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Thin-Walled Structures xxx (xxxx) xxx–xxx
Contents lists available at ScienceDirect
Thin-Walled Structures
journal homepage: www.elsevier.com/locate/tws
Full length article
Strain rate effect on the mechanical behavior of basalt: Observations from
static and dynamic tests
⁎
Akx Malika, Tanusree Chakrabortyb, , K. Seshagiri Raob
a
b
Department of Civil & Environment Engineering, The NorthCap University, Gurugram, India
Department of Civil Engineering, Indian Institute of Technology (IIT) Delhi, India
A R T I C L E I N F O
A B S T R A C T
Keywords:
Deccan Basalt
Dynamic increase factor
Laboratory testing
Strain rate
SHPB
Basalt rock is often used as a building material and in architectural design of building by constructing thin
veneer and facade. Thus, dynamic characterization of basalt rock is of utmost importance in blast resistant
structural design. This paper discusses static and dynamic, compressive and tensile mechanical behavior of
Deccan Basalt obtained from Deccan plateau, India. The dynamic tests have been performed at strain rates
ranging from 200 to 1600/s using split Hopkinson pressure bar (SHPB) with certain modifications in a conventional setup. The present test results are compared with other available data from the literature on igneous
rocks to understand the influence of loading rate on Deccan Basalt in terms of the peak failure stress, modulus of
elasticity, deformation modulus, and strain energy. An empirical correlation on dynamic increase factor (DIF) for
the compressive and tensile strength of Basalt is proposed by comparing present experimental results with all
other available data from the literature on Basalt.
1. Introduction
1.1. Background of the work
Basalt rock is often used as a building material and in architectural
design of building by constructing thin veneer and facade and foundations for many high-rise buildings and dams. In important structures,
thin basalt facades are often used as sacrificial layers in front of the
buildings. Blast loading near the building could cause fragmentation of
thin basalt facade causing damage to the surrounding structures and
injuries to people nearby. Hence, it is of utmost importance to study the
stress-strain response of basalt under high loading rate equivalent to
blast loading. Basalt is a volcanic igneous rock available in plenty in
India. The Indian subcontinent is covered with a remarkable volcanic
province in the west-central India popularly known as Deccan plateau.
It occupies an area of 512,000 km2 and thickness ranging from a few
meters to 2 km [1]. This region is covered with layers of Basaltic rocks.
It has various hidden tectonic features and remains to be an area of
interest among researchers [2–6]. Previous studies on Deccan trap basalt rocks are concentrated on geology, petrology and chemical compositions which are very useful in mineral and water resource exploration studies, topographical and structural mapping. However,
strength characteristics become one of the most important parameters
required during mechanical analysis, for applications in the blast resistant design of civil and military infrastructure.
The compressive and tensile strength of Nagpur Basalt from the
eastern Deccan Plateau under static conditions has been characterized
and reported in [7]. Static tests on rocks from the central region of
Deccan plateau have been conducted by [8], but only under saturated
conditions. Static compressive strength of Deccan rocks using indirect
mechanical methods has been determined by [9]. Very few data are
available in the literature which discusses the influence of strain rate on
the strength of Deccan plateau rocks. Many studies have established
that high strain rate is generated in rocks when high rate of loading is
applied, and behavior of rock materials is influenced by the strain rate
[11–18]. A general variation of the yield strength of rocks with strain
rate is shown in the Fig. 1 [19].
The compressive strength of some Indian sedimentary rocks at different strain rates has been discussed in [17,18]. Characterizing
strength behavior of rocks under static conditions is relatively simple,
but characterizing the strength of any material under dynamic loads
requires special testing methods. Kolsky [20] developed a split Hopkinson pressure bar (SHPB) and used it to determine the dynamic response of materials. Since then, researchers have modified SHPB and
used it extensively to determine the dynamic behavior of various materials like metals, ceramics, ice, glass and human tissues [21–23].
⁎
Corresponding author.
E-mail addresses: akx.malik@gmail.com, akxmalik@ncuindia.edu (A. Malik), tanusree.chakraborty@gmail.com, tanusree@civil.iitd.ac.in (T. Chakraborty),
raoks@civil.iitd.ac.in (K.S. Rao).
http://dx.doi.org/10.1016/j.tws.2017.10.014
Received 23 February 2017; Received in revised form 28 August 2017; Accepted 8 October 2017
0263-8231/ © 2017 Elsevier Ltd. All rights reserved.
Please cite this article as: Malik, A., Thin-Walled Structures (2017), http://dx.doi.org/10.1016/j.tws.2017.10.014
Thin-Walled Structures xxx (xxxx) xxx–xxx
A. Malik et al.
Brazilian disc (BD) specimens with parallel flat ends as suggested in
[30] have been used, which have proven to be helpful in minimizing
the stress concentration problem at the loading ends as highlighted in
[27]. The results are analyzed and compared with other data from the
literature on compressive and tensile behavior different varieties of
Basalt and other igneous rocks under different strain rates
[7–10,16,32–37,42]. Compressive strength, tensile strength, deformation modulus and strain energy of Deccan Basalt have been found to be
increasing with increase in strain rate.
3.0
Yield Strength (GPa)
2.5
2.0
1.5
1.2. Factors affecting dynamic testing
1.0
A conventional SHPB system is based on the assumptions that stress
and strain in the specimen are considered to be uniform in the axial
direction as per 1-D wave propagation theory and the effect of friction
and inertia are considered to be negligible. For rocks, it is difficult to
achieve these assumptions due to dispersion, inertial and frictional effects but various modifications and measures can be taken to achieve
them.
During static testing, when the load is applied to a specimen, the
specimen deforms and develops strain. In response to this deformation,
stress is developed in the specimen. The same stress-strain phenomenon
occurs during high strain rate testing but with greater complexity.
During high strain rate test, the inertia effects and the wave propagation effects become significant and dominate the test results. As the
strain rate is increased, the stress measurement starts getting affected.
The deformation within the sample is no more constant and at strain
rates of the order of 103–104/s, the effect of shock wave propagation
becomes highly critical. Due to these effects, there is the tendency of
developing stress non-uniformity which distorts the force equilibrium
and maintaining a constant stress-strain state throughout the specimen
becomes difficult.
The main causes of developing stress non-uniformity in rocks during
SHPB test are poor parallelism between specimen/bar interfaces, misalignment of bars and specimen indentation into bar end faces [38]. A
high-frequency wave dispersion is inevitable in brittle materials [39].
However, a polished specimen/bar surface and pulse shaper can minimize the inertial and frictional effects. Frew et al. [40] suggests pulse
shaper as a correction measure to minimize these effects. In the case of
static and quasi-static compression experiments on rocks, the length/
diameter ratio of the specimen is usually 2:1 to minimize the end effects, as specified by ASTM standard C39 [41]. However, in SHPB
testing on rocks, the specimen thickness decision is made not only by
end effects but also by stress equilibrium and strain rate level. For a
rock with small failure strain, a thick specimen will fail from the impact
end before the specimen gets fully loaded across its thickness [15]. Our
static test results show Deccan trap basalt to be highly brittle in nature.
Thus, an optimal length/diameter ratio has to be chosen to obtain stress
uniformity. To consider these scaling effects, length/diameter ratio of
0.5 and 1 has been used. In ISRM suggested methods for dynamic
compression tests, both length/diameter ratio 0.5 and 1 are acceptable
[43].
For heterogeneous brittle materials like rocks, a large diameter bar
corresponds to a longer length of bar and specimen. Due to this, the
applied strain rate is severely limited due to the length of the sample.
Further, a longer incident and transmission bars can cause strong wave
dispersion and oscillation and so the one-dimensional stress wave
theory and uniform stress-strain may no longer be valid. A 20 mm
diameter SHPB setup with certain modifications is used in the present
study.
0.5
0.0
-4
-2
0
2
4
6
Log (Strain Rate) (/sec)
Fig. 1. Variation of yield strength of rock with strain rate [19].
Fig. 2. Strain rates with respect to real load conditions and testing methods [23,24].
Various researchers have extended the utility of SHPB to determine the
dynamic strength behavior of rocks at high strain rates [11–18]. There
are other experimental techniques also available to characterize the
strength of materials at high strain rate (Fig. 2) however, the ISRM
commission on rock dynamics recommends split Hopkinson pressure
bar (SHPB) for a strain rate range of 100–1000/s [23].
Determination of dynamic compressive strength using SHPB is
comparatively easier than determining the dynamic tensile strength.
For the dynamic tensile test, [25] adopted the use of anvils between the
specimen, using different sizes of anvils for different sizes of specimens.
A modified design of Kolsky tension bar was given by [26] which was
further used by many researchers. Dynamic splitting test on ceramic
materials were conducted by [27] using SHPB, highlighting some aspects for future researchers when their observations showed broken
pieces of specimen near the point of loading indicating the presence of
stress concentration. In order to reduce the errors in dynamic tensile
testing, various studies have been conducted by modifying the SHPB
setup and the special mechanical test procedures have been presented
in and [28–31] to determine the tensile behavior of brittle rocks by
making flattened Brazilian specimens.
Lack of the literature on strain rate sensitivity of Deccan rocks
emphasizes the need of this study to characterize the material properties and mechanical behavior under static and dynamic loading conditions of these rock materials. The purpose of this study is to characterize Deccan Basalt under static and dynamic compressive and
tensile loading conditions up to a strain rate of 10−4 to 103/s. The static
tests are performed in the Rock Engineering laboratory, IIT Delhi. The
dynamic SHPB tests are performed in Terminal Ballistic Research
Laboratory (TBRL), Chandigarh. The SHPB device in TBRL Chandigarh
has been used for testing at high strain rates with some modifications in
the experimental procedures. For dynamic tensile testing in SHPB,
2. Materials and methods
2.1. Sample collection and specimen preparation
A thorough site investigation of the Deccan trap region is conducted
2
Thin-Walled Structures xxx (xxxx) xxx–xxx
A. Malik et al.
Fig. 3. Deccan Basalt specimens for (a) static test; (b)
for Brazilian and dynamic test.
and Deccan Basalt blocks are collected from the Koyna Dam region. The
Koyna Dam site is the largest hydroelectric power project in India. The
Deccan Basalt obtained from the field is fresh in nature and has undergone very less degree of change since the time of its formation. First
petrographic tests are performed using the scanning electron micrograph (SEM) device and further, the static and dynamic tests are carried
out.
Fig. 3 shows the specimens prepared for conducting index properties tests and mechanical tests (static and dynamic). Basalt cores are
drilled from the block samples using rock drilling machine to prepare
the specimen for static tests of NX size (54 mm diameter). Subsequently
cutting, lapping and finishing are done and specimens are prepared in
accordance to the ISRM: 1981(b). A total of 12 specimens of NX size are
prepared with L/D ratio of 2:1 as specified by ASTM standard C39 for
compressive strength test of cylindrical specimen (Fig. 3). For Brazilian
test [44], 12 specimens of two thicknesses are prepared to understand
the size effect of the specimen on the tensile strength. All the specimens
are oven dried at 105° Celsius for 24 h. For the slake durability test, 10
spherical specimens weighing 50 g each are prepared as specified in IS10050-1981 [45]. For specific gravity test, powdered specimen passing
through 475 µm sieve size is prepared. For dynamic testing in SHPB
setup, core samples of 18 mm diameter are used. For cutting 18 mm
diameter samples safely, indigenously crafted cutting machine having
fine blade is used. The size of specimen and accuracies of machine met
the requirements of ISRM (1979) suggested methods. Care is taken to
prepare samples which are free from flaws.
Fig. 4. SEM image under 10,000 magnification Deccan Basalt.
2.3. Ultrasonic tests
Ultrasonic pulse velocity test is conducted herein to determine the
primary wave velocity and understand the degree of fissuring and anisotropy of rock. The direct testing method is adopted. Two transducers
of 50 kHz frequency are used to detect the P-wave velocity. A thin film
of grease is distributed on the sample - transducer interfaces as the
coupling fluid to reduce errors in measurement due to the presence of
air. The variation in P-wave velocity is due to anisotropy and heterogeneity in the rock. The time of travel of the wave through the rock
specimen is calculated which is then used to compute the P-wave velocity, dynamic elastic modulus, shear modulus and index quality of the
rocks as displayed for some specimens in Table 1 The average P-Wave
velocity for Deccan Basalt was 5400 m/s. Dynamic Elastic modulus was
calculated from the P-Wave velocity VP using Eq. (1). The required
material parameters are taken from the results obtained from the static
compression tests.
2.2. SEM tests
Index tests provide the basic information on the physical properties
of the rocks in order to assist in their classification for the nature and
behavior of the rock. Herein, the SEM petrographic studies are carried
out to know the mineralogical composition, grain size, and arrangement of particles in the rocks as they help in understanding the failure
pattern of rocks. For SEM analysis, 6 test samples of 5 mm thickness are
tested. The SEM uses a focused beam of high-energy electrons to generate a variety of signals at the surface of solid specimens. The signals
that derive from electron sample interaction reveal information about
the sample including external morphology (texture), chemical composition, crystalline structure and orientation of materials. The microscope accelerating voltage is varied from 2 to 5 kV. The working distance is taken between 9 and 12 mm. The magnification ranges taken
are 1000 × to 10,000 × for Deccan Basalt. The SEM image of Deccan
Basalt is shown in Fig. 4 and the image is interpreted from the morphology produced and textural aspects of the rock samples. The Deccan
Basalt showed a highly laminated structure without pores visible at
lower magnifications. At 10,000 × the subrounded and fine grains are
seen attached to the surface.
VP =
E
ρ
(1)
Table 1
Sonic wave velocity for Deccan Basalt.
3
S. No
Time (ms)
Length
(mm)
P-wave
velocity
(m/s)
Dynamic
modulus
(GPa)
Shear
modulus
(GPa)
Index
quality
(IQ)
B4
B5
B6
B7
B8
B11
20.2
20.1
20.8
20
20.1
20.2
109
107.9
109
109.1
109
109
5396.04
5368.16
5240.38
5455
5432.84
5396.04
87.06
86.16
82.11
88.97
88.25
87.06
38.01
37.62
35.85
38.85
38.53
38.01
83.1
82.5
80.6
83.9
83.5
83.1
Thin-Walled Structures xxx (xxxx) xxx–xxx
A. Malik et al.
Fig. 5. Unconfined compression equipments (a)
2000 kN capacity (b) servo-control machine with
3000 kN capacity.
where E is Young's modulus and ⍴ is material density.
and compressive bearing strength of 607 MPa. The loading jaws are
designed so as to contact the disc-shaped specimen at diametrically
opposed surfaces over an arc of contact of nearly 10° at failure. The
radius of jaws is taken as 29 mm in diameter, which is 1.6 times of that
the specimen size. The samples taken are dry as per standards suggested
by ISRM (1978d) and IS: 10082-1981 [44]. The test is performed by
placing disc-shaped specimen in the middle of the jaws and the compressive load is applied. The deformation rate for Brazilian test is kept
constant at 2.5 mm/min. The tensile strength (σt) of the specimen is the
maximum stress obtained in the specimen during tension and it is calculated as:
2.4. Mechanical experiments
Both static and dynamic tests are conducted on Deccan Basalt in dry
conditions and discussed in the following paragraphs.
2.4.1. Static compression tests
The unconfined compressive strength (UCS) tests are performed on
NX size cylindrical specimens of L/D ratio 2:1 under dry condition. For
each rock, 6 specimens are tested with strain gages without strain
control, and another 6 specimens are tested using strain control technique. For tests with strain gages, a loading frame of 2000 kN is used.
Axial and diametrical deformation response are measured by properly
fixing 4 strain gauges of 120-Ω resistance in all four directions on the
tested specimen. These strain gauges are carefully connected with wires
to a double channeled strain indicator setup designed in the IIT-Delhi
rock laboratory. The test set-up is shown in Fig. 5. The strain rate for the
static tests is measured to be in the order of 10−1/s. Teflon sheets are
put on the end surfaces of specimen and platen to minimize the end
friction. Readings of axial and diametrical responses are taken after
every 500 kg load. The results from stress-strain plots are used to produce a well-quantified data for determining Young's modulus and Poison's ratio. For tests with strain control, the servo-controlled machine of
capacity 3000 kN is used and strains are measured using LVDT with
proper care. For a servo-controlled machine, strain-deformation rate is
varied to obtain strain rate in the order of 10−4 to 10−2/s and stressstrain behavior is analyzed. Unconfined compression strength (UCS) is
the maximum axial stress of the specimen during compression and
critical strain (Ec) is the corresponding strain at peak stress.
σt =
2P
πBD
(2)
2.4.3. Dynamic compressive tests
Dynamic tests are performed in SHPB located at the Terminal
Ballistic Research Laboratory (TBRL), under Defense Research and
Development Organization (DRDO), Govt. of India. The SHPB setup
mainly consists of a gas gun, a striker, an incident bar, a transmission
bar, a pressure gas gun and an output bar, as shown in Fig. 7. High
strength maraging steel having a yield strength of 1750 MPa are used in
bars. The length of the incident and transmission bars used is 2000 mm
each. The length of striker bar is 300 mm, while diameter of all the bars
are 20 mm.
For the testing, the specimen is sandwiched between the incident
and the transmission bar using a small amount of grease. The gas gun is
loaded at a required pressure. The pressure valve is opened and the
striker bar is pushed ahead due to the release of pressure. The striker
bar strikes the incident bar and an elastic compressive stress wave
called the incident wave is generated and it travels through the incident
bar. The incident wave passes through the specimen and a part of the
incident wave reflects back from the interface of the incident bar and
the specimen, which is called the reflected wave. The remaining part of
the incident wave travels through the output bar, which is called the
transmission wave. The readings of the waves are recorded with the
help of an oscilloscope attached to the strain gages pasted at the middle
of the incident bar and the transmission bar.
With the help of an oscilloscope, the strain histories in the input and
output bars are recorded using strain gauges I & II (120 Ω, 90° tee
2.4.2. Static tensile tests
Brazilian tensile strength test is conducted as per the IS: 10082-1981
[44]. The tests are conducted on discs of L/D ratio 0.5. Two different
diameter of samples- 54 mm and 18 mm are chosen to understand the
effect of sample size. For the 18 mm diameter specimen, a small apparatus is designed in accordance to the IS: 10082-1981 [44]. The test
set-up is shown in Fig. 6. Aluminum is used to carve the apparatus,
having an elastic modulus of 68.5 GPa, the tensile strength of 324 MPa,
4
Thin-Walled Structures xxx (xxxx) xxx–xxx
A. Malik et al.
Fig. 6. Brazilian tensile test equipment (a) loading frame; (b) NX size apparatus; (c) 18 mm diameter apparatus.
(a)
Compressive test
Loading angle < (2α)
Tensile test
P1 = EA (εi + εr )
(5a)
P2 = EAεt
(5b)
Pa = EA
Gas Gun
Wave Shaper
Strain gauge I (Ch A)
Striker
Incident Bar
ε i + εr + εt
2
(5c)
For force equilibrium to be maintained, forces at both ends of the
sample have to be equal. i.e., P1 = P2; which gives εi + εr = εt . So, when
the sample is in equilibrium, strain rate and strain are gives as:
Strain gauge II (ChB)
−2c
∂ε
εr = s
l0
∂t
Transmitted Bar
εs =
(b)
−2c
l0
∫0
(6)
t
εr τ ∂τ
(7)
Compressive stresses, elastic modulus (E) and deformation modulus
(D) are calculated as:
σa = EA
E=
σ0.6 − σ0.4
ε0.6 − ε0.4
D=
σP
εc
Fig. 7. (a) A schematic diagram of SHPB setup used with different orientation sample for
compressive and tensile tests (b) data acquisition system.
rosette precision strain gages designated as EA-06-125TM-120)
mounted at the mid-point positions of incident and transmission bars,
which are at 1000 mm from the specimen - bar interface. In total three
strain signals are recorded as shown in Fig. 7(b). These signals are from
the incident strain, εi (Strain Gauge I); reflected strain, εr (Strain Gauge
I) and the transmitted strain, εt (Strain gauge II). These measured
strains provide the required data for the stress-strain relation of the
sample material. For the purpose of reducing wave dispersion, a copper
pulse shaper of 10 mm diameter and 1 mm thickness is used as shown
in Fig. 7(a). For the analysis of stress, strain and strain rate in the
specimen using 1-Dimensional wave propagation theory, the following
equations are used:
εs =
l1 − l2
l0
∂εs
v − v2
= 1
∂t
l0
∂εs
ε − εr − εt
=c i
∂t
l0
ε i + εr + εt
2As
(8)
(9)
(10)
where σp is the peak failure stress, εc is the critical strain at failure, σ0.6
is the stress at 0.6 times the peak stress, and σ0.4 is the stress at 0.4 times
the peak stress. The ε0.6 and ε0.4 are the respective strains for σ0.6 and
σ0.4. In this study, the dynamic compressive strength of Basalt is evaluated.
2.4.4. Dynamic tensile tests
The same SHPB setup is used herein for conducting tensile tests at
high strain rates with certain modifications. The specimens are modified by flattening their loading ends and making them parallel to each
other. Specimens of two different sizes of 18 mm diameter and 38 mm
diameter are prepared as shown in Fig. 3. For tensile testing, the specimen is sandwiched diametrically between the incident and the
transmission bar along the flat ends as shown in Fig. 7(a). The ends of
the specimen are flattened to an angle 2α, also called the loading angle,
to reduce the stress concentration. As per the IS specifications, while
preparing the specimen, care is taken to limit the loading angle 2α
between 10° to 20°. Similarly, like dynamic compression tests, for the
purpose of reducing dispersion, a copper pulse shaper of 10 mm diameter and 1 mm thickness is used. The equations used to calculate
strain and strain rate are as similar to the compressive test. For tensile
strength (σt), the equation used is as follows [28]:
(3a)
(3b)
(4)
where l1 and l2 are the displacements at sample-bar interfaces, v1 and v2
are the respective particle velocities at sample-bar interfaces, c is the
longitudinal stress wave velocity in the bar. In terms of measured strain
pulses, forces at the end of the specimen and average forces are:
σt = −0.95
5
2P
πdL
(11)
Thin-Walled Structures xxx (xxxx) xxx–xxx
A. Malik et al.
Table 2
Physical properties.
Table 3
Static properties of Deccan Basalt.
Rock type
Dry
density
(g/cm3)
Porosity (%)
Specific
gravity
Sonic Wave
Velocity (m/
s)
Durability
Index
Rock
UCS
(MPa)
Critical strain
Elastic
modulus
(GPa)
Deformation
modulus
(GPa)
Poisson
ratio (µ)
Strain
energy
(MJ)
Deccan
Basalt
2.98
0.2
3.02
5380
98 (very
high)
Basalt
85.7
0.007–0.01
11.67
9.87
0.19
0.29–0.41
where P is the load at failure calculated from Eq. (5c), d is the diameter
of the specimen and L is the length of the specimen. Tensile stress is
taken as negative and compressive stress is taken as positive.
3. Results and discussions
3.1. Physical properties
The physical properties such as dry densities, porosity, void ratio
and specific gravity are determined for basalt in its natural state following the standard test procedures suggested by IS:13030 (1991) [46].
The specific gravity is determined as per the standard procedures
mentioned in IS: 1122 – 1974 [47]. The values are given in Table 2.
3.2. Static tests
Fig. 9. Failure under static compression tests of Deccan Basalt.
The results and parameters obtained from the static compression
tests on basalt under static and dynamic loading conditions are discussed in this section.
3.2.1. Compressive testing
Unconfined compressive tests are carried out on basalt and stressstrain curves obtained are shown in Fig. 8.
It is observed that for Deccan Basalt the critical strain (ε) which is
the strain at peak stress varied from 0.005 to 0.01 which shows that
Deccan Basalt is very brittle in nature. The static properties and modulus parameters are presented in Table 3. The compressive strength of
Deccan Basalt with a displacement rate in the range of 0.001–0.01/s
results in an averaging peak value of 85.7 MPa. Fig. 9 indicates shear
failure for Deccan Basalt with splitting along one major surface. Parameters like Elastic modulus (E), Deformation modulus (D) are calculated using Eqs. (9) and (10).
The standard deviation for deformation modulus of Deccan Basalt is
founded to be 1.56 whereas the standard deviation for elastic modulus
of Deccan Basalt is 2.85.
Fig. 10. Failure under static Brazilian tensile test Deccan Basalt.
3.2.2. Tensile testing
Brazilian tensile strength test is conducted at a loading rate of
0.2 kN/s. A desirable failure mode is obtained for basalt as shown in
Fig. 10. The results of tensile strength test on different sizes (18 mm and
54 mm diameter) are shown in Fig. 11. The tensile strength of basalt is
found to be consistent with a particular size. For NX size samples, the
average tensile strength of Deccan Basalt obtained was 13.13 MPa.
Tensile strength was found to be 20–25% higher for 18 mm diameter
samples as compared to NX size samples.
Deccan Basalt
140
Sample Numbers
120
Stress (MPa)
100
80
B1
B2
B3
B4
B5
B6
B8
B9
60
3.3. Dynamic tests using SHPB
40
3.3.1. Compressive testing on Deccan Basalt
Dynamic tests are carried out in SHPB at room temperature for both
types of rocks. For Deccan Basalt, 14 specimens are tested and force
equilibrium is maintained for 9 specimens. The remaining samples resulted poor reading due to heterogeneity in the specimens and some
defects in parallelism. Table 4 presents the summary of the results. For
each test, strain-time history curves are obtained (Fig. 12(a)) and incident strain, transmitted strain and reflected strain are calculated using
20
0
0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014
Strain
Fig. 8. Stress-strain plots obtained from static compressive testing of Deccan Basalt.
6
Thin-Walled Structures xxx (xxxx) xxx–xxx
A. Malik et al.
24
anisotropy and heterogeneity in the rocks. However, the strain rate
generated varied with L/D ratios. For higher L/D ratio of 1, the strain
rate generated was lower, which was 200–700/s for a pressure of
1–1.5 bar. For L/D ratio 0.5 the strain rate generated was in the range of
360–1600/s by varying pressure from 1 to 2.5 bar.
Fig. 13(a) represents the stress-strain curves obtained for strain rates
varying from 359 to 1604/s at L/D ratio 0.5. An increase in the compressive strength is found. Comparing the stress-strain curves for a
strain rate of 992/s to 0.001/s (Fig. 13(b)) an increase in compressive
strength and stiffness of specimen is observed. An increase in deformation modulus with strain rate is also found (Fig. 14(a)). However,
no direct relation between deformation modulus and strain rate could
be suggested. Fig. 14(b) shows a linear increase in strain energy (SE),
with strain rate given in the following equation:
Deccan Basalt (54 mm)
Deccan Basalt (18 mm)
Tensile Strength (MPa)
20
16
12
8
4
0
15
20
25
30
35
40
45
50
55
The dynamic increase factor (DIF), i.e. the ratio of dynamic to static
peak stress is calculated for Deccan Basalt and is compared with the
available literature on Basalt from North America and other igneous
rocks like granite, Porphyritic Tonalite as shown in Fig. 15, and the
increasing trend of compressive strength with strain rate is validated.
By using the literature available on Basalt for effect of strain rate ε̇ on
compressive strength, an equation is proposed:
Diameter (mm)
Fig. 11. Tensile strength of Deccan Basalt.
Table 4
Compressive strength results for Deccan Basalt specimen at high strain rates.
Sample ID
2
B
B3
B10
B5
B8
B4
B11
B12
B14
L/D ratio
0.5
0.5
0.5
0.5
0.5
0.5
1
1
1
Pressure used
(bar)
Strain rate
(/s)
Peak stress
(MPa)
1
1
1
2
2.5
2.5
1
2
2
359
361
602
992
1264
1605
202
659
740
175.7
173.4
186.6
212.4
249
262
156.6
200.1
251.3
DIF = 1.5407(log ε̇)0.0492 with R2 = 0.78
3.3.2. Dynamic tensile test on Deccan Basalt
The values of tensile strength at high loading rates are presented in
Table 5. Several specimens are tested and satisfactory results are obtained for 5 specimens. Few samples showed high dispersions and were
discarded. There were cases of pre-mature failure observed during trial
testing when specimen broke while the stress wave is still rising inside
the specimen and the specimen being not fully loaded and thus, stress
equilibrium not being developed in the specimen. Use of pulse shaper
helped in reducing the rising front as the wave reverberates inside the
specimen and a uniform stress distribution is achieved after a period of
time. The plots for strain vs time history, force equilibrium at sample
bar interfaces with time, and tensile strength vs. strain are shown in
Fig. 17.
The strain rate generated for different samples is in the range of
(b)
1250
1000
Transmitted Wave (Ch B)
Incident Wave (Ch A)
Reflected Wave (Ch A)
750
70
Incident Bar Side
Transmission Bar Side
60
50
500
250
Force (kN)
Strain (microdef)
(13)
The failed specimen is obtained in the form of multiple elongated
pieces, 3–6 mm long along with crushed particles as shown in Fig. 16.
For some specimen, completely crushed particles are obtained. The
dynamic modulus is also found to be increasing at higher strain rates as
compared to the static elastic modulus.
Eqs. (2)–(7). From the ultrasonic tests, the average value of P-wave
velocity in Deccan Basalt samples was observed to be 5400 m/s. For a
specimen of length 9 mm, the time of travel of the wave from one end of
sample to the another comes out as 1.65 μs. And for stress uniformity to
be maintained [48] the wave must travel 4 times inside the specimen
which translates the time of travel to be nearly 6.6 μs. It was observed
that the peak stresses in various tests are obtained in a time frame of
60–100 μs, which validates that force equilibrium (Fig. 12(b)) could be
maintained in the specimen after about 6.6 μs. Deccan Basalt has high
resistance to breakage and 1 bar pressure produced nearly 300–600/s
strain rate. Different strain rates are generated at same pressure due to
(a)
(12)
SE = 0.0006ε̇ + 0.3497 with R2 = 0.72
60
0
-250
-500
40
30
20
-750
10
-1000
-1250
0
200
400
600
800
1000
1200
Time (microseconds)
0
0
20
40
60
80
100
120
140
160
Time (microseconds)
Fig. 12. (a) Strain time curves with the incident, reflected and transmitted pulses (b) force equilibrium between the specimen and bar interfaces.
7
Thin-Walled Structures xxx (xxxx) xxx–xxx
A. Malik et al.
(a)
(b) 250
250
Strain Rates
Stress (MPa)
Stress (MPa)
200
602 /sec
359/sec
361/sec
1604/sec
1264/sec
200
150
100
Static (Strain rate 0.001/sec)
Dynamic (Strain rate 992/sec)
150
100
50
50
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16
3.5
Strain
Strain(%)
Fig. 13. (a) Stress-strain curves for Deccan Basalt (a) at strain rates from 359 to 1604/s (b) comparison of static (0.001/s) and dynamic (992/s) stress-strain results.
(a)
(b)
2.0
1.5
40
y = 0.0006(x) +0.3497
2
R = 0.72
3
Strain energy(J/m )
Deformation Modulus (GPa)
50
30
20
1.0
0.5
10
0
0.0
0
400
800
1200
1600
0
400
800
1200
1600
Strain Rate (/sec)
Strain Rate (/sec)
Fig. 14. Variation of (a) deformation modulus and (b) strain energy with strain rate for Deccan Basalt.
3.0
with time. In the time duration in which sample failed, the rate of strain
generation is found to be fairly constant. Fig. 17(b) shows the force
equilibrium being maintained in the specimen during loading up to
peak stress equilibrium. The results can be considered valid only in a
specimen where force equilibrium is developed and constant strain rate
is generated. The tensile strength vs strain curves for the different
specimens are shown in Fig. 17(c). The results show an increase in
tensile strength as compared to the static tensile strength. The average
factor of increase comes out to be 1.75. The average peak stress observed was 22.9 MPa, and the average strain at failure was 1.3%.
The DIF for tensile strength is compared with the literature on other
igneous rocks [16,37,49,50] as shown in Fig. 18. No direct co-relation
for an increase in tensile strength of rocks can be proposed. There is
high variation in the increase in tensile strength of different rocks with
strain rate due to heterogeneous and intrinsic characteristics of rocks.
A recovered basalt specimen after dynamic tensile test is shown in
Fig. 19. The splitting of the sample is observed from the center. Unlike
axial loading in dynamic compression testing, crushing is not observed
during the tensile test. No multiple cracks are observed in the specimen
as well. Very negligible crushing is observed at the point of loading. The
failure of the sample observed is as desired for a static Brazilian test.
Deccan Basalt (Current Study)
Tuff [16]
Basalt [32]
Basalt [33]
Basalt [10]
Granite [32]
Porphyritic Tonalite [42]
Granite [35]
2.5
DIF
2.0
1.5
1.0
0.5
-6
-4
-2
0
2
4
Log Strain Rate (/sec)
Fig. 15. Comparison of DIF for Deccan Basalt with the DIF of other igneous rocks and
Basalt.
281/s to 601/s, with peak tensile strength varying from 18 to 27 MPa.
The strain rate generated at 1 bar pressure is in the range of 280–360/s
and the average tensile strength obtained is 22.22 MPa. Fig. 17(a) explains the generation of the incident, reflected and transmitted pulses
8
Thin-Walled Structures xxx (xxxx) xxx–xxx
A. Malik et al.
Fig. 16. Deccan Basalt specimen (a) before SHPB test
(b) after failure in SHPB test.
4. Conclusions
Table 5
Peak tensile stress at varying strain rates for Deccan Basalt.
Sample
number
L/D ratio
Pressure used
(bar)
Strain rate
(/s)
Peak stress
(MPa)
B21
B23
B24
B26
B27
0.5
0.5
0.5
0.5
0.5
1
1
1
1.5
1
556
281
359
601
357
18
23
27
25
21
Dynamic compressive and tensile experiments for Deccan Basalt is
performed herein. Deccan Basalt is highly brittle in nature and its
strength is found to be sensitive to strain rate. Material parameters for
Deccan Basalt may be used in the design and analysis of various above
and underground structures subjected to impact loading. From the test
results, it is concluded that both the compressive strength and tensile
strength, deformation modulus, stiffness and fracture energy increase
with increasing strain rate. The factor of increase in compressive
strength
of
Basalt
with
strain
rate
is
proposed
as
(a) 1500
(b)
Incident Wave (Strain Gage I)
Transmitted Wave (Strain Gage II)
Reflected Wave (Strain Gage I)
1000
Force Equillibrium for Deccan Basalt
(Dynamic Tensile Test)
Incident Force, F1(kN)
Transmitted Force, F2(kN)
30
20
Force (kN)
Strain (microdef)
25
500
0
-500
10
-1000
-1500
15
5
0
200
400
600
0
800 1000 1200 1400 1600
0
40
Time (microseconds)
80
120
Time (microseconds)
160
200
(c) 30
Tensile Strength (MPa)
25
20
15
10
Strain Rates
556/sec
601/sec
281/sec
357/sec
5
0
0.0
0.5
1.0
1.5
2.0
Strain (%)
Fig. 17. (a) Incident, reflected and transmitted pulses (b) force equilibrium during tensile test (c) stress-strain curves for tensile strength at high loading.
9
Thin-Walled Structures xxx (xxxx) xxx–xxx
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5
Deccan Basalt
Tuff [16]
Sandstone [49]
Barre Granite [50]
Granite [37]
DIF (Tensile)
4
3
2
1
-6
-4
-2
0
2
4
Log Strain Rate (/sec)
Fig. 18. DIF for tensile strength of Deccan Basalt and other rocks.
Fig. 19. Failure of Deccan Basalt under dynamic tensile test.
DIF = 1.5407(log ε̇)0.0492 with R2 = 0.78. A linear response for increase
in strain energy of Deccan Basalt with strain rate is given as
SE = 0.0006ε̇ + 0.3497 with R2 = 0.72 . This increase in energy is consumed in fragmentation of the particles. During drilling and blasting
operations in rocks, the factor of increase in strength and strain energy
could play an important role in determining the efficiency of the operations.
Acknowledgments
The authors are thankful to Defense Research and Development
Organisation (DRDO), Ministry of Defense (ARMREB/CDSW/2013/
151 Dated: 30-07-2013), Govt. of India for funding this research and
providing their Terminal Ballistic Research laboratory (TBRL) for
testing. We are thankful to Ministry of Human Resource and
Development, Govt. of India for their financial support.
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11
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