Case Studies in Construction Materials 17 (2022) e01602

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Case Studies in Construction Materials

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Case study

Experimental study on shear performance of basalt fiber concrete

beams without web reinforcement
Yu Jianbing *, Xia Yufeng, Liu Saijie, Xu Zhiqiang
College of Civil Science and Engineering, Yangzhou University, Yangzhou, Jiangsu 225127, China

A R T I C L E I N F O A B S T R A C T

Keywords: In this study, we report the results of an experimental investigation conducted under a four-point
Basalt fiber concrete beams bending loading in order to evaluate the shear performance of concrete beams reinforced with
Failure morphology basalt fiber without web reinforcement. According to the experimental results, it is evident that
Bearing capacity
the final failure morphology of concrete-basalt fiber concrete composite beams and conventional
Finite element analysis
concrete beams was shear failure, whereas the failure morphology of concrete beams reinforced
with full basalt fiber was bending failure. Moreover, the results also indicate that the cracking
load and ultimate bearing capacity of concrete composite beams reinforced with concrete-basalt
fiber are lower than those of conventional concrete beam. This is mainly due to the interface
between ordinary post-cast concrete and concrete reinforced with hardened basalt fiber. Due to
the superior tensile properties of fiber, composite beams and all basalt fiber concrete beams
exhibit a higher degree of ductility than conventional concrete beams. Utilizing the existing
calculation theory for concrete beams reinforced with fiber, it was calculated that the cracking
load and ultimate load of basalt fiber beams were calculated, and the calculation results were
consistent with the experimental results. Based on the results of the evaluation and the theoretical
analysis, this study proposes a finite element modeling method for basalt fiber composite beams.
The results of the analysis were consistent with the experimental results of all investigated beams.
The established model was employed in order to investigate the influence of shear span ratio on
the shear performance of basalt fiber beams.

1. Introduction

As of today, concrete is the most commonly utilized building material in the construction industry. In addition to its high degree of
plasticity, it is also convenient to draw materials, and it allows the control of structural deformations. Since concrete and steel bars can
be combined to realize their respective advantages, they are commonly utilized in the construction of ports, civil buildings, roads, and
bridges [1]. However, due to the corrosion damage induced by chloride ions, a large number of reinforced concrete structures require
an overhaul after approximately 30 years, such as bridges, ports, railways, etc. In recent years, numerous studies have been conducted
to overcome the shortcomings of concrete, with the objective of making the material lighter, more resilient, and more durable [2–5].
Accordingly, it was proposed to utilize composite beams reinforced with fibers in order to overcome these shortcomings [6–8].
Carbon, aramid, polyethylene, glass, and basalt fibers are highly advanced fibers that can be utilized in the production of fiber-
reinforced concrete [9]. In recent years, basalt fibers derived from igneous basalt rocks have been commonly utilized in concrete

* Corresponding author.
E-mail address: jbyu@yzu.edu.cn (Y. Jianbing).

https://doi.org/10.1016/j.cscm.2022.e01602
Received 15 August 2022; Received in revised form 4 October 2022; Accepted 20 October 2022
Available online 4 November 2022
2214-5095/© 2022 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
Y. Jianbing et al. Case Studies in Construction Materials 17 (2022) e01602

Nomenclature

Δu Ultimate displacement.
Δy yield displacement.
γc Non-fiber safety factor of concrete.
ks size coefficient.
fut− FRC Ultimate tensile residual strength of fiber reinforced concrete.
fc Compressive strength of ordinary concrete.
ft Tensile strength of ordinary concrete.
σ cp The average normal stress of loading or prestress on concrete section.
b Section width.
d Section height.
Vfcr Cracking load of inclined section of fiber reinforced concrete beam.
fft Tensile strength of fiber reinforced concrete.
λf steel fiber content characteristic value.
ρ longitudinal reinforcement ratio.
βcr Influence coefficient of basalt fiber on shear cracking load of beam oblique section，take βcr = 0.049.
Vc Design value of shear capacity of inclined section concrete.
Vfc Design value of shear capacity of steel fiber reinforced concrete.
βv Influence coefficient of fiber on shear capacity of concrete on inclined section of flexural member，specific values
determined by experiments.
εt,r Peak tensile strain corresponding to uniaxial tensile strength.
εc,r Peak compressive strain corresponding to uniaxial compressive strength.
x The location of the truncation is defined by the ratio of strain to peak strain, values according to the strength grade of
concrete.
σ The stress.
Ec Elasticity modulus of concrete.
dt The uniaxial tensile damage evolution coefficient of concrete.
dc The uniaxial compression damage evolution coefficient of concrete.
αt Parameter values of descending section of uniaxial tensile curve of concrete.
ft,r The representative value of uniaxial tensile strength of concrete.
fc,r The representative value of uniaxial compression strength of concrete.
n variable.
ρc a parameter in the derivation process and has no practical significance.
ρt a parameter in the derivation process and has no practical significance.
E0 The elastic modulus of concrete.
ED The damage elastic modulus of concrete.
d The damage factor. d= 0 represents non-destructive state, d= 1 represents completely damaged, 0 <d< 1
corresponding to different degrees of damage.
ft Axial tensile strength.
fts Splitting tensile strength of basalt fiber concrete.
εt Peak tensile strain.
Eft Initial tensile elastic modulus of basalt fiber reinforced concrete.
Ep secant modulus at peak point of basalt fiber reinforced concrete.
ES elastic modulus of steel bar.
σs reinforcement stress.
εs reinforcement strain.
fy,r Representative value of yield strength of steel bar.
fst,r Representative value of ultimate strength of steel bar.
εy Yield strain of steel bar corresponding to fy,r .
k Slope of reinforcement hardening.

structures across the globe [10]. Basalt fiber is a new green-colored industrial material that can be manufactured with a reduced level
of emissions. Furthermore, the amount of energy consumed in the manufacturing process of composite beams reinforced with basalt
fiber is 1/16 of that of carbon fiber, the manufacturing cost is 1/6 of that of carbon fiber, and the creep rate is 1/4 of that of aramid
fiber. In addition, the corrosion resistance of composite beams reinforced with basalt fiber is also superior to that of glass fiber [11].
James [10,12,13] has conducted a number of studies on basalt fiber concrete, ranging from basalt fiber concrete materials to basalt
fiber concrete beams. He examined the mechanical properties of basalt fiber-reinforced concrete at high temperatures. Based on the

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Table 1
Concrete mix ratio.
Water（kg/m3） Cement（kg/m3） Sand（kg/m3） Crushed stone（kg/m3） Water reducer (%)

190 485 700 1080 0.8

Table 2
The major mechanical properties of basalt fiber.
Diameter（μm） Density（kg/m3） Elastic modulus（GPa） Tensile strength（MPa）

10 2.65 93–115 3300–4800

experimental results, he proposed a constitutive model of concrete reinforced with basalt fiber and verified that the proposed model is
capable of accurately predicting the bearing capacity of concrete structures reinforced with basalt fiber. Ao [14] conducted a study on
the shear performance of concrete beams reinforced with FRP bar-basalt fiber. Ao discovered that in cases where the concrete spec­
imens reinforced with basalt fiber were subjected to compression failure, they developed more fine cracks than ordinary concrete
specimens. In cases where the fiber content was 0.1%, the compressive strength and splitting tensile strength of the concrete specimens
reinforced with fiber were enhanced, however, in cases where the fiber content exceeded a certain threshold, the compressive strength
decreased. Zhang et al. [15] conducted four-point concentrated loading tests on four concrete beams reinforced with BFRP-reinforced
basalt fiber without web reinforcement in addition to another individual BFRP-reinforced concrete beam without web reinforcement.
The results demonstrated that the increase in basalt fiber content led to the specimen changing from baroclinic failure to shear
compression failure. In addition, it also led to a decrease the mid-span deflection and crack width of the specimen, as well as an in­
crease the shear cracking load and ultimate bearing capacity of the specimen. Jabbar et al. [16] applied basalt fiber to ultra-high
performance concrete T-beams. According to the test results, it was demonstrated that basalt fiber is capable of delaying the obli­
que cracking of ultra-high performance concrete more than steel fiber. Moreover, adding 0.5% and 1% basalt fiber to ultra-high
performance concrete T-beams enhanced their shear strength significantly more than adding the same volume fraction of steel
fiber. Abed et al. [17] conducted shear tests on eight BFRP-RC deep beams reinforced with basalt fiber. The results indicated that the
overall stiffness, toughness, and ultimate shear strength of the concrete beams reinforced with basalt ultra-fine fiber exhibited a 42%
increase. Murad et al. [18] conducted shear tests on eight concrete beams reinforced with basalt fiber and polypropylene fiber. It was
found that the shear strength, peak deflection, ductility, and initial stiffness of the beam containing 2.5% basalt fiber increased by 20%,
64%, 121%, and 21%, respectively.
According to the aforementioned research, it is evident that unlike concrete reinforced with basalt fiber, ordinary concrete ma­
terials are characterized by brittleness, poor impact resistance, and low tensile strength. Incorporating an appropriate amount of basalt
fiber in the manufacturing of concrete results in a significant improvement in the static and dynamic mechanical properties of concrete
as well as its brittleness. However, there are also a number of studies on the shear performance of basalt fiber and ordinary concrete
composite beams. In this study, we propose to utilize basalt fiber concrete partially instead of ordinary concrete within beams. In other
words, the purpose here is to examine the shear performance of basalt fiber concrete beams in part by replacing the concrete in the
tensile zone with basalt fiber concrete. According to previous research, it is evident that when the volume content of basalt fiber was
0.1%, the mechanical properties of concrete were superior; therefore, the volume content of basalt fiber was set to 0.1% in this paper
[7,13,14,17].

2. Shear performance test scheme

2.1. Materials

The strength grade of matrix concrete was C40, and the cementitious material was ordinary Portland cement with a strength of
42.5 MPa, and its performance index also achieved the specification requirements [19]. The coarse aggregate consisted of gravel with a
particle size between 5 and 25 mm, and the fine aggregate consisted of yellow sand with a fineness modulus between 2.5 and 2.8. Tap
water containing 40% poly-carboxylate superplasticizer was used, and the performance indicators of the water reducing agent ach­
ieved the anticipated specifications. The specific concrete mix ratio is provided in Table 1. The basalt fibers were short-cut to 15 mm in
length and 10 µm in diameter. The major mechanical properties of basalt fiber are provided in Table 2. In order to produce basalt fiber
concrete, 0.1% basalt fiber was added to the C40 matrix concrete. In addition, HRB400 steel bars were utilized as a means of rein­
forcing the longitudinal tensile strength. Since the stirrups were arranged at the mid-span loading point and also at both ends of the
bearing in order to reinforce the erection, the bending and shear spans did not contain any stirrups.

2.2. Performance test of concrete materials

The compressive and splitting tensile tests were carried out on C40 ordinary concrete and concrete reinforced with 0.1% basalt
fiber [20–22]. The cylinder compressive strength test was conducted by utilizing three standard specimens of ϕ150 × 300 mm cylinder
block, the cylinder splitting tensile test was conducted by utilizing three standard specimens of ϕ150 × 300 mm cylinder block, the

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Fig. 1. Test block pouring.

Fig. 2. Splitting tensile test.

Fig. 3. Concrete cylinder compression test.

Table 3
Material properties of concrete.
Concrete Compressive strength fc（MPa） Tensile strength ft（MPa） Elastic modulus Ec（GPa）

Ordinary concrete 38.56 3.38 34.46

basalt fiber reinforced concrete 40.35 4.01 35.08

cube compressive strength test was conducted by utilizing six standard specimens of 150 × 150 × 150 mm block. Fig. 1 depicts field
production. Figs. 2 and 3 depict the mechanical properties of the tested concrete，the test results of material properties of concrete are
shown in Table 3.

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Fig. 4. Details of specimen design.

Table 4
The specific parameters of the test beams.
Specimens Reinforcement for the upper Reinforcement for the bottom Shear zones Shear span he Number of test
beam beam stirrups ratio (mm) specimens

I1 2 2 0 4.25 0 1
10 18 + 3

12
I2 2 2 0 4.25 100 1
10 18 + 3

12
I3 2 2 0 4.25 150 1
10 18 + 3

12
I4 2 2 0 4.25 300 1
10 18 + 3

12

2.3. Specimen design

In this paper, a total of four beams were tested. The bottom of the beams were reinforced by utilizing two rows of HRB400 ordinary
steel bars with diameters of 12 mm and 18 mm, respectively. As depicted in Fig. 4, the diameter of the upper reinforcement was
10 mm, the diameter of the stirrup was 8 mm, and the spacing was 200 mm. The major variable for each specimen was the height he of
the fiber concrete at the bottom of the beam, and the values he of each specimen are 0, 100 mm, 150 mm, and 300 mm, respectively.
The specific parameters of the test beams are provided in Table 4.

2.4. Manufacture of specimen

In the production process of all specimens, the longitudinal reinforcement and stirrups of the beams were bound together in order
to form a reinforcement cage for each specimen. Furthermore, the strain gauge was installed according to the design requirements.
Subsequently, the bottom and side template of the beam were supported. Specimens I1 and I4 concrete were one-time pours of or­
dinary concrete and basalt fiber concrete. Specimens I3 and I4 were first poured with basalt fiber concrete at the bottom of the beams.
The ordinary concrete was poured into the upper framework after the strength of the basalt fiber concrete reached 80% of the design
strength. Following removal of the formwork, a plastic film is installed on the beams in order to cover and maintain each specimen. The
entire production process of the specimens is depicted in Fig. 6.

2.5. Test loading device and loading system

A four-point symmetrical loading shear test was conducted on all beams; the loading device is depicted in Fig. 5. In this case, the
loading method was monotonic loading. In the test loading process, the specimen was preloaded first in order to determine whether the
loading instrument was capable of functioning properly. During the formal loading process, the applied load of each stage was strictly
controlled at approximately 10% of the ultimate bearing capacity. When the applied load reached 75% of the calculated cracking load,
the loading value of each stage was adjusted to approximately 5% of the cracking load value in order to facilitate the accurate
measurement of the cracking load of the specimens. (Fig. 7).

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Fig. 5. Test loading device.

3. Analysis of test results

3.1. Failure morphology

During the loading process of the four beams, a number of vertical cracks first developed at the lower portions of both sides of the
bending section of the beam, and gradually expanded as the load increased. Considering the load applied by the four beams during
cracking, it is evident that the cracking load increased in proportion to the increase in basalt fiber concrete height, as demonstrated in
Table 5.
When the load of specimen I1 was increased to 20 kN, the beam developed several vertical cracks on both sides, around the bending
section. When the load was increased to 40 kN, the beam developed multiple vertical cracks at the lower part of both sides around the
bending shear section. As the load continued to be applied, the cracks around the joint action section of bending and shearing
expanded obliquely to the loading point, resulting in multiple oblique cracks. When the load was increased to 120 kN, as a result, the
vertical cracks around the mid-span bending section expanded to approximately half the height of the beam, such that the oblique
cracks on both sides of the beam became connected. When the load was increased to 150 kN, it led to a rapid increase in the width of
the diagonal cracks, whereas the cracks around the pure bending section no longer expanded at approximately half the height of the
beam. Subsequently, the test beam rapidly lost its bearing capacity, resulting in its brittle failure. The final failure mode was diagonal
tension failure; the final failure mode of specimen I1 is depicted in Fig. 4(a). In the case of specimen I2 and specimen I3 the crack
development during loading was essentially the same as that of specimen I1. As compared to I1, I2 and I3 exhibited a significant
increase in the number, as well as density of cracks. However, the vertical cracks around the pure bending section only expanded up to
the interface between the fiber-reinforced concrete and the ordinary concrete, leaving the middle portion of the beam unaffected. The
ultimate bearing capacity of specimen I2 was significantly lower than that of specimen I1, and the ultimate bearing capacity of
specimen I3 was slightly lower than that of specimen I1. The final failure modes of specimens I2 and I3 were all diagonal tension
failure, as depicted in Fig. 4(b) and (c). Regardless of the cracking load or ultimate load, specimen I4 exhibited superior results as
compared to specimen I1. Moreover, it was also found that the final failure mode of the concrete beam reinforced with basalt fiber also

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Fig. 6. Test beam fabrication.

changed, its failure mode was bending failure. The final failure mode is depicted in Fig. 4(d).

3.2. Cracking load and analysis of the ultimate bearing capacity

Based on Table 5 and Fig. 8, it is evident that the incorporation of basalt fiber results in an increase in the cracking load of the beams
of the normal section. As Compared to I1, the cracking load of the normal section of specimens I3 and I4 increased by 25% and 40%,
respectively, whereas the cracking load of the normal section of specimen I2 remains unaffected. In terms of cracking load, the cracking
load of the oblique section in the case of all concrete beams reinforced with fiber is the highest, which is 12.5% higher than that of
specimen I1. Moreover, as compared to specimen I1, the cracking load of the oblique section of specimen I2 is reduced by 12.5%. In
terms of ultimate bearing capacity, the all-fiber concrete beam exhibits the highest ultimate bearing capacity, which is 15.3% higher
than that of specimen I1. As compared to specimen I1, the ultimate bearing capacity of specimen I2 and I3 decreased by 8% and 2%,
respectively. In the case of specimen I4, the basalt fiber is capable of changing the failure morphology of the component by utilizing the
failure morphology, thereby improving its cracking load and ultimate bearing load.

3.3. Loading-displacement curves

Fig. 9 depicts the load-deflection curves of all test beams. According to Fig. 9, it is evident that all beams were in the elastic stage
before the specimens developed cracks, and that there is a linear variation between the deflection and the load. The deflection values of
each specimen were essentially the same under the same load. As compared to specimen I1, the ultimate load of I2 was significantly
reduced, whereas the ultimate load of I3 was only slightly reduced. The decrease in the ultimate bearing capacity of I2 and I3 can be
attributed to the presence of a composite layer between the ordinary concrete and the basalt fiber concrete. As compared to I1, both the
cracking load and ultimate load of the concrete beam reinforced with basalt fiber in I4 were increased. As the bearing capacities of
specimens I1, I2, and I3 reached their ultimate loads, the beams exhibited a rapid decrease in their bearing capacities, which caused the
specimens to exceed their limit states. In terms of ductility, specimen I4 was the best. After the load reached the ultimate bearing
capacity, the load did not decrease rapidly, and the deflection value increased, in other words, it was capable of carrying the weight,.
According to Fig. 10, it is evident that when the load is applied to 70 kN, 90 kN, 110 kN, 130 kN, and 150 kN, the mid-span
deflection value of the ordinary concrete beam I1 is greater than the deflection value of beam I2, I3, and I4. This indicates that
basalt fiber is capable of effectively improving the tensile capacity, the crack resistance, and the overall stiffness of the concrete
components. Under the same load, the deflection of basalt fiber concrete beams is significantly less than that of conventional concrete

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Fig. 7. Final failure morphology of test beams.

Table 5
Experimental results.
Specimens Fiber volume content he Normal section cracking Oblique section cracking Ultimate load Failure morphology
（%） （mm） load（kN） load（kN） （kN）

I1 0 0 20 40 150 diagonal tension

failure
I2 0.1 100 20 35 138 diagonal tension
failure
I3 0.1 150 25 40 147 diagonal tension
failure
I4 0.1 300 28 45 173 bending failure

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Fig. 8. Load comparison.

Fig. 9. Load-deflection curves of specimens.

Fig. 10. Variation of beam deflection under different loads.

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Fig. 11. Strain distribution of mid-span section along specimen depth.

test specimens.

3.4. Strain analysis of concrete

In the mid-span pure bending section, there were five concrete strain gauges bonded uniformly along the height of the beam from
top to bottom. The spacing between each strain gauge was 50 mm, and the strain gauges from top to bottom were labeled C1, C2, C3,
C4, and C5, respectively. Fig. 11 depicts the mid-span concrete strain of the five strain gauges of each specimen under the ultimate
loads of 20%, 40%, 60%, 80%, and 100%, respectively. According to Fig. 11, it is evident that the strain of the mid-span section of each
specimen changes linearly, which is consistent with the plane section assumption. Moreover, it is evident that in all specimens the
upper part of the axial beams moves in response to the load.
Fig. 12 depicts the strain curve of concrete on one side of the beam bending shear section. As a result of the joint action of shear
force and bending moment, oblique cracks develop between the bearing and the loading point. Before the loading of specimen I1
reached 40 kN, the strain of the concrete remained relatively stable. Although, when the loading exceeded 40 kN, the tensile strain of
concrete measured by strain gauges FC3 and FC4 increased in proportion with the increase in the loading. The increase in strain is
primarily due to the strain gauge being pasted only in the development areas of cracks. The strain gauge FC5 was subjected to tensile
stress, as a result, at first there was an increase in the concrete strain, but then it decreased in proportion with the increase in the load.
Since there was relatively no crack development in the strain gauge FC1 paste area, as a result, the strain value was also unaffected. The
change in the concrete strain of specimens I2 and I3 were relatively similar to that of specimen I1 on one side of the bending-shear
section. However, since the crack development in the case of specimen I4 was more sparse, it is evident that except for the rapid
increase in the strain value of strain gauge PC7, the concrete strain at the rest of the areas was relatively stable.

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Fig. 12. Load-strain curve in bending-shear section.

3.5. Displacement ductility coefficient

In the case of concrete structures, it is imperative that structures meet both strength and ductility requirements. Ductility is the
deformation capacity of a member from the beginning of yielding to the ultimate bearing capacity [23]. The ductility coefficient was
introduced in order to investigate the ductility of concrete beams reinforced with basalt fiber without web reinforcement under shear
failure. The ductility coefficient refers to the ratio of the displacement Δu corresponding to 0.85 Pmax in the load-displacement curve
and the deflection Δy corresponding to the initial yield point [24]. As indicated by the following formula:
Δu
μΔ = (1)
Δy

Since the specimens in this test were all beams without web reinforcement, the longitudinal reinforcements of specimens I1, I2, and
I3 did not yield when the component was damaged. The initial yield point was obtained by applying the energy approach; as depicted
in Fig. 13. Line OA, AN, OA, and the load-displacement curve intersect at point B, and indicate that the area of two shadow parts in the
graph is equal, and the corresponding displacement of point A is Δy . The calculation results of the displacement ductility coefficient are

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Fig. 13. Determination of yield displacement by energy method.

Table 6
Ductility coefficient.
Specimens Δy /mm Δu /mm μΔ
I1 8.7 14.5 1.66
I2 7.3 13.6 1.85
I3 8.4 15.5 1.88
I4 9 84 9.33

provided in Table 6.
According to Table 6 and Fig. 9, it is evident that the ordinary concrete test beam I1 exhibited the smallest ductility, and the full-
fiber concrete member I4 exhibited the largest ductility. Its μΔ was 5.6 times that of specimen I1, 5 times that of specimen I2, and 4.9
times that of specimen I3. Secondly, basalt fiber concrete accounted for half of the height of the beam I3, its μΔ was 13% higher than I1,
and 2% higher than I2. In the case of beam I2, the basalt fiber concrete accounted for 1/3 of the height of the beam, and its μΔ was 11%
higher than specimen I1. Based on the results, It is evident that the addition of basalt fiber to concrete structures was conducive to
improving the ductility of all members and enhancing their deformation capacity.

3.6. Oblique section cracking load calculation

The formula for calculating the cracking load of the inclined section is not given in the Code for the design of concrete structures
[25] as well as the design standard of concrete structures reinforced with steel fiber [26]. Therefore, the calculation formula of the
cracking load of the inclined section in this paper refers to the theoretical formula obtained from previous research.
Reference [27] proposed the calculation formula of the cracking load for the diagonal section of concrete beams reinforced with
basalt fiber as follows:
( )( )
2.4ft 40ρ
Vfcr = + 1 + βcr λf bh0 (2)
λ+5 λ
Reference [28] proposed the calculation formula of the cracking load for the diagonal section of concrete beams reinforced with
basalt fiber as follows:
2.45fft
Vfcr = bh0 (3)
λ + 3.5
Reference [29] proposed the calculation formula of the cracking load for the diagonal section of concrete beams reinforced with
basalt fiber as follows:
( )
2.45 20ρ
Vfcr = + fft bh0 (4)
λ + 3.5 λ + 1.1
Reference [30] proposed the calculation formula of the cracking load for the diagonal section of concrete beams reinforced with
basalt fiber as follows:
( )
20ρ
Vfcr = 0.24fft + + 0.5λf bh0 (5)
λ
Reference [31] proposed the calculation formula of the cracking load for the diagonal section of concrete beams reinforced with

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Fig. 14. Comparison of calculated cracking load of inclined section with experimental value.

basalt fiber as follows:

( ( ) )
1.25 20 1 + 2λf ρ
Vfcr = + fft bh0 (6)
2λ + 0.5 2λ + 0.5
Reference [32] proposed the calculation formula of the cracking load for the diagonal section of concrete beams reinforced with
basalt fiber as follows:
( )
0.67 35.6ρ
Vfcr = + fft bh0 (7)
λ + 0.13 λ + 5.9
In the calculation process, due to the lack of a calculation theory for composite beams, in the calculation of the cracking load of the
inclined section of I2 and I3, the calculation theory of the full section concrete beam reinforced with fiber was utilized. According to
Fig. 14, it is evident that the cracking load value of the beam calculated by applying the relevant theory was greater than the
experimental value. In the case of specimens I2, I3, and I4, the theoretical value of the cracking load of the inclined section calculated
in reference [32] is the closest one to the experimental value. Therefore, this formula is best suited for predicting the cracking load of
the inclined section of the component.

3.7. Calculation of the ultimate bearing capacity

Calculation of the shear capacity of the rectangular concrete beams reinforced with basalt fiber should meet the requirements of
reference [26].
( )
Vfc = Vc 1 + βv λf (8)

Concrete reinforced with fiber is utilized in tension zones and ordinary concrete is utilized in compression zone. In formula (8), λf
should be replaced by λfp, and λfp, and must meet the following requirements.
In cases where shear span ratio λ > 2 and the load is concentrated, λfp is calculated as follows：
( )
2hf 4
λfp = λf − 1 (9)
h λ
In cases where the shear span ratio λ ≤ 2 and the load is a concentrated load or uniform load, λfp is calculated according to the
following formula：
2hf
λfp = λf (10)
h
In cases where the height of the concrete beam reinforced with fiber in the tension zone he is 0.5 times higher than the full height of
section h, take he= 0.5 h.
Calculation of ultimate bearing capacity of fiber reinforced concrete beams in ACI Committee 544 as follow [33]：
{ [ ( ) ]13 }
0.18 fut− FRC
VFRC = ks 100ρ 1 + 7.5 fc + 0.15σ cp bd (11)
γc ft

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Table 7
Comparison between experimental value and theoretical value.
Specimens Vefcu /kN /kN reference [26] Vefcu /Vcfcu Vcfcu /kN reference [33] Vefcu /Vcfcu

I1 150 82.3 1.82 64.5 2.32

I2 138 94.5 1.46 131.3 1.05
I3 147 100.8 1.46 131.3 1.12
I4 173 137.5 1.26 131.3 1.32

Fig. 15. Stress-strain curves of concrete.

√̅̅̅̅̅̅̅̅
200
ks = 1 + (12)
d
In Table 7, the theoretical calculation value and the test value of the ultimate load are compared. According to Table 7, it is evident
that the theoretical calculation value is conservative regardless of whether the American code or the Chinese code is adopted.

4. Development of the finite element model of the beams

4.1. Material constitutive

4.1.1. Concrete constitutive modeling

According to the existing research results, ordinary concrete and basalt fiber concrete exhibit similar failure mechanisms and
deformation. In both types of concrete, elastic deformations occur first and then non-linear elastic deformations occur due to cracks.
Concrete cracking is caused by the fact that internal tensile stress is greater than the cracking stress of concrete. As a result of
incorporating basalt fibers into the concrete matrix, the cracking stress is increased and the development of cracks is delayed, without
affecting the form of cracks. Accordingly, it is evident that the constitutive model of basalt fiber concrete is significantly similar to the
constitutive model of ordinary concrete [34].
In the process of concrete deformation, the internal micro-cracks continue to expand and evolve. Moreover, the concrete also
exhibits softening and attenuation of elastic modulus. In order to demonstrate the inelastic behavior of concrete, the damage plasticity
model in combination with the elastic damage model, as well as the tensile and compressive plasticity theories were selected.

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Y. Jianbing et al. Case Studies in Construction Materials 17 (2022) e01602

Fig. 16. Stress-strain curve of steel bar.

Additionally, these models and theories are also capable of demonstrating the cracking and crushing phenomenon of concrete. The
stress-strain relationship of ordinary concrete and fiber concrete is depicted in Fig. 15.
The mathematical expression formula of stress-strain constitutive relation curve of ordinary concrete under uniaxial tension is as
follows [25]:
σ = (1 − dt )Ec ε (13)
⎧ ( 5
)
⎨ 1 − ρt 1.2 − 0.2x x≤1
dt = ρt (14)
⎩1 − x>1
αt (x − 1)1.7 + x

ε
x= (15)
εt,r

ft,r
ρt = (16)
Ec Et,r

The mathematical expression formula of stress-strain constitutive relation curve under uniaxial compression is as follows:
σ = (1 − dt )Ec ε (17)

⎧ ρc n
⎨ 1 − n − 1 + xn
⎪ x≤1
dc = ρc (18)
⎪
⎩1 − x>1
αc (x − 1)2 + x

fc,r
ρc = (19)
Ec Ec,r

ε
x= (20)
εc,r

Ec εc,r
n= (21)
Ec εc,r − fc,r

The stress-strain relation curve of basalt fiber reinforced concrete under uniaxial tension adopts the mathematical expressions
proposed in reference [35–37] as follows：

ft = − 0.4142f 3ts + 5.4768f 2ts − 22.856fts + 33.378 (22)

εt = 65f 0.54
t × 10− 6
(23)

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Y. Jianbing et al. Case Studies in Construction Materials 17 (2022) e01602

Table 8
Concrete material parameters.
Concrete E /GPa ν Expansion angle Eccentricity fbo /fco K Viscous coefficient

C40 34.46 0.2 30 0.1 1.16 0.6667 0.005

BFRP 35.08 0.2 30 0.1 1.16 0.6667 0.005

Table 9
Steel material parameters.
Steel E /GPa ν fy /MPa fst /MPa

HRB400 200 0.3 400 570

⎧ ( ) ( )
⎪
⎪ Eft Eft 2 Eft
⎪
⎨E x + 1.5 − 1.25 x + 0.25 − 0.5 x4 0≤x≤1
Ep Ep
(24)
p
y=
⎪
⎪ x
⎪
⎩ x≥1
αf (x − 1)1.7 + x

0.312f 2t
αf = l
(25)
1 + 3.58ρf dff

Concrete beams develop cracks as a result of the tensile stress within them. The incorporation of basalt fiber into the beams does not
affect the morphology of crack development; however, it does delay the development of cracks. As a result, the stress-strain consti­
tutive relation curve of concrete reinforced with basalt fiber under uniaxial compression can be modeled in the same manner as the
stress-strain constitutive model of ordinary reinforced concrete under uniaxial compression.

4.1.2. Constitutive modeling of steel

The constitutive model of steel bars in this paper is applied to a trilinear model under monotonic loading; as depicted in Fig. 16.
The mathematical expression formula of the trilinear model of reinforcement is as follows：
⎧ ⎫
⎪
⎪ Es εs εs ≤ εy ⎪
⎪
⎨ ⎬
σs = ( fy εy <)εs ≤ εs,h (26)
⎪
⎪ f + k ε − ε ε < ε ≤ ε ⎪
⎪
⎩ y s s,h s,h s s,u
⎭
0 εs > εs,u

4.1.3. Material parameter values

The material parameters of C40 concrete and basalt fiber concrete entered in ABAQUS are provided in Table 8.
The steel cushion block in ABAQUS was an ideal elastic-plastic material by default. The Poisson’s ratio was 0.3 and the elastic
modulus was 200 GPa. Material parameters for steel bars are provided in Table 9.

4.2. Model development

4.2.1. Interface simulation

Considering the stress characteristics of concrete, while disregarding its tensile strength and interface bonding force, the hardened
concrete and the post-cast concrete contact interface are considered primarily to be responsible for bearing the normal extrusion force
and tangential friction [38]. ABAQUS software is capable of quickly simulating the normal extrusion force and tangential friction force
of the concrete interface. In the simulation process of the software, it is necessary to simulate the characteristics of the contact by
defining the tangential behavior and the normal behavior in order to achieve the mechanical properties of the contact surface
simulation. For the tangential behavior, this paper chooses ’ Penalty ’ friction function, the friction coefficient is 0.6, according to the
value of friction coefficient between rough concrete surface. For normal behavior, this paper chooses hard contact to consider the
contact pressure interference problem and allows post-contact separation.
The contact surface between the concrete beam and the steel cushion block was set as the binding relationship. The concrete
contact surface was set as the main surface, and steel cushion block surface was set as the slave surface. The steel cushion block was
distributed and coupled with the reference point, and the load was transmitted to the surface of the cushion block through the
reference point.

4.2.2. Element selection and meshing

In the modeling process, considering the beam model was relatively simple, so the full beam finite element model was established
instead of using symmetrical model. In the Meshing process, the smaller the mesh size, the more modeling calculations are required,
resulting in a higher computational cost, and the accuracy will also be affected. In order to achieve the necessary calculation speed and

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Y. Jianbing et al. Case Studies in Construction Materials 17 (2022) e01602

Fig. 17. Finite element model.

accuracy of both requirements, the concrete element and the steel cushion block adopt the hexahedral 3D solid element C3D8R. The
mesh size of concrete and steel cushion blocks was divided into 20 mm; the finite element analysis model is depicted in Fig. 1. As part of
the steel frame, 3D truss elements were utilized and the mesh size was 10 mm. In order to obtain the mesh division of the beam, the grid
seeds are first arranged on the two rectangular components of the beam, and then the division accuracy is determined by utilizing
structured technology. In the meshing division, considering the concrete section size was larger, so the grid division was sparser, and
the section size of the steel bar was smaller, so the grid size was smaller, which could increase the accuracy of the calculation.

4.2.3. Boundary and load application

In one end of the beam, it was possible to constrain the displacements in x, y, and z directions as well as the rotations along x and y
directions, whereas on the other end, only the displacements in y direction were constrained. The loading method was displacement
loading. Two reference points were set above the cushion blocks of the loading point of the specimen, and the reference points were
coupled with the cushion blocks. Subsequently, two linearly increased, equal displacement loads were applied to the two reference
points.(Fig. 17).

4.3. Finite element analysis results

4.3.1. Analysis of failure morphology

Fig. 18 depicts the damage nephogram of the four specimens obtained by applying the finite element software ABAQUS. According
to Fig. 18, it is evident that there is no peeling phenomenon at the interface between ordinary concrete and concrete reinforced with
basalt fiber. The final failure morphology of the four specimens was the same as that of the test results. Shear failure occurred in
specimens I1, I2, and I3, and bending failure occurred in specimen I4. The comparison between the ultimate load calculated by the
finite element method and the test value is shown in Table 10. This phenomenon demonstrates that the calculated results of the stress-
strain curves of ordinary concrete and concrete reinforced with basalt fiber that were selected by applying ABAQUS, were consistent
with the actual situation. As a result, it is possible to accurately represent the failure characteristics of basalt fiber beams without web
reinforcement.

4.3.2. Deflection analysis

Fig. 19 depicts a comparison of load-deflection curves between the test and the finite element calculation. Fig. 19 demonstrates
that, in the elastic stage, although the finite element calculation results were relatively consistent with the test results, there is also a
linear variation between the resulting load-deflection curves. In the rising section of the simulated load-deflection curves, the slope of
the load-deflection curves was greater than that of the test results. Under the same load, the actual deflection of the specimens was
greater than that of the simulation results, which indicates that the actual stiffness of the specimen was less than that of the simulation.
This is primarily due to the fact that in the elastic stage, the results of the finite element analysis were idealized, and the defects in the
processing and maintenance of actual components led to the decrease in stiffness. In the case of specimens I1, I2, and I3, the beams
exhibited brittle failure during the test process. However, the beams simulated by applying the finite element method exhibited plastic
deformation capabilities. As a result, the load-deflection curves obtained by the simulation of the descending section exhibited a more
gentle downward trend. The bending failure and the ductility of specimen I4 were favorable, and the simulated load-deflection curve
was also in accordance with the experimental value.

4.3.3. Parametric analysis

Shear span ratio is the most direct factor affecting the bearing capacity of concrete beams without web reinforcement. The influence
of the four different shear span ratios on the shear capacity of the concrete beams reinforced with basalt fiber was analytically
investigated. The four shear span ratios were 1.7, 2.55, 3.4, and 4.2, respectively. Fig. 20 depicts the load-deflection curves of the four
specimens under different shear span ratios.
Fig. 20 demonstrates that the bearing capacity of all beams decreased in proportion to the increase in shear span ratios. In addition,
it was also found that under a lower shear span ratio, the specimen suddenly exceeds limit states after reaching the ultimate load, thus
resulting in a rapid decline in the bearing capacity. Under a higher shear span ratio, the specimen exhibited a lower ultimate load;

17
Y. Jianbing et al. Case Studies in Construction Materials 17 (2022) e01602

Fig. 18. Comparison of failure morphology between test and finite element calculation.

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Y. Jianbing et al. Case Studies in Construction Materials 17 (2022) e01602

Table 10
Ultimate load comparison.
Specimens FEA/kN EX/kN Failure morphology

I1 145 150 shear failure

I2 155 133 shear failure
I3 159 147 shear failure
I4 173 173 bending failure

Fig. 19. Comparison of load-deflection curves between test and finite element calculation.

however, it maintained a favorable deformation capacity.

5. Conclusion

(1) During the shear process of concrete beams reinforced with basalt fiber, the generation and development of cracks exhibit the
characteristics of being late, dense, and concentrated.

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Y. Jianbing et al. Case Studies in Construction Materials 17 (2022) e01602

Fig. 20. Load-deflection curves of beams under different shear span ratios.

(2) The ultimate failure mechanism of concrete beams reinforced with basalt fiber and ordinary concrete composite beams is still
shear brittle failure, and the failure mode of concrete beams reinforced with fiber is bending failure, which indicates a favorable
deformation capability.
(3) For I2, I3 and I4 specimens, the increase in the height of basalt fiber concrete beams, results in an increase in the ultimate
bearing capacity, cracking load of the inclined section, and the cracking load of the normal section of composite beams.
(4) In terms of ductility, regardless of whether it is a composite beam or a full-fiber concrete beam, the incorporation of basalt fiber
enhances the ductility of the specimen.
(5) The material constitutive model selected in this paper is capable of accurately predicting the failure characteristics and bearing
capacity of basalt fiber beams.
(6) Due to the limited number of test specimens, no theoretical formula could be developed for calculating the cracking load and
ultimate load of the inclined sections of composite beams composed of concrete reinforced with fiber and ordinary concrete
according to the test results.

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.

Data availability

Data will be made available on request.

Acknowledgments

The research work described in this paper was financially supported by the grants from the Major National Projects of China
(2016YFC0701703), Yangzhou Youth Fund Project (YZ2017101), Yangzhou Housing System Project (202004), Yangzhou School
Cooperation Project (YZ2021168). Their supports are gratefully acknowledged by the authors. The authors would like to express their
gratitude to EditSprings (https://www.editsprings.cn) for the expert linguistic services provided.

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