Composite Structures 259 (2021) 113233
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Composite Structures
journal homepage: www.elsevier.com/locate/compstruct
Dynamic compressive behavior of concrete confined with unidirectional
natural flax FRP based on SHPB tests
Yu-lei Bai a, Zhi-Wei Yan a, Jun-Feng Jia a, Togay Ozbakkaloglu b,⇑, Yue Liu a
a
b
Key Laboratory of Urban Security and Disaster Engineering of Ministry of Education, Beijing University of Technology, Beijing, China
Ingram School of Engineering, Texas State University, San Marcos, Texas, USA
A R T I C L E
I N F O
Keywords:
Natural flax FRP
Concrete
Split Hopkinson pressure bar (SHPB)
Dynamic compressive behavior
Strain rate effect
A B S T R A C T
This paper presents an experimental study on the dynamic compressive behaviors of concrete confined with
unidirectional natural flax fiber reinforced polymers (FFRPs) under an axial impact load. A total of 80 specimens were prepared and tested using a 75 mm diameter split Hopkinson pressure bar (SHPB) at different strain
rates varying from 50 to 200 s−1. The experimental results showed that the failure modes and dynamic compressive mechanical properties (i.e., dynamic compressive strength, critical compressive strain, and energy
absorption capacity) of FFRP‐confined concrete were sensitive to the strain rate. The unconfined concrete specimens were crushed into small pieces at relatively low strain rates, whereas the FFRP‐confined concrete specimens failed with FRP rupture and partial damage to the core concrete at relatively high strain rates. This
indicates that the confinement of FFRP jackets can alleviate concrete damage and improve impact resistance.
Compared with unconfined concrete, the application of the FFRP jacket remarkably improves the compressive
strength, critical strain, and toughness, which indicates outstanding impact resistance. Increasing the confinement stiffness of the FFRP contributed to increasing the compressive strength, critical strain, and toughness.
Based on the experimental results, the confinement mechanism of external flax FRP jackets on concrete was
discussed, and a new dynamic strength model was proposed to predict the dynamic compressive strength of
FFRP‐confined concrete within the investigated strain rate range.
1. Introduction
Fiber‐reinforced polymer (FRP) composites are commonly used in
the fields of civil, aerospace, and automotive engineering as protective
and strengthening tools, due to their high strength‐to‐weight ratio,
excellent fatigue and corrosion resistance, and relatively low manufacturing cost. Providing confinement for existing reinforced concrete
(RC) columns as the external jackets for seismic retrofitting is a popular application of FRP composites. Numerous investigations of the
structural performance of FRP‐confined RC columns under static or
seismic loads have been performed [1–12]. Nevertheless, it is worth
noting that in addition to static/seismic loading, RC structures may
also encounter blast/impact loading during their service life [13,14].
For example, bridge piers may encounter collisions with moving vehicles or ships and military facilities may be subjected to bomb attacks or
accidental impacts. Despite many investigations on the impact resistance of concrete and RC structures have been carried out [15–22],
few studies on the impact resistance of the concrete specimen confined
with FRP jackets have been carried out [13,23–28].
Xiao and Shen [25] found that the damage to a concrete‐filled steel
tube could be significantly alleviated by the application of external
carbon FRP (CFRP) jackets at a high level of impact energy. Pham
and Hao [26] observed that the impact resistance of the concrete column can be significantly improved by the confinement of the FRP jackets, and the failure mode of the FRP‐confined concrete was sensitive to
strain rate. Pham et al. [27] numerically investigated the impact‐
resistant performances of FRP‐confined concrete columns using LS‐
DYNA, which produced a reliable prediction of its impact resistance
using the finite element model. Huang et al. [28] observed that the
failure mode of the GFRP (glass FRP)‐SR (spiral reinforcement)‐
confined concrete column was closely related to the impact energy.
The impact‐resistant capacity can be remarkably enhanced by increasing the GFRP tube thickness and volumetric ratio of SR.
Compared with the studies on the impact‐resistant behaviors (e.g.,
drop hammer test, light‐gas gun test) of FRP‐confined concrete
⇑ Corresponding author.
E-mail addresses: baiyulei@bjut.edu.cn (Y.-l. Bai), yanzhw@126.com (Z.-W. Yan), jiajunfeng@bjut.edu.cn (J.-F. Jia), togay.oz@txstate.edu (T. Ozbakkaloglu), yliu@bjut.edu.cn
(Y. Liu).
https://doi.org/10.1016/j.compstruct.2020.113233
Received 8 September 2020; Revised 16 October 2020; Accepted 30 October 2020
Available online 6 November 2020
0263-8223/© 2020 Published by Elsevier Ltd.
Y.-l. Bai et al.
Composite Structures 259 (2021) 113233
strength model was proposed to predict the dynamic compressive
strength of FFRP‐confined concrete at different strain rates and serves
as a basic design model for the design of FFRP‐confined reinforced
concrete structures against impact loading.
members, there have been fewer studies conducted on the impact
resistance of the concrete specimens confined with FRP jackets, in
terms of the SHPB test [29–32]. Yang et al. [29–31] applied external
aramid FRP (AFRP) jackets to wrap the concrete specimen and pointed
out that its dynamic compressive strength, toughness, and ultimate
strain were significantly improved when the strain rate rose from 80
to 170 s−1. Xiong et al. [32] found that the strength and ductility of
the concrete under dynamic loading were improved with an increase
in the layer of external CFRP jacket, while the dynamic increase factor
(DIF) was not sensitive to the strain rate for CFRP‐confined concrete
within the strain rate range of 10–80 s−1. Apart from Yang et al.’s
and Xiong et al.’s work, very few research can be found on this topic
in the existing literature. An in‐depth understanding of the impact‐
resistant behaviors of FRP‐confined concrete is of vital significance
to the reliable impact‐resistant retrofitting applications of RC structures strengthened with FRP composites. Therefore, more studies need
to be done in this field.
Many studies [33–35] indicated that the DIF of concrete‐like materials was not only contributed by strain rate effects but also included
many structural effects, such as the interface friction, lateral inertia,
confining pressure, etc. Cui et al. [33] investigated the effect of confining pressure on the dynamic compressive strength of concrete by
intensive numerical simulations. It was found that the strain rate sensitivity of the concrete material with lateral confinement was less than
the unconfined specimen. Hao et al. [34] experimentally verified that
the lateral inertia confinement had an important role in the dynamic
compressive mechanical properties of concrete‐like materials. Flores‐
Johnson and Li [35] explored the structural effects (interface friction,
radial inertia, lateral confinement, Poisson’s ratio, specimen diameter,
etc.) on the DIF of concrete‐like materials. The simulation results
showed that the interface friction and redial inertia were two external
sources to produce the lateral confinement, which can increase the
DIF.
Recently, the use of natural fibers (e.g., jute, kenaf, sisal, ramie,
hemp, flax, cotton, and coir) as building materials has gained attention
from both researchers and engineers throughout the world due to
increasing environmental concern and the globally promoted concept
of sustainability [36–41]. Compared with conventional FRPs (carbon
FRP, aramid FRP, and glass FRP), natural fiber materials are cost‐
effective and characterized by low density. Nevertheless, the natural
fibres have the poor durability and weak fibre‐matrix interface that
is due to their small water absorbance [42–44]. Interfacial adhesion
of the matrix fibres has a significant role in the tensile mechanical
properties of natural fibres, which can be modified by the surface
treatment of fibres or matrix. Flax fiber, a new type of natural fiber
made from the flax plant [45], is extensively distributed around the
world and has emerged as an alternative to conventional FRP composites for the strengthening/retrofitting of RC structures [37,46,47].
Wang et al. [48] investigated the dynamic compressive mechanical
properties of FFRP‐confined concrete specimens at the strain rate from
0.2 to 30 s−1, and found that the FFRP‐confined concrete exhibited an
outstanding impact performance. Apart this research, few studies have
been conducted on the dynamic compressive mechanical properties of
FFRP‐confined concrete. Thus, new studies should be conducted to
explore the dynamic compressive mechanical properties of FFRP‐
confined concrete at intermediate strain rates (50–200 s−1) for the
application of this natural fiber material in the field of protection engineering and blasting.
This paper presents a study on the dynamic compressive mechanical behaviors of the concrete wrapped with FFRP jackets at intermediate strain rates (50–200 s−1). The effects of the strain rate and
confinement stiffness (i.e., the product of FRP thickness and elastic
modulus) on the dynamic compressive strength, critical strain, toughness, and failure mode of FFRP‐confined concrete were discussed and
analyzed. The findings provide a better understanding of the behavior
of FFRP‐confined concrete at an intermediate strain rate. A new
2. Experimental program
2.1. Material
2.1.1. Concrete
Ordinary Portland cement, crushed granite with a nominal size of
5–10 mm, and natural sand were used in the concrete mix with a target
strength of 20 MPa. Two concrete cylinders, 150 mm in diameter and
305 mm in height, were prepared in a standard laboratory environment to determine concrete strength with a density of 2.38 g/mm3.
The 28‐day compressive strength of these two specimens was
18.5 MPa on average according to a standard compressional test.
2.1.2. FRP sheets
Unidirectional flax fabric, which was manufactured by the Nanjing
High‐tech Composites Institute of Technology, China, was employed to
externally strengthen the concrete (Fig. 1). The area density, bulk density and nominal thickness of the flax fibers were 210 g/mm2, 1.55 g/
mm3 and 0.135 mm, respectively. The mechanical properties of the
FFRP coupon were obtained by flat coupon tensile tests, and presented
in Table 1 as well as the epoxy resin adhesive used in this test. Flat coupon tensile tests were conducted following ASTM standard D3039‐
M08 [49] on the flax FRP composites to obtain their tensile properties.
Five identical coupons (one layer of flax fiber sheet, l×w=250×25
mm) were prepared and tested (Fig. 2). Aluminum tabs (l×w×t=6
1×25×1 mm) were used to reduce stress concentration. Two strain
gauges were glued on both sides of each FRP coupon to record the tensile strain. The crosshead displacement rate was constant at 1.5 mm/
minute.
Fig. 3 shows the failure modes of FFRP coupons under the quasi‐
static loading. All of the coupons failed at either the center or near
the end of the gauge length. The latter may have been caused by stress
concentration. Fig. 4 presents the tensile stress‐strain curves of the
FFRP coupons. The linear elastic behaviors of FFRP coupons were
maintained until they ruptured, which exhibits the behavior of brittle
fracture. The average tensile strength, rupture strain, and elastic modulus of the FFRP coupon were obtained with values of 788.0 MPa,
1.36%, and 58.0 GPa, respectively (Table 1).
2.2. Specimens preparation
A total of 88 concrete specimens were cast, of which 80 specimens
were used for dynamic tests. Among the specimens prepared for the
dynamic tests, three sets of 20 specimens were wrapped with two,
Fig. 1. Flax fiber sheet.
2
Composite Structures 259 (2021) 113233
Y.-l. Bai et al.
Table 1
Mechanical properties of FFRP coupon and epoxy resin adhesive.
Type
Tensile strength
(MPa)
Rupture strain
(%)
Elastic modulus
(GPa)
FFRP coupon
Epoxy resin
788.0
33.0
1.36
3.54
67.2
2.35
3000 mm, an energy source, a damper, a velocity testing system,
and a digital oscilloscope, as shown in Fig. 6.
A key issue with the SHPB apparatus employed for the determination of the dynamic mechanical properties of materials is the decoupling between the stress wave effect and strain rate effect
[15,50,51]. On one hand, the incident and transmission bars are in a
state of elasticity during the propagation of the stress wave so that
the strain rate effect on the bars can be negligible. Therefore, only
the stress wave effect is considered for the bars. On the other hand,
the design of the specimen size makes the time for the stress wave
to propagate through the specimen much shorter than the total duration of loading. Thus, the stress wave effect is ignored and only the
strain rate effect is considered for the specimen.
The projectile, incident bar, and transmission bar used in this test
are made of 48CrMoA whose density (ρ) and elastic modulus (E) are
7,800 kg/m3 and 210 GPa. Thus, its wave velocity (C) can be computed as 5189 m/s using the following equation:
pffiffiffiffiffiffiffiffi
C ¼ E=ρ
ð1Þ
four, and six layers of FFRP jackets respectively, while the remaining
20 unconfined concrete specimens were tested for comparison. The
diameter and height of specimens for the dynamic tests were 70 and
38 mm respectively while the specimens for the quasi‐static tests were
designed with 70 mm in diameter and 140 mm in height. Previous
researchers (e.g., Xiao et al. [20], Wang et al. [50]) indicated that this
specimen sizes are suitable for determining the dynamic increase factor (DIF) based on the similar stress state and failure pattern.
The manual wet lay‐up installation process was used to produce the
specimen, as per the process used by Dai et al. [4]. The side surface of
the concrete specimen was polished before the application of a two‐
component (the main resin component and a hardener) primer with
a mixing ratio of 2:1. Afterward, a single continuous flax fiber sheet
that was impregnated with epoxy resin adhesives was wrapped around
the side surface of the concrete specimen with the orientation of the
main fibers circumferential. The lengths of the fiber sheets in the overlapping region for all specimens were 110 mm covering half of the
perimeter.
The specimen was placed between the incident and transmission
bars (Fig. 6). The two ends of the specimen were polished until the
non‐parallelism of the two ends was less than 0.1 mm to minimize
the effect of the non‐parallelism on the obtainment of the dynamic
mechanical properties [52]. Two strain gauges with 10 mm in gauge
length were mounted on the surface of the external FFRP jacket to
record the tensile strain (although the gauges failed in this test).
Another two strain gauges were permanently installed on the incident
bar and the transmission bar. They were 2,340 mm and 2,000 mm
away from the interface between the specimen and the bar, respectively. Vaseline was applied to the ends of the bar and specimen to
alleviate the friction effect of the interface between the specimen
and bars. To reshape the waveform of the incident wave and eliminate the high‐frequency oscillation of the stress wave [53], a rubber
shaper (D×t=20×1 mm) was used as shown in Fig. 6. A velocity
testing system was used to measure the initial velocity of the
projectile.
The time histories of the stress σ(t), strain ε(t) and strain rate ɛ_ ðtÞ of
specimens were determined according to the Two‐Wave Theory [29],
which can be expressed by the following equations.
2.3. Test program
2.3.1. Quasi-static test
The quasi‐static compressional test was conducted by a servo‐
hydraulic testing system with a capacity of 3,000 kN (Fig. 5). All specimens in the quasi‐static tests were tested with a constant loading rate
of 0.15 mm/min. All data during the test was simultaneously recorded
by a data logger system.
2.3.2. SHPB test
An SHPB device with a diameter of 75 mm was employed to obtain
the dynamic compressive behaviors of FFRP‐confined concrete. The
apparatus is comprised of a 600 mm long projectile, an incident bar
with a length of 5000 mm, a transmission bar with a length of
ɛðtÞ ¼
2C
Ls
Z
t
½ɛ i ðtÞ ɛ t ðtÞdt
0
Fig. 2. Flat coupon tensile test: (a) FFRP coupon; (b) Test apparatus.
3
ð2Þ
Y.-l. Bai et al.
Composite Structures 259 (2021) 113233
3. Test results
3.1. Quasi-static test results
The failure modes of specimens wrapped with different FFRP jackets subjected to static loading are shown in Fig. 9. All specimens failed
by a single, straight, and vertical rupture in the external FRP jackets,
indicating the brittle failure of the FFRP jackets. This phenomenon is
similar to that reported by Yan and Chouw [39]. Nevertheless, this
is different from that of concrete cylinders confined with other types
of FRP (e.g., CFRP, GFRP, and AFRP) whose external FRP jacket ruptures usually only occurred at the mid‐height of the column (e.g.,
Lam and Teng [56], Dai et al. [4]). This may be due to the unique tensile behaviors of FFRP composite materials. The failure of the flax fiber
at the weak point gives rise to a progressive failure process.
As listed in Table 3, the compressive strength of the concrete specimen wrapped with FFRP jackets increased with the layer of the FFRP
jackets growth under the quasi‐static loading. The deviation of compressive strength between two identical specimens was not more than
5%, which indicates a small dispersion of compressive strength.
Fig. 3. The failure mode of FFRP coupons.
3.2. SHPB test results
3.2.1. Stress waves
A typically shaped pulse wave of the SHPB test is shown in Fig. 10
(a). The sum of the incident wave σi and the reflected wave σr should
be equal to the transmission wave σt to achieve stress balance, according to the one‐dimensional stress wave theory, which can be expressed
as
σi þ σr ¼ σt
ð5Þ
where σi, σr and σt are the dynamic stress of the incident, reflected, and
transmission wave, respectively. By processing the recorded wave signals, Fig. 10(b) exhibits the comparison of both waves, which indicates
that stress balance was achieved.
Fig. 4. Tensile stress-strain relation of FFRP coupons.
ð4Þ
3.2.2. Determination of strain rate
The strain rate is time‐dependent and is usually not constant
throughout the entire duration of loading. Various definitions of the
representative strain rate in SHPB tests were provided in the open literature [18–20]. Chen et al. [18] utilized the strain rate that corresponds to the failure point, which may not reflect the strain rate of
the entire duration. Grote et al. [19] adopted the average strain rate,
which was defined as the quotient of the maximum strain divided by
the entire duration of loading. This definition may cause the obtained
strain rate to be less than the actual strain rate because the duration of
the initial strain was not excluded in the calculation. Xiao et al. [20]
employed the slope of the main linear part of the strain–time curve
as the representative strain rate, which may more accurately represent
the actual strain rate of the specimen, as depicted in Fig. 11. Therefore,
the method by Xiao et al. was adopted in this study.
where εi(t) is the strain of the incident bar and εt(t) is the strain of the
transmission bar. As and Ls are the initial cross‐sectional area and
height of the specimen, respectively. A is the cross‐sectional area of
the bars.
To reduce test dispersion, four identical specimens were tested at
the same launch pressure and a similar strain rate was achieved. For
a reliable result, an average stress‐strain curve was generated from
four raw stress‐strain curves at a similar strain rate, which was adopted
as the representative result for the discussion [20,54,55]. Fig. 7 presents the average stress‐strain curve for the unconfined concrete at a
launch pressure of 0.15 MPa as an example. And Fig. 8 shows the
stress‐strain curve of 6 layers of FFRP‐confined concrete at a similar
strain rate of 153 s‐1. Details about the experimental data of SHPB tests
are shown in Table 2.
3.2.3. Failure mode
Fig. 12 shows a picture of a typical unconfined concrete specimen
after the SHPB test. Due to the relatively low compressive strength, all
specimens were crushed into small pieces at a relatively low strain rate
of 56 s−1. Fig. 13 shows the typical failure modes of specimens confined with two, four, and six layers of FFRP jackets at different strain
rates. It can be seen that the damage to the concrete was greatly
reduced with the confinement of the external FFRP jackets. This shows
that the application of FFRP greatly improves the impact resistance of
the concrete material, prompting brittle concrete with sufficient
deformability. With an increase in the confinement stiffness, the damage to the concrete was significantly alleviated. Compared with the
first figures of Fig. 13a‐c, it is found that although the specimens with
higher confinement stiffness were subjected to greater impact energy,
Fig. 5. Quasi-static compression test.
σðtÞ ¼ E
ɛ_ ðtÞ ¼
A
ɛt ðtÞ
As
2C
½ɛ i ðtÞ ɛ t ðtÞ
Ls
ð3Þ
4
Composite Structures 259 (2021) 113233
Y.-l. Bai et al.
Fig. 6. SHPB apparatus: (a) Full-scale photo; (b) Technical illustration.
Fig. 7. Stress-strain curve of unconfined concrete: (a) before average; (b) after average.
increases rapidly when loading at high speed. After some fibers fractured, the stress in the FRP failed to redistribute. Similarly, for the
specimen confined with four layers of FFRP, the external FFRP jackets
experienced no rupture, one big crack, two big cracks and four big
cracks when the strain rate was increased from 118 to 182 s−1. Without the confinement of the external FFRP jackets, the core concrete
was broken into small fragments. For the specimen wrapped with six
layers of FFRP, the failure mode of the specimen changed from concrete falling off to the crushed concrete surface when the strain rate
was increased from 140 to 153 s−1. The rupture of the external FFRP
jackets was observed until the strain rate arrived at about 163 s−1.
there was less damage to the core concrete. For the specimen confined
with two layers of FFRP jackets at the strain rate of 87 s−1, about half
of the core concrete was damaged with the external FFRP jackets
failed. For the specimen wrapped with four layers of FFRP jackets,
the core concrete was cracked and crushed, whereas the external FFRP
remained intact at the strain rate of 118 s−1. For the specimen confined with six layers of FFRP jackets at the strain rate of 140 s−1, only
a little concrete fell off from the surface of the specimen and the FFRP
remained intact. Therefore, it was concluded that an increase in the
confinement stiffness could remarkably improve the impact‐resistant
capacity of the concrete
It also can be seen in Fig. 13 that the damage of the FFRP‐confined
concrete specimen was aggravated with the strain rate growth. The
specimen confined with two layers of FFRP jackets experienced the
cracking failure, crushing failure, smashing failure and FRP rupture
when the strain rate increased from 87 to 162 s−1. In particular, when
the strain rate increased from 128 to 162 s−1, the fracture sites of the
external FFRP jackets changed from one to two and the core concrete
was severely crushed into pieces. This is because the stress of FRP
3.2.4. Stress-strain curves
As seen in Section 2.3.2, the average stress‐strain curves of unconfined specimens and specimens confined with different layers of FFRP
jackets at different strain rates are obtained and presented in Fig. 14.
The curves of the unconfined concrete specimen under dynamic compressive loading are similar in shape to those under quasi‐static uniaxial compression. The stress‐strain curve initially has a parabolic
5
Y.-l. Bai et al.
Composite Structures 259 (2021) 113233
Fig. 8. Stress-strain curve of 6 layers of FFRP-confined concrete: (a) before average; (b) after average.
Table 2
Key results of SHPB tests.
Specimen
D (mm)
H (mm)
Layers of FFRP
Launch pressure (MPa)
Strain rate (s−1)
Peak stress (MPa)
Peak strain (%)
Toughness (kJ/m3)
DIF for Strength
F-0-1
F-0-2
F-0-3
F-0-4
F-0-5
F-2-1
F-2-2
F-2-3
F-2-4
F-2-5
F-4-1
F-4-2
F-4-3
F-4-4
F-4-5
F-6-1
F-6-2
F-6-3
F-6-4
F-6-5
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
38
38
38
38
38
38
38
38
38
38
38
38
38
38
38
38
38
38
38
38
0
0
0
0
0
2
2
2
2
2
4
4
4
4
4
6
6
6
6
6
0.15
0.16
0.18
0.20
0.22
0.18
0.21
0.24
0.28
0.30
0.24
0.27
0.30
0.33
0.35
0.30
0.30
0.33
0.33
0.35
56
70
97
131
147
87
101
128
162
173
118
140
154
169
182
128
140
153
163
172
18.1
19.5
21.5
23.9
25.5
51.6
56.4
57.8
60.7
62.7
75.5
77.0
77.9
80.6
82.4
85.9
91.7
96.2
101
103
0.720
0.760
0.932
1.00
1.08
1.78
1.91
2.17
2.38
2.21
2.16
2.45
2.54
2.52
2.49
2.57
2.80
2.88
2.91
3.17
97.5
105
152
172
206
729
812
926
1112
1138
1202
1429
1480
1574
1604
1586
1898
2041
2214
2436
0.981
1.06
1.17
1.30
1.38
1.18
1.28
1.32
1.38
1.43
1.19
1.21
1.23
1.27
1.30
1.07
1.15
1.20
1.26
1.28
Notes: Specimens were donated as “A-B-C”, where A, B, and C represent the type of FRP, the layer number of FRP, and the number of strain rates.
4. Discussion and analysis
4.1. Dynamic compressive strength and dynamic increase factor (DIF)
0
Dynamic compressive strength (f c ) is determined as the peak stress
of the stress‐strain curve. Fig. 15 showed that the dynamic compressive strength linearly increases with an increase in the strain rate for
both unconfined concrete and FFRP‐confined concrete, which can be
expressed as Eqs. (6)–(9). Specifically, the compressive strength of
the unconfined concrete increased by 40.9% from 18.1 to 25.5 MPa
with an increase in the strain rate from 56 to 147 s−1. The dynamic
compressive strength of the concrete specimen confined with two,
four, and six layers of FFRP jackets increased by 21.5%, 9.14%, and
19.4% when increasing the strain rate from 87 to 173 s−1, 118 to
182 s−1, and 128 to 172 s−1, respectively. The damage to concrete
materials is caused by the generation and development of cracks.
According to the perspective of fracture mechanics, the energy
required in the process of crack formation is much higher than that
in the process of crack development. The higher the loading speed
is, the more cracks will be generated and the more energy will be dissipated. Under a high strain rate, the duration of the impact load is
Fig. 9. Failure mode after static compression test.
portion and declines after the peak stress. For the FFRP‐confined specimens with the same confinement stiffness, typical curves can be
divided into three parts: a parabolic portion, a linear ascending portion
that is nearly tangential to the parabola at the transition point, and a
descending portion after the peak stress of the curves due to the rupture of the FFRP jacket. It is indicated in Fig. 14 that an increase in
the strain rate leads to an increase in the peak axial stress and peak
axial strain (i.e., a strain that corresponds to the peak stress) of unconfined concrete and FFRP‐confined concrete.
6
Composite Structures 259 (2021) 113233
Y.-l. Bai et al.
Table 3
Quasi-static test results.
D (mm)
H (mm)
Layers
f 0co (MPa)
f 0cc (MPa)
Average strength (MPa)
f 0cc =f 0co
70
70
70
70
70
70
70
70
140
140
140
140
140
140
140
140
0
0
2
2
4
4
6
6
18.6
18.3
–
–
–
–
–
–
–
–
43.3
44.5
62.0
65.1
80.6
79.3
18.5
–
–
2.3
2.4
3.4
3.5
4.4
4.3
43.9
63.6
80.0
Fig. 10. Stress waves of 2-layer flax FRP-confined concrete after single impact: (a) Typically shaped waveforms during SHPB tests; (b) Incident + Reflected.
Fig. 11. Determination of the strain rate.
Fig. 12. Unconfined concrete specimen after impact.
very short, and the concrete material does not have enough time for
energy accumulation. The impact loading is withstood by the increasing stress of specimens. Thus, the strength of concrete materials
increases with the strain rate growth. According to damage mechanics,
there are two kinds of effects in concrete at a high strain rate: the
strain rate strengthening effect and the damage softening effect. Under
the impact load, micro‐cracks need time to penetrate each other and
the damage softening effect will lag while the strain rate strengthening
effect is increasing. At high strain rates, the damage softening effect in
concrete materials lags behind the damage to the concrete, which correspondingly increases the strength of the concrete materials.
For a similar strain rate, an increase in the confinement stiffness in
the external jackets leads to the dynamic compressive strength growth.
For example, when the strain rate is at 140 s−1, the dynamic compressive strength (91.7 MPa) of six layers of FFRP‐confined concrete is larger than that (77.0 MPa) of the specimen confined with four layers of
FFRP jackets. Notably, the slope of the empirical formula for the
dynamic compressive strength has a large increase from 0.11 to
0.385 when the number of layers of FFRP jackets was increased from
four to six. This indicates that the six layers of FFRP‐confined concrete
7
Y.-l. Bai et al.
Composite Structures 259 (2021) 113233
Fig. 13. Typical failure modes of concrete wrapped with different layers of FFRP jackets: (a) 2 layers; (b) 4 layers; (c) 6 layers.
growth rate of the DIF. From Table 4 and Fig. 15, it can be seen that
the specimen confined with six layers of FFRPs had the largest value
of A of 1.65. This indicates that the specimen confined with six layers
of FFRPs had a significant strain rate effect on the dynamic compressive
strength with the largest growth rate of the DIF among all specimens.
Nevertheless, at a similar strain rate (e.g., 130 s−1), the DIF of the specimen confined with six layers of FFRPs was the smallest of all, although
it had a largest growth rate of the DIF. This phenomenon was due to
that its transition point of the strain rate sensitivity is larger than that
of other specimens.
From Figs. 14 and 15, it can be seen that the dynamic compressive strength of the unconfined concrete is smaller than that of the
FFRP‐confined concrete, but its DIF is larger than the FFRP‐
confined concrete (excluding the concrete confined by two layers
of FFRP). This observation can be explained as follows. Under the
quasi‐static loading, the unconfined concrete was in a uniaxial compressive state, whereas the FFRP‐confined concrete was in a three‐
dimensional pressure state. Thus, the compressive strength of the
FFRP‐confined had a larger value. Under the dynamic loading, the
stress state of the unconfined concrete changed to a three‐
dimensional pressure state due to the existence of the lateral inertia
effect. For the FFRP‐confined concrete, it was still in a three‐
dimensional pressure state with the combined confinement of the
external FRP jackets and the lateral inertia effect of concrete. The
change of the failure mode for the unconfined concrete resulted in
its larger DIF compared to that of the FFRP‐confined concrete. With
an increase in the layer of external FFRP jackets, the role of the
external FFRP jackets was more prominent than the lateral inertia
effect of concrete in constraining the lateral deformation of concrete,
which led to a decreased DIF.
provided strong confinement. The concrete specimens that had two or
four layers of FFRP were moderately confined. As the confining pressure increases, the internal cracks in the concrete gradually close with
the compactness of the concrete increased.
Unconfined concrete f 0c ðMPaÞ ¼ 0:0784_ɛ þ 13:8; 50 ⩽ ɛ_ ⩽ 200s1 ; R2 ¼ 0:99
ð6Þ
2 layer FFRP confined concrete f 0c ðMPaÞ ¼ 0:110_ɛ þ 43:6; 50
⩽ ɛ_ ⩽ 200s1 ; R2 ¼ 0:89 ð7Þ
4 layer FFRP confined concrete f 0c ðMPaÞ ¼ 0:109_ɛ þ 62:1; 50
⩽ ɛ_ ⩽ 200s1 ; R2 ¼ 0:93 ð8Þ
6 layer FFRP confined concrete f 0c ðMPaÞ ¼ 0:385_ɛ þ 37:2; 110 ⩽ ɛ_
⩽ 200s1 ; R2 ¼ 0:99
ð9Þ
To further investigate the strain rate effect on the compressive
strength of specimens, the DIF is used and defined as the ratio of the
dynamic compressive strength to the quasi‐static compressive
strength. As shown in Fig. 16, the relationship between the DIF and
_ presents a trend that is increasing
the logarithm of the strain rate (ɛ)
almost linearly, which can be approximately expressed as
DIF ¼ Alg_ɛ þ B
ð10Þ
where parameters A and B can be obtained from the regression analysis
of the experimental results (Table 4). A indicates the strain rate effect
coefficient of the dynamic compressive strength of FFRP‐confined concrete. A high value of parameter A indicates a significant strain rate
effect on the dynamic compressive strength, which reflects a high
8
Composite Structures 259 (2021) 113233
Y.-l. Bai et al.
Fig. 14. Average stress-strain curves of concrete wrapped with different layers of FFRP jackets: (a) Control specimens; (b) 2 layers; (c) 4 layers; (d) 6 layers.
Fig. 15. Dynamic compressive strength versus strain rate.
Fig. 16. Dynamic increase factor for dynamic compressive strength.
4.2. Critical compressive strain
Fig. 17 shows the critical compressive strain of specimens at different strain rates. The critical compressive strain increases with the
strain rate growth. Specifically, the critical compressive strain of the
unconfined concrete increased by 50% from 0.72% to 1.08% with
the strain rate increasing from 56 to 147 s−1. The critical compressive
strain of the specimen confined with two, four, and six layers of the
Critical compressive strain (εcr) is defined as the axial strain that
corresponds to the peak stress of the stress‐strain curves for both
unconfined concrete and FFRP‐confined concrete. It is an important
index for characterizing the deformation behavior of the specimen.
9
Y.-l. Bai et al.
Composite Structures 259 (2021) 113233
Table 4
Values of the parameters A and B.
Parameters
Unconfined
2-layer FFRP confined concrete
4-layer FFRP confined concrete
6-layer FFRP confined concrete
A
B
R2
0.92
−0.64
0.99
0.73
−0.21
0.93
0.58
−0.03
0.89
1.65
−2.40
0.99
FFRP jackets increased by 24.2%, 15.3%, and 23.3% with the increase
of the strain rate from 87 to 173 s−1, 118 to 182 s−1, and 128 to
172 s−1, respectively. This can be explained as follows. For the unconfined concrete, the existence of the lateral inertia confinement alleviates the formation of macro cracks and promotes the formation of
microcracks. At high strain rates, the damage softening effect of concrete materials lags behind the damage to the concrete. For the
FFRP‐confined concrete, except for the damage softening effect, the
application of FFRP makes the internal cracks in the concrete gradually close and increases the compactness of concrete, prompting brittle
concrete with sufficient deformability. Thus, the critical compressive
strain of the FFRP‐confined concrete was substantially larger than that
of the unconfined concrete at the same strain rate (e.g., 130 s−1). It
can be concluded that applying external FFRP jackets to confine the
concrete can increase the ductility of concrete under impact loading.
4.3. Energy absorption capacity
Fig. 18. Energy absorption capacity.
crack tends to lag behind the loading rate [29], although the cracking
rate simultaneously increases with the strain rate growth. The energy
may be partly consumed by the generation of micro‐cracks and partly
transferred to the elastic strain energy of the specimen (i.e., energy
stored in the specimen during the load and released after the load).
Thus, additional micro‐cracks and greater elastic deformation are generated for the specimens that are under a dynamic compressive load
compared with the quasi‐static compression test, which may contribute to the high toughness at a high strain rate. For the FFRP‐
confined concrete, except for the cracking propagation effect, the existence of external FFRP jackets limits the lateral expansion of the core
concrete and hinders the generation of microcracks. Thus, the axial
strain and dynamic compressive strength improved significantly, and
more energy was absorbed.
The increase in the toughness of the FFRP‐confined concrete is
more remarkable than that of the unconfined concrete, which can be
observed when comparing the slopes of the linear fitting curves in
Fig. 18. This indicates that the FFRP‐confined concrete is more sensitive to the strain rate effect in regards to the toughness. As discussed
in Section 4.1, the concrete specimens with two or four layers of FFRP
jackets were strongly confined. Under impact, the external FFRP jackets of the moderately confined specimen can only absorb limited
energy. After the rupture of the external FFRP jackets, the stress state
of the specimen varied from three‐dimensional pressure to axial compression with the sudden brittle failure of the concrete. For the specimen with strong confinement, the amount of energy absorbed by the
external FFRP jackets was larger than that of the moderately confined
specimen. The specimen was in the three‐dimensional pressure state
for a longer duration. Thus, the lateral expansion of concrete was more
effectively hindered and fewer micro‐cracks were formed. Therefore,
the application of external FFRP jackets, that is, an increase in the confinement stiffness, can improve the impact‐resistant capacity of
concrete.
Unconfined concrete Wp kJ=m3 ¼ 1:16_ɛ þ 30:4; 50 ⩽ ɛ_
Energy absorption capacity, commonly referred to as toughness, is
used to reflect the impact‐resistant capacity of the specimen and is
defined as the area under the stress‐strain curve, which can be calculated by Eq. (11).
Z ɛcr
Wp ¼
σdɛ
ð11Þ
0
where Wp stands for the peak toughness of the specimen when the
strain reaches the critical strain (εcr) [54,55] and σ and ε represent
the stress and strain of the stress‐strain curve, respectively.
The correlations between the toughness and strain rate are shown
in Fig. 18 and listed in Table 2. The toughness of the specimen
increases with the increase of the strain rate for both unconfined concrete and FFRP‐confined concrete, which can be expressed as Eqs.
(12)–(15). Specifically, the toughness of the unconfined concrete
increases by 111% when the strain rate increases from 56 to
147 s−1. For the concrete confined by two, four and six layers of FFRP,
the toughness increases by 56.1%, 33.4% and 53.6% when the strain
rate varied from 87 to 173 s−1, 118 to 182 s−1 and 128 to 172 s−1,
respectively. This can be explained as follows. The development of a
⩽ 200s1 ; R2 ¼ 0:96
ð12Þ
2 layer FFRP confined concrete Wp kJ=m3 ¼ 4:82_ɛ þ 316; 50 ⩽ ɛ_
⩽ 200s1 ; R2 ¼ 0:99 ð13Þ
Fig. 17. Critical compressive strain versus strain rate.
10
Composite Structures 259 (2021) 113233
Y.-l. Bai et al.
4 layer FFRP confined concrete Wp kJ=m3 ¼ 6:20_ɛ þ 511; 50 ⩽ ɛ_
where f l is the lateral pressure of the FRP jackets on the concrete;
ɛl , Efrp and tfrp are the hoop strain, the elastic modulus of FRP jacket,
and nominal thickness of the FRP jacket, respectively, and R is the
radius of the core concrete. The peak stress of the FRP‐confined concrete can be expressed as [4]
⩽ 200s1 ; R2 ¼ 0:92 ð14Þ
6 layer FFRP confined concrete Wp kJ=m3 ¼ 18:1_ɛ 701; 110 ⩽ ɛ_
⩽ 200s1 ; R2 ¼ 0:98 ð15Þ
f 0 cc ¼ f 0co þ k1f l
0
4.4. Confinement mechanism of flax FRP and dynamic strength model
E frp t frp ɛ l
R
0
where f cc and f co are the axial compressive strength of FRP‐confined
concrete and unconfined concrete, respectively, and k1 is the confinement effectiveness coefficient with the suggested value of 3.5 [4].
According to Eq. (17), the axial compressive strength of the concrete wrapped with FFRP jackets increases with an increase in the
compressive strength of the unconfined concrete and the lateral pressure from the external FFRP jackets under the quasi‐static load, which
applies to the specimen subjected to the axial impact load after some
revisions. That is, for the dynamic compressive tests, the dynamic compressive strength of the unconfined concrete increases with the strain
4.4.1. Confinement mechanism
The increase in the compressive strength of the FFRP confined concrete under static loading is due to the confinement mechanism of the
external FRP jackets. The relationship between the lateral pressure and
strain of the FRP jacket under a quasi‐static axial compressive load can
be expressed as
fl ¼
ð17Þ
ð16Þ
Table 5
Database: Dynamic compressive tests of FRP-confined concrete.
0
No.
Ref.
f co (MPa)
FRP type
Efrp (GPa)
Tensile strength (MPa)
Thickness (mm)
f l (MPa)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
Present study
18.5
FFRP
67.2
788
Yang and Song [30]
48.9
AFRP
131
2206
Yang et al. [29]
48.9
AFRP
131
2206
0.135
0.135
0.135
0.135
0.135
0.27
0.27
0.27
0.27
0.27
0.405
0.405
0.405
0.405
0.405
0.286
0.286
0.286
0.286
0.286
0.572
0.572
0.572
0.572
0.572
0.286
0.286
0.286
0.286
0.286
0.286
0.286
0.286
0.286
0.286
0.286
0.286
0.286
0.572
0.572
0.572
0.572
0.572
0.572
0.572
0.572
0.572
0.572
0.572
0.572
0.572
6.09
6.09
6.09
6.09
6.09
12.2
12.2
12.2
12.2
12.2
18.3
18.3
18.3
18.3
18.3
12.9
13.1
13.0
13.0
13.0
26.2
25.8
25.6
26.3
25.5
13.0
13.0
13.0
13.0
13.0
13.0
13.0
13.0
13.0
13.0
13.0
13.0
13.0
26.0
26.0
26.0
26.0
26.0
26.0
26.0
26.0
26.0
26.0
26.0
26.0
26.0
11
D × h (mm)
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
97.9
96.5
96.9
97.2
97.2
96.5
97.7
98.4
96.0
98.8
97
97
97
97
97
97
97
97
97
97
97
97
97
97
97
97
97
97
97
97
97
97
97
97
97
97
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
38
38
38
38
38
38
38
38
38
38
38
38
38
38
38
50.3
48.9
48.5
46.8
48.4
49.5
49.5
48.8
50.5
48.5
48
48
48
48
48
48
48
48
48
48
48
48
48
48
48
48
48
48
48
48
48
48
48
48
48
48
Strain rate (s−1)
(MPa)
f cc;d
87
101
128
162
173
118
140
154
169
182
128
140
153
163
172
51
74.3
83.6
95.3
128
56.7
74.5
105
119
120
89.8
95.9
106
110
115
121
127
132
135
137
139
143
147
87.2
92.7
100
107
113
119
121
126
131
135
139
142
147
51.6
56.4
57.8
60.7
62.7
75.5
77
77.9
80.6
82.4
85.9
91.7
96.2
101
103
79.5
100
120
122
147
117
123
169
187
192
128
133
134
141
140
147
148
151
150
154
156
156
160
154
154
162
177
176
189
190
189
193
205
201
207
214
0
Y.-l. Bai et al.
Composite Structures 259 (2021) 113233
rate growth due to the Stefan effect, transverse inertia effect, and
cracking propagation effect [20,29,57,58]. Due to these three effects,
the dynamic compressive strength of the FFRP‐confined concrete is larger than the quasi‐static strength of the FFRP‐confined concrete. The
external jackets provide additional lateral pressure to the core concrete, which ensures that the dynamic compressive strength of the
FFRP‐confined concrete is larger than that of the unconfined concrete
at a similar strain rate.
It is often challenging to achieve a genuine strain rate effect in
concrete‐like materials that are hydrostatic pressure sensitive
[33–35]. Many structural effects are often contained in a pseudo strain
rate effect, such as the specimen geometry, interface friction, lateral
confinement, radial inertia, etc. An increase in the interface friction,
lateral confinement and radial inertia can enhance the dynamic compressive strength. This is because these effects can increase the lateral
pressure on the concrete materials and in turn improve its axial compressive strength.
Fig. 19. Performance of a new dynamic compressive strength model in
predicting the dynamic compressive strength of FRP-confined concrete at
intermediate strain rates.
4.4.2. Dynamic strength model
Through analysis that was conducted using the static strength
model of confined concrete (Eq. (17)), a new model was proposed
for describing the axial compressive strength of FRP‐confined concrete
under the dynamic impact, expressed as
f 0 cc;d ¼ f 0co;d þ 3:5f l;d
0
includes Yang and Song [30] and Yang et al. [29] as listed in Table 5.
Since the external AFRP jackets of specimens confined with three layers of AFRP had no rupture under axial impact [30], the related data
was excluded. Through the regression analysis of the data in Table 5,
the values of the four parameters a, b, c and d in Eq. (21) can be
obtained as 3.26, −4.47, 0.260 and 0.192 respectively. By comparing
the experimental data with the model data, it is found that both two
data have good consistency (Fig. 19). This new model can accurately
predict the dynamic compressive strength of the FRP‐confined normal
concrete at strain rates ranging from 50 to 200 s−1. Hence, the
dynamic compressive strength model is expressed as
50 ⩽ ɛ_ ⩽ 200s1
f 0 cc;d ¼ f 0co ð3:26log_ɛ 4:47Þ þ 3:5f l ð0:26log_ɛ þ 0:192Þ;
f 0co ⩽ 50MPa
ð18Þ
0
where f cc;d
and f co;d are the dynamic compressive strength of FRP‐
confined concrete and unconfined concrete, respectively, and f l;d is
the dynamic lateral pressure of the FRP jackets on the concrete.
Due to the strain rate effect on the compressive strength of concrete, the dynamic compressive strength of the unconfined concrete
0
(f co;d ) can be expressed as Eq. (19), based on the experimental results
by this test, Yang and Song [30], Xie et al. [59], Yang et al. [29] and
Al‐Salloum et al. [15]. Therefore, it can be expressed as
f 0co;d ¼ f 0co ðalog_ɛ þ bÞ
ð19Þ
ð22Þ
where a and b are the parameters. In general, it is difficult to determine
the dynamic confining pressure of external FRP jackets on the core concrete under axial impact load. Through the dynamic tensile tests of
FRPs [60–63], it is concluded that FRP materials are strain‐rate sensitive material, whose dynamic tensile strength is linearly related to
the strain rate logarithm. Therefore, the expression of dynamic confining pressure can be expressed as
It is worth noting that the proposed dynamic strength model is only
based on the experimental data. The structural effects is not reflected
in the model, which needs to be resolved in future research.
f l;d ¼ f l ðclog_ɛ þ dÞ
5. Conclusions
Using the SHPB technique, the failure modes of the FFRP‐confined
concrete and dynamic compressive stress‐strain curve were investigated and discussed. The strain rate effect on the dynamic compressive
strength, critical compressive strain and toughness were investigated
and analyzed. The main conclusions drawn are as follows:
ð20Þ
where c and d are the parameters. Thus, the dynamic compressive
strength of FRP‐confined concrete can be calculated as
f 0 cc;d ¼ f 0co ðalog_ɛ þ bÞ þ 3:5f l ðclog_ɛ þ dÞ
ð21Þ
1. An increase in the strain rate leads to an increase in concrete damage due to the increase in input energy. The unconfined concrete
was crushed into small pieces at a low strain rate while the damage
to the FFRP‐confined concrete was significantly reduced even at a
high strain rate. This indicates that the application of FFRP greatly
improves the impact resistance of the concrete material, prompting
brittle concrete with sufficient deformability.
2. The dynamic compressive strength linearly increases with the
strain rate growth for both unconfined concrete and FFRP‐
confined concrete. As the confining pressure increases, the internal
cracks in the concrete gradually close, and the compactness of the
concrete increases. Thus, for a similar strain rate, an increase in the
confinement stiffness of the external jackets leads to an increase in
the dynamic compressive strength. The dynamic compressive
strength of the unconfined concrete is smaller than that of FFRP‐
confined concrete, while the DIF of the unconfined concrete is larger than that of FFRP‐confined concrete, which is due to the effect
of the confinement stiffness on the stress state of the specimen.
It is worth noting that the strain rate of the external FRP jackets is
in the same order of magnitude as the axial strain rate of concrete.
Since the strain rate of fiber cloth is not easy to determine, to facilitate
the calculation, the concrete and external FRP share the same strain
rate.
When determining the lateral pressure of the FRP jackets on the
concrete (f l ), the hoop rupture strain of an external FRP jacket is an
important parameter. Several previous investigations (e.g., Dai et al.
[4], Lam and Teng [56], Lim and Ozbakkaloglu [64]) revealed that
the hoop rupture strain of an external FRP jacket is usually substantially lower than the rupture strain from the coupon test. Nevertheless,
Xia et al. [37] reported that the rupture strain of an FFRP jacket from
the compression test is similar to that from the flat coupon tensile test.
For the convenience of the calculation and engineering application,
the rupture strain of an FFRP coupon is used.
To propose a new dynamic compressive strength model for FRP‐
confined concrete, existing experimental data was collected, which
12
Composite Structures 259 (2021) 113233
Y.-l. Bai et al.
[7] Zeng J-J, Guo Y-C, Gao W-Y, Chen W-P, Li L-J. Stress-strain behavior of concrete in
circular concrete columns partially wrapped with FRP strips. Compos Struct
2018;200:810–28. https://doi.org/10.1016/j.compstruct.2018.05.001.
[8] Wang Z, Wang D, Smith ST, Lu D. CFRP-Confined square RC columns. I:
Experimental investigation. J Compos Constr 2012;16(2):150–60. https://doi.
org/10.1061/(ASCE)CC.1943-5614.0000245.
[9] Ribeiro F, Sena-Cruz J, Branco FG, Júlio E. Hybrid FRP jacketing for enhanced
confinement of circular concrete columns in compression. Constr Build Mater
2018;184:681–704. https://doi.org/10.1016/j.conbuildmat.2018.06.229.
[10] Lee KS, Lee BY, Seo SY. A seismic strengthening technique for reinforced concrete
columns using sprayed FRP. Polymers 2016;8(4):107–28.
[11] Ozbakkaloglu T, Saatcioglu M. Seismic behavior of high-strength concrete columns
confined by fiber-reinforced polymer tubes. J Compos Constr 2006;10(6):538–49.
https://doi.org/10.1061/(ASCE)1090-0268(2006)10:6(538).
[12] Gholampour A, Ozbakkaloglu T. Behavior of steel fiber-reinforced concrete-filled
FRP tube columns: experimental results and a finite element model. Compos Struct
2018;194:252–62. https://doi.org/10.1016/j.compstruct.2018.03.094.
[13] Pham TM, Hao H. Review of concrete structures strengthened with FRP against
impact
loading.
Structures
2016;7:59–70.
https://doi.org/10.1016/j.
istruc.2016.05.003.
[14] Bai YL, Yan ZW, Ozbakkaloglu T, Dai JG, Jia JF, Jia JB. Dynamic behavior of PET
FRP and its preliminary application in impact strengthening of concrete columns.
Appl Sci 2019;9(23):4987–97.
[15] Al-Salloum Y, Almusallam T, Ibrahim SM, Abbas H, Alsayed S. Rate dependent
behavior and modeling of concrete based on SHPB experiments. Cem Concr
Compos 2015;55:34–44. https://doi.org/10.1016/j.cemconcomp.2014.07.011.
[16] Li L-J, Tu G-R, Lan C, Liu F. Mechanical characterization of waste-rubber-modified
recycled-aggregate concrete. J Cleaner Prod 2016;124:325–38. https://doi.org/
10.1016/j.jclepro.2016.03.003.
[17] Chen X, Xu L, Zhu Q. Mechanical behavior and damage evolution for concrete
subjected to multiple impact loading. KSCE J Civ Eng 2017;21(6):2351–9. https://
doi.org/10.1007/s12205-016-1143-8.
[18] Chen X, Wu S, Zhou J. Experimental and modeling study of dynamic mechanical
properties of cement paste, mortar and concrete. Constr Build Mater
2013;47:419–30. https://doi.org/10.1016/j.conbuildmat.2013.05.063.
[19] Grote DL, Park SW, Zhou M. Dynamic behavior of concrete at high strain rates and
pressures: I. experimental characterization. Int J Impact Eng 2001;25(9):869–86.
https://doi.org/10.1016/S0734-743X(01)00020-3.
[20] Xiao J, Li L, Shen L, Poon CS. Compressive behaviour of recycled aggregate
concrete under impact loading. Cem Concr Res 2015;71:46–55. https://doi.org/
10.1016/j.cemconres.2015.01.014.
[21] Zhao D-B, Yi W-J, Kunnath SK. Numerical simulation and shear resistance of
reinforced concrete beams under impact. Eng Struct 2018;166:387–401. https://
doi.org/10.1016/j.engstruct.2018.03.072.
[22] Zhao D-B, Yi W-J, Kunnath SK. Shear mechanisms in reinforced concrete beams
under impact loading. J Struct Eng 2017;143(9):04017089. https://doi.org/
10.1061/(ASCE)ST.1943-541X.0001818.
[23] Shan JH, Chen R, Zhang WX, Xiao Y, Yi WJ, Lu FY. Behavior of concrete filled
tubes and confined concrete filled tubes under high speed impact. Adv Struct Eng
2007;10(2):209–18. https://doi.org/10.1260/136943307780429725.
[24] Uddin N, Purdue JD, Vaidya U. Feasibility of thermoplastic composite jackets for
bridge impact protection. J Aerosp Eng 2008;21(4):259–65. https://doi.org/
10.1061/(ASCE)0893-1321(2008)21:4(259).
[25] Yan X, Yali S. Impact behaviors of CFT and CFRP confined CFT stub columns. J
Compos Constr 2012;16(6):662–70. https://doi.org/10.1061/(ASCE)CC.19435614.0000294.
[26] Pham TM, Hao H. Axial impact resistance of FRP-confined concrete. J Compos
Constr
2017;21(2):04016088.
https://doi.org/10.1061/(ASCE)CC.19435614.0000744.
[27] Pham TM, Chen WS, Hao H. Failure and impact resistance analysis of plain and
FRP-confined concrete cylinders under axial impact loads. Int J Protective Struct
2017;9(4):4–29.
[28] Huang L, Sun X, Yan L, Kasal B. Impact behavior of concrete columns confined by
both GFRP tube and steel spiral reinforcement. Constr Build Mater
2017;131:438–48. https://doi.org/10.1016/j.conbuildmat.2016.11.095.
[29] Yang H, Song H, Zhang S. Experimental investigation of the behavior of aramid
fiber reinforced polymer confined concrete subjected to high strain-rate
compression. Constr Build Mater 2015;95:143–51. https://doi.org/10.1016/
j.conbuildmat.2015.07.084.
[30] Hui Y, Hengwen S. Dynamic compressive behavior of FRP-confined concrete under
impact and a new design-oriented strength model. Polym Polym Compos 2016;24
(2):127–31. https://doi.org/10.1177/096739111602400207.
[31] Song H, Yang H, Zhang S. Study on dynamic behavior of AFRP-wrapped circular
concrete specimens under repeated impacts. Polym Polym Compos 2017;25
(1):103–12. https://doi.org/10.1177/096739111702500114.
[32] Xiong B, Demartino C, Xiao Y. High-strain rate compressive behavior of CFRP
confined concrete: large diameter SHPB tests. Constr Build Mater
2019;201:484–501. https://doi.org/10.1016/j.conbuildmat.2018.12.144.
[33] Cui J, Hao H, Shi Y. Numerical study of the influences of pressure confinement on
high-speed impact tests of dynamic material properties of concrete. Constr Build
Mater 2018;171:839–49. https://doi.org/10.1016/j.conbuildmat.2018.03.170.
[34] Hao Y, Hao H, Jiang GP, Zhou Y. Experimental confirmation of some factors
influencing dynamic concrete compressive strengths in high-speed impact tests.
Cem
Concr
Res
2013;52:63–70.
https://doi.org/10.1016/j.
cemconres.2013.05.008.
3. The critical compressive strain of the unconfined concrete increases
with an increase in the strain rate, due to the existence of the lateral
inertia confinement and damage softening effect. The application
of FFRP makes the internal cracks in the concrete gradually close
and increases the compactness of the concrete, prompting brittle
concrete with sufficient deformability. Thus, the critical compressive strain of the FFRP‐confined concrete was substantially larger
than that of the unconfined concrete at the same strain rate.
4. The toughness of the specimen increases with the strain rate
growth for both unconfined concrete and FFRP‐confined concrete,
due to the cracking propagation effect and that the external FFRP
jackets hinder the lateral expansion of concrete and generation of
microcracks. The increase in the toughness of the concrete specimen wrapped with FFRP jackets is more remarkable than that of
the unconfined concrete, which indicates that the FFRP‐confined
concrete is more sensitive to the strain rate effect in regards to
the toughness. The application of external FFRP jackets can
improve the impact‐resistant capacity of concrete.
5. By modifying the existing dynamic strength model, a new dynamic
strength model is proposed to predict the dynamic compressive
strength of FRP‐confined normal concrete at strain rates from 50
to 200 s−1. This new model provides a good prediction of the
dynamic compressive strength of the concrete specimens wrapped
with FFRP jackets.
CRediT authorship contribution statement
Yu‐lei Bai: Conceptualization, Methodology, Funding acquisition,
Supervision, Project administration. Zhi‐Wei Yan: Investigation, Data
curation, Writing ‐ original draft. Jun‐Feng Jia: Conceptualization,
Funding acquisition, Supervision. Togay Ozbakkaloglu: Methodology, Supervision. Yue Liu: Methodology, Supervision.
Declaration of Competing Interest
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
The authors are grateful for the financial support received from the
National Natural Science Fund of China (No. 51678014, 51778019,
51978017), Beijing Nova Programme (No. Z201100006820095),
Young Talents Cultivation Project of Beijing Municipal Institutions,
the China Postdoctoral Science Foundation (No. 2018T110021) and
the First Laboratory of Hefei Jiangshui Dynamic Mechanics Experimental Technology Co., Ltd.
References
[1] Teng JG, Chen JF, Smith ST, Lam L. FRP: Strengthened RC Structures. Frontiers in
Physics 2002:266.
[2] Hollaway LC, Teng JG. Strengthening and rehabilitation of civil infrastructures
using fibre-reinforced polymer (FRP) composites. UK: Woodhead Publishing Ltd;
2008.
[3] Seyhan EC, Goksu C, Uzunhasanoglu A, Ilki A. Seismic behavior of substandard RC
columns retrofitted with embedded aramid fiber reinforced polymer (AFRP)
reinforcement. Polymers 2015;7(12):2535-57.
[4] Dai J-G, Bai Y-L, Teng JG. Behavior and modeling of concrete confined with FRP
composites of large deformability. J Compos Constr 2011;15(6):963–73. https://
doi.org/10.1061/(ASCE)CC.1943-5614.0000230.
[5] Ouyang L-J, Gao W-Y, Zhen B, Lu Z-D. Seismic retrofit of square reinforced
concrete columns using basalt and carbon fiber-reinforced polymer sheets: a
comparative study. Compos Struct 2017;162:294–307. https://doi.org/10.1016/
j.compstruct.2016.12.016.
[6] Zeng J-J, Guo Y-C, Gao W-Y, Li J-Z, Xie J-H. Behavior of partially and fully FRPconfined circularized square columns under axial compression. Constr Build Mater
2017;152:319–32. https://doi.org/10.1016/j.conbuildmat.2017.06.152.
13
Y.-l. Bai et al.
Composite Structures 259 (2021) 113233
[50] Wang SS, Zhang MH, Quek ST. Effect of specimen size on static Strength and
dynamic increase factor of high-strength concrete from SHPB test. J Test Eval
2011;39(5):898–907.
[51] Wang S, Zhang M-H, Quek ST. Mechanical behavior of fiber-reinforced highstrength concrete subjected to high strain-rate compressive loading. Constr Build
Mater 2012;31:1–11. https://doi.org/10.1016/j.conbuildmat.2011.12.083.
[52] Liu P, Hu D, Wu Q, Liu X. Sensitivity and uncertainty analysis of interfacial effect
in SHPB tests for concrete-like materials. Constr Build Mater 2018;163:414–27.
https://doi.org/10.1016/j.conbuildmat.2017.12.118.
[53] Li W, Xu J. Impact characterization of basalt fiber reinforced geopolymeric
concrete using a 100-mm-diameter split Hopkinson pressure bar. Mater Sci Eng, A
2009;513-514:145–53. https://doi.org/10.1016/j.msea.2009.02.033.
[54] Ren GM, Wu H, Fang Q, Liu JZ. Effects of steel fiber content and type on dynamic
compressive mechanical properties of UHPCC. Constr Build Mater
2018;164:29–43. https://doi.org/10.1016/j.conbuildmat.2017.12.203.
[55] Zhang H, Liu Y, Sun H, Wu S. Transient dynamic behavior of polypropylene fiber
reinforced mortar under compressive impact loading. Constr Build Mater
2016;111:30–42. https://doi.org/10.1016/j.conbuildmat.2016.02.049.
[56] Lam L, Teng JG. Ultimate condition of fiber reinforced polymer-confined concrete.
J Compos Constr 2004;8(6):539–48. https://doi.org/10.1061/(ASCE)1090-0268
(2004)8:6(539).
[57] Fu Q, Niu D, Zhang J, Huang D, Wang Y, Hong M, Zhang Lu. Dynamic compressive
mechanical behaviour and modelling of basalt–polypropylene fibre-reinforced
concrete. Archiv Civ Mech Eng 2018;18(3):914–27. https://doi.org/10.1016/j.
acme.2018.01.016.
[58] Rossi P, Toutlemonde F. Effect of loading rate on the tensile behaviour of concrete:
description of the physical mechanisms. Mat Struct 1996;29(2):116–8. https://doi.
org/10.1007/BF02486201.
[59] Xie ZH, Duan ZJ, Guo YC, Li X, Zeng JJ. Behavior of fiber-reinforced polymerconfined high-strength concrete under Split-Hopkinson Pressure Bar (SHPB)
impact compression. Appl Sci 2019;9(14):2830. https://doi.org/10.3390/
app9142830.
[60] Al-Zubaidy H, Zhao X-L, Al-Mahaidi R. Mechanical characterisation of the dynamic
tensile properties of CFRP sheet and adhesive at medium strain rates. Compos
Struct 2013;96:153–64. https://doi.org/10.1016/j.compstruct.2012.09.032.
[61] Zhang X, Zhu D, Zhang H, Yao Y, Mobasher B, Huang L. Experimental study of
dynamic behavior of AFRP under different strain rates and temperatures. J Struct
Integrity Maint 2016;1(1):22–34.
[62] Chen W, Hao H, Jong M, Cui J, Shi Y, Chen Li, Pham TM. Quasi-static and dynamic
tensile properties of basalt fibre reinforced polymer. Compos B Eng
2017;125:123–33. https://doi.org/10.1016/j.compositesb:2017.05.069.
[63] Chen W, Meng Q, Hao H, Cui J, Shi Y. Quasi-static and dynamic tensile properties
of fiberglass/epoxy laminate sheet. Constr Build Mater 2017;143:247–58. https://
doi.org/10.1016/j.conbuildmat.2017.03.074.
[64] Lim JC, Ozbakkaloglu T. Hoop strains in FRP-confined concrete columns:
experimental observations. Mater Struct 2015;48(9):2839–54. https://doi.org/
10.1617/s11527-014-0358-8.
[35] Flores-Johnson EA, Li QM. Structural effects on compressive strength
enhancement of concrete-like materials in a split Hopkinson pressure bar test.
Int
J
Impact
Eng
2017;109:408–18.
https://doi.org/10.1016/j.
ijimpeng.2017.08.003.
[36] Yan L, Chouw N, Jayaraman K. Flax fibre and its composites – a review. Compos B
Eng 2014;56:296–317. https://doi.org/10.1016/j.compositesb:2013.08.014.
[37] Xia Y, Xian G, Wang Z, Li H. Static and cyclic compressive properties of selfcompacting concrete-filled flax fiber–reinforced polymer tubes. J Compos Constr
2016;20(6):04016046. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000706.
[38] Summerscales J, Dissanayake NPJ, Virk AS, Hall W. A review of bast fibres and
their composites. Part 1 – Fibres as reinforcements. Compos A Appl Sci Manuf
2010;41(10):1329–35. https://doi.org/10.1016/j.compositesa:2010.06.001.
[39] Yan L, Chouw N. Natural FRP tube confined fibre reinforced concrete under pure
axial compression: a comparison with glass/carbon FRP. Thin-Walled Struct
2014;82:159–69. https://doi.org/10.1016/j.tws.2014.04.013.
[40] Ku H, Wang H, Pattarachaiyakoop N, Trada M. A review on the tensile properties
of natural fiber reinforced polymer composites. Compos B Eng 2011;42
(4):856–73. https://doi.org/10.1016/j.compositesb:2011.01.010.
[41] Reis JML. Fracture and flexural characterization of natural fiber-reinforced
polymer concrete. Constr Build Mater 2006;20(9):673–8. https://doi.org/
10.1016/j.conbuildmat.2005.02.008.
[42] Kandemir A, Pozegic TR, Hamerton I, Eichhorn SJ, Longana ML. Characterisation
of natural fibres for sustainable discontinuous fibre composite materials. Materials
2020;13(9):doi:10.3390/ma13092129.
[43] Karim MRA, Tahir D, Haq EU, Hussain A, Malik MS. Natural fibres as promising
environmental-friendly reinforcements for polymer composites. Polym Polym
Compos
2020.
https://doi.org/10.1177/0967391120913723:10.1177/
0967391120913723.
[44] Nechwatal A, Mieck K-P, Reußmann T. Developments in the characterization of
natural fibre properties and in the use of natural fibres for composites. Compos Sci
Technol 2003;63(9):1273–9. https://doi.org/10.1016/S0266-3538(03)00098-8.
[45] Betts D, Sadeghian P, Fam A. Tensile Properties of Flax FRP Composites, 6th AsiaPacific Conference on FRP in Structures. APFIS; 2017.
[46] Yan L, Su S, Chouw N. Microstructure, flexural properties and durability of coir
fibre reinforced concrete beams externally strengthened with flax FRP composites.
Compos
B
Eng
2015;80:343–54.
https://doi.org/10.1016/
j.compositesb:2015.06.011.
[47] Yan L, Chouw N. Dynamic and static properties of flax fibre reinforced polymer
tube confined coir fibre reinforced concrete. J Compos Mater 2014;48
(13):1595–610. https://doi.org/10.1177/0021998313488154.
[48] Wang W, Zhang X, Mo Z, Chouw N, Li Z, Xu Z-D. A comparative study of impact
behaviour between natural flax and glass FRP confined concrete composites.
Constr
Build
Mater
2020;241:117997.
https://doi.org/10.1016/
j.conbuildmat.2020.117997.
[49] American Society for Testing Materials (ASTM). Standard test method for tensile
properties of polymer matrix composite materials. D3039M-08 2008b;West
Conshohoken:PA.
14