addition to the above parameters, the plastic behavior of concrete as well as the
damage coefficient of concrete in pressure and tension should also be entered into
the software. To simulate the behavior of concrete under compression, the EC2 model
is used (Puurula et al. 2015):
Table 1 Concrete damaged plasticity model parameters
|
Parameter
|
Unit
|
Value
|
|
Elastic modulus
|
MPa
|
36,267
|
|
Poisson's ratio
|
-
|
0.20
|
|
Dilation angle
|
degree
|
35
|
|
Eccentricity
|
-
|
0.10
|
|
fb0/fc0
|
-
|
1.16
|
|
K
|
-
|
0.667
|
|
Viscosity parameter
|
-
|
0.00
|
where, $\sigma_{c}$ : Compressive stress
$\eta =\epsilon_{c}/\epsilon_{c1}$
$\epsilon_{c}$ : Compressive strain
$\epsilon_{c1}$ : Strain at the compressive strength of concrete
$f_{cm}$ : Mean compressive strength of concrete at 28 days age
$k=1.05E_{cm}\left |\epsilon_{c1}\right | /f_{cm}$
$E_{cm}$ : Elastic modulus of concrete
Fig. 6 shows the concrete stress-strain diagram in compression computed using the EC2 equation.
To define the non-linear behavior of concrete in tension, a bilinear model has been
used, which is defined based on the area under the stress-crack width diagram, which
is the fracture energy. The fip 1990 standard code has been used to compute the fracture
energy (CEB-FIP 1991). The stress-crack width diagram of concrete is shown in Fig. 7.
The behavior of CFRP before rupture is linear and elastic, so the elastic model has
been used to define this material, and its strength has been input into the model
to simulate the rebar rupture. For simplicity, the rebar slip in concrete was ignored,
and then the interaction between concrete and CFRP rebars was considered fully constrained.
In order to increase the accuracy of finite element analysis, the studied models have
been simulated in three-dimensional and analyzed using the quasi-static nonlinear
analysis method with a dynamic explicit solver. Using a boundary condition at the
desired location, displacement control methodology was implemented in these models.
Since these locations are different in each model, these points are explained in the
results section. Concrete parts have meshed with three-dimensinal (3D) eight-node
cubic elements and CFRP rebars have meshed with beam elements. The finite element
model of the beam is shown in Fig. 8.
Fig. 6 Stress-strain diagram of concrete in compression
Fig. 7 Stress-crack width diagram of concrete in tension
Fig. 8 Concrete beam finite element model
3.1 Verification
To verify the FEM modeling method used in this paper, a concrete column reinforced
with longitudinal and transverse CFRP rebars was considered. The size and details
of this column are shown in Fig. 9.
The properties of CFRP rebars used in the column are presented in Table 2. The compressive strength of the concrete of the column was considered as 42.9 MPa.
Afifi et. al has been performed experiments on columns with these characteristics
(Afifi et al. 2014). They applied axial load on the top face of the column and the axial force-displacement
diagram was provided as output. Also, this column has been modeled in Abaqus software
and analyzed under axial load using FEM and the results have been compared with the
experimental results (Fig. 10).
Table 2 CFRP rebar properties, as used in the verification model
|
Bar size
|
Diameter (m)
|
Area (m2)
|
E (GPa)
|
Ft (MPa)
|
|
#3
|
9.5×10-3
|
7.1×10-5
|
120
|
1,596
|
|
#4
|
1.27×10-2
|
1.29×10-4
|
140
|
1,899
|
As can be seen, the results of the finite element analysis agree with the experimental
results.
Fig. 9 Verified column detail
Fig. 10 Comparison of experimental and FEM results
4. Results
4.1 Column model
In the Fig. 11, Tresca stress is shown in the column. As can be seen, the maximum stress in concrete
occurs at the support, which is due to the conditions of the applied boundary conditions.
In Fig. 12, the axial stress of the column’s rebars is shown. The stress distribution in these
rebars is also as expected and the highest compressive stress in the rebars can be
seen at the support.
In Fig. 13, the force-displacement curve of the column is presented. The column totally loses
its strength after peak stress.
Fig. 11 Tresca stress in the column model
Fig. 12 Axial stress in the Column’s CFRP rebars
Fig. 13 Force-Displacement diagram of the column model
4.2 Beam model
Considering that the studied beam was under gravity load in the middle of its span,
there is an internal shear force and bending moment at the same time almost throughout
the beam length. The simultaneous effect of these two forces on the Tresca stress
of the beam can be seen in Fig. 14.
In Fig. 15, the axial stress in the beam rebars is shown. As expected, the maximum stress of
the rebar is located in the middle of the beam bay and the minimum stress is located
at both ends of the beam.
The behavior of the beam under the applied load can be better understood using the
force-deformation diagram. Therefore, in Fig. 16, the graph of the force applied to the beam against the displacement of the beam
at the mid-span is drawn. As can be seen, when the force reaches about 300 KN, the
curve dropped suddenly, which is due to the failure of the concrete in the compressive
area of the beam. Because the rebars are not damaged, the beam can still withstand
further deformation.
Fig. 14 Tresca stress in Beam model
Fig. 15 Axial stress on CFRP rebars in Beam model
Fig. 16 Force-Deflection diagram on the beam model
4.3 Shear wall model
To see the stress distribution in the shear wall, the Tersca stress in the studied
wall is shown in Fig. 17. As can be seen, the location of maximum compressive stress is near the support.
It should be noted that the maximum internal moment is located at the support point
in the wall.
Fig. 18 shows the stress distribution in the shear wall rebars. The vertical rebars on the
right side of the wall are under compression and the vertical rebars on the left side
of the wall are under tensile stress. Also, the place of maximum tensile and compressive
stress of rebars is located near the support.
As can be seen in Fig. 19, although the initial lateral stiffness of the shear wall is high, it decreases sharply
after reaching the maximum strength, which is mainly caused by concrete cracking under
tensile stress.
Fig. 17 Tresca stress in the shear wall model
Fig. 18 Stress distribution in the CFRP rebars of the shear wall model under lateral load
Fig. 19 Lateral displacement-force diagram on the shear wall
4.4 Two-way slab model
According to the ratio of the length to the thickness of the slab (22.26), it is expected
that the studied slab behaves as a shell under the applied loads. As a result, to
study the distribution of cracking due to tensile stress in this slab, the distribution
of the damage ratio in tension is shown in Fig. 20. The highest value of this parameter occurs in the corners and edges of the slab
due to the concentration of stress caused by the application of boundary conditions,
while in the middle of the slab we see cracking due to internal tensile stress.
Fig. 21 shows the stress distribution in the rebars of this slab. The maximum stress is located
in the center of the slab, and the amount of stress decreases as you move away from
the center of the slab. As expected, the stress in the rebars is tensile.
To study the effect of the plastic behavior of the slab, the change of the total force
applied to the slab against the displacement of the center of the slab is shown in
Fig. 22. As the force applied to the slab increases, the stiffness of the slab decreases,
which is mainly caused by concrete cracking under tensile stress. and CFRP rebars
should withstand higher loads.
Fig. 20 Tresca stress distribution in the two-way slab
Fig. 21 Axial Stress in the CFRP rebars of the two-way slab model
Fig. 22 Force-Displacement diagram of the two-way slab
4.5 Beam-column connection model
In Fig. 23, the Tresca stress in the beam-column connection is shown. The maximum stress occurs
at the connection of the beam to the column and at the lower face of the beam, which
is caused by the presence of the maximum moment force in this place.
The beam cracked at the interface of the beam to the column connection because the
tensile stress in the upper face and compressive stress in the bottom face of the
beam is more than concrete strength.
Fig. 24 shows the axial stress of the beam-column connection rebars.
As can be seen, there is no significant stress in the column rebars, while the maximum
tensile stress is located in the beam bars, especially near the intersection of the
beam and the column.
The diagram of force versus vertical displacement at the free end of the beam of the
studied connecting is shown in Fig. 25. As can be seen, this connection can withstand acceptable plastic deformation.
Fig. 23 Tresca stress in the Beam-Column connection model
Fig. 24 Axial stress in the CFRP rebars of Beam-Column connection model
Fig. 25 Force-Displacement diagram of the beam-column connection
5. Conclusion
To investigate the behavior of reinforced concrete structures with CFRP rebars, a
beam, column, shear wall, two-way concrete slab, and a beam-column connection were
analyzed using the FEM under applied loads and the results were presented. Considering
that CFRP rebars are not ductile, therefore, in the design of structures where these
rebars are used to reinforce concrete, the required rebar area is calculated in such
a way that the rebar does not fail under the loads applied to the structure. There
was such a situation in all the investigated models and despite the occurrence of
tensile cracks and even the compression plastic deformation of concrete, the internal
stress of the rebars was lower than the rupture strength, and the structure model
was not destroyed. Also, from the results of these analyses, it was determined that
a brittle behavior can be expected in columns and beams where there is little possibility
of force redistribution after the concrete has been crushed in compression. While
due to the redistribution of internal force from the crushed concrete to the CFRP
rebars in the shear wall, the beam-column connection, and the two-way slab, much more
ductility was observed.
In general, it can be concluded that the replacement of steel rebars with CFRP rebars
in reinforced concrete structures, while making the structure durable against corrosion
and increasing the life cycle of the structure, did not cause a significant change
in the behavior of the structure under loads in the plastic range.
Acknowledgement
This research is supported by the Korea Agency for Infrastructure Technology Advancement
(KAIA) grant funded by the Ministry of Land, Infrastructure and Transport (Grant 22CFRP-
C163381-02).
References
Afifi, M. Z., Mohamed, H. M., and Benmokrane, B. (2014) Strength and Axial Behavior
of Circular Concrete Columns Reinforced with CFRP Bars and Spirals. Journal of Composites
for Construction 18(2). https://doi.org/10.1061/(ASCE)CC.1943-5614.0000430
Aljazaeri, Z., Alghazali, H. H., and Myers, J. J. (2020) Effectiveness of Using Carbon
Fiber Grid Systems in Reinforced Two- way Concrete Slab System. ACI Structural Journal
117(2), 81-89. 10.14359/51720198.
Cao, X., Chen, Y., Wang, H., Cheng, C., Zhou, X., Zhang, H., Kim, S. E., and Kong,
Z. (2023) Experimental and Numerical Investigation of 800 MPa HSS welded T-section
Column Strengthened with CFRP. Thin-Walled Structures 184. 10.1016/j.tws.2022.110510.
CEB (2010) CEP-FIP Model Code 2010. Lausanne, Switzerland; International Federation
for Structural Concrete (fib), Comite Euro-International du Beton (CEB).
Chin, S. C., and Shafiq, N. (2012). Strengthening of RC Beams with Large Openings
in Shear by CFRP Laminates: Experiment and 2D Nonlinear Finite Element Analysis. Research
Journal of Applied Sciences, Engineering and Technology 4(9), 1172-1180.
Choi, S. Y., Hong, S. C., Park, S. K., and Jeong, S. W. (2022) Effects of Diameter-to-thickness
Ratio on Impact Energy Absorption Capability of CFRP Cylindrical Crash Box. International
Journal of Automotive Technology 23(6), 1663- 1671. 10.1007/s12239-022-0144-5.
Erfan, A. M., Abd Elnaby, R. M., Aziz Badr, A., and El-sayed, T. A. (2021) Flexural
Behavior of HSC One Way Slabs Reinforced with Basalt FRP Bars. Case Studies in Construction
Materials 14. 10.1016/J.CSCM.2021.E00513.
Fiedler, B., Hojo, M., Ochiai, S., Schulte, K., and Ochi, M. (2001) Finite-element
Modeling of Initial Matrix Failure in CFRP under Static Transverse Tensile Load. Composites
Science and Technology 61(1), 95-105. 10.1016/S0266-3538(00)00198-6.
Garcez et al. 2022;
Higuchi, R., Aoki, R., Yokozeki, T. and Okabe, T. (2020) Evaluation of the In-situ
Damage and Strength Properties of Thin- ply CFRP Laminates by Micro-scale Finite Element
Analysis. Advanced Composite Materials 29(5), 475-493. 10.1080/09243046.2020.1740867.
Ibrahim. A. M., and Salman, W. D. (2009) Finite Element Analysis of Reinforced Concrete
Beams Strengthened with CFRP in Flexural. Diyala Journal of Engineering Sciences 02(02).
https://www.iasj.net/iasj/download/7d92e70202d6b45c.
Jawdhari, A., and Harik, I. (2018) Finite Element Analysis of RC Beams Strengthened
in Flexure with CFRP Rod Panels. Construction and Building Materials 163, 751-766.
Kim, J.-S., Jeong, S.-M., Kim, H.-J., Kim, Y.-J., and Park, S.-G. (2022) Bond Strength
Properties of CFRP Bars according to W/C Ratios and Diameters of the CFRP. Journal
of the Korea Concrete Institute 34(6), 675-680.
Kim, K. M., and Cheon, J. H. (2022) Flexural Behavior of One- Way Slab Reinforced
with Grid-Type Carbon Fiber Reinforced Plastics of Various Geometric and Physical
Properties. Applied Sciences (Switzerland, 12(23). 10.3390/app122312 491.
Ouria, A., Toufigh, V., Desai, C., Toufigh, V., and Saadatmanesh, H. (2016) Finite
Element Analysis of a CFRP Reinforced Retaining Wall. Civil and Architectural Engineering
and Mechanics 18(6), 757-774. 10.12989/gae.2016.10.6.757.
Parvin, A., and Wang, W. (2002) Concrete Columns Confined by Fiber Composite Wraps
under Combined Axial and Cyclic Lateral Loads. Composite Structures 58(4), 539-549.
10.1016/S0263-8223(02)00163-0.
Peng, S., Xu, C., Lu, M., and Yang, J. (2018) Experimental Research and Finite Element
Analysis on Seismic Behavior of CFRP-Strengthened Seismic-Damaged Composite Steel-
Concrete Frame Columns. Engineering Structures 155, 50-60. 10.1016/j.engstruct.2017.10.065.
Puurula, A. M., Enochsson, O., Sas, G., Blanksvärd, T., Ohlsson, U., Bernspång, L.,
Täljsten, B., Carolin, A., Paulsson, B., and Elfgren, L. (2015) Assessment of the
Strengthening of an RC Railway Bridge with CFRP Utilizing a Full-scale Failure Test
and Finite-element Analysis. Journal of Structural Engineering 141(1). 10.1061/(ASCE)ST.1943-541X.0001116.
Shill, S. K., Garcez, E. O., Al-Ameri, R., and Subhani, M. (2022) Performance of Two-Way
Concrete Slabs Reinforced with Basalt and Carbon FRP Rebars. Journal of Composites
Science 6(3), 74. 10.3390/JCS6030074.
Simulia (2017) Abaqus 6.11 Theory Manual. Providence, RI, USA: DS SIMULIA Corp.
Szczecina, M., and Winnicki, A. (2015) Calibration of the CDP Model Parameters in
Abaqus. Berkeley, California, USA; Structures and Materials Research, Department of
Civil Engineering Series 100, University of California.
Yoo, S. W., and Choo, J. F. (2022) Behavior of CFRP-reinforced Concrete Columns at
Elevated Temperatures. Construction and Building Materials 358. 10.1016/j.conbuildmat.2022.129425.
Zhang, D., Wang, H., Burks, A. R., and Cong, W. (2020) Delamination in Rotary Ultrasonic
Machining of CFRP Composites: Finite Element Analysis and Experimental Implementation.
International Journal of Advanced Manufacturing Technology 107(9-10), 3847-3858. 10.1007/S00170-020-05310-0.
Zhao, Q., Zhao, J., Dang, J. T., Chen, J. W., and Shen, F. Q. (2019) Experimental
Investigation of Shear Walls Using Carbon Fiber Reinforced Polymer Bars under Cyclic
Lateral Loading. Engineering Structures 191. 10.1016/j.engstruct.2019.04.052.