Journal of Civil Engineering and Management

ISSN 1392-3730 / eISSN 1822-3605

2022 Volume 28 Issue 7: 523–535
https://doi.org/10.3846/jcem.2022.16683

INVESTIGATION OF THE PERFORMANCE OF RC BEAMS

REINFORCED WITH FRP AND ECC MATERIALS

Guorui SUN1, 2, Jie LAI3, Yuzhou ZHENG4, Kaikai ZHENG2, Jun SHI1, 5*
1School
of Civil Engineering, Central South University, Changsha, China
2KeyLab of Structures Dynamic Behavior and Control of the Ministry of Education,
Harbin Institute of Technology, Harbin, China
3Academy of Combat Support, Rocket Force University of Engineering, Xi’an, China
4School of Field Engineering, Army Engineering University of PLA, Nanjing, China
5National Engineering Laboratory for High Speed Railway Construction, Changsha, China

Received 15 October 2021; accepted 18 January 2022

Abstract. This paper investigates the structural working behavior of reinforced concrete beams bonded with fiber rein-
forced polymer and engineered cementitious composite materials subjected to bending using structural stressing state the-
ory. First, six reinforced concrete beams externally bonded with composite reinforcement layer and one control beam are
tested to investigate the effects of the bond length, fiber reinforced polymer grid thickness and fiber content on the flexural
behavior. Then, the finite strain data of RC beams are interpolated by the numerical shape function method. The gener-
alized strain energy density model is established to characterize the stressing state of the structure. Through the Mann-
Kendall criterion, the characteristics load P and Q of the beams are detected, and the whole loading process is divided into
three stage. Finally, the analysis of the strain and deformation on the beams reveals the effect of different parameters on
different stage. The characteristic load P increases as the bond length increases, and the characteristic load Q increases as
the thickness of the FRP and the fiber content increase. The vertical deformation of the strengthened beam for the charac-
teristic load Q and ultimate load is significantly smaller than that of the unreinforced beam.
Keywords: fiber reinforced polymer, composite reinforcement layer, stressing state, characteristic load, reinforcement con-
crete beam.

Introduction
Over the past few decades, the demand for repairing and ronment, the bearing capacity of an FRP-reinforced beam
strengthening reinforced concrete (RC) structures has is also significantly improved. In the case of steel corro-
steadily increased. Among them, fiber reinforced polymer sion, the ultimate load of an FRP-reinforced beam was
(FRP) has been widely used in the repair and reinforce- 14.8% higher than that of the unreinforced beam (Kadhim
ment of RC beams due to its convenient construction, et al., 2019). The reason for this may be that the FRP plays
light weight and high strength (Godat et  al., 2020; He an important role in resisting the load after the reinforce-
et al., 2020; Sogut et al., 2021). ment yields (Kara et al., 2015). The bonding property be-
In recent years, many valuable experimental studies tween FRP and concrete is the key factor for controlling
have been carried out to investigate the working behavior the behavior of RC structures strengthened with FRP (Yao
of beams strengthened with FRP. The curvature, deflection et al., 2005). However, traditional bonding materials, such
and flexural performance of RC beams determined using as epoxy resins, are susceptible to environmental effects.
different reinforcement methods were compared through Therefore, many scholars have attempted to utilize other
experimental and theoretical analyses. The results show innovative bonding materials to replace epoxy resins and
that the bearing capacity of RC beams strengthened with update the FRP strengthening system (Al-Salloum et al.,
the FRP method is better than that achieved by other re- 2011; Dai et al., 2014; Escrig et al., 2015; Ge et al., 2017).
inforcement methods (Li et al., 2020). In a corrosive envi-

*Corresponding author. E-mail: csushijun@csu.edu.cn

Copyright © 2022 The Author(s). Published by Vilnius Gediminas Technical University

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unre-
stricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
524 G. Sun et al. Investigation of the performance of RC beams reinforced with FRP and ECC materials

Engineered cementitious composite (ECC) materi- CRL through the bending test. Based on the numerical
als with high ductility and multipoint uniform cracking shape function (NSF) method, the limited strain data of
have a wide range of applications in civil engineering (Ma the beams are interpolated to obtain more detailed strain
et al., 2021; Shanmugasundaram & Praveenkumar, 2021). information. Then, through structural stressing state the-
When FRP and ECC materials are combined to reinforce a ory, the generalized strain energy density (GSED) model
structure, the properties of both can be effectively utilized, is introduced to analyze the stressing state of the struc-
and the ultimate load of the structure can be significantly ture. The leap characteristic in the Ej,norm-Fj curve can be
increased. Hence, researchers have used ECC materials as detected by the Mann-Kendall (M-K) criterion, and the
the transition layer to investigate the flexural behaviors of loading stages of the structure can be divided through the
RC beams strengthened with FRP (Afefy et al., 2015; Yuan characteristic load. In addition, according to the strain
et  al., 2021). The results show that ECC materials could mode and the deformation of the experimental beams,
avoid the premature shedding of FRP sheets and improve the reliability of the characteristic load is verified. Finally,
the ultimate load of the test beams. Ge et al. investigated the influence of different parameters on the structure at
the effect of the FRP content and ECC thickness on the different loading stages can be determined by comparing
flexural properties of RC beams. Based on the test results, the characteristic load, section strain and displacement.
the failure modes of the strengthened beams were deter-
mined, and a formula for calculating the bearing capacity 1. Experiments for RC beams strengthened with CRL
was proposed (Ge et  al., 2019). Zheng et  al. proposed a
new strengthening method for RC beams by combining 1.1. Configuration of the experimental RC beams
basalt FRP grid and ECC materials as a composite rein- The flexural experiment was performed on RC beams
forcement layer (CRL). The proposed technique is effec- strengthened with an FRP grid and an ECC Southeast
tive for suppressing the debonding of externally bonded University, and the dimensions of the structure are shown
materials and fully utilizing the strength of the material in Figure 1. The experimental RC beam was 1800 mm in
(Zheng & Wang, 2015; Zheng et al., 2016, 2018). length, 200 mm in width and 300 mm in height. The effec-
In summary, a great deal of research has been con- tive length of the beam was 1700 mm with two ends sim-
ducted on strengthening RC structures with FRP. Howev- ply supported. The yield stress and fracture strength of the
er, there are still two problems to be solved in the analysis longitudinal reinforcement were 560 MPa and 640 MPa,
of structures strengthened with FRP and ECC materials, respectively. And the compressive strengths of concrete
which are summarized below: were 35 MPa. After the RC beams were maintained for 28
1. The reliability of the reinforced system must still be days and polished with a grinding wheel, the BFRP grid
verified due to the limited experimental data. At the was first fixed to the bottom surface of the RC beams by
same time, the existing analytical methods cannot means of pre-built steel studs. After that, a 30 mm thick
effectively investigate the stressing state character- ECC layer was placed along the longitudinal direction of
istics of the structure, and the limited experimental the beam to form the CRL. The CRL is located below the
test data cannot be fully exploited. beam with a width of 200 mm. The CRL was fabricated
2. Researchers have concentrated on studying the in- into a plate with dimensions of 400 mm (length) × 100 mm
crease in the ultimate load of beams rather than (width) × 30 mm (thickness) for the tensile test. The ul-
clarifying the effects of the reinforcement methods timate loads of CRL for 0 mm, 1 mm, 3 mm and 5 mm
on the different loading stages. The effect of different thick BFRP grids were 8.5 kN, 12 kN, 16.8 kN and 20.1 kN,
parameters on the flexural properties of the struc- respectively. No relative slip occurred between FRP and
ture at different loading stages is not clear. ECC, while the damage mode of CRL was FRP fracture
In view of the above problems, this paper investigates damage. The properties of FRP and ECC in CRL are
the working behavior of RC beams strengthened with a shown in Table 1 to Table 3.

Figure 1. Structural dimensions of the experimental RC beam

Journal of Civil Engineering and Management, 2022, 28(7): 523–535 525

Table 1. Properties of ECC placements were recorded in the mid-span cross section
and the loading cross section through the displacement

fiber (%)
meter. The distance between the mid-span cross section

Flay ash
Cement
(kg/m3)

(kg/m3)

(kg/m3)

(kg/m3)

(kg/m3)

(kg/m3)
reducer
Quartz
Water

Water
Silica
and the loading cross section was 250 mm.

fume
sand

PVA
During the test, four-point bending tests were used
1.4 1 4 0.15 0.15 0.05 1.3/2.0 for all beams. First, the concentrated load was applied
through the jack at the top of the experimental setup, and
Table 2. Properties of FRP then the concentrated load was distributed to two loading
points through the distributed beam, as shown in Figure
Thickness Tensile Modulus of 2b. The distance between the loaded section and the cen-
Elongation
of FRP grid strength of elasticity
(mm) FRP (MPa)
(%)
(GPa)
ter section of the span was 250 mm. The loads were ap-
plied in a step-by-step approach, each step was held for 5
1 357 0.27 51
minutes and the deformation and crack development of
3 386 0.26 53 the beams were recorded. The magnitude of the concen-
5 416 0.22 57 trated load was recorded by a loading sensor connected to
a hydraulic jack. The increment of the concentrated load
Table 3. Different factors of the experimental RC beams was fixed at 5 kN/ grade before the concrete crack and
10 kN/ grade after the concrete crack. When the experi-
Bond length Fiber Thickness Compressive mental beam was broken, the test ended and the damage
Number of CRL content of of FRP strength of model was recorded.
(mm) ECC (%) grid (mm) ECC (MPa)
BB0 None None None None
2. Theoretical analysis method
BB1 500 1.3 1 31
BB2 500 1.3 3 31 2.1. Numerical shape function method
BB3 500 1.3 5 31 In structural analysis, the experimental data can charac-
BB4 450 1.3 3 31 terize the working behavior of a structure to some extent,
BB5 400 1.3 3 31 but the response mechanism and characteristics of the
BB6 500 2.0 3 33 structure cannot be fully presented due to a limitation in
the measuring instrument. Hence, to obtain more infor-
mation regarding the response mechanism and charac-
1.2. Distribution of the measurement teristics of the structure, the NSF method was proposed,
points and loading scheme which can accurately interpolate or extend experimental
Figure 2a shows the distribution of the displacements and data with clear physical significance. The NSF method is a
strain measurement points of the experimental beams. The new and effective interpolation method that directly inter-
strains of the longitudinal reinforcement were recorded in polates experimental data fields through traditional shape
the mid-span cross section, the loading cross section and functions and finite element simulations. This approach
the bearing cross section. The strains of the concrete, CRL not only overcomes the disadvantages of traditional shape
and FRP grid were recorded in the mid-span cross section. functions but also meets the accuracy requirements of ex-
Among them, G1–G5 represent the strain of the concrete, perimental analysis.
and G6 represents the strain of the CRL. G7, G9 and G10 To vividly introduce the NSF method, the strain field
represent the strain of the steel bar at different cross sec- of the experimental beam numbered BB5 is taken as an ex-
tions. G8 represents the strain of the FRP grid. The dis- ample. As shown in Figure 3a, the mid-span cross section

a) b)

Figure 2. Experimental device: a – Distribution of the strain and displacement measurement points of the RC experimental beams;
b – Loading scheme of the RC experimental beam
526 G. Sun et al. Investigation of the performance of RC beams reinforced with FRP and ECC materials

was constructed by using ANSYS software. Shell unit 181 a) b) c)

was used for the concrete slab and CRL slab with a thick-
ness of 5 mm, and the unit area was 5×5 square mm. The
beam 188 elements were used to simulate ordinary steel
rebar and FRP in the cross-section. Its thickness was also
5 mm, and their area was the actual area. Additionally, it
was assumed that the connection between the steel bar
and the concrete is was rigid. Moreover, 16 measurement
nodes in the mid-span cross section were taken as the ba-
sic nodes of the numerical shape function. By applying
displacement at the i-th measuring nodes and limiting dis-
placement at other measurement nodes, the shape func- Figure 3. Finite element model: a – Measuring point;
tion Ni of the measuring nodes i can be obtained from b – Node 3; c – Node 9
the finite element simulation, such as N3 and N9 shown
in Figure 3b and 3c. the real measured values, and the error between them can
Without considering large deformation and elasto- be calculated by Eqn (3):
plasticity, the simulation results calculated by this method
can be superimposed linearly. Therefore, the NSF method εijs − εije
can be used to calculate the interpolation field of the mid- dij = × 100% , (3)
εije
span cross section of the experimental beam as follows:

 ( )
Ni =  N i ( x1 ) , N i ( x2 )N i x j N i ( xn )  , (1)

where dij is the error of the i-th node at the j-th load step
between the interpolation and experiment and εs ij and
where Ni is the numerical shape function of the i-th meas- εe ij are the interpolating and experimental strains of the
uring node, Ni(xj) is the simulated value at element node i-th node at the j-th load step, respectively. The average
xj and n is the total node of the plate. error of the i-th node in the whole loading process can be
m estimated by Eqn (4):
D= ∑ ui Ni , (2) 1
N
i =1
di =
N ∑ dij , (4)
j
where D is the deflection field of the section, ui repre-
sents the measuring samples and m is the total number of where`di is the average error of the i-th node and N is the
measured nodes. Among them, there is no CRL section of total number of load steps. Hence, the precision of the
the experimental beam BB0. Therefore, m = 12 when the NSF method can be determined through the error values
experimental beam is BB0, and m = 16 when referring to and the comparison curves comparing the interpolated
the other experimental beams. and experimental data.
Accordingly, the finite measured strain in the cross Taking measuring nodes 2 and 13 as examples, the
section can be interpolated by shape function expansion experimental and interpolation curves of the measuring
to obtain the strain field. To verify the precision of the points are shown in Figure 4a, and the fitting degree of
NSF method, 14 out of 16 measured strain nodes on the the data can be clearly observed. During the entire load-
mid-span cross section are adopted to construct the strain ing process, the curves for the same point have very high
field, and then the interpolation results at the other two fitting degrees. The error of all measuring points is shown
points can be obtained. These values are compared with in Figure 4b, and the error results are relatively small, and

a) b)

Figure 4. The error results of strain data mid-span section: a – Comparison curve of measuring points in mid-span section;
b – Error of all measuring points
Journal of Civil Engineering and Management, 2022, 28(7): 523–535 527

the average errors are less than 9% and the maximum er- N
rors are less than 15% throughout the loading period, thus ∑ Eij
fully meeting the application requirements. Therefore, the E j ,norm = i =1
, (8)
NSF method can be used to sufficiently and accurately ex- EM
tend the experimental data to explore the potential char- where Ej,norm is the normalized GSED sum under the j-th
acteristics of the structural forces in depth. load; EM is the maximum strain energy value over the load-
The working behavior and failure mechanism of the ing process; and N is the total number of measured points.
structure can be investigated more comprehensively Thus, the structural stressing state could be appropriate-
through the changing characteristics of the internal forces. ly characterized by the GSED values, and the Ej,norm -Fj
Therefore, the in-plane bending moment of the mid-span curve of the structure could be plotted to investigate the
cross section can be constructed by the NSF method. The stressing state characteristics of the structure.
calculation method of the in-plane bending moment was
achieved by summing the product of the longitudinal 2.3. M-K criterion
stress, vertical distances and area for each element:
The M-K criterion is a widely used trend analysis tool that
Mj= ∫A ∑
σydA = σij yi Ai , (5) does not need to comply with a certain distribution or
adapt to the interference of individual outliers (Kendall &
A
where σij is the stress of the i-th element at the j-th load Gibbons, 1990; Shi et al., 2019; Xiao et al., 2021). Hence,
step, Ai is the area of the i-th element, Mj is the in-plane the M-K criterion is applied to identify the mutation of
bending moment at the j-th load step, and yi is the vertical the structural stressing state from the Ej,norm-Fj curve. It
distance of the i-th element from the neutral axis. is assumed that the sequence of Ej,norm (the j-th load step,
where j is 1, 2, …, n) is statistically independent. Then, the
M-K criterion procedure is as follows:
2.2. Structural stressing state concept
For the Ej,norm-Fj curve, the cumulative number mi and
To resolve the problem that the definition of the struc- stochastic variable dk are calculated by the following equa-
tural stressing state is not uniform and accurate, this paper tions:
defines the stressing state of the loaded structure as the +1 E j ,norm ( i ) > E j ,norm ( j )(1 ≤ j ≤ i )
structural working behavior. In other words, the stress- mi =  ; (9)
ing state of the structure is defined as the internal or ex- 0 otherwise
k
ternal mode of the structure under a certain load, which
is characterized by the numerical model of the structural
= dk ∑
mi ( 2 ≤ k ≤ n ). (10)
i
responses such as strains, displacements, and GSEDs. The
stressing state of the structure will change with increas- The “+1” value means adding one more to the existing
ing load, showing different characteristics at certain load value if the inequality on the right side is satisfied for the
levels, which is in accordance with the law of the quanti- j-th comparison. The mean value E(dk) and the variance
tative to qualitative change of the system. To determine V(dk) of dk can be calculated by the following equations:
the corresponding numerical model and characteristic k ( k − 1)
parameters of the structure, the GSED is introduced to =E ( dk ) ( 2 ≤ k ≤ n ) ; (11)
4
express the stressing state of the measured point (Huang
k ( k − 1)( 2k + 5 )
et al., 2014; Mann, 1945). Hence, the GSED can be calcu- = V ( dk ) ( 2 ≤ k ≤ n ). (12)
lated by Eqn (6): 72
εij By normalizing dk, the gradient UFk can be calculated
Eij =
∫0 σdε , (6) by Eqn (13):
(dk − E(dk ))
where Eij is the GSED value of the i-th measured point UFk = . (13)
under the j-th load and εij is the strain value of the i-th v(dk )
point under the j-th load. The strain of every node on the Finally, the UFk-F curve can be plotted. The proceed-
cross section is obtained through the NSF method, and ing inverse E’ sequence is consistent with the prior se-
the GSED values can be summed by Eqn (7): quence, which can form the UBk -F curve. Therefore, the
N leap points of the Ej,norm -Fj curve can be determined by
Ej = ∑ Eij Ai , (7) the intersection of the UFk and UBk curves.
i =1
where Ej is the GSED value of the measured section at the 3. Analysis of experimental results
j-th load step; N is the number of elements; and Ai is the
area of the i-th element. Then, a normalized GSED value 3.1. Ultimate loads and failure modes
is adopted as a characteristic parameter of the structural For beam BB0, the concrete at the bottom cracked when
stressing state, and the normalized GSED sum is calcu- the load was 31 kN. With increasing load, the cracks con-
lated by Eqn (8): tinued to expand along the height direction of the beam,
528 G. Sun et al. Investigation of the performance of RC beams reinforced with FRP and ECC materials

while the number of microcracks at the bottom continued 3.2. Investigation into the Ej,norm-Fj curve
to increase. After the reinforcement yielded, the deforma-
In order to study the effect of each influencing factor
tion of the structure increased rapidly. With a further in-
on the beam at each stage of the loading process after
crease in load, the concrete in the compression zone was
strengthening, the structural stressing state theory and
damaged. For beams BB1~BB6, when the load was 51~61
NSF method are used to study the sudden change charac-
kN, the concrete at the bottom cracked, while multiple mi-
crocracks appeared in the CRL. As the load increased, the teristics of the structure. The stressing state model of the
width and number of cracks at the bottom increased, and RC beam is represented by the GSED value composed of
the number of microcracks extended toward the loading the strain data, which can be calculated from Eqn (6). The
point. After the reinforcement yielded, the CRL showed Ej,norm-Fj curve can be described to investigate the devel-
multipoint uniform cracking. Microcracks started to ap- oping tendency and sensitivity of the RC beam’s stressing
pear at the interface between the CRL and concrete for state during the entire loading process.
beams BB3 and BB6. With the further increase in load, In this section, taking the experimental beam BB5 as
the FRP of the beams fractured, and the structure reached an example, the Ej,norm-Fj curve is plotted to analyze the
the ultimate load. working behavior of the RC beam, as shown in Figure 6.
The ultimate loads and damage modes of the speci- Characteristic load P (50 kN) and characteristic load Q
mens are shown in Figure 5. The damage mode of RC (110 kN) in the Ej,norm-Fj curve are distinguished by the
beam BB0 in the control group is concrete crushing after M-K criterion. Before characteristic load P is reached, the
yielding of the reinforcement. The damage mode of RC curve increases slowly and approaches a straight line, in-
beam BB0 in the control group is concrete crushing af- dicating that the experimental beam is in a stable stressing
ter yielding of the reinforcement. The damage modes of state. After that, the curve still increases slowly, but the
beams BB1, BB2, BB4 and BB5 are that the FRP fractures growth rate increases and is curvilinear, indicating that
first, and then, the concrete is crushed in the compressed the test beam undergoes some plastic deformation and the
area. The damage mode of beam BB3 is first FRP fracture, stressing state of the structure changes. Beyond character-
and then, the interface between the CRL and concrete is istic load Q, the curve increases sharply compared with
separated and damaged. The damage mode of test beam the previous stage, displaying a different tendency, indicat-
BB6 is that the FRP fractures first, then partial separa- ing that the RC beam changes from a stable stressing state
tion between the CRL and concrete occurs, and finally, to an unstable stressing state.
the concrete in the compression zone is crushed. The bond In conclusion, characteristic load P can be regarded as
length of the CRL does not change the damage mode of the demarcation point of the RC beam from one working
the beam. The results show that with the increase in the state to another. At this time, although the working state
fiber content in the ECC and the thickness of the FRP, the changes, the whole structure remains in a stable working
damage pattern changes, and separation of the CRL and state. The working state of the structure changes qualita-
concrete interface may occur. The bond length of the CRL tively beyond characteristic load Q and is different from
does not change the damage mode of the beam. Compar- the working state of the previous stage. The RC beam can
ing the ultimate loads of different beams shows that the be seen as the demarcation point from a stable working
ultimate loads of RC beams keep increasing as the thick- state to structural failure. Characteristic load Q is differ-
ness of the FRP grid, the fiber content of the ECC and the ent from the ultimate load and is the starting point of the
bond length of the CRL increase. structure failure process.

Figure 5. Ultimate loads and failure modes

Journal of Civil Engineering and Management, 2022, 28(7): 523–535 529

(characteristic load P), the region beyond the ultimate

tensile strain appears and expands with an increase in the
load. At the same time, the strain of the longitudinal rein-
forcement and FRP grid increases rapidly, and the maxi-
mum tensile strain of the mid-span cross section is con-
centrated in the CRL and reinforcement region. As shown
in Figure 7b, beyond characteristic load Q, the maximum
tensile strain of the mid-span cross section is concentrated
in the CRL region. Compared with the previous stage, the
gap between the strain of the FRP grid and the strain of
Figure 6. The Ej,norm-Fj curve and M-K statistic curves of the the reinforcement increases rapidly, indicating that the
experimental RC beam numbered BB5 tensile strain is mainly borne by the FRP grid during the
failure stage. The strain distribution of the CRL in beam
3.3. Investigation into the characteristics BB5 is relatively uniform, indicating that the CRL could
of the strain fields uniformly bear the tensile stress.
The mid-span cross section of the experimental beam is
meshed through the finite element method, and the meas- 3.4. Analysis of the structural stressing state mode
ured strain is interpolated according to the NSF method Based on the strain data obtained by extending the NSF
to obtain the strain field. The strain contour map near the method, the stressing state model of the RC beams was
characteristic loads P and Q was analyzed, as shown in established. The strain of a measuring point can represent
Figure 7. To analyze the strain distribution of the mid- the stressing state of this point, which leads to the strain
span cross section, dotted lines of different colors are used of the measuring points of the different cross sections be-
to represent the different strain values. Among them, the ing assembled to cause the stressing state mode of the RC
separatrix of 0 με is marked with a red dotted line to iden- beam into a vector. Then, the Sstrain-Fj curves are plotted
tify the distributions of the compression zone and ten- based on the experimental data to analyze the changing
sion zone of concrete. The ultimate tensile strain of the characteristics of the stressing state mode and the working
concrete is marked with a black dotted line to show the performance of the RC beam. The Sstrain-Fj curve of RC
working condition of the concrete. beam BB5 is shown in Figure 8. Among them, the ultimate
At the beginning of loading, the strain of the mid-span tensile strain of concrete (ey) and yield strain of steel bar
cross section is small, and the distribution is uniform, as (e′y) were obtained experimentally.
shown in Figure 7a. The strain of concrete is less than the Before characteristic load P (50 kN) is reached, the
ultimate tensile strain, indicating that the stressing state of strain of the beam increases slowly, and the Sstrain-Fj curve
concrete does not change. When the load reaches 50 kN can be approximately regarded as a straight line, indicat-

a)

b)

Figure 7. The strain contour maps of BB5: a – The strain contour maps corresponding to the characteristic load P;
b – The strain contour maps corresponding to the characteristic load Q
530 G. Sun et al. Investigation of the performance of RC beams reinforced with FRP and ECC materials

ing that the structural stressing state remains stable. When The leap characteristics of the structural working perfor-
the load reaches 50 kN, cracks appear at the bottom of the mance of the beam at characteristic loads P and Q are
concrete in the mid-span cross section. The tensile strain consistent with the law revealed in Figure 8. At the initial
of concrete gradually reaches the ultimate tensile strain stage of loading, the strain increment of the FRP grid is
and no longer bears tensile stress. The strain curve of con- small, the strain increment increases beyond characteris-
crete in the compression zone gradually shows a curvi- tic load P, and the strain increment beyond characteristic
linear distribution. The tension assumed by the concrete load Q increases suddenly compared with the previous
at the bottom before cracking is transferred to the steel two stages, indicating that the structural stressing state
bar and CRL, which results in a sudden increase in the mode has changed at the failure load ascertained by the
strain of the steel bar and CRL. Compared with the load- M-K criterion. Hence, the rationality of the M-K criterion
ing cross section, cracks appear earlier in the mid-span and the stressing state theory was verified by analyzing the
cross section of concrete. Thus, when the load is 50 kN, strain trends and distribution laws.
the strain of longitudinal reinforcement in mid-span cross
section suddenly increases, and when the load is 60 kN, 4. Experimental study on RC beams
the strain of longitudinal reinforcement in bearing cross strengthened by different CRL schemes
section suddenly increases.
Beyond the characteristic load Q (110 kN), the strain 4.1. Investigation into the Ej-Fj curve and in-plane
growth rate of concrete in the tension zone remains stable bending moment of the mid-span cross section
because the concrete has been damaged. The compressive According to the NSF method, the GSED values of the
strain of the concrete in the compression zone increased different RC beams of the mid-span cross section are
rapidly until the experimental beam is fractured. Com- plotted in Figure 10 to further investigate the common
pared with the previous stage, the tensile strain of the FRP and different working characteristics. The stressing state
grid increases rapidly. The reason may be that after the of each beam is divided into three stages by the charac-
steel bar reaches the yield load, the tensile force of the teristic loads. The lower the GSED value is, the better the
steel bar gradually transfers to the FRP grid. In the whole stability of the structure. Under the same load, the GSED
process of the experiment, the strain of the CRL is higher value of the strengthened beam is less than that of the
than that of the concrete, and the strain of the FRP grid in control beam, indicating that the reinforcement method
the CRL is higher than that of the longitudinal reinforce- can improve the stability of the beam. The longer the bond
ment, indicating that the CRL plays a significant role in length of the CRL is, the lower the GSED value is, indicat-
the bearing tensile stress. ing that the bond length of the CRL has a certain effect on
The variation trend of the strain at key points of the the bearing capacity of the strengthened beam. The GSED
mid-span cross section of the beam is shown in Figure 9. values of different reinforced RC beams are approximated

a) b)

Figure 8. The Sstrain-Fj curves of RC beam numbered BB5: a – The Sstrain-Fj curves for the concrete and CRL;
b – The Sstrain-Fj curves for the longitudinal reinforcement and FRP grid

Figure 9. The stressing state of the structure at measuring points of beam numbered BB5
Journal of Civil Engineering and Management, 2022, 28(7): 523–535 531

before the characteristic load P is reached. Beyond charac- commodate more load during the elastic stage. With an
teristic load P, the GSED value of the strengthened beam increase in the thickness of the FRP grid and the fiber
is incrementally smaller than that of the control beam. content, the strengthened beams are able to endure more
Beyond characteristic load Q, the GSED value of the rein- loads during the elastic-plastic stage, which indicates that
forced beam is much smaller than that of the unreinforced the thickness of the FRP grid has a certain influence on
beam. This result further verifies the reliability of the char- the elastic-plastic stage of the beam. With a reduction in
acteristic load and shows that the effect of the reinforce- the bond length of the CRL, the load that the strengthened
ment method on the structure is mainly concentrated after beam can bear in the elastic stage decreases, indicating
the characteristic load. that the influence of the bond length of the CRL of the
Based on the NSF method, the in-plane bending mo- beam in the elastic stage is greater than that in other stag-
ment can be obtained, as shown in Figure 10b. Under the es. In summary, the bond length of the CRL, the thickness
same load, the bending moment value of the strengthened of the FRP grid and the fiber content in the CRL can be
beam is smaller than that of the control beam, but the used to increase the ultimate bearing capacity of the ex-
gap is not large, which indicates that the strengthening perimental beam by increasing the load that can be borne
method has little influence on the bending moment. in the elastic stage or elastic-plastic stage.
The proportions of the different loading stages during
4.2. The characteristic points of different schemes the test are shown in Figure 11b. Compared to control
beam BB0, strengthened beams have a greater proportion
The cracking load of the concrete is close to characteristic
of the elastic stage in the overall loading process. The fail-
load P, and the yield load of the reinforcement is close to
ure stage of the strengthened beam accounts for a rela-
the characteristic load Q. The gap between the cracking
tively small percentage of the overall loading process.
load and the characteristic point P is less than 10%, and
the gap between the yield load and the characteristic load
4.3. Investigation into the characteristics
Q is less than 6%. Hence, based on the stressing state of
of strain fields
the beam, the elastic stage is determined from the initial
load to characteristic load P, the elastic-plastic stage is de- To further investigate the effect of the strengthening meth-
termined from the characteristic load P to characteristic od, the strain contour map of the beam is shown in Fig-
load Q, and the failure stage is beyond the characteristic ure 12, and the strain contour maps of the experimental
load Q. beams BB6 and BB0 are compared. At the initial loading
The loads of the beam at different stages are shown stage, the strain distribution of the test beam is approxi-
in Figure 11a. Beams bonded with CRL are able to ac- mate, indicating that the strengthening method has little

a) b)

Figure 10. The Ej-Fj curves and in-plane bending moment with different beams of the mid-span cross section:
a – The Ej-Fj curve; b – The in-plane bending moment

a) b)

Figure 11. Three stages in the test: a – Loads at different stages; b – The proportion of the different loading stages
532 G. Sun et al. Investigation of the performance of RC beams reinforced with FRP and ECC materials

influence on the strain distribution of the test beam in in Figure 13a. In the elastic stage, the strain of the rein-
the elastic stage. The crack area of the control beam ap- forcement is small, and the reinforcement strain of the
pears earlier than in the strengthened beam. In the elastic- strengthened beam is close to that of the control beam.
plastic stage and failure stage, the maximum tensile strain In the elastic-plastic stage, the strain of the reinforcement
of the beam BB0 is mainly concentrated in the reinforce- increases rapidly. Since the CRL could assist the reinforce-
ment area, while the maximum tensile strain of the beam ment in bearing tensile force, the reinforcement strain of
BB6 is mainly concentrated in the CRL area. In summary, the strengthened beam under the same load is less than
the reinforcement method could change the distribution the strain of the control beam. At this point, due to the
of the tensile strain in the elastic-plastic and failure stages different thicknesses of the FRP grid, the reinforcement
of the structure. strain is different. In the failure stage, the strain of the
The strain of the longitudinal reinforcement at the reinforcement increases rapidly compared with that in the
mid-span cross section is analyzed, as shown in Figure previous stage, and the reinforcement strain value of the
13. Among them, ε P represents the reinforcement strain control beam is much higher than that of the strengthened
of the experimental beam BB0 when it reaches character- beam.
istic load P, and ε Q represents the reinforcement strain of The influence of the CRL bonding length and fiber
the experimental beam BB0 when it reaches characteristic content on the steel bar strain is shown in Figure 13b and
load Q. The influence of the thickness of the FRP grid 13c. Here, the shorter the bond length of the CRL is, the
on the strain of the reinforcement is studied, as shown greater the final strain value of the reinforcement, but the

a)

b)

Figure 12. The strain contour maps: a – Beam numbered BB0; b – Beam numbered BB6
Journal of Civil Engineering and Management, 2022, 28(7): 523–535 533

fiber content has little influence on the final strain. In con- ment. With the reduction of the bond length of CRL, the
clusion, the method proposed in this paper could reduce gap between the strain of reinforcement and the strain
the tensile stress of steel reinforcements in the elastic-plas- of concrete measuring point G5 decreases. The effects of
tic stage and failure stage due to the partial tensile stress strengthening method on the strain of concrete and rein-
borne by the CRL. forcement mainly concentrated in the elastic-plastic stage
Figure 14 shows the strain modes at the mid-span and the failure stage.
cross section of experimental beams with different bond
length of CRL. By comparing the compressive strain of 4.4. Investigation into the structural deformation
different experimental beams, the strengthening method of the experimental beams
has little effect on concrete strain in compression zone. The effects of the strengthening schemes on structural de-
During the whole loading process, the tensile strain of the formation are studied, as shown in Figure 15. Here, dP and
concrete of the beam BB0 is much smaller than that of the dQ represent the vertical displacement of the experimen-
reinforcing steel. Compared with the experimental beam tal beam BB0 when it reaches characteristic load P and
BB0, the tensile strain of the concrete of the other experi- characteristic load Q, respectively, and dF represents the
mental beams increasees and the strain of the steel bars vertical displacement of the beam numbered BB1 when it
decrease. When the experimental beam numbered BB2, reaches the breaking load.
BB4 and BB6 entered the elastic-plastic stage, the strain The vertical deformation of the experimental beams
of CRL increased rapidly, and the strain corresponding to numbered BB0, BB1, BB2 and BB3 is investigated, as
the breaking load was greater than that of the reinforce- shown in Figure 15a. In the elastic stage, the vertical dis-

a) b) c)

Figure 13. Strain of reinforcement in different experimental beams: a – Experimental beams with different thicknesses of FRP grid;
b – Experimental beams with different bond lengths of CRL; c – Experimental beams with different fiber contents

a) b)

c) d)

Figure 14. Strain of mid-span cross section in different experimental beams: a – Experimental beam numbered BB0;
b – Experimental beam numbered BB2; c – Experimental beam numbered BB4; d – Experimental beam numbered BB6
534 G. Sun et al. Investigation of the performance of RC beams reinforced with FRP and ECC materials

placement increases slowly, and the deformation of the method adopted in this paper could reduce the vertical
strengthened beam is close to that of the unreinforced deformation of the beam in the elastic-plastic stage and
beam, which indicates that the strengthening method has the failure stage, especially in the failure stage. The final
little effect on the deformation. In the elastic-plastic stage, vertical deformation of the strengthened beam is signifi-
the vertical displacement growth rate of the experimen- cantly lower than that of the control beam. The thickness
tal beams increases, and the growth rate of different ex- of the FRP grid, bond length of the CRL and fiber content
perimental beams are different. Under the same load, the have little influence on the final vertical deformation of
deformation of all strengthened beams is less than that the beam.
of the control beam, indicating that the method could re-
strain the deformation of the beam in the elastic-plastic Conclusions
stage. Although the displacement of the beams increased
at different rates, the vertical deformation of the beams The flexural tests of RC beams bonded with FRP grids and
was close to each other when the experimental beams ECC materials were carried out, and the GSED parameters
reached the yield load. In the failure stage, the vertical were constructed based on the structural stressing state
displacement increases rapidly compared to the previous theory and NSF method. Using the M-K criterion tool, the
stage, and the deformation of the strengthened beam is leap characteristics of the strengthened RC beams were
much smaller than that of the control beam during the revealed, and the hidden mechanical properties under dif-
whole failure stage. Under the same load, as the thickness ferent strengthening conditions were reflected. The main
of the FRP grid increases, the vertical deformation of the conclusions are as follows:
beam decreases. When the experimental beams reach the (1) The damage mode of the control set is typical
breaking load, the vertical deformation of the strength- concrete damage, and the damage mode of the
ened beams is similar and much smaller than that of the strengthened beam is mainly FRP fracture. The ul-
control beam. timate load of RC beams strengthened with CRL is
The vertical deformation of other experimental beams significantly improved compared to control beams
is shown in Figure 15b and 15c. Under the same load, the and increases with the increase of bond length of
CRL, fiber content in ECC and FRP thickness.
a)
(2) The Ej,norm-Fj curve is constructed using the struc-
tural stressing state theory, and the M-K criterion
is used to identify the leap characteristics (char-
acteristic loads P and Q) of the structure from
the stable state to the unstable state. The essential
changes of the structural stress state are revealed,
and the loading process is divided into the elas-
tic stage and the elastic-plastic stage as well as the
failure stage.
b) (3) The analysis of deformation, strain of different ma-
terials and the trend of GSED further reveals the
abrupt change characteristics at the characteristic
load. The experimental strain data do not reflect
the working characteristics of the overall structure,
so the NSF method is introduced to give the strain
fields at critical sections. The method directly re-
flects the stress state characteristics of beams un-
der different loads, highlights the variation at the
characteristic loads, and further verifies the reli-
c) ability of the M-K criterion.
(4) Different influencing factors have different effects
on different loading stages of the beam. The longer
the bond length of CRL the higher the characteris-
tic load P. The higher the FRP thickness and fiber
content the higher the characteristic load Q. Com-
pared to unreinforced beam, the reinforced beam
has less vertical deformation in the elastic-plastic
and failure stages.
Figure 15. The vertical displacement of different experimental
beams: a – The experimental beams with different thicknesses Acknowledgements
of the FRP grid; b – The experimental beams with different
bond lengths of the CRL; c – The experimental beams with The authors would like to thank the members of the CSU
different fiber contents 1004 office for their selfless help and useful suggestions.
Journal of Civil Engineering and Management, 2022, 28(7): 523–535 535

Funding Kadhim, A. M., Numan, H. A., & Özakça, M. (2019). Flexural

strengthening and rehabilitation of reinforced concrete beam
This work was financially supported by the National Natu- using BFRP composites: Finite element approach. Advances
ral Science Foundation of China (Grant Nos. 52008399). in Civil Engineering, 2019, 4981750.
https://doi.org/10.1155/2019/4981750
Kara, I. F., Ashour, A. F., & Köroğlu, M. A. (2015). Flexural be-
Author contributions havior of hybrid FRP/steel reinforced concrete beams. Com-
Guorui Sun and Yuzhou Zheng conceived the study and posite Structures, 129, 111–121.
were responsible for the design and development of the https://doi.org/10.1016/j.compstruct.2015.03.073
Kendall, M. G., & Gibbons, J. D. (1990). Rank correlation meth-
data analysis. Jie Lai and Yuzhou Zheng were responsible
ods (5th ed.). Edward Arnold.
for data collection and analysis. Kaikai Zheng and Jun Shi Li, D., Zhou, J. L., & Ou, J. P. (2020). Damage, nondestructive
were responsible for data interpretation. Guorui Sun wrote evaluation and rehabilitation of FRP composite-RC structure:
the first draft of the article. A review. Construction and Building Materials, 271, 121551.
https://doi.org/10.1016/j.conbuildmat.2020.121551
Disclosure statement Xiao, H. H., Luo, L., Shi, J., Jiang, H. C., & Wu Z. W. (2021).
Stressing state analysis of multi-span continuous steel-
The authors declare no conflict of interest. concrete composite box girder. Engineering Structures, 246,
113070. https://doi.org/10.1016/j.engstruct.2021.113070
Mann, H. B. (1945). Nonparametric tests against trend. Econo-
References metrica, 13, 245–259. https://doi.org/10.2307/1907187
Ma, H., Yi, C., & Wu, C. (2021). Review and outlook on durabil-
Afefy, H. M., Kassem, N., & Hussein, M. (2015). Enhancement of
ity of engineered cementitious composite (ECC). Construc-
flexural behaviour of CFRP-strengthened reinforced concrete
beams using engineered cementitious composites transition tion and Building Materials, 287(2), 122719.
layer. Structure and Infrastructure Engineering, 11(8), 1042– https://doi.org/10.1016/j.conbuildmat.2021.122719
1053. https://doi.org/10.1080/15732479.2014.930497 Shanmugasundaram, N., & Praveenkumar, S. (2021). Influence
Al-Salloum, Y. A., Siddiqui, N. A., Elsanadedy, H. M., Abadel A. A., of supplementary cementitious materials, curing conditions
& Aqel M. A. (2011). Textile-reinforced mortar versus FRP and mixing ratios on fresh and mechanical properties of en-
as strengthening material for seismically deficient RC beam- gineered cementitious composites-A review. Construction and
column joints. Journal of Composites for Construction, 15, Building Materials, 309(22), 125038.
920–933. https://doi.org/10.1016/j.conbuildmat.2021.125038
https://doi.org/10.1061/(ASCE)CC.1943-5614.0000222 Shi, J., Zheng, K. K., Tan, Y. Q., Yang K. K., & Zhou, G. C. (2019).
Dai, J. G., Munir, S., & Ding, Z. (2014). Comparative study of Response simulating interpolation methods for expanding
different cement-based inorganic pastes towards the develop- experimental data based on numerical shape functions. Com-
ment of FRP strengthening technology. Journal of Composites puters and Structures, 218, 1–8.
for Construction, 18(3), A4013011. http://doi.org/10.1016/j.compstruc.2019.04.004
https://doi.org/10.1061/(ASCE)CC.1943-5614.0000420 Sogut, S., Dirar, S., Theofanous, M., Faramarzi, A., & Nayak, A.
Escrig, C., Gil, L., Bernat-Maso, E., & Puigvert, F. (2015). Ex- N. (2021). Effect of transverse and longitudinal reinforcement
perimental and analytical study of reinforced concrete beams ratios on the behaviour of RC T-beams shear-strengthened
shear strengthened with different types of textile-reinforced with embedded FRP BARS. Composite Structures, 262(5),
mortar. Construction and Building Materials, 83, 248–260. 113622. http://doi.org/10.1016/j.compstruct.2021.113622
https://doi.org/10.1016/j.conbuildmat.2015.03.013 Yao, J., Teng, J. G., & Chen, J. F. (2005). Experimental study on
Ge, W. J., Ashour, A. F., Ji, X., Cai, C., & Cao, D. F. (2017). Flex- FRP-to-concrete bonded joints. Composites Part B: Engineer-
ural behavior of ECC-concrete composite beams reinforced ing, 36(2), 99–113.
with steel bars. Construction and Building Materials, 159, https://doi.org/10.1016/j.compositesb.2004.06.001
175–188. https://doi.org/10.1016/j.conbuildmat.2017.10.101 Yuan, W. Y., Han, Q., Bai, Y. L., Du, X. L., & Yan, Z. W. (2021).
Ge, W. J., Ashour, A. F., Cao, D., Lu W., Gao, P., Yu, J., Ji, X., & Compressive behavior and modelling of engineered cementi-
Cai, C. (2019). Experimental study on flexural behavior of tious composite (ECC) confined with LRS FRP and conven-
ECC-concrete composite beams reinforced with FRP bars. tional FRP. Composite Structures, 272(15), 114200.
Composite Structures, 208, 454–465. https://doi.org/10.1016/j.compstruct.2021.114200
https://doi.org/10.1016/j.compstruct.2018.10.026 Zheng, Y. Z, & Wang, W. W. (2015). Tensile behaviour of FRP
Godat, A., Hammad, F., & Chaallal, O. (2020). State-of-the- grid strengthening ECC composite under a uniaxial loading.
art review of anchored FRP shear-strengthened RC beams: In Second International Conference on Performance-based and
A study of influencing factors. Composite Structures, 254, Lifecycle Structural Engineering (pp. 529–535), Brisbane, Aus-
112767. https://doi.org/10.1016/j.compstruct.2020.112767 tralia. https://doi.org/10.14264/uql.2016.1149
He, W., Wang, X., & Wu, Z. (2020). Flexural behavior of RC Zheng, Y. Z., Wang, W. W., & Brigham, J. C. (2016). Flexural
beams strengthened with prestressed and non-prestressed behaviour of reinforced concrete beams strengthened with
BFRP grids. Composite Structures, 246, 112381. a composite reinforcement layer: BFRP grid and ECC. Con-
https://doi.org/10.1016/j.compstruct.2020.112381 struction and Building Materials, 115, 424–437.
Huang, Y., Zhang, Y., Ming, Z., & Zhou, G. (2014). Method for https://doi.org/10.1016/j.conbuildmat.2016.04.038
predicting the failure load of masonry wall panels based on Zheng, Y. Z., Zhang, L. F., & Xia, L. P. (2018). Investigation of
generalized strain-energy density. Journal of Engineering Me- the behaviour of flexible and ductile ECC link slab reinforced
chanics, 140(8), 04014061. with FRP. Construction and Building Materials, 166, 694–711.
https://doi.org/10.1061/(ASCE)EM.1943-7889.0000771 https://doi.org/10.1016/j.conbuildmat.2018.01.188