Numerical Investigation of the Effect of Varying Levels of Corrosion on
Seismic Performance of Beam-Column Joints
Pradeep Singh Shekhawat1, Shubham Dangwal2, Heaven Singh3
1 Scientist-D,
Bureau of Indian Standards, New Delhi-110002
Email address-pardeepshekhawat@bis.gov.in
2 Research Scholar, Civil Engineering Department, Thapar Institute of Engineering and Technology, Patiala-147004, India.
E-mail address- sdangwal_phd18@thapar.edu
3 Assistant Professor, Civil Engineering Department, Thapar Institute of Engineering and Technology, Patiala-147004, India.
E-mail address- heaven.singh@thapar.edu
Abstract
Corrosion of reinforcement bars in a reinforced concrete (RC) structure poses a potential threat to its strength and serviceability
under a seismic environment. The severity of damage due to corrosion on RC structures primarily depends on the magnitude
and location of the steel corrosion. In the present study, the numerical simulation of the seismic behavior of RC Exterior beam-
column joints (BCJ) subjected to non-uniform corrosion was performed. A total of three non-seismically detailed BCJ
specimen models were developed using three-dimensional (3D) nonlinear finite element (FE) analysis with the aid of the
software ABAQUS. The reduction of the cross-sectional area of corroded bars, the mechanical properties of reinforcement
bars, and the deterioration of concrete strength due to splitting cracks and spalling of the concrete cover were considered the
main analytical parameters. From the simulation, it can be observed that the seismic performance degrades significantly as the
level of corrosion increases. The high corrosion rate leads to the brittle fracture of the reinforcement bars, resulting in the
premature failure of the structural member.
Keywords: Finite element modeling, Beam-column joint, Corrosion
1 Introduction
The corrosion damage has been considered a major reason for the premature deterioration of the RC structures.
For RC structures located near the coastal regions and in earthquake-prone regions, the corrosion can severely
degrade the seismic capacity and ultimately endanger the safety of the structures [1–3]. Several experimental
investigations have been conducted to investigate the seismic performance of corrosion-damaged RC members.
The experimental studies stated the cross-sectional area reduction of reinforcing bars, decrease in ductility of steel
bars, and deformation of concrete due to propagation of cracks [4,5]. Even though accelerated corrosion is adopted
to replicate the corrosion damage within the structural member, the process is still tedious and time-consuming.
The experimental setup demands open space and is associated with high costs. Therefore, to evaluate the
performance of corroded RC members, a numerical analysis can render a potentially cost-effective alternative
over experimental tests. Some studies have been conducted on the analytical modeling of the behavior of
corrosion-damaged structural members. The structural response and strength parameters can be numerically
assessed with great reliability using Non-linear Finite element analysis [6–9].
Certain numerical simulation methods have been proposed to determine and investigate the behavioral
changes experienced in corroded RC structural members under seismic loading [10–13]. Fayaz et al. [14]
performed numerical modeling to analyze the seismic performance of beam-column joints strengthened with high
UHPFRC and CFRP. The hysteresis performance of corrosion-damaged RC columns was numerically simulated
using finite element models [15]. As per the previous researchers, the one factor that plays a crucial role in
simulating the behavior of corroded RC structural components is material constitutive relations. In most numerical
studies, a material damage model considering the degradation of concrete strength and steel reinforcements was
adopted to efficiently simulate the behavior of structural components [16–18]. When it comes to simulating
corrosion damage on the FE model, previous studies have shown that it is very difficult to model pitting corrosion
1
due to the randomness of pit distribution. Therefore, most of the numerical studies have modeled pitting corrosion
as uniform corrosion based on average cross-section loss along with empirical coefficients. D. Coronelli et al. [19]
proposed a numerical model in which uniform corrosion was adopted with pitting parameters. Zhao et al. [20]
modeled corrosion-damaged RC beams using a uniform corrosion state along with empirical coefficients
representing the reduction in the strength and ductility of corroded reinforced bars and also by reducing the cross-
sectional area of damaged bars.
Numerical modeling and analysis using modern-day computational software require a much shorter time
and can cover the effects of a wide range of parameters and has been widely applied in civil engineering.
Therefore, a numerical simulation can be proposed based on the experimental data to analyze the hysteretic
performance of corrosion-damaged members under different loading conditions. According to the above analysis,
an Exterior beam-column joints having two different levels of corrosion damage was numerically studied in terms
of hysteresis performance using the non-linear FE software ABAQUS. The two different corrosion levels were
taken from the experimental study performed by S. Dangwal & H. Singh [21] and were introduced in the FE
models. Thereafter, the seismic parameters such as energy dissipation and stiffness were evaluated and compared
with the uncorroded/control specimen.
2 Significance
Analyzing the corrosion effect on the structural member in real site conditions will comprise of high capital
investment, and time taking procedure. Moreover, the necessity of open space and large infrastructure will be a
big challenge. Therefore, the numerical simulation will render a potentially time-saving and cost-effective
alternative, also covering several other parameters. In this numerical study, a Finite element (FE) model is
proposed to analyze the seismic performance of corrosion-damaged structural member under the influence of
seismic loading. The model was expected to provide a simple, reliable computational basis for seismic safety
analysis, reliability assessment, reinforcement, and reconstruction of corroded RC frame structures.
3 Finite element modeling of corroded RC exterior beam-column joints (BCJs)
3.1 Modelling of reinforced concrete BCJ and test parameters
The configuration of the three BCJ specimens (i.e. one control and two corrosion-damaged) to prepare numerical
models was selected from S. Dangwal & H. Singh [21]. For the description and reinforcement detailings of the
BCJ specimen, the experimental study [21] can be referred to. Of the three specimens, one specimen is
uncorroded/control (U), one corroded specimen has a corrosion rate of less than 10% (C-1) while the other
specimens have a corrosion rate of more than 10% (C-2), corrosion rate taken from the experimental study [21],
where U represent uncorroded and C represents corroded.
To simulate the seismic performance of test specimens, a three-dimensional FE model has been proposed
by using ABAQUS software. The concrete was modeled by using an eight-node brick element C3D8R, and the
non-linear behavior was simulated by using the concrete damage plasticity (CDP) model. The CDP parameters
for the normal strength concrete are shown in Table 1. The uncorroded and corroded reinforcement bars were
modeled by using a two-noded truss element (T3D2). The bond between concrete and reinforcement steel was
modeled by imposing a constraint using “EMBEDDED REGION”. Through this constraint, the reinforcement
bars are in perfect bond with the concrete surface. The concrete surface was selected as the host region while the
reinforcement bars cage was embedded inside it, as shown in Fig. 1. Since the specimens have to be tested under
the influence of cyclic loading, displacement-controlled cycles were provided at the top of the beam. To assign
the displacement, a reference point “RP-1” was selected on the top surface of the beam and was bonded to the
surface of the beam with another constraint named “TIE”, as shown in Fig. 2. This TIE bond holds the two
individual surfaces together by avoiding any relative motion between them. The reference point “RP-1” was
selected as the master surface while the beam region was selected as the slave region.
2
Table 1. Concrete damage plasticity parameters for normal strength concrete [14].
Material Dilation Angle Eccentricity fbo/fco k Viscosity Parameter
Normal
35 0.1 1.16 0.667 0.007985
concrete
3.2 Modeling of concrete
Concrete in Compression
The compression behavior of the concrete has been simulated as per the model proposed by Mander and Priestly
[22]. The important parameters such as Peak compressive strength, Poisson ratio, and Modulus of elasticity were
24 MPa, 0.2, and 23 GPa, respectively obtained from the experimental results. Due to the reinforcement corrosion,
spalling and cracking occur on the surface of concrete resulting in reduced strength of concrete. To consider the
corrosion damage on the concrete, Coronelli and Gambarova [19] proposed an equation, representing the
reduction in the strength of the concrete cover.
1
ƒccor= 𝜀 𝑓𝑐′ (1)
1+𝑘 1
𝜀𝑐𝑜
𝜀1 = (bf – bo)/bo (2)
Where,
• 𝑓𝑐′ and ƒccor represents the compressive strength of uncorroded and corrosion-damaged concrete,
• 𝑘 is the coefficient related to bar roughness and diameter (for ribbed bars of medium diameter, 𝑘=0.1),
as suggested by Cape [23],
• 𝜀𝑐𝑜 is strain corresponding to peak compressive stress 𝑓𝑐′ ,
• 𝜀1 is the average tensile strain perpendicular to the direction of the applied compression, in the cracked
concrete,
• bo represents section width with no corrosion cracks,
• bf represents beam width increased by corrosion cracking.
Concrete in Tension
The concrete tensile behavior was modeled through the softening function proposed by [24,25] based on the
tensile peak strength of 2.5 MPa obtained from experimental data.
Modeling of corroded steel bars
For uncorroded reinforcement bars, the mechanical properties are taken as per the experimental data obtained
from the tensile strength testing [21]. To simulate the corrosion damage within the model, parameters like the
3
cross-sectional area of the rebars, elastic modulus, yield strength, ultimate strength, and ultimate strain were
modified as per the proposed model [26,27] and empirical equations given by various researchers [28,29].
𝜋𝐷2 𝑋𝐶𝑅
As(XCR) = (1 − ) (3)
4 100
𝑤0 −𝑤𝑐
XCR = * 100 (4)
𝑤0
Where,
• As represents the reduced cross sectional area of corroded bars
• D represents the diameter of reinforcement bars
• wo and wc represents the weight of uncorroded and corroded reinforcements
• XCR represents the corrosion ratio [21]
ƒyc = (1- 0.00198 XCR)ƒy (5)
Esc = (1- 0.00113 XCR)Es (6)
ƒuc = (1- 0.0019 XCR)ƒu (7)
Ɛuc = (1- 0.021 XCR)Ɛu (8)
Where,
• ƒy and ƒyc represent the nominal yield strength before and after corrosion
• Es, and Esc represent the nominal elastic modulus before and after corrosion
• ƒu and ƒuc represent nominal ultimate strength before and after corrosion
• Ɛu and Ɛuc represent nominal ultimate strain before and after corrosion
3.3 Boundary condition and loading protocol
The boundary condition and the loading conditions applied to the FE model are similar to that provided in the
experimental study [21]. Fig. 2 shows the column end fixed by “ENCASTRE” boundary conditions, column axial
load applied at one end of the column, and also displacement cycles provided at the reference point “RP-1”. The
displacement cycles were set as per the guidelines of American concrete institute (ACI 374.1-05) [30], which can
be referred to [21,31] for a detailed description. A meshing of 50 mm element size has been selected for this
model.
4 Results and Discussion
4.1 Hysteresis behavior of BCJ specimens
The load-displacement hysteretic behavior of the control and two corroded BCJ specimens are shown in Fig. 3.
The control specimen (U) shows wide and large hysteresis loops during the elastic stage. When compared to the
corroded specimen (C-1), the control specimen shows wide loops even at the post-elastic stage resulting in higher
stiffness. Due to corrosion damage, the reinforcement bar has suffered significant degradation in ductility. From
the hysteresis curve of the corroded specimen (C-2), it can be observed that the specimen was not able to dissipate
the energy after the elastic stage. Due to severe corrosion damage at the C-2 specimen, the tensile properties of
the reinforcement bar were significantly distorted and were not able to withstand higher displacement which
resulted in the brittle fracture of the reinforcement bar. The brittle fracture of the reinforcement bar under the
cyclic loading led to the absence of the hysteresis loop in the negative direction for the C-2 specimen. The C-2
specimen showed tensile damage at a severe pitting location (i.e. at 8 mm diameter bar where the fracture
occurred) on the surface of the beam. It can be observed that the concrete will experience cracks and steel-concrete
bonding will worsen due to corrosion damage resulting in the degraded load-bearing capacity.
4
4.2 Load-Displacement Envelope Curves
The envelop curves represent the peak load at each displacement cycle in both positive and negative directions
thereby displaying the decline in the seismic performance at the elastic and post-elastic stage during the entire
loading cycle. Fig. 4 shows the envelop curves of all the specimens. From Fig. 4, it can be observed that at high
displacement specimen C-1 showed a decline in the load-carrying capacity along with the reduced ductility when
compared to the control specimen (U). Specimen C-2 showed a significant decline in the load-carrying capacity,
as the tensile strength of the corroded reinforcement bars was degraded at an alarming rate due to the fracture of
corrosion-damaged bars. The fracture of the 8mm diameter bars can be seen in Fig. 5. It was determined by the
Von Mises stress representation, as the von Mises stress exceeded the tensile stress of the 8mm diameter
reinforcement bars obtained experimentally, after the displacement of 7.8 mm.
(a) (b) (c)
Fig. 3. Hysteresis behavior of (a) Control (b) Corroded specimen (less than 10%, C-1), and (c) Corroded specimen (more than
10%, C-2).
Fig. 4. Load-Displacement Envelop curve of all specimens. Fig. 5. Von Mises stress representation of C-2 specimen.
4.3 Energy Dissipation
Energy dissipation is one of the important seismic parameters indicating the behavior of structural members during
post-elastic deformation. Cumulative energy dissipation is the summation of dissipated energy at each cyclic peak.
Fig. 6 shows the cumulative energy dissipation curve with respect to the drift ratios for all the specimens. When
compared to the control specimen (U), the C-1 specimen shows slightly less energy dissipation. However, the C-
2 specimen showed an alarming reduction in energy dissipation at higher displacement. When compared to the
control specimen (U), the C-2 specimen showed a significant reduction of 46.3% at the drift ratio of 4.36%.
5
However, it can be observed that all the specimens showed similar energy dissipation during the initial drifts and
showed rapid reduction at later drifts indicating the effect of corrosion on the seismic performance of specimens.
4.4 Stiffness Degradation
The inelastic behavior of the BCJ specimens can be analyzed by determining the stiffness degradation over the
post-elastic range. Fig 7. shows the stiffness degradation plot with respect to the drift ratio for all the specimens.
When compared to the control specimen (U), the C-1 and C-2 specimens showed a decrement of 5% and 13%,
16.6%, and 23.21% in the initial stiffness values in the positive and negative cycles, respectively. At the drift of
1%, the C-2 specimen showed a stiffness degradation of approximately 10.5% and 45.45% in the positive and
negative cycle, when compared to that of the control specimen (U). After the drift ratio of 1%, the corroded
reinforcement bar suffered a brittle fracture in the negative cycle.
Fig. 6. Cumulative energy dissipation of all specimens Fig. 7. Stiffness degradation vs Drift ratio plot of all specimens
5 Conclusion
In this paper, a numerical simulation of the seismic performance of the RC beam-column joint having two different
levels of corrosion damage was performed by using ABAQUS software. By analyzing the simulation and the
results, the following conclusions can be drawn:
• The corrosion damage on the reinforcement bars will significantly affect the load-displacement behavior
of reinforced concrete BCJ but has little effect on the elastic stage. The peak load, ultimate load, and
ultimate deflection significantly decrease with the increase in corrosion rate.
• At a severe corrosion rate (i.e., corrosion rate greater than 10%), a brittle fracture of corroded rebars was
experienced in the numerical model during ongoing cyclic displacement resulting in the deterioration of
load-carrying capacity and ductility leading to the premature failure of the specimen.
• The cumulative energy dissipation of the C-2 specimen showed approximately 46% reduction when
compared to that of the control specimen (U), representing a significant deterioration of energy
dissipation capacity at a higher corrosion level.
• The stiffness has shown an alarming decrement with an increase in corrosion rate. For the C-2 specimen,
a stiffness degradation of approximately 45.45 % was observed at the drift ratio of 1%, after that
fracture of reinforcement bars was seen.
6
References
[1] A. Kanchanadevi, K. Ramanjaneyulu, Effect of corrosion damage on seismic behaviour of existing reinforced
concrete beam-column sub-assemblages, Eng. Struct. 174 (2018) 601–617.
https://doi.org/10.1016/j.engstruct.2018.07.094.
[2] J. Cairns, G.A. Plizzari, Y. Du, D.W. Law, C. Franzoni, Mechanical Properties of Corrosion-Damaged
Reinforcement, (2005) 2005.
[3] Q. Li, D. tao Niu, Q. hui Xiao, X. Guan, S. jie Chen, Experimental study on seismic behaviors of concrete columns
confined by corroded stirrups and lateral strength prediction, Constr. Build. Mater. 162 (2018) 704–713.
https://doi.org/10.1016/j.conbuildmat.2017.09.030.
[4] W. Zhu, R. François, Corrosion of the reinforcement and its influence on the residual structural performance of a 26-
year-old corroded RC beam, Constr. Build. Mater. 51 (2014) 461–472.
https://doi.org/10.1016/j.conbuildmat.2013.11.015.
[5] J. Cheng, X. Luo, P. Xiang, Experimental study on seismic behavior of RC beams with corroded stirrups at joints
under cyclic loading, J. Build. Eng. 32 (2020). https://doi.org/10.1016/j.jobe.2020.101489.
[6] J. Cairns, Z. Zhao, Behaviour of concrete beams with exposed reinforcement, Proc. Inst. Civ. Eng. Struct. Build. 104
(1994) 351–355. https://doi.org/10.1680/istbu.1994.26785.
[7] J.R. de B. Silva, B. Horowitz, Nonlinear finite element analysis of reinforced concrete shear walls, Rev. IBRACON
Estruturas e Mater. 13 (2020). https://doi.org/10.1590/s1983-41952020000600003.
[8] F.J. Vecchio, Non-linear finite element analysis of reinforced concrete: at the crossroads?, Struct. Concr. 2 (2001)
201–212. https://doi.org/10.1680/stco.2.4.201.40356.
[9] B.Y. Yuan, ANALYSIS OF CORRODED RE INFOR C ED C O N C R E T E, 117 (2018) 2018–2034.
[10] M.M. Kashani, L.N. Lowes, A.J. Crewe, N.A. Alexander, A multi-mechanical nonlinear fibre beam-column model
for corroded columns, Int. J. Struct. Integr. 7 (2016) 213–226. https://doi.org/10.1108/IJSI-09-2014-0044.
[11] F. Di Carlo, A. Meda, Z. Rinaldi, Numerical evaluation of the corrosion influence on the cyclic behaviour of RC
columns, Eng. Struct. 153 (2017) 264–278. https://doi.org/10.1016/j.engstruct.2017.10.020.
[12] A.S. Rao, M.D. Lepech, A.S. Kiremidjian, X.Y. Sun, Simplified structural deterioration model for reinforced concrete
bridge piers under cyclic loading1, Struct. Infrastruct. Eng. 13 (2017) 55–66.
https://doi.org/10.1080/15732479.2016.1198402.
[13] X. Zhang, B. Li, Shear-Strength Capacity Assessment of Corroded Reinforced Concrete Beam-Column Joints, J.
Perform. Constr. Facil. 32 (2018) 04018067. https://doi.org/10.1061/(asce)cf.1943-5509.0001216.
[14] Q. Fayaz, G. Kaur, P.P. Bansal, Numerical Modelling of Seismic Behaviour of an Exterior RC Beam Column Joint
Strengthened with UHPFRC and CFRP, Arab. J. Sci. Eng. 47 (2022) 4971–4986. https://doi.org/10.1007/s13369-
021-06334-8.
[15] G. Zhao, M. Zhang, Y. Li, D. Li, The Hysteresis Performance and Restoring Force Model for Corroded Reinforced
Concrete Frame Columns, J. Eng. (United Kingdom). 2016 (2016). https://doi.org/10.1155/2016/7615385.
[16] F. Biondini, M. Vergani, Deteriorating beam finite element for nonlinear analysis of concrete structures under
corrosion, Struct. Infrastruct. Eng. 11 (2015) 519–532. https://doi.org/10.1080/15732479.2014.951863.
[17] E. Afsar Dizaj, R. Madandoust, M.M. Kashani, Exploring the impact of chloride-induced corrosion on seismic
damage limit states and residual capacity of reinforced concrete structures, Struct. Infrastruct. Eng. 14 (2018) 714–
729. https://doi.org/10.1080/15732479.2017.1359631.
[18] E.A. Dizaj, R. Madandoust, M.M. Kashani, Probabilistic seismic vulnerability analysis of corroded reinforced
concrete frames including spatial variability of pitting corrosion, Soil Dyn. Earthq. Eng. 114 (2018) 97–112.
https://doi.org/10.1016/j.soildyn.2018.07.013.
[19] D. Coronelli and P. Gambarova, Structural Assessment of Corroded Reinforced Concrete Beams: Modeling
Guidelines, AUGUST. Vol. 130 (2004) 1214–1224. https://doi.org/10.1061/~ASCE!0733-9445~2004!130:8~1214!
[20] G. Zhao, J. Xu, Y. Li, M. Zhang, Numerical Analysis of the Degradation Characteristics of Bearing Capacity of a
Corroded Reinforced Concrete Beam, Adv. Civ. Eng. 2018 (2018). https://doi.org/10.1155/2018/2492350.
[21] S. Dangwal, H. Singh, Seismic performance of corroded non-seismically and seismically detailed RC beam-column
7
joints rehabilitated with High Strength Fiber Reinforced Concrete, Eng. Struct. 291 (2023) 116481.
https://doi.org/10.1016/j.engstruct.2023.116481.
[22] P.R. Mander JB, Priestley MJN, THEORETICAL STRESS-STRAIN MODEL FOR CONFINED CONCRETE By,
114 (1989) 1804–1826.
[23] M. Capé, Residual service-life assessment of existing R/C structures, Chalmers Univ. Technol. Goteborg Milan Univ.
Technol. Italy Erasmus Progr. (1999).
[24] Hordijk DA., Local approach to fatigue of concrete [phD thesis ] Delft university of Technology, (1991).
[25] H.A.W. Cornelissen, D.A. Hordijk, H.W. Reinhardt, Cornelissen, Hordijk, Reinhardt - 1986.pdf, Heronjournal.Nl.
(1986) 45–56. http://heronjournal.nl/31-2/6.pdf.
[26] R.K. Biswas, M. Iwanami, N. Chijiwa, K. Uno, Effect of non-uniform rebar corrosion on structural performance of
RC structures: A numerical and experimental investigation, Constr. Build. Mater. 230 (2020).
https://doi.org/10.1016/j.conbuildmat.2019.116908.
[27] W. Zhang, X. Song, X. Gu, S. Li, Tensile and fatigue behavior of corroded rebars, Constr. Build. Mater. 34 (2012)
409–417. https://doi.org/10.1016/j.conbuildmat.2012.02.071.
[28] X.H. Wang, X. La Liu, Modeling the flexural carrying capacity of corroded RC beam, J. Shanghai Jiaotong Univ. 13
E (2008) 129–135. https://doi.org/10.1007/s12204-008-0129-1.
[29] Q. Wu, Y. Yuan, Experimental study on the deterioration of mechanical properties of corroded steel bars, Tumu
Gongcheng Xuebao/China Civ. Eng. J. 41 (2008) 42–47.
[30] ACI 374.1-05, Acceptance Criteria for Moment Frames Based on Structural Testing and Commentary, ACI Comm.
374. (2005) 1–9.
https://www.concrete.org/store/productdetail.aspx?ItemID=374105&Format=DOWNLOAD&Language=English&
Units=US_Units.
[31] S. Dangwal, H. Singh, Behavior of corrosion damaged non-seismically and seismically detailed reinforced concrete
beam-column sub-assemblages under cyclic loading, Eng. Fail. Anal. 146 (2023) 107135.
https://doi.org/10.1016/j.engfailanal.2023.107135.
