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Research Article
Investigations of Dynamic Mechanical Performance of Rubber
Concrete under Freeze-Thaw Cycle Damage
Jingli Zhang
College of Civil Engineering, Zhengzhou University of Science and Technology, Zhengzhou Henan 450064, China
Correspondence should be addressed to Jingli Zhang; zhangjingli@zit.edu.cn
Received 4 May 2023; Revised 18 September 2023; Accepted 27 September 2023; Published 25 October 2023
Academic Editor: Andrea Spaggiari
Copyright ©2023 Jingli Zhang. is is an open access article distributed under the Creative Commons Attribution License, which
permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
In order to study the eect of the freeze-thaw cycle on the integrity and dynamic mechanical performance of rubber concrete, the
wave speed of rubber concrete specimens with 10% rubber volume was measured by a nonmetallic ultrasonic detector. e impact
tests were also performed on rubber concrete specimens with dierent numbers of freeze-thaw cycles (0, 25, 50, 75, 100, and 125)
at dierent impact air pressures (0.3, 0.4, 0.5, and 0.6 MPa) using a 74 mm diameter split Hopkinson pressure bar (SHPB) device,
peak stress, ultimate strain dynamic intensity enhancement factor (DIF), and energy absorption eect. e results show that with
the increase of freeze-thaw cycles, the wave speed decreases, and the freeze-thaw action will damage the rubber concrete and
reduce the longitudinal wave velocity. Under the same freeze-thaw cycles, with the rise of strain rate, the peak stress, limit strain,
DIF, and absorbed energy increase, and there is an obvious strain rate eect; under the pressure of 0.6 MPa, the peak stress of 25,
50, 75, 100, and 125 freeze-thaw cycles decreases by 25.1%, 37.1%, 46%, 52.5%, and 54.8%. With the increase of the freeze-thaw
cycles, the peak stress of the specimen decreases, and the decrease gradually decreases. After the number of cycles exceeds 100, the
stress decrease of the specimen is no longer obvious, the limit strain increases, and the absorbed energy decreases. e freeze-thaw
environment signicantly reduces the strength and integrity of rubber concrete specimens.
1. Introduction
e annual production of waste rubber products is huge
worldwide, and if they are directly disposed of in landlls
and incinerators, it will not only cause waste of resources but
also cause environmental pollution. erefore, the reuse of
waste rubber materials is important for the protection of
resources and the environment [1–3]. At present, the do-
mestic construction industry advocates energy saving, en-
vironmental protection, and green development, and
research has shown that mixing a certain amount of rubber
particles into concrete can eectively improve its mechanical
performance [4]. Hu et al. [5] found that as the amount of
rubber admixture increased, the compressive, tensile, and
shear strengths of the specimens subsequently decreased and
the ductility increased. Son et al. [6] found that the in-
corporation of rubber in concrete reduces its compressive
strength and modulus of elasticity, but its deformation and
absorption energy increases, and its curvature ductility
increases by nearly 90%. Zhao et al. [7] carried out dynamic
compression tests on rubber concrete using the SHPB test
apparatus and found that its damage level was signicantly
lower than ordinary concrete and its energy dissipation
capacity was signicantly higher.
e northeast and northwest of China are in the
monsoon freeze zone, and concrete buildings are in the
freeze-thaw environment [8]. It has been shown that freeze-
thaw cycling changes the internal structure of the specimen,
thus changing its mechanical properties. Zhou et al. [9, 10]
studied the uniaxial compressive mechanical properties of
fractured sandstone under freeze-thaw fatigue damage. e
results indicate that freeze-thaw cycles can cause fatigue
damage to the specimen, leading to new microcracks and
micropores, thereby reducing the mechanical properties of
the specimen. Tian et al. [11] studied the deterioration
mechanism of concrete, and the tests showed that the elastic
modulus and strength decreased signicantly with the in-
crease of the freeze-thaw. Cao et al. [12] found that the peak
Hindawi
Shock and Vibration
Volume 2023, Article ID 6621439, 14 pages
https://doi.org/10.1155/2023/6621439
strain of concrete specimens increased with the increase of
the freeze-thaw eect. Zhou et al. [13] found that freeze-thaw
cycles reduce the ultimate compressive strength of steel ber
concrete and the rate of decline increases signicantly after
100 freeze-thaw actions. Wang et al. [14] found that the
strengths of recycled concrete under freeze-thaw cycles were
subsequently reduced, and their deterioration was higher
than that of ordinary concrete. Fan et al. [15] found that the
compressive and exural properties all decreased with the
action of the freeze-thaw eect. Freeze-thaw cycles can cause
damage to rubber concrete and reduce its mechanical
performance. However, the present research results only stay
under static load, and there is little research on the me-
chanical performance of rubber concrete under dynamic
load after freeze-thaw cycles. Concrete materials are often
subjected to dynamic loads such as impacts and vibrations
during their design service life and their mechanical per-
formance under dynamic loads dier in many ways from
those under static loads [16].
To further study the mechanical performance of rubber
concrete under dynamic load after freeze-thaw cycles,
a sonic detector was used to measure the degree of damage to
rubber concrete under freeze-thaw times. e uniaxial
impact compression test of freeze-thaw rubber concrete was
carried out by using φ74 mm SHPB device to analyze the
inuence law of the freeze-thaw cycles and strain rate on the
longitudinal wave velocity, peak stress, ultimate strain, and
energy absorption eect of rubber concrete, so as to provide
a test basis for rubber concrete engineering.
2. Program
2.1. Materials. e test uses P·O 42.5 cement, the ne ag-
gregate is sand, the coarse aggregate uses the particle size less
than 18 mm gravel, and tap water. e selected rubber
particles have a particle size range of 1∼3 mm, as shown in
Figure 1.
It was shown that the best volume dosage of rubber
granules in rubber concrete is 10%, and the design strength
of the base concrete was 30 MPa [17]. Rubber replaces sand
by 10% of equal volume, and the mass ratio is cement : sand :
rubber : water : stone �1 : 1.125 : 0.052 : 0.4 : 2.3 after the
specimen is poured and placed under standard maintenance
conditions for maintenance. After maintenance, the speci-
mens will be processed into φ50 ×100 mm and φ74 ×37 mm
cylindrical standard specimens by taking the core, cutting,
and grinding, with 3 specimens in each group. A total of 18
rubber concrete specimens were tested in a static com-
pression test, and 72 specimens were tested in a dynamic
compression test. e nonparallelism of both end surfaces of
the specimens was less than 0.05 mm, and the atness of one
side was within 0.02 mm [18].
2.2. Test Equipment and Method. e freeze-thaw cycles are
0, 25, 50, 75, 100, and 125 times, respectively. During the
freeze-thaw cycle, the minimum temperature in the center of
the specimen was controlled at (−18 ±2)°C and the maxi-
mum temperature was controlled at (5 ±2)°C. A group of
specimens was selected for ultrasonic testing immediately.
e compression test was carried out immediately after the
freeze-thaw cycle. Uniaxial compression tests were con-
ducted to obtain macroscopic mechanical indices. A 74 mm
diameter SHPB test apparatus was used to get dynamic
compression tests. e structure of the test setup is shown in
Figure 2.
e dynamic test was carried out by the impact dynamics
laboratory φ74 mm variable section SHPB test device, using
dierent impact air pressures (0.3, 0.4, 0.5, and 0.6 MPa) on
the specimen. e bullet acquires a velocity vunder the
impact air pressure to strike the incident bar, and an incident
wave is formed by the pulsing of the incident bar. When the
wave reaches the contact surface between the end of the
incident rod and the specimen, part of the pulse is reected
back to form a reected wave, and the other part is trans-
mitted to form a transmitted wave in the transmission rod.
e pulse signals are collected and displayed by an oscil-
loscope, whose wave forms are shown in Figure 3. In order to
ensure the validity of the impact test data, stress balance
testing is required for each impact data. e stress balance is
shown in Figure 4 [19].
e collected data are solved by applying the corre-
sponding calculation formulae, some of which are described
in the following [20, 21]:
5 mm
Figure 1: Selection of rubber particles.
2Shock and Vibration
ε
•
(t) � C0
ls
εi(t) − εr(t) − εt(t)
,
ε(t) � C0
lt
0
εi(t) − εr(t) − εt(t)
dt,
σ(t) � AE
2AS
εi(t) + εr(t) + εt(t)
,
⎧
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎩
Wi(t) � AEC0t
0
εi
2(t)dt,
Wr(t) � AEC0t
0
εr
2(t)dt,
Wt(t) � AEC0t
0
εt
2(t)dt.
⎧
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎩
(1)
Ws(t) � Wi(t) − Wr(t) − Wt(t),(2)
εd�Ws(t)
V,(3)
where Wiis the incident energy, J; Wtis the transmitted
energy, J; Wris the reected energy, J; Wsis the energy
absorbed, J; C0is the longitudinal wave speed in the
compressional rod, m/s; εdis the unit absorbed energy
density, J. cm
−3
; and Vis the volume, cm
3
.
3. Results
3.1. Comparison of Mechanical Performance of Two Concrete
Materials. In order to analyze the mechanical performance
of plain concrete and rubber concrete under dynamic load
when the rubber substitution rate is 10%, quasi-static
compression and dynamic impact tests were conducted
on two types of specimens with the same ratio, and the
results are shown in Table 1. e stress-strain curves of plain
concrete and rubber concrete at dierent average strain rates
(whose values are the average values of the stable section of
bullet
tachymeter
entrance bar strain gauge transmission rod strain gauge
damping devicetest piece
oscilloscopecomputer
Dynamic
strain gauge
Figure 2: Schematic diagram of SHPB device.
0 200 400 600 800 1000
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
Voltage (V)
Time (µs)
Transmissive rod signal
Incident rod signal
Reflected Wave
Transmitted wave
Incident wave
Figure 3: Measured waveform.
Time (µs)
0 50 100 150 200 250 300
-40
-20
0
20
40
60
Incident stress
Reflected Stress
In+Reflective stress
Transmittance stress
Stress (MPa)
Figure 4: Stress equilibrium curve.
Shock and Vibration 3
the reected waves) are shown in Figures 5 and 6, the change
in toughness is shown in Figure 7, and the density of
absorbed energy per unit is shown in Figure 8.
From Table 1, Figures 5, and 6, it can be seen that the
peak stresses in plain concrete are overall higher than those
in rubber concrete at dierent impact air pressures, which
shows consistency with the results of numerous studies
[5, 6]. However, rubber concrete is signicantly more ductile
than plain concrete and has a higher deformation capacity.
Toughness refers to the ability of a material to deform under
external load and is a reection of the comprehensive
performance of material ductility and strength, which can be
expressed using the area enclosed between the stress-strain
curve and the coordinate axis of the specimen under external
load [22]. As can be seen from Figure 7, the toughness of
rubber concrete is signicantly higher than that of plain
concrete, which can eectively prevent the building from
brittle damage under external load.
To further study the energy absorption eect of rubber
concrete, the energy change under dierent impact air
pressures was analyzed, and the results are shown in Table 1
and Figure 8. With the rise of pressure, the incident and
absorbed energy increased, and the energy absorption rate of
rubber concrete was signicantly higher than that of plain
concrete. Figure 8 shows that with the rise of air pressure, the
density of absorbed energy per unit increases, and the
density of absorbed energy of rubber concrete is signicantly
higher than that of plain concrete, and the incorporation of
rubber can eectively enhance the energy absorption eect
of concrete materials. Rubber as an elastic material can
increase the plastic deformation capacity of concrete.
Rubberized concrete specimens in the external load after the
external part of the energy will be stored in the way of elastic
energy in the rubber particles, which greatly enhances the
specimen’s energy consumption eect. At the same time, the
incorporation of rubber particles can also improve the
bonding characteristics between the cementitious material
and the aggregate, which also greatly improves the ductility
of the specimen.
3.2. Ultrasonic Testing of Specimens under Freeze-aw Cycles.
e internal integrity of the material can be measured by the
ultrasonic inspection principle [23]. ere are cracks and
pores inside the concrete material, and the elastic wave
propagation inside the material will reect, refract, and
bypass when it encounters the cracks. e macroscopic
expression is the increase of the elastic wave propagation
path and the decrease of the wave speed. e wave speed of
Table 1: Mechanical performance of two concrete materials.
Number Average strain
rate (s
−1
)
Dynamic
strength (MPa)
Toughness
(J)
Static average compressive
strength (MPa)
Wi
(J)
Ws
(J)
Energy absorption
rate (%)
εd
(J·cm
−3
)
XJ-0-0.3 75.1 40.1 0.43
34.2
63.2 18.6 29.5 0.12
XJ-0-0.4 99.8 46.8 0.66 85.4 26.7 31.3 0.17
XJ-0-0.5 127.2 60.2 0.80 106.7 36.1 33.8 0.23
XJ-0-0.6 155.9 74.5 1.17 146.8 47.6 32.4 0.30
XJ-10-0.3 72.3 37.5 0.60
31.5
60.3 24.7 41.0 0.16
XJ-10-0.4 96.7 45.7 0.79 79.5 33.8 42.5 0.22
XJ-10-0.5 124.6 57.3 1.05 103.2 49.7 48.2 0.32
XJ-10-0.6 151.7 70.6 1.33 141.7 61.6 43.4 0.38
Note. XJ-10-0.3 in XJ indicates rubber concrete, 10 indicates rubber admixture of 10%, 0.3 indicates impact air pressure of 0.3 MPa.
0.000 0.005 0.010 0.015 0.020
0
10
20
30
40
50
60
70
80
Stress (MPa)
Strain
0.3 MPa
0.4 MPa
0.5 MPa
0.6 MPa
Figure 5: Stress-strain curves of plain concrete.
0.000 0.005 0.010 0.015 0.020 0.025
0
10
20
30
40
50
60
70
80
0.3 MPa
0.4 MPa
0.5 MPa
0.6 MPa
Stress (MPa)
Strain
Figure 6: Stress-strain curves of rubber concrete.
4Shock and Vibration
rubber concrete was measured at the end of the freeze-thaw
cycles, and the damage degree was calculated under freeze-
thaw cycles, and the test results are shown in Table 2,
Figures 9, and 10.
As shown in Table 2 and Figure 9, with the rise of freeze-
thaw cycles, the longitudinal wave velocity of rubber con-
crete specimens tends to decrease. Compared with the
unfreeze-thaw specimens, the longitudinal wave velocity of
specimens with 25 freeze-thaw cycles decreases by 9.5%,
16.1% at 50 cycles, and 23.4% and 24.7% at 100 and 125
cycles, respectively.
To further evaluate the internal damage of the rubber
concrete specimens after freezing cycles, the damage degree
was dened as D, which is calculated as shown in (2) [24],
and the damage degree under dierent numbers of freeze-
thaw cycles is shown in Figure 10.
D�1−VT
V0
,(4)
where Dis the degree of damage; V
T
is the wave speed after
the freeze-thaw cycle, m/s; and V
0
is the wave speed without
freeze-thaw cycle, m/s.
Figure 10 shows that with the rise of freeze-thaw cycles,
the degree of rubber concrete damage increases, and the
increase gradually decreases, which shows consistency with
the law of change of the wave speed. Analysis of the reason:
there is a large amount of pore water inside the rubber
concrete specimen, and research shows that the pore water
will produce about 9% volume expansion due to freezing
[25], causing the expansion of the native pores inside the
concrete, while the expansion of the water volume will
produce stress inside the specimen, causing the expansion of
0.3 0.4 0.5 0.6
0.4
0.6
0.8
1.0
1.2
1.4
Vegetal concrete
Rubberized concrete
Toughness (J)
Shock pressure (MPa)
Figure 7: Toughness of specimens under dierent impact pressure.
0.3 0.4 0.5 0.6
Vegetal concrete
Rubberized concrete
Shock pressure (MPa)
0.10
0.15
0.20
0.25
0.30
0.35
0.40
εd (J.cm-3)
Figure 8: Unit absorbed energy density of specimen under dierent impact pressure.
Shock and Vibration 5
the internal cracks. In the process of alternating positive and
negative temperature will generate a certain tensile stress, so
that the rubber concrete produces fatigue damage, and
under the repeated action of freeze-thaw cycles, the internal
pore cracks expand and the damage degree increases [26].
When the wave propagates inside the specimen, reection
and bypassing will occur when it encounters pore cracks,
making the wave speed decrease. Longitudinal wave velocity
and damage reduction amplitude gradually decreased, which
is due to the repeated expansion of pore water to increase the
porosity, the late freeze-thaw eect on the internal structure
of concrete reduced, the amount of new pores subsequently
reduced, and the longitudinal wave velocity reduction
amplitude and damage increase decreased.
3.3. Stress-Strain Curve. e three-wave method was used to
process the data collected from the specimens, and the test
results are shown in Table 3. e stress-strain curves of
rubber concrete under static load are shown in Figure 11.
e average strain rates obtained under dierent pressures
are shown in Figure 12, and the stress-strain curves of freeze-
thaw cycles under 0.4 MPa are shown in Figure 13.
Due to the existence of a large number of primary cracks
inside the concrete material, the stress-strain curve under
static load includes four stages: pore compacting, elasticity,
yielding, and damage. Unlike the static load action, the
stress-strain curve under dynamic load includes three stages:
elasticity, yield, and damage. Under the action of a high
strain rate, the specimen is subjected to the load for a very
Table 2: Longitudinal wave velocity of specimen under freeze-thaw cycle.
Number Specimen height
L(mm)
Initial sound time
value (s)
Measured sound time
value (s) Wave speed (m·s
−1
) Average (m·s
−1
)D
XJ-0-1 99.8 3.2 31.8 3490
3552 0XJ-0-2 100.3 3.2 31.4 3557
XJ-0-3 100.3 3.2 31.0 3608
XJ-25-1 99.73 3.2 34.8 3156
3215 0.095XJ-25-2 101.14 3.2 34.0 3284
XJ-25-3 99.13 3.2 34.2 3204
XJ-50-1 100.59 3.2 37.0 2891
2979 0.161XJ-50-2 98.74 3.2 36.8 2939
XJ-50-3 100.06 3.2 35.4 3107
XJ-75-1 99.37 3.2 37.8 2872
2826 0.204XJ-75-2 98.89 3.2 38.4 2809
XJ-75-3 100.42 3.2 39.2 2798
XJ-100-1 99.26 3.2 39.2 2757
2722 0.234XJ-100-2 99.42 3.2 39.8 2716
XJ-100-3 100.21 3.2 40.4 2694
XJ-125-1 99.46 3.2 38.6 2710
2673 0.247XJ-125-2 99.42 3.2 40.4 2673
XJ-125-3 101.21 3.2 41.6 2636
Note. XJ-0-1 in XJ means rubber concrete, 0 means the number of freeze-thaw cycles is 0, 1 means the test piece number is 1.
0 20 40 60 80 100 120 140
2600
2800
3000
3200
3400
Longitudinal wave velocity
Average longitudinal wave velocity
Longitudinal wave velocity (m.s-1)
Freeze-thaw cycle (time)
3600
Figure 9: Relationship between freeze-thaw cycle times and longitudinal wave velocity.
6Shock and Vibration
short time, the specimen internal primary pore cracks
cannot be compressed directly into the elastic deformation
phase, the curve in this phase is approximately a straight line
up, the slope of the curve is close to a constant value, the
constant value can be used as the dynamic elastic modulus.
Figure 12 shows that as the air pressure increases, the av-
erage strain rate increases, and there is a linear positive
correlation between the two. Figure 13 shows that with the
rise of the freeze-thaw cycles, the peak stress of the rubber
concrete specimen decreases, the drop rate gradually
decreases, and the ultimate strain increases. When the
number of freeze-thaw cycles exceeds 75, the change in peak
stress in the specimen will no longer be signicant. is is
due to the freezing eect and alternating temperature dif-
ferences in the internal stress, the specimen internal pore
crack expansion, in the cementitious material and aggregate,
rubber contact surface to produce new cracks, while the
rubber in repeated freeze-thaw damage will also occur,
resulting in damage to the specimen, the stress is then re-
duced. With the rise of freeze-thaw cycles, the freezing eect
0 20 40 60 80 100 120 140
Freeze-thaw cycle (time)
0.00
0.05
0.10
0.15
0.20
0.25
D
Figure 10: Relationship between freeze-thaw cycle times and damage degree.
Table 3: Test results of rubber concrete under freeze-thaw cycle.
Number Average strain
rate (s
−1
)
Specimen
height (mm)
Diameter
(mm)
Dynamic
compressive
strength (MPa)
Dynamic ultimate
strain (10
−3
)
Static average
strength (MPa) DIF Absorption energy (J)
XJ-0-0.3 72.3 36.98 74.12 37.5 19.8
31.5
1.19 24.7
XJ-0-0.4 96.7 37.02 73.56 45.7 21.6 1.45 33.8
XJ-0-0.5 124.6 36.38 73.98 57.3 23.3 1.82 49.7
XJ-0-0.6 151.7 37.72 74.00 70.6 24.1 2.24 61.6
XJ-25-0.3 78.1 37.78 73.78 31.2 21.5
25.8
1.21 19.5
XJ-25-0.4 99.6 37.01 73.78 36.4 22.5 1.41 28.4
XJ-25-0.5 127.1 36.02 73.97 44.1 24.1 1.71 40.6
XJ-25-0.6 155.4 37.18 73.89 52.9 24.6 2.05 53.5
XJ-50-0.3 74.6 36.78 74.34 25.8 22.1
22.4
1.15 18.6
XJ-50-0.4 102.6 37.16 74.21 31.6 23.1 1.41 26.7
XJ-50-0.5 128.7 37.32 73.42 36.3 24.8 1.62 37.8
XJ-50-0.6 156.3 37.67 74.22 44.4 25.7 1.98 52.1
XJ-75-0.3 77.4 36.76 73.98 24.2 22.6
20.7
1.17 16.7
XJ-75-0.4 99.2 36.59 73.78 27.9 23.9 1.35 28.3
XJ-75-0.5 130.9 37.18 74.57 34.0 25.5 1.64 33.8
XJ-75-0.6 154.3 37.38 74.25 38.1 26.7 1.84 49.3
XJ-100-0.3 73.2 37.25 74.06 22.3 22.5
18.6
1.20 14.1
XJ-100-0.4 95.6 36.87 74.10 25.7 24.8 1.38 23.6
XJ-100-0.5 133.5 36.77 74.02 29.8 26.1 1.60 29.5
XJ-100-0.6 158.2 36.85 74.06 33.5 27.5 1.80 40.2
XJ-125-0.3 74.4 37.08 73.95 21.7 23.3
17.9
1.21 15.3
XJ-125-0.4 98.2 37.42 73.92 27.4 25.5 1.53 25.1
XJ-125-0.5 129.6 37.30 74.11 29.2 26.7 1.63 28.9
XJ-125-0.6 157.7 37.05 74.15 31.9 27.9 1.78 35.7
Note. XJ-0-0.3 in XJ means rubber concrete, 0 means the number of freeze-thaw cycles is 0, 0.3 means the air pressure is 0.3 MPa.
Shock and Vibration 7
will no longer be obvious, and the incremental damage to the
specimen will be reduced.
3.4. Peak Stress and Absorbed Energy. e peak stresses of
freeze-thaw cycled rubber concrete at dierent impact air
pressures are shown in Figure 14, and the relationship be-
tween the absorbed energy and the air pressure is shown in
Figure 15.
Figure 14 shows that as the shock pressure increases,
the peak stress increases, and the specimen shows an
obvious strain rate eect. e dashed line in Figure 14
indicates that the stress increase in the specimen increases
signicantly when the air pressure reaches 0.4 MPa at
0 and 25 freeze-thaw cycles. When the air pressure
reached 0.5 MPa at 50 freeze-thaw cycles, the stress in-
crease in the specimen increased signicantly, and the
specimen no longer showed such a phenomenon after
75 freeze-thaw cycles. With the rise in freeze-thaw cycles,
the degree of internal damage to the rubber concrete
specimen increases, and the increase in impact air pres-
sure specimen stress no longer increases.
Figure 15 shows that the absorbed energy shows an
obvious strain rate eect. As the air pressure increases, the
energy absorption value increases. Freeze-thaw cycles will
0.000 0.001 0.002 0.003 0.004 0.005
0
5
10
15
20
25
30
35
Stress (MPa)
Strain
0
25
50
75
100
125
Figure 11: Stress-strain curve under static load.
0.3 0.4 0.5 0.6 0.7
60
80
100
120
140
160
180
Average strain rate (s-1)
Shock pressure (MPa)
0 y=266.1x-8.42
(R2=0.999)
25 y=259.4x-1.68
(R2=0.994)
50 y=271.2x-6.49
(R2=0.999)
75 y=262.4x-2.63
(R2=0.993)
100 y=292.9x-16.68
(R2=0.985)
125 y=281.3x-11.61
(R2=0.996)
Figure 12: Relationship between pressure and strain rate.
8Shock and Vibration
reduce the energy absorption capacity of rubber concrete
specimens, but this eect will gradually decrease with the
increase in freeze-thaw cycles. e freeze-thaw energy
absorbed by the specimens at 0.4 MPa air pressure for 25, 50,
75, 100, and 125 times decreased by 16%, 21%, 16.3%, 30.2%,
and 25.7%. As the impact pressure increases, the incident
energy increases, and the energy absorbed by the specimen
in this process increases according to the conservation of
energy. Rubber particles in concrete have a good energy
absorption eect, but the rubber itself will be damaged by the
freeze-thaw action, and its energy absorption eect will be
reduced [27]. e rubber damage increment will no longer
be obvious, and the test piece will reduce the magnitude of
the change in energy absorption.
3.5. Eect of Freeze-aw Cycles on the Dynamic Mechanical
Performance of Rubber Concrete. e eect of freeze-thaw
cycles on the stress of rubber concrete under the same
pressure is shown in Figure 16, and its ultimate strain and
absorbed energy change law is shown in Figures 17 and 18.
Figure 16 shows that there is an obvious strain rate eect
on the peak stress of the rubber concrete specimen, and the
peak stress increases with the rise of the impact air pressure
under the same number of freeze-thaw cycles. e peak
stress of the specimens under 0 freeze-thaw cycles increased
by 88.3% compared to 0.3 MPa air pressure at 0.6 MPa, while
the peak stress increased by 69.6%, 72.1%, 57.4%, 50.2%, and
47.0% at 25, 50, 75, 100, and 125 freeze-thaw cycles, and the
strain rate eect under freeze-thaw cycles was signicantly
Stress (MPa)
0.000 0.005 0.010 0.015 0.020 0.025 0.030
0
10
20
30
40
50
Strain
0
25
50
75
100
125
Figure 13: Stress-strain curves under freeze-thaw cycle.
0.30 0.35 0.40 0.45 0.50 0.55 0.60
20
30
40
50
60
70
80
Shock pressure (MPa)
0
25
50
75
100
125
Stress (MPa)
Figure 14: Relationship between impact pressure and peak stress.
Shock and Vibration 9
reduced. Under the same impact pressure, the peak stress
of the rubber concrete specimen decreases with the in-
crease of the number of freeze-thaw cycles, and the two are
logarithmically related. e peak stresses of the specimens
were reduced by 25.1%, 37.1%, 46%, 52.5%, and 54.8% for
25, 50, 75, 100, and 125 freeze-thaw cycles under 0.6 MPa
air pressure, and the stress reduction rate gradually de-
creased, and the stress reduction rate would no longer be
obvious after the cycle times exceeded 100. Figure 17
shows that as the freeze-thaw cycles increases, the ulti-
mate strain of the specimen increases with the same
impact air pressure, and the relationship is linear. e
pore water inside the specimen will produce freezing
expansion during the freeze-thaw cycle, causing the ex-
pansion of pores and cracks inside the specimen, while
there are dierences in thermal expansion coecients
between rubber, cement, and aggregates [13]. In the
process of repeated temperature dierences between the
three interfaces will produce stress dierences, so that the
expansion of primary cracks and the generation of new
cracks, crack penetration between each other to increase
the degree of damage to the rubber concrete, the test piece
integrity is reduced, the ability to withstand external loads
is weakened, the stress of the test piece under the same
impact pressure is reduced, and the ultimate strain in-
creases. With the rise of freeze-thaw cycles, the stress drop
in the specimen decreases, which is due to the increase in
the number of freeze-thaw cycles to rise the porosity of the
specimen, the later freeze-thaw action of the pore water
output of the freezing and swelling eect will no longer be
obvious, the increase in the porosity of the specimen so that the
temperature dierence in the aggregate interface generated by
0.30 0.35 0.40 0.45 0.50 0.55 0.60
10
20
30
40
50
60
70
Absorptive energy (J)
Shock pressure (MPa)
0
25
50
75
100
125
Figure 15: Relationship between shock pressure and absorbed energy.
0 20 40 60 80 100 120 140
0.3 MPa
0.4 MPa
0.5 MPa
0.6 MPa
Freeze-thaw cycle (time)
20
30
40
50
60
70
80
Stress (MPa)
y=28.5+41.8e-0.02x (R2=0.998)
y=27.6+29.7e-0.023x (R2=0.996)
y=25.3+20.5e-0.025x (R2=0.987)
y=20.2+17.4e-0.021x (R2=0.995)
Figure 16: Relationship between the freeze-thaw cycles and peak stress.
10 Shock and Vibration
the stress dierence is reduced, and the specimen produces new
damage to reduce the degree of stress drop.
Figure 18 shows that as freeze-thaw cycles rises, the
absorbed energy of rubber concrete decreases. e absorbed
energy reductions of the specimens under four dierent
impact air pressures were 38.1%, 25.7%, 41.9%, and 42%,
respectively, which were linearly related. e rubber material
itself has a good energy absorption eect, and the specimen
will be damaged by the concrete itself and the rubber under
the action of freeze-thaw cycles, thus reducing its own
energy absorption eect, and with the rise of the freeze-thaw
cycles, the energy absorption energy will gradually decrease.
3.6. Eects of Shock Pressure and Freeze-aw Cycles on DIF.
It was shown that the mechanical performance of concrete
materials is improved under dynamic loading, and to further
investigate the strain rate eect of rubber concrete under
freeze-thaw cycles, DIF was introduced to analyze the
specimens, whose value is the ratio of dynamic strength to
quasi-static strength [28, 29], calculated as follows:
DIF �fd
f,(5)
where fdis the compressive strength, and fis the com-
pressive strength under quasi-static load.
e variation pattern of DIF for rubber concrete under
freeze-thaw cycles with dierent impact air pressure is
shown in Figure 19.
Figure 19 shows that the specimen DIF increases with
the rise of pressure, which is consistent with the results of
the study on the mechanical performance of concrete in
the documentation [30], where the increase of strain rate
can signicantly enhance the strength of the material.
With the increase of the number of freeze-thaw cycles, the
0 20 40 60 80 100 120 140
20
22
24
26
28
30
Extreme strain (10-3)
Freeze-thaw cycle (time)
y=0.033x+24.03 (R2=0.983)
y=0.027x+23.39 (R2=0.997)
y=0.024x+20.47 (R2=0.852)
y=0.031x+21.62 (R2=0.997)
0.3 MPa
0.4 MPa
0.5 MPa
0.6 MPa
Figure 17: Relationship between the freeze-thaw cycles and ultimate strain.
0.3 MPa
0.4 MPa
0.5 MPa
0.6 MPa
10
20
30
40
50
60
70
Absorbed energy (J)
y=-0.197x+61.0 (R2=0.96)
y=-0.161x+46.8 (R2=0.93)
y=-0.074x+22.8 (R2=0.72)
0 20 40 60 80 100 120 140
Freeze-thaw cycle (time)
y=-0.074x+22.8 (R2=0.85)
Figure 18: Relationship between the freeze-thaw cycles and absorbed energy.
Shock and Vibration 11
DIF increase of rubber concrete specimens decreased.
Compared with ordinary rubber concrete, the DIF of
specimens with freeze-thaw cycles at 0.6 MPa air pressure
decreased by 8.5%, 11.6%, 17.9%, 19.6%, and 20.5%.
Freeze-thaw cycles will weaken the strain rate eect of
specimens and reduce the DIF increase of rubber con-
crete, and the higher the pressure, the more obvious the
phenomenon. is is due to the freeze-thaw cycle, which
will cause damage to the test piece, reducing its own load-
bearing capacity, with the cycle number of test piece
damage increases, the integrity of the lower DIF. With the
increase in impact air pressure, the overall trend of in-
creasing DIF and freeze-thaw cycle on the test piece will
become more obvious.
0.30 0.35 0.40 0.45 0.50 0.55 0.60
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
DIF
Shock pressure (MPa)
0
25
50
75
100
125
Figure 19: Relationship between impact pressure and DIF.
0 12575
(a)
0 12575
(b)
Figure 20: Specimen rupture crushing pattern. (a) Plain concrete. (b) Rubber concrete.
12 Shock and Vibration
e rupture and crushing patterns of concrete specimens
with dierent numbers of freeze-thaw cycles under 0.4 MPa
air pressure are shown in Figure 20.
Figure 20 shows that the two types of specimens coexist
in split tensile and crushing damage modes under loading.
With the increase in the number of freeze-thaw cycles, there
is a signicant increase in the degree of rupture and frag-
mentation of both types of concrete specimens, and the
specimen rupture fragmentation decreases in size and in-
creases in number. Freezing and thawing concrete cause
damage to the concrete material itself, and the greater the
number of cycles, the greater the degree of damage, the
specimen’s ability to withstand loading is reduced, and the
degree of fragmentation increases. Comparing the rupture
and crushing degrees of two kinds of concrete specimens
under the same number of freeze-thaw cycles, it can be seen
that the crushing degree of rubberized concrete specimens is
signicantly lower than that of plain concrete. e in-
corporation of rubber particles enhances the ductility of
concrete specimens and their resistance to deformation
under external loads. e rupture and crushing degree of the
specimens are signicantly reduced under the same impact
load, and the incorporation of rubber particles enhances the
deformation resistance of concrete materials.
4. Conclusions
(1) e peak stress of plain concrete under load is higher
than that of rubber concrete as a whole, but its
toughness and energy absorption density are sig-
nicantly lower than that of rubber concrete, and the
incorporation of rubber enhances the ductility and
energy absorption eects of concrete materials.
(2) Freeze-thaw cycles under the action of rubber concrete
longitudinal wave velocity decreases with the increase
of freeze-thaw, and the degree of damage increases. e
freeze-thaw action will cause fatigue damage to rubber
concrete, with the increase in the number of freeze-
thaw cycles test specimens wave speed decrease, and
the increase in the degree of damage decreases.
(3) Freeze-thaw cycles can cause damage to the internal
structure of concrete and rubber particles. e peak
stress and absorbed energy decrease with the in-
crease of freeze-thaw cycles, which are logarithmi-
cally and linearly correlated, respectively, and the
ultimate strain increases with the rise of freeze-thaw
cycles, which are linearly correlated.
(4) e DIF of rubber concrete under freeze-thaw cycles
increased with the rise of impact air pressure, and the
increase of specimen DIF decreased with the increase
of freeze-thaw times, and the DIF of specimens
under freeze-thaw cycles at 0.6 MPa air pressure
decreased by 8.5%, 11.6%, 17.9%, 19.6%, and 20.5%
compared to that of ordinary rubber concrete.
Data Availability
e data used to support the ndings of the study are
available from the corresponding author upon request.
Conflicts of Interest
e author declares that they have no conicts of interest.
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14 Shock and Vibration
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