Construction and Building Materials 199 (2019) 244–255
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Construction and Building Materials
journal homepage: www.elsevier.com/locate/conbuildmat
Mechanical properties of coral concrete subjected to uniaxial dynamic
compression
Linjian Ma a,b, Zeng Li a,⇑, Jiagui Liu a, Liqun Duan a, Jiawen Wu a
a
b
State Key Laboratory of Disaster Prevention and Mitigation of Explosion and Impact, Army Engineering University of PLA, 210007 Nanjing, China
State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, 221116 Xuzhou, China
h i g h l i g h t s
Mechanical properties of coral concrete under quasi-static and dynamic compressions are investigated.
Coral concrete exhibits high-early strength and more brittle characteristics.
The compressive strength and failure pattern are sensitive to strain rate.
Energy dissipation and fractal dimension are calculated and found to be rate-dependent.
Differences of failure pattern and mechanism between coral and conventional concrete are analyzed.
a r t i c l e
i n f o
Article history:
Received 16 September 2018
Received in revised form 4 December 2018
Accepted 6 December 2018
Keywords:
Coral aggregate concrete
Dynamic compressive strength
Failure pattern
Energy dissipation
Fractal dimension
a b s t r a c t
The uniaxial compressive behavior of coral aggregate concrete was experimentally investigated under
quasi-static to dynamic loading rates. Quasi-static compression tests of coral concrete at different curing
ages were performed at a constant strain rate of 105 s1 using an electro-hydraulic servo-controlled test
machine. Dynamic impact loading tests were conducted at stain rates from 101.48 s1 to 102.16 s1 utilizing a 100-mm-diameter split Hopkinson pressure bar (SHPB) system. The strain rate effects on the
mechanical properties of coral concrete were assessed in terms of the uniaxial compressive strength,
energy dissipation, fractal dimension and failure pattern. The coral concrete exhibits high-early strength
and the post-peak stress-strain curves behave in a more brittle manner than conventional concrete. A
more remarkable rate-dependence in the compressive strength of coral concrete than other cementbased composites was observed as the dynamic increase factor (DIF) increased from 1.73 to 2.56 with
the strain rate increasing from 30.12 s1 to 143.32 s1. Different from the failure pattern of conventional
concrete, the fracture plane of coral concrete directly penetrated through the coral shingles rather than
cracking in the interface between the cement mortar and the coarse aggregate under both quasi-static
and dynamic loadings, ascribing to the low strength of coral aggregates and the high intensity of bonding
interface. The ratio of the absorbed energy to incident energy is between 0.3–0.5 and tends to decrease
with an increase in strain rate. A higher loading rate may lead to more energy absorption consumed by
generating more fracture planes and smaller fragments, which is in consistent with a higher value of fractal dimension. The fractal dimension in the range of 2.027–2.302 for coral concrete was also found to be
proportional to the logarithm of the loading strain rate.
Ó 2018 Elsevier Ltd. All rights reserved.
1. Introduction
Recent developments of marine industry and island engineering
have driven a dramatic increase in demand for construction materials such as steel, wood, natural rock and concrete. Cement based
materials play a dominant role in the highly corrosive marine envi⇑ Corresponding author.
E-mail address: lzx2447@163.com (Z. Li).
https://doi.org/10.1016/j.conbuildmat.2018.12.032
0950-0618/Ó 2018 Elsevier Ltd. All rights reserved.
ronment of remote island reef engineering on account of the properties of cost efficiency, durability, and workability. Nowadays, the
feasibility and suitability of coral aggregates as a locally available
alternatives to conventional aggregates for concrete preparation
have gained widespread acceptance [1–7]. Coral aggregate concrete normally refers to the cement based composites made with
coral aggregates and seawater. It has been extensively applied for
a variety of marine structures such as sea embankments, coastal
breakwaters, ship wharf, and other offshore structures since World
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L. Ma et al. / Construction and Building Materials 199 (2019) 244–255
War II. Coral concrete structures on islands are subjected to environmental and artificial impacts during the service life. Therefore,
there is a need to explore the mechanical properties of coral concrete under various circumstances for its application in marine
engineering.
Considerable efforts have been made to assess the performance
characteristics of coral concrete in respect of mix proportion
design, workability, durability, strength, as well as other basic
physical and mechanical properties. The physical and mechanical
properties of coral concrete were found to be different from conventional concrete, and in some ways, were similar with lightweight aggregate concrete [8]. The differences of mechanical
behaviors between coral and conventional concrete are mainly
attributed to the high compressibility and low crushing strength
of corals with remarkable intra-granular voids and highly irregular
shape [9,10]. It was reported that due to the high porosity of coral
aggregates, coral concrete demanded more water than Portland
cement concrete during the mixing procedure to achieve proper
workability and strength [11]. The coral concrete exhibits highearly strength or rapid hardening phenomena, that is the strength
of concrete mixed with coral aggregates and seawater grows faster
at early age then slower at later age [12]. In fact, coral concrete of
moderate strength up to 50 MPa can be easily prepared, whereas a
higher designed strength grade is limited to the low strength of
coral aggregates [13]. It was also confirmed that the long-term
strength of coral concrete could maintain a high level and meet
the engineering requirements [3]. While in the challenging marine
environment with high temperature, high humidity and high salinity, the speed of carbonization and corrosion of concrete grows faster, especially for the steel reinforced concrete. The durability and
service life of concrete structures on the remote islands are found
to be shorter than that on the mainland [14,15]. Although the coral
sand and seawater may help improve the pore structure and interfacial transition zone [16], the major factor restricting the use of
coral concrete remains the chloride corrosion due to the inherent
porous structure of corals and plenty of chloride ions from itself
and seawater [17]. The chloride diffusion of coral concrete in tropical marine environment is characterized by low chloride binding
capacity, high surface free chloride concentration and high apparent chloride diffusion coefficients [15]. With the exploration of
active admixtures and composite fiber reinforcement, the performances of coral concrete in strength, corrosion resistance and brittleness can be remarkably improved [18].
The mechanical behaviors of coral concrete depend not only on
the material compositions (concrete type, water-to-cement ratio,
and size gradation of aggregates, etc.) but also on the loading conditions (temperature, stress state, loading rate, etc.). It is noted that
the aforementioned literatures have been rarely involved in complicated stress states that the coral concrete is potentially subjected to, especially under dynamic loading scenarios, e.g.,
seismic oscillation, impacts induced by waves and ships, even
bomb explosions in military activities, etc. As a matter of fact, it
is well recognized that the inherent strain-rate sensitive property
of concrete-like materials has a prominent effect on the mechanical characteristics. Therefore, a systematic evaluation on the
dynamic properties of coral aggregate concrete can provide the
main basis for improving the design and protective ability of marine engineering structures. This paper aims to experimentally
assess the static and dynamic compression behavior of coral concrete at different loading rates. The effects of strain rate on uniaxial
compressive strength enhancement, energy dissipation and failure
pattern were evaluated. Furthermore, the fractal characteristics of
coral concrete fragments under impact loads were also examined
adopting the method of mass-frequency.
2. Materials and experimental procedure
2.1. Raw materials and mix proportion
Both coral debris and coral sand adopted as coarse and fine
aggregates were directly shipped from the islands in South China
Sea. Unlike natural quartz sand or mineral rocks having a physical
(a) Coral debris
(b) Coral fragments
(c) Coral sand
Fig. 1. Corse and fine coral aggregates from the South China Sea Island.
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L. Ma et al. / Construction and Building Materials 199 (2019) 244–255
tional aggregates. Thus, in view of the specification for mix proportion design of lightweight and conventional concrete, the mix
proportion of the coral concrete in this study was determined
and detailed in Table 4. Besides, a super plasticizer (SP) accounting
for 0.1% of the mass of seawater with a water-reducing ratio of 25%
was adopted considering the high water absorption characteristic
of coral aggregates (around 10%). Meanwhile, the water-tocement ratio was kept near 0.5 to assure the workability.
2.2. Specimen preparation and basic physical properties
The raw materials were stirred using a concrete blender with
the sequence of cement, coral sand, coral fragments and seawater.
To ensure a uniform mixing of raw materials, half of the seawater
was first blended into the mixture after 60 s of dry-mixing for 30 s,
then the other half was added and mix for 120 s. A slump of around
35 mm was achieved for the coral concrete mixture through slump
test. After the mixing process, the mixture was then poured into
the inside surface-oiled moulds (300 100 100 mm and
270 270 60 mm) for compaction on a vibrating table. The cast
coral concrete was placed in the curing room at constant temperature of 20 ± 2 °C and relative humidity of 95%. The specimens
were demoulded from the moulds after 3 d and were continually
cured there for 28 d.
In the present study, a set of fifteen cubic specimens with
dimensions of 100 100 100 mm were fabricated for quasistatic tests. Nine specimens for dynamic experiments was cut into
a standard cylinder with dimensions of U 100 50 mm followed
the recommendation of L/D = 0.5–1 to limit the axial inertial effect
[19]. The density of test samples is 2000–2200 kg/m3, which is
much smaller than that of conventional concrete and a little larger
than lightweight concrete. Ultrasonic pulse velocity (UPV) tests
were performed using an RSM-SY5 (T) non-metal ultrasonic detection analyzer. UPV is an important parameter to tell whether the
material is dense or porous since wave travels faster in solid phase
than that in gaseous phase. The UPV of coral concrete is in the
range of 2500–3000 m/s, which is remarkably slower than that of
Fig. 2. Particle size distribution of coral sand.
or chemical origin, coral debris and coral sand are the accumulation of died skeletal bodies of hermatypic polypary corals and
shells, that is, mainly of biological sedimentary origin. The mineral
composition of corals consists of as high as 97% calcium carbonate
with specific gravity of 2.7–2.85. The coral debris (Fig. 1a) were
first broken into smaller fragments (Fig. 1b) with a maximum
diameter of 10 mm and were then sieved into a continuous gradation of 5–10 mm for coarse aggregates. The size distribution of
coral sand is present in Fig. 2 with a fineness modulus of 2.24.
The basic physical properties of coarse and fine aggregates including the bulk and apparent densities, porosity, water absorption,
and mud content are detected complying with the Chinese standards GB/T 14684-2011, and the test results are listed in Tables 1
and 2, respectively. The cement used for concrete preparation
was 42.5 ordinary Portland cement (P.O. 42.5), which was produced by China Anhui Conch Cement Co., Ltd. Artificial seawater
was prepared in accordance with the American ASTM D11412003 and its chemical composition is given in Table 3.
As shown in Table 1, the apparent density of coarse aggregate is
2564 kg/m3, which is between that of lightweight and convenTable 1
Physical properties of coral fragment.
Bulk density/kg/m3
Apparent density/kg/m3
Porosity/%
Water absorption/%
Mud content/%
Cylindrical compressive strength/MPa
981.9
2564
61.7
8.6
6
2.83
Table 2
Physical properties of coral sand.
Bulk density/kg/m3
Apparent density/kg/m3
Porosity/%
Water absorption/%
Mud content/%
1228
2632
53.3
9.2
10.4
Note: The porosities
of coral fragments and coral sand are calculated as following equation (Chinese National Standards – Sand for Construction (GB/T 14684-2011)):
V 0 ¼ 1 qq1 100%
2
where V0 is the porosity, q1 and q2 are bulk density and apparent density of the tested material, respectively.
Table 3
Chemical composition of artificial seawater.
NaCl/kg/m3
MgCl26H2O/kg/m3
Na2SO4/kg/m3
CaCl2/kg/m3
KCl/kg/m3
24.5
11.1
4.1
1.2
0.7
Table 4
Mix proportion of coral concrete.
Cement/kg/m3
Coral fragment/kg/m3
Coral sand/kg/m3
Artificial seawater/kg/m3
SP/kg/m3
W/C
500
714
586
238
0.24
0.476
Note: SP: superplasticizer; W/C = seawater/cement.
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L. Ma et al. / Construction and Building Materials 199 (2019) 244–255
Table 5
Comparison of basic physical and mechanical properties of different types of concretes.
Concrete type
Density/kg/m3
UPV/m/s
Elastic modulus/GPa
Poisson’s ratio
Coral concrete
Conventional concrete [16]
Lightweight concrete [17]
2000–2200
2400–2800
560–1950
2500–3000
4200–4700
3500–3800
21–32
32.5–34.5
10–30
0.22–0.25
0.20–0.22
0.20–0.25
conventional and lightweight concrete, indicating the porous characteristic of the specimens. A comparison of basic physical and
mechanical properties of three types of concretes were given in
Table 5.
2.3. Quasi-static tests
The MTS 647.250 electro-hydraulic servo-controlled test system is utilized to conduct the uniaxial quasi-static compression
test. It is composed of the main machine, oil source, control system
and loading frame. The maximum static and dynamic loading
forces are 2500 kN and 2750 kN, respectively. The displacement
control mode was adopted and applied at a loading speed of
0.001 mm/s or at a constant strain rate of 105 s1. PTFE films were
placed on the contact position between the specimen and two
loading platens to mitigate the end effect. The extensometers with
a gauge length of 25 mm and a resolution of 0.00001 mm were
attached on the tested specimen along two perpendicular directions to monitor the axial and horizontal deformations.
2.4. Split Hopkinson pressure bar (SHPB) tests
As a widely used apparatus developed by Kolsky [20], the split
Hopkinson pressure bar (SHPB) was applied to quantify the
dynamic compressive response of coral concrete under intermediate strain rate range of 101–103 s1. The SHPB technique is valid
based on the assumptions that the stress wave propagates onedimensionally in an elastic bar without dispersion while the stress
and strain within the specimen remains in an axially uniform state
during the loading process [21]. The shape and amplitude of the
induced incident pulse depend on the impact velocity and the
length of the striker. A slowly rising ramped pulse is preferred
not only to facilitate stress equilibrium but also to generate a
nearly constant strain rate state in the sample [22]. However, during large diameter SHPB tests, a rectangular stress pulse with steep
ramp is always generated by the impact of the striker, which arises
the difficulty of achieving dynamic stress equilibrium for concretelike materials. It is also well known that the induced rectangular
pulse consists of different frequency components, which propagate
Loading System
Gas gun
Laser
speedometer
8
rðtÞ ¼ AAbs Eb et ðtÞ
>
>
>
<
Rt
b
eðtÞ ¼ 2C
e ðtÞds
0 r
Ls
>
>
>
:_
2C b
eðtÞ ¼ Ls er ðtÞ
ð1Þ
where the subscripts b, s, i, r, t denotes the bar, specimen, incident,
reflected and transmitted pulses, respectively.
Bar System
Pulse shaper
Strike bar
with different velocities in the bar system, leading to the wave dispersion effect. The dispersion of stress pulse have great effect on
the validity of the test data and become more severe as the bar
diameter increases. Therefore, necessary pulse shaping technique
is needed to adjust the incident waveform to half-sine-like pulse
with high frequency oscillations being filtered out. Approaches of
pulse shaping technique have been proposed for brittle materials
such as rocks, concrete and ceramics in pioneering works [23–
25]. In the present study, a thin rubber disk named pulse shaper
with 10 mm in diameter and 2 mm in thickness was placed in front
of the incident bar to effectively minimize pulse dispersion in all
tests. Furthermore, the lubricant was evenly smeared on the two
ends of the specimen to reduce the effects of end friction and stress
concentration [21,26,27].
The adopted 100 mm-diameter SHPB system is presented
schematically in Fig. 3, which consists of a gas gun chamber, a striker bar (0.8 m in length), an incident bar (4 m in length) and a
transmitted bar (3 m in length). The modulus of high-strength
alloy steel bars is 205.6 GPa with a density of 7767 kg/m3, thus
the velocity of wave propagating in the bars could be simply calcupffiffiffiffiffiffiffiffiffi
lated as C ¼ E=q = 5145 m/s. The velocity of the strike bar is
measured by a laser speedometer. The failure progress of specimens is captured using a high-speed camera with 105 fps. The incident, reflected and transmitted stress pulses are monitored with
four semiconductor strain gauges mounted in the middle of the
incident and transmitted bars through Wheatstone bridge, which
is connected to a digital oscilloscope with a sampling frequency
of 2 106 s1. According to the one-dimensional stress wave theory, these strain measurements are used to determine the time histories of stress r(t), strain e(t) and strain rate e_ (t) within the
specimen as [20]:
Specimen
Incident bar
Strain gauges
Transmitted bar
Computer
Compression test：
：
BD test：
Data Acquisition and
Recording System
Fig. 3. Schematic of a typical SHPB system.
Damper
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L. Ma et al. / Construction and Building Materials 199 (2019) 244–255
3. Results and discussions
3.1. Quasi-static test results
3.1.1. Complete stress-strain curves
By combing the simultaneously measured results of the load
transducer of MTS and extensometers fixed on the specimens,
the non-linear stress-strain relationships of coral concrete under
uniaxial compression are plotted in Fig. 4. As can be seen from
Fig. 4, the complete compressive stress-strain curves of coral concrete can be divided into four stages: consolidation stage, elastic
stage, plastic stage and fracture stage. Specifically, the consolidation stage is observed as an upward concave in the initial portion
of the complete stress-strain curve, which is different from that
of conventional concrete. This may be mainly caused by the pore
structures of coral aggregates and the voids inside the concrete
matrix being compacted as the loading stress increases. The consolidation stage indicates the typical porous and loose features of
the microstructure of the coral concrete. The slope of the ascent
linear stress-strain curve is between those of the lightweight and
conventional concrete with the same strength grade. The descend
stage of the stress-strain curve is much more abrupt and steeper
compared to other concrete types. It is evident that the postpeak stress-strain relationship of coral concrete behaves in a more
brittle manner. The low crushing strength of coral particles and
special failure mode are the two main reasons resulting in the significant brittleness of coral aggregate concrete compared to normal
concrete. The crushing strength of coral aggregates is much lower
than gravels and pebbles and itself exhibits evident brittle characteristic [28]. Furthermore, owing to the high intensity of bonding
interface, the fracture plane of coral concrete tends to penetrate
directly through the coral aggregates rather than the interface
between the cement mortar and the aggregates.
The average compressive strength of coral concrete is
40.08 MPa and the corresponding failure strain is 0.185%, which
is slightly larger than that of the conventional concrete. The elastic
modulus was calculated by the slope of the approximate linear part
of ascent stage of the stress-strain curve, and the average value
appears to be 29.60 GPa, which is consistent with the research of
pioneer experts [29–31]. Time history curves of transverse strain,
longitudinal strain and Poisson’s ratio were together displayed in
Fig. 5. Under uniaxial compression state, the Poisson’s ratio of coral
Fig. 4. Stress-strain curves of coral concrete under quasi-static compression.
Fig. 5. Time history curves of transverse strain, longitudinal strain and Poisson’s
ratio.
concrete specimen is around 0.254, which is basically the same as
the other two types of concretes.
3.1.2. Compressive strength for different curing ages
The tested average compressive strength of coral concrete cured
for 3 d, 7 d, 14 d, 21 d and 28 d are 32.14 MPa, 35.43 MPa,
37.51 MPa, 38.04 MPa and 40.04 MPa, respectively. The normalized strength with respect to the 28-day strength of coral concrete
along with the conventional and lightweight concrete are plotted
against the curing age in Fig. 6. It is seen that the strength of coral
concrete tends to increase faster during early period then slower
during later period as compared to the conventional and lightweight concrete. Specifically, the coral concrete strength at 3 d
and 7 d reaches over 80% and 90% of that at 28 d, whereas the
development of the rest 10% of the ultimate curing strength lasts
for three weeks. The high-early strength behavior of coral concrete
is mainly caused by the chlorides in the coral aggregates and seawater and its inherent porous structure. The high content of chloride salts in coral concrete mixed with corals and seawater plays
the role as rapid hardening agents [32,33]. In addition, the porous
microstructure of coral aggregates performs the function of ‘‘water
bag”. It absorbs and reserves a certain amount of water from the
concrete slurry and releases the water in the hydration and
Fig. 6. Strength development of three types of concretes for different curing ages.
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L. Ma et al. / Construction and Building Materials 199 (2019) 244–255
3.2. SHPB test results
3.2.1. Dynamic stress-strain curves
Typical waveform of signals measured by the strain gauges
mounted on the incident and transmitted bars are presented in
Fig. 7a. As seen in Fig. 7a, a tender and smoother ramp waveform
is realized with a pulse shaper. The rising time of shaped incident
pulse is nearly up to 250 ls, which is sufficient for five to ten wave
reverberations in the sandwiched specimens to achieve a stress
equilibrium state during impact loading. To qualitatively check
the validity of the SHPB tests, time histories of dynamic strain
pulses on the incident and transmitted ends of the specimen calculated using Eq. (1) and the strain rate with respect to time are plotted together in Fig. 7b. As illustrated in Fig. 7b, the difference of the
transmitted and reflected pulses coincides approximately with the
incident pulse, which indicates a dynamic equilibrium of the action
and reaction forces is satisfied on both ends of the specimen
throughout the loading process. The curve of strain rate as a function of time exists an evident platform, thus facilitating a roughly
constant strain rate state for the duration of loading. To further
quantitatively assess the dynamic stress state, the stress equilibrium factor d accounting for the relative stress difference is defined
as [34]:
Rt
dðtÞ ¼
30
20
10
0
.
DC-1 (ε = 30.12 s-1)
t = 250 μs
-10
-20
-30
0
100
200
300
400
Rt
ðei þ er Þdt 0 et dt
DrðtÞ
i.
¼h 0
raver ðtÞ R t ðei þ er Þdt þ R t et dt 2
0
where Dr and ravg are the stress difference and average stress at
both ends of the specimen, respectively.
In general, a dynamic stress equilibrium is achieved when d(t) is
smaller than 5%. The curves of stress equilibrium factor with
respect to time for different strain rates are plotted in Fig. 8. As
demonstrated in Fig. 8, a long rising action time of more than
200 ls is obtained for various loading strain rates, which is 10–
12 times of the travelling time (16.7–20 ls) in the specimen to
δ
hardening process, which also enhances the early strength of coral
concrete [8,31].
500
600
700
800
t / μs
(a)
ð2Þ
30
0
20
δ
10
0
t = 205 μs
-10
DC-5 (ε = 90.03 s-1)
-20
-30
0
100
200
300
400
500
600
700
800
t / μs
(b)
30
20
δ
10
0
t = 220 μs
.
DC-9 (ε = 143.32 s-1)
-10
-20
-30
0
100
200
300
400
500
600
700
t / μs
(c)
Fig. 7. (a) Typical waveforms monitored from strain gauges; (b) dynamic strain
pulses on both ends of specimen and strain rate history with a pulse shaper.
Fig. 8. d as a function of time for different strain rates.
800
250
L. Ma et al. / Construction and Building Materials 199 (2019) 244–255
guarantee the stress equilibrium. It can also be determined from
Fig. 8 that the specimens remain a stable stress equilibrium state
during the most of the action time of incident stress pulse. Besides,
the uniform state of stress and deformation along the length of the
specimens have achieved prior to failure.
The dynamic compressive stress-strain curves of coral concrete
at strain rate ranging from 30.12 s1 to 143.32 s1 are shown in
Fig. 9. Most of the stress-strain curves possess a similar shape
and the post-peak stages demonstrate a strain-softening behavior
due to fragmentation and granular flow. However, the shape of
the DC-1 and DC-2 curves is apparently different from the other
specimens, in which the strain decreased slightly after the peak
stress. That was mainly due to the following reason: under the condition of relatively low impact speed, the specimen was not damaged thoroughly thus the deformation had a certain recovery after
the impact, whereas the other specimens were pulverized when
the impact speed was greatly higher. An obvious change in the
stress-strain response of the coral concrete with increasing strain
rate can be found. At a strain rate of 143.3 s1, the compressive
strength of coral concrete is 102.5 MPa, which is approximately
2.6 times the quasi-static strength of 40.08 MPa. Both the dynamic
compressive strength and deformation are sensitive to the loading
strain rate caused by the combined effects of Stefan, cracking propagation and inertia. It is widely accepted that the viscous effect of
110
3.2.2. Strain rate effect on compressive strength
The dynamic increase factor (DIF) defined as the ratio of
dynamic compressive strength to quasi-static is regarded as an
important parameter for the characterization of the ratedependence of material strength. Fig. 10 depicts the relationship
between DIF and strain rate for coral concrete. A significant
increase in dynamic compressive strength of coral concrete is
observed over the applied strain rate. As shown in Fig. 10a, within
the same regime of strain rate, the tested value of DIF of coral concrete is in the range of 1.73–2.56, which is slightly higher than that
of conventional (between 1.5 and 2.25) [35–38]. The remarkable
DC-1 (30.12 s-1)
DC-2 (49.12 s-1)
DC-3 (59.43 s-1)
DC-4 (79.81 s-1)
DC-5 (90.03 s-1)
100
90
80
σ / MPa
free water in the micropores of concrete could increase the cohesive strength between coral aggregates and cement mortar with
strain rates. Hence, the Stefan effect plays a dominant role in the
elastic deformation stage before the initiation of microcracks. The
propagation of microcracks with irreversible deformation always
lags behind the dynamic loading. According to the theorem of
impetus, the stress level of coral concrete specimen improves to
counteract the external impulse, which is considered the main reason of rate-dependence of dynamic strength. As the lateral deformation is restricted by its inertia effect, the dynamic compressive
strength increases with this equivalent confining pressure. The
inertia effect may be more dominant in the post-peak stage.
70
60
50
40
30
20
10
0
0.00
0.01
0.02
0.03
0.04
0.05
ε
(a)
110
DC-6 (97.34 s-1)
DC-7 (100.58 s-1)
DC-8 (123.66 s-1)
DC-9 (143.32 s-1)
100
90
σ / MPa
80
70
60
50
40
30
20
10
0
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
ε
(b)
Fig. 9. Stress-strain relationships of coral concrete under SHPB tests: (a) DC-1–DC5; (b) DC-6–DC-9.
Fig. 10. (a) Strain rate sensitivity of compressive strength; (b) fitting results of
different empirical equations.
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L. Ma et al. / Construction and Building Materials 199 (2019) 244–255
strength enhancement demonstrates a more intense ratesensitivity of coral concrete than other cement-based composites.
Different empirical formulas have been proposed to account for
the strain rate sensitivity of the uniaxial compressive strength of
concrete. Fig. 10b presents the comparison of fitted results using
four equations suggested by Al-Salloum [38], CEB [39], Ngo [40]
and Grote [41]. The four fitting equations are listed as follows:
DIF ¼
3:248e_ þ 77:946
e_ þ 75:763
8 >
1:03as
>
< e_e_s DIF ¼
1
>
>
: cs _e_ 3
es
9
>
; e_ 6 30 s1 >
=
>
;
; e_ > 30 s1 >
ð3Þ
ð4Þ
where cs ¼ 10ð6:16as 2:0Þ ; as ¼ 1=ð5 þ 9f cs =f co Þ; f co ¼ 10 MPa; e_ s ¼ 3
105 s1 .
Fig. 11. Typical energy evolution in a SHPB compression test.
0:056
e_
DIF ¼ 0:952 ; e_ s ¼ 3:33 105 s1
e_ s
ð5Þ
DIF ¼ 0:177 lge_ þ 1:832
ð6Þ
As illustrated in Fig. 10b, all the predicted values of CEB formula
are lower than the tested data, whereas the fitted results using
exponential formula by Ngo and linear formula by Grote which
describe DIF as a function of the logarithm of strain rate are in better agreement. By comparison, the adopted formula proposed by
Yousef Al-Salloum turns to be the best candidate for predicting
the dynamic strength enhancement of coral concrete. However,
the application scope of the empirical formulas is still restricted
due to the lack of available experimental data between the
quasi-static and the intermediate strain rate regime.
3.2.3. Strain rate effect on energy dissipation
In SHPB tests, the propagation of the waves in bars is an essential way to transfer the impact energy to the specimen. It is
assumed that the dynamic loading process is adiabatic and the
energy loss at the interfaces between the bars and the specimen
are negligible [42]. Hence, the total absorbed energy can be indirectly derived from the difference of the incident, reflected and
transmitted stress wave energy, which have the following
expressions:
8
Ws ¼ Wi Wr Wt
>
>
R
>
>
< W i ¼ AB C B EB 0t e2i ðsÞds
Rt
>
W r ¼ AB C B EB 0 e2r ðsÞds
>
>
>
Rt
:
W t ¼ AB C B EB 0 e2t ðsÞds
ð7Þ
where Wi, Wr, Wt, Ws represent the energy of incident, reflected,
transmitted and absorbed energy, respectively. The amount of
energy decrease as the aspect ratio of specimens increases, while
the volume-specific energy absorbed by the specimen tend to be
higher, which results in finer fragment size distribution [43–45].
The energy absorption mainly consumes as the fracture energy
in the process of crack initiation and extension, the kinetic energy
of the fragments and other forms of energy such as heat, sound and
radiation. Therefore, the impact damage of concrete can be characterized by the energy dissipation during fracture process. From the
perspective of energy evolution, the deformation and failure mechanisms of materials subjected to dynamic loading might be closely
correlated. The typical energy evolution curves of coral concrete in
SHPB tests are plotted in Fig. 11. As shown in Fig. 11, the incident,
reflected and absorbed energy increase continually with time until
they ultimately reach an upper limit value, whereas the transmitted energy remains constant occupying less than 5% of the total
incident energy. Specifically, the moments of stress equilibrium
t1, critical fracture t2, end of the plateau with constant strain rate
t3, and end of the energy absorption t4 might divide the energy
evolution process into five portions. The first portion (0–t1) is the
initial unstable period before the valid stress equilibrium state,
corresponding to the compaction stage in the stress-strain curve.
As seen in Fig. 11, only little energy is absorbed during this period.
The second (t1–t2) and third (t2–t3) portions are the steady period
as the energy absorption maintains a constant rate and accounts
for most of the total absorbed energy. During the fourth portion
(t3–t4), the energy absorption keeps increasing while the growth
rate decreases to nil, which might be named the transient period.
The fifth portion is the last period in which the energy maintains
its maximum value, implying that the specimen is completely
destroyed by the impact.
More specific representative energy measured at fracture
moment t2 for different stain rates are listed in Table 6 and plotted
in Fig. 12. Clearly, the specific incident and reflected energy
increased nonlinearly with growing strain rate, while the transmitted energy exhibited a slight decayed tendency. An evident linear
relationship was found between the absorbed energy and loading
strain rate. An indicator Ws/Wi defined as the ratio of the absorbed
energy to the incident energy is commonly adopted to evaluate the
energy dissipation performance of porous materials [46]. Theoretical derivations by Lundberg proved that Ws/Wi owned an extreme
value of 50%, and it could be attained only when the amplitude of
the incident pulse was twice the yield stress of the specimen [42].
As illustrated in Fig. 13, a comparison of the energy absorption
ratios of normal concrete [47], sandstone [48] and rock salt [49]
have the same trend to decrease as the strain rate increases. It is
obvious that the energy absorbability of coral concrete is between
30% and 50%, which is higher than that of other three materials.
Table 6
Representative energy measured at time t1 for different loading rates.
Specimen
Strain
rate/s1
Wi/J
Wr/J
Wt/J
Ws/J
Ws/V/
kJ/m3
Ws/
Wi/%
DC-1
DC-2
DC-3
DC-4
DC-5
DC-6
DC-7
DC-8
DC-9
30.12
49.12
59.43
79.81
90.03
97.34
100.58
123.66
143.32
284.15
338.41
359.27
481.39
657.45
513.66
756.97
644.11
959.35
43.63
99.34
98.95
185.56
329.24
196.27
401.85
315.19
577.46
101.21
70.11
84.58
60.51
53.88
70.51
50.83
63.87
32.06
139.30
168.96
175.74
235.31
274.33
246.88
304.29
265.05
349.82
377
471
477
639
743
669
825
719
973
49.02
49.93
48.92
48.88
41.73
48.06
40.20
41.15
36.46
252
L. Ma et al. / Construction and Building Materials 199 (2019) 244–255
100
M/MT / %
10
DC-1 (R2 = 0.909)
D = 2.027
DC-2 (R2 = 0.906)
D = 2.076
DC-3 (R2 = 0.971)
D = 2.149
DC-4 (R2 = 0.990)
D = 2.194
DC-5 (R2 = 0.974)
D = 2.240
1
0.1
0.01
1E-3
0.01
0.1
1
10
100
d / dmax
(a)
Fig. 12. Relationship between specific energy and strain rate.
100
0.6
Ws/Wi
0.4
M/MT / %
0.5
Coral concrete
Normal concrete Tai (2009)
Sandstone Li & Mao (2014)
Rock salt You, et al. (2017)
0.3
10
DC-6 (R2 = 0.989)
D = 2.276
DC-7 (R2 = 0.973)
D = 2.289
DC-8 (R2 = 0.982)
D = 2.280
DC-9 (R2 = 0.969)
D = 2.302
0.2
0.1
1
1E-3
0.0
1.0
0.01
0.1
1
10
100
d/dmax
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
(b)
.
lgε / s-1
Fig. 14. Relative mass versus fragmentation size: (a) DC-1–DC-5; (b) DC-6–DC-9.
Fig. 13. Ws/Wi as a function of strain rate.
This may be mainly attributed to the peculiar porous and loose
structure of coral aggregates. The porous microstructure plays an
important role in the energy absorption of coral aggregate concrete
under dynamic impacts. The energy dissipation ratio could be
quantitatively correlated to the strain rate using an inverse linear
equation:
Ws
¼ 0:18 lge_ þ 0:79
Wi
ð8Þ
3.2.4. Strain rate effect on fractal dimension
Generally, crushed parts of a solid material have a selfsimilarity to the whole in geometry [50]. Fractal theory is an effective approach for the estimation of the geometric and mechanical
characteristics of solid and granular materials after crushing.
Therefore, the fractal crushing property of coral concrete subjected
to dynamic loads can be quantitatively assessed by fractal dimension. A fractal model based on mass-frequency is described as a
power law function in the cumulative mass-size distribution
curves, which can be written as [43]:
Z
M/
3
3D
d dN / d
ð9Þ
where M refers to the cumulative mass after sieving, d and D are the
sieve diameter and fractal dimension, respectively.
The fragment size distributions of broken coral concrete specimens under dynamic compression were obtained by sieving with
standard sieve series and the results were plotted in a log-log scale
in Fig. 14. The fragments of coral concrete exhibited pronounced
fractal feature since the cumulative mass appeared to be linearly
related to fragment size. The slope of the fitted straight line is 3D according to Eq. (9). Fig. 15 depicts the fractal dimension of coral
concrete at different strain rates. The fractal dimension increased
from 2.027 to 2.302 as the strain rate increased from 30.12 s1 to
143.32 s1, implying a higher degree of fragmentation and selfsimilarity. The fractal dimension was found to be proportional to
the logarithm of the loading strain rate. The value of fractal dimension as a function of strain rate can be further expressed as:
D ¼ 0:46 lge_ þ 1:34
ð10Þ
3.2.5. Failure pattern and mechanism
Fig. 16 depicts the failure mode of coral concrete under quasistatic compression. In quasi-static compression cases, several
visible macro-cracks originated at the upper and lower ends of
concrete cubes as the axial strain reached a threshold value around
103. With an increase in the irreversible deformation, the macrocracks extend mainly in the axial direction with few inclined
fissures. The coral concrete ultimately split into multiple columns
accompanied with the concentration of macro-cracks and the formation of fracture surfaces. From Fig. 16b we can see that the main
253
L. Ma et al. / Construction and Building Materials 199 (2019) 244–255
Fig. 15. Fractal dimension of coral concrete with respect to strain rate.
failure plane directly penetrates through the coral debris rather
than cracking in the interface between the cement and aggregates,
which is quite different from the failure pattern of the conventional
concrete.
Fig. 17 presents the failure patterns of coral concrete specimens
at different strain rates. With an increase in the loading rate, the
damage level of the coral concrete disc undergoes edge crack, edge
broken, major breakage, crushing and grinding. At lower strain
rate, the specimen failed with few pieces of columns while the central core kept its integrity. As the strain rate grew higher, the specimen split into smaller fragments even powders. Fundamentally,
higher impact velocity with more absorbed energy is consumed
by generating more cracks and fracture planes resulting in the
breakage of the coral concrete specimen into smaller pieces.
Generally, the fracture of concrete begins and follows the weakest route with a least energy consumption. Internal flaws like
pores, micro-cracks and weak bonding interface between cement
mortar and coarse aggregate tend to be the weak regions in conventional concrete matrix. Consequently, the special failure mode
of coral concrete is mainly caused by the low strength of coral
aggregate and the high intensity of bonding interface. As demonstrated in Fig. 18, the interfacial transition zone between the coral
aggregates and cement matrix is highly dense without any visible
flaws. Due to the porous microstructure, coral aggregates can
absorb and reserve water in the early stage of the mixing and
release water during the hydration and hardening process. The
local water-cement ratio is adjusted by the ‘‘absorption-release”
action to enhance the adhesive strength between the aggregates
and cement mortar [31]. On the other hand, the peculiar rough
and porous surface texture of coral aggregates also contributes to
a high frictional strength on the interface. The hydration products
together with matrix may easily attach and accumulate on the
rough surface and embed into the porous microstructures of coral
aggregates, resulting in the high bonding intensity and frictional
strength of the interfacial transition zone.
4. Conclusions
Uniaxial quasi-static and dynamic compression tests on coral
concrete specimens were conducted utilizing servo-hydraulic
machine and split Hopkinson pressure bar system. The effects of
loading strain rate on compressive strength, energy dissipation
and failure pattern were evaluated. The main conclusions are
drawn as follows.
(a)
Internal
pores
Broken coral
coarse aggregates
(b)
Fig. 16. Failure pattern of coral concrete under quasi-static compression: (a)
surface cracks; (b) fracture plane.
The coral concrete exhibits high-early strength or rapid hardening phenomena for the 7 d compressive strength attains 90% of that
at 28 d. The brittleness of coral concrete is more evident than that
of conventional or lightweight concrete due to the high compressibility and low crushing strength of corals with remarkable intragranular voids and highly irregular shape. The average quasistatic compressive strength and elastic modulus of the coral
concrete are 40.08 MPa and 29.60 GPa, which are slightly lower
than the corresponding conventional concrete.
The loading rate is proved to have significant effects on the
dynamic compressive strength, energy dissipation, fractal dimension and failure pattern. The value of dynamic increase factor is
in the range of 1.73–2.56 with the strain rate increasing from
30.12 s1 to 143.32 s1. An empirical formula accounting for the
strength enhancement with respect to strain rate is found to be
more satisfying with the experimental results. Unlike the failure
pattern of conventional concrete, the main fracture cracks directly
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L. Ma et al. / Construction and Building Materials 199 (2019) 244–255
Fig. 17. Failure pattern of coral concrete under dynamic compression.
the work described is an original research that has not been published previously, and not under consideration for publication elsewhere, in whole or in part.
Interface
Acknowledgment
The authors would like to express their grateful appreciations to
the National Natural Science Foundation of China (Grant Nos.
51774295 and 51808551) for the financial support to this research.
Coral
aggregates
Cement
crystal
Fig. 18. Micro-morphology of the interface of coral concrete.
propagate through the coral shingles rather than breaking in the
interface between the cement mortar and the aggregate, which is
due to the low strength of coral aggregate and the high intensity
of bonding interface.
The incident, reflected and absorbed energy develop with an
increase in the strain rate, while the transmitted energy approximately keeps unchanged. The ratio of absorbed energy to the incident energy is in the range of 0.3–0.5 and seems to be inversely
proportional to the logarithm of the strain rate. More energy
absorbed by the coral concrete specimen with higher loading rate
is mainly consumed for generating new fracture surfaces resulting
in smaller fragments. Fractal dimension is further adopted to characterize the breakage degree in response to various strain rates.
The fractal dimension of coral concrete under impact loading varies in the range of 2.027–2.302 and can be related to the logarithm
of the strain rate using a linear equation.
Conflict of interest statement
No conflict of interest exits in the submission of this manuscript, and the manuscript has been approved by all authors for
publication. I would like to declare on behalf of my co-authors that
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