Novel Three-dimensional Rock Dynamic Tests Using the True Triaxial Electromagnetic Hopkinson Bar System

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Rock Mechanics and Rock Engineering
https://doi.org/10.1007/s00603-020-02344-4
TECHNICAL NOTE
Novel Three‑dimensional Rock Dynamic Tests Using theTrue Triaxial
Electromagnetic Hopkinson Bar System
HepingXie1,2· JianboZhu1,2· TaoZhou1,2 · JianZhao3
Received: 27 February 2020 / Accepted: 12 December 2020
© The Author(s), under exclusive licence to Springer-Verlag GmbH, AT part of Springer Nature 2021
Keywords 3D rock dynamics· True triaxial electromagnetic Hopkinson bar· Rock dynamic test
1 Introduction
With increasingly more large rock structures built in
regions where severe dynamic disturbance and complex
tectonic stress present, the engineering disturbance induced
dynamic disasters (e.g., rockburst, coal bump, landslide)
are becoming more frequent and severe, resulting in huge
casualties and property losses (Jiang etal. 2017; Linzer
etal. 2007). This is mainly because rock engineering built
in those regions not only bears triaxial static loads (e.g.,
crustal stress) but also is subjected to multi-axial dynamic
disturbances such as blasting and earthquake. Therefore,
understanding the dynamic response and behavior of rocks
subjected to multi-axial dynamic and static loads is of great
significance for the design, construction and operation of
rock engineering.
Many efforts have been devoted to investigating the
mechanical and fracture behavior of rocks under dynamic
compression, dynamic tension and coupled dynamic uni-
axial compression and static confinement loading condi-
tions using the split Hopkinson bar (SHB) system (Cho
etal. 2003; Doan and Gary 2009; Frew etal. 2001; Gary
and Bailly 1998; Huang etal. 2010; Li etal. 2008, 2013;
Nemat-Nasser etal. 2000; Xie etal. 2020; Zhang and Zhao
2014; Zhou etal. 2020; Zhu etal. 2018). For instance, Doan
and Gary (2009) revealed the mechanism of rock pulveriza-
tion at the strain rate of 102s−1. Li etal. (2017) for the first
time revealed the influence of joint interface characteristics
on wave propagation across rocks. Cadoni (2010) showed
that the dynamic tensile strength of Orthogneiss rock is sen-
sitive to strain rate and load-schistosity inclination. Liu etal.
(2019) reported the earliest study on the dynamic mechani-
cal and fracture behavior of sandstone under the coupled
dynamic uniaxial impact and true triaxial static confinement.
However, rock dynamic behavior under the coupled multi-
axial dynamic and static stresses have not been investigated.
One of the major reasons is the lack of a true triaxial syn-
chronized impact testing device that can apply both the tri-
axial dynamic disturbances and the triaxial insitu stresses.
To solve this problem, a true triaxial electromagnetic Hop-
kinson bar (TEHB) system has recently been developed by
Xie etal. (2018), which provides a cutting-edge testing plat-
form for studying the three-dimensional (3D) rock dynamic
behavior subjected to the coupled triaxial dynamic impacts,
under triaxial insitu stress as well as under strain rates from
101s−1 to 103s−1. The superiorities of the TEHB over the
conventional dynamic testing apparatuses, in particular the
SHB, mainly include: (1) the controllable and adjustable
generation of stress pulse; (2) the synchronous, repeatable
and precise generation of multiple identical stress pulses; (3)
the convenient and precise achievement of the stress equi-
librium of the specimen; (4) the easy replicability of the
coupled triaxial dynamic impact and triaxial insitu stress
conditions. Therefore, the TEHB can overcome the limita-
tions of the current SHB techniques and is applicable to
systematically carry out rock dynamic tests.
* Jianbo Zhu
jianbo.zhu@szu.edu.cn
* Tao Zhou
tzhou@szu.edu.cn
1 Guangdong Provincial Key Laboratory ofDeep
Earth Sciences andGeothermal Energy Exploitation
andUtilization, Institute ofDeep Earth Sciences andGreen
Energy, College ofCivil andTransportation Engineering,
Shenzhen University, Shenzhen, China
2 Shenzhen Key Laboratory ofDeep Underground Engineering
Sciences andGreen Energy, Shenzhen University, Shenzhen,
China
3 Department ofCivil Engineering, Monash University,
Melbourne, Australia

H.Xie et al.
1 3
This paper aims to introduce novel and essential 3D rock
dynamic tests that can be only performed with the TEHB.
Firstly, the TEHB was briefly introduced. Subsequently, rock
dynamics tests and studies that could be performed using the
TEHB were introduced and analyzed in detail. The antici-
pated findings can pave the way for future rock dynamics
investigations and facilitate the development of the 3D rock
dynamics theories.
2 Testing Apparatus
Figure1 shows the schematic view of the TEHB, which
mainly consists of a six orthogonal triaxial frame con-
structed from square bars made of high strength anti-mag-
netic titanium alloy (50 × 50 × 3000mm3), a servo-controlled
confining pressure system, a stress pulse generation system
and a data acquisition and analysis system.
The servo-controlled confining pressure system consists
of a servo control system, a hydraulic pump station and three
hydraulic cylinders. It can apply true triaxial pressures to a
rock specimen in the three orthogonal directions in accord-
ance with the insitu stress condition. The maximum con-
fining pressure in each axis is 300MPa. During testing,
the confining pressures are applied to the specimen before
impact loading. Notably, because the response time of the
servo control system to the load is too long (approximately
10ms) to exactly maintain the stability of the confining pres-
sures. Therefore, due to the Poisson’s effect on rock speci-
men, the confining pressures will be slightly changed when
the specimen is subjected to a triaxial impact.
The stress pulse generation system is composed of six
electromagnetic pulse generators. With the aid of the elec-
tromagnetic energy conversion technique and the synchro-
nous control technique, the stress pulse generation sys-
tem can synchronously/asynchronously generate multiple
half-sine stress pulses with high consistency, accuracy and
repeatability, enabling to conduct synchronously/asynchro-
nously triaxial impact loading tests on the rock specimen.
The data acquisition and analysis system includes the
contact (e.g., strain gauges) and non-contact (e.g., acoustic
emission, electromagnetic radiation and infrared radiation)
signal capture apparatuses, the real-time monitoring (e.g.,
high-speed camera) system and the post-test characterization
tools (e.g., X-ray CT and scanning electron microscope),
which can be integrated to comprehensively analyze the
dynamic responses and behavior of rock specimens from
macro to meso and micro scales.
In dynamic tests performed with the TEHB, the impact
loads are symmetrically applied to the two sides of the rock
specimen in each axis, which is superior over the conven-
tional SHB technique. The symmetrical loading can quickly
achieve dynamic stress equilibrium in the rock specimen,
particularly at the early loading stage of the test. The time to
reach stress equilibrium in symmetrical loading is approxi-
mately 1/3 of that in the conventional SHB test (Nie etal.
2018). In addition, the symmetrical loading with the same
incident stress pulse yields a higher strain rate than the con-
ventional SHP technique. Due to the large size of the rock
specimen, the upper limit of strain rate in conventional SHB
tests is usually ~ 102s−1, while the symmetrical loading can
achieve a higher strain rate up to ~ 103s−1.
In true triaxial impact tests, when the specimen is triaxi-
ally loaded, three waves, i.e., the elastic wave induced by the
Poisson’s effect, the transmitted wave and reflected wave,
are generated in each bar. Because these three waves are
successively generated in a very short time (within approxi-
mately 10μs) and propagate along the same direction, they
superpose into one wave, propagating away from the speci-
men in each axis. In addition, the propagation of superim-
posed waves does not interfere with each other in the three
orthogonal directions (Cadoni and Albertini 2011), and con-
sequently, the interpretation of dynamic strain data obtained
in true triaxial impact tests still follows the one-dimensional
(1D) elastic wave propagation theory (Liu etal. 2019).
Figure2 shows a synchronous symmetric impact loading
in the x-axis. Two identical incident stress waves, generated
by electromagnetic pulse generators, propagate from the
incident ends of the left and right incident bars, respectively.
Herein, the incident pulses propagate from the left and right
are termed as the left incident wave (εL_inc) and right incident
wave (εR_inc), respectively. When the left incident wave arrives
at the interface between the left incident bar and the specimen,
a portion of the wave is reflected back into the left incident
bar as a reflected wave, while the remaining passes through
the specimen and enters the right incident bar as a transmitted
wave. Likewise, the right incident wave propagates in accord-
ance with the same principle. Because the travel time of the
left incident wave in the specimen is much shorter than the
duration of the incident wave, the reflected wave recorded by
Fig. 1 The schematic diagram of the TEHB (Xie etal. 2018)

Novel Three-dimensional Rock Dynamic Tests Using theTrue Triaxial Electromagnetic Hopkinson…
1 3
the strain gauge at the midpoint of the right incident bar is
actually a superposition of the reflected wave from the right
incident wave, the transmitted wave from the left incident wave
and the elastic wave induced by the Poisson’s effect due to the
impact from the other two orthogonal directions. The super-
imposed wave in the right incident bar is termed as the right
reflected wave (εR_ref). Similarly, the superimposed wave in
the left incident bar is termed as the left reflected wave (εR_ref).
As aforementioned, dynamic stress equilibrium in the rock
specimen in each axis can be well achieved under synchronous
symmetric loading using the TEHB. Therefore, according to
the 1D stress wave theory, the dynamic stress
𝜎(t)
, dynamic
strain
𝜀(t)
and strain rate
̇𝜀 (t)
of the specimen in each axis can
be determined as (Nie etal. 2018):
(1)
𝜎
(t)=
1
2
A
A
s
E
(
𝜀L_inc +𝜀R_inc +𝜀L_reft +𝜀R_ref
)
where C, A and E are the longitudinal wave speed, cross-sec-
tion area and Young’s modulus of the incident bar, respec-
tively. Ls and As are the length and cross-section area of the
specimen, respectively.
Under the coupled true triaxial static confining pressures
and true triaxial impact, the stress applied to the specimen
in each axis is the sum of the static confining pressure and
the dynamic stress. Therefore, the equivalent stress (
𝜎
) and
equivalent strain (
𝜀
) can be applied to evaluate and analyze
the dynamic strength and deformation of the specimen under
coupled true triaxial static confining pressures and true triaxial
impact, which can be determined as (Xu etal. 2020):
(2)
𝜀
(t)= C
L
s
∫
t
0
(
𝜀L_inc +𝜀R_inc −𝜀L_reft −𝜀R_ref t
)dt
(3)
̇𝜀
(t)=
C
L
s
(
𝜀L_inc +𝜀R_inc −𝜀L_reft −𝜀R_ref
)
(4)
𝜎
=
√
1
2[(
𝜎x_dyn +𝜎x_sta −𝜎y_dyn −𝜎y_sta
)
2+
(
𝜎y_dyn +𝜎y_sta −𝜎z_dyn −𝜎z_sta
)
2+
(
𝜎z_dyn +𝜎z_sta −𝜎x_dyn −𝜎x_sta
)
2
]
(5)
𝜀
=
√
2
9[(
𝜀x_dyn +𝜀x_sta −𝜀y_dyn −𝜀y_sta
)
2+
(
𝜀y_dyn +𝜀y_sta −𝜀z_dyn −𝜀z_sta
)
2+
(
𝜀z_dyn +𝜀z_sta −𝜀x_dyn −𝜀x_sta
)
2
]
Fig. 2 Schematic diagram of wave propagation during symmetric loading in x-axis
where
𝜎i_dyn
,
𝜎i_sta
,
𝜀i_dyn
and
𝜀i_sta
represent the dynamic
stress, static confining pressure, dynamic strain and static
strain corresponding to the peak static confining pressure
along the i-axis (i = x, y, and z), respectively.
3 Rock Dynamic Testing
As aforementioned, the TEHB is superior over the con-
ventional SHBs. The TEHB can precisely, repeatedly and
synchronously generate multiple identical half-sine stress
pulses, which is essential for the dynamic tests on brittle
rocks. It can also achieve multi-directional dynamic (e.g.,
from symmetric/bidirectional to biaxial/four-directional
and true triaxial impact loading) impact under in situ

H.Xie et al.
1 3
Fig. 3 Schematic diagram of triaxial compression on a specimen: a
The triaxial dynamic compression; b the coupled triaxial static and
triaxial dynamic compression; c, d the typical loading paths during
synchronous and asynchronous triaxial and six-directional compres-
sions, respectively; e, f schematic diagram of thermo-mechanical
coupling loading device from the overview and cross-section view,
respectively. ∆t means the loading time delay along one axis with
respect to the first loaded axis. σ1, σ2 and σ3 represent the maxi-
mum, intermediate and minimum principal stresses along x, y and z
axes, respectively; σdx, σdy and σdz represent the dynamic compres-
sive stresses applied to specimen along x, y and z axes, respectively.
The pink arrow refers to the wave propagation direction. Waveform
with convex shape is defined as compressive wave. The two pulses
in opposite direction represent synchronous and symmetrical loading
along a certain axis

Novel Three-dimensional Rock Dynamic Tests Using theTrue Triaxial Electromagnetic Hopkinson…
1 3
conditions (e.g., stress and thermal fields). With these
functions and features, a series of innovative and essen-
tial rock dynamic tests can be conducted, which typically
include 3D dynamic compression tests under the coupled
true triaxial impact and static triaxial insitu stress and
real-time thermal conditions, 3D dynamic tension tests
under the triaxial confining pressure, and 3D dynamic
fracturing tests under the coupled static and dynamic
loading conditions. The detailed introduction and analy-
sis of these typical rock dynamic tests are presented in
this section.
3.1 3D Dynamic Compression
TEHB tests are conducted to investigate the dynamic
response and behavior of rock specimens under multi-axial
and multi-directional dynamic compression with or with-
out the consideration of the insitu static stress and ther-
mal conditions. Figure3a–d demonstrate the schematic
diagram of the typical 3D dynamic compression test and
the typical loading paths of synchronous and asynchro-
nous dynamic compression tests. In TEHB tests, both the
dynamic loads and static confining pressure can be inde-
pendently adjusted and applied in the three orthogonal
directions in accordance with the insitu stress conditions.
Notably, to avoid the collision of bars due to the volu-
metric compaction of the specimen under the true triaxial
impact, the side length of the cubic specimen is 1mm
longer than the side length of the square bar (50mm).
To avoid the mismatch between the side surfaces of the
specimen and the square bars, a 0.5mm chamfer is manu-
factured at each edge of the cubic specimen, as shown
in Fig.3a. Figure3e, f illustrate the schematic diagram
of the thermo-mechanical coupling loading device. The
rock specimen is first placed at the center of the triaxial
bars, and the static insitu confining pressures are applied
to the specimen via the elastic bars. Then, the heating fur-
nace is installed on the square bars to heat the rock speci-
men. When the specimen is evenly heated to the targeted
temperature (e.g., 20–400°C), the true triaxial dynamic
loads are synchronously or asynchronously applied to the
rock specimen to perform the dynamic thermo-mechanical
coupling test.
With the testing results, the influences of the confin-
ing pressure (in particular the intermediate (σ2) and the
minimum (σ3) principal stresses), the loading paths of the
static confining pressure and the dynamic compression,
the thermal effect, the strain rate and the synchronous and
asynchronous impact on the dynamic mechanical behav-
ior of rocks can be determined. The dynamic compressive
strength, deformation, fracture and failure mechanism of
rocks from macro and micro scales under the above loading
conditions can be derived. Consequently, the dynamic con-
stitutive models (e.g., viscoelastic constitutive model, strain
rate-dependent dynamic constitutive model, etc.) and the
strength and failure criteria considering the coupled multi-
directional static confining pressures and multi-directional
dynamic compression and thermal conditions are able to be
established.
3.2 3D Dynamic Tension
Rock is more vulnerable to tension than compression
because its tensile strength is significantly lower than its
compressive strength. As rocks are also often subjected to
Fig. 4 Schematic diagram of the dynamic biaxial tension test under
static triaxial confining pressure: a The dynamic and static loadings
on a rock specimen; b a typical loading path of the coupled triaxial
confining pressure and biaxial dynamic tensile load. σtx and σty rep-
resent the dynamic tensile stress applied to specimen along x and y
axes, respectively. Waveform with concave shape is defined as tensile
wave

H.Xie et al.
1 3
tensile loading especially in underground structures, under-
standing the dynamic tensile behavior of rock is of great
importance to the design, construction and stability assess-
ment of rock structures. Although many studies have been
conducted to investigate the mechanical behavior of rock
under dynamic tension, the previous investigations are lim-
ited to 1D loading conditions (Cadoni 2010; Cho etal. 2003;
Huang etal. 2010). Few studies have been performed to
investigate the dynamic tensile strength of rocks under 1D
dynamic tension and hydrostatic static confining pressure
(Zeng etal. 2019). The tensile behavior of rock under the
coupled 3D dynamic tension and static triaxial insitu stress
conditions has not been investigated.
Since the TEHB is capable of applying the coupled multi-
axial static compression and multi-axial dynamic tension on
the rock specimen, it has the ability to carry out the dynamic
tensile test under static confining pressure. Figure4 shows
the schematic diagram of a typical dynamic biaxial tension
test under static triaxial confining pressure, where the static
true triaxial insitu stress is applied to the rock specimen
prior to the biaxial and four-directional synchronous tensile
impact loading. Notably, the static confining pressure can be
applied uniaxially, biaxially or triaxially, and the dynamic
tension can be symmetric/bidirectional, biaxial/four-direc-
tional or true triaxial tension. In addition, the dynamic ten-
sion can be applied to the specimen in an asynchronous
manner similar to the loading paths presented in Fig.3d.
In this way, the dynamic tensile strength, tensile strain and
failure behavior of rocks under the aforementioned loading
conditions can be determined. Consequently, the laboratory
results can be used to build the dynamic tensile constitutive
models and dynamic tensile failure criteria of rocks consid-
ering the coupled multi-directional static confining pressure
and multi-directional dynamic tensile stress.
3.3 3D Dynamic Fracturing
Rock failure is a complex 3D dynamic fracture process under
the impact of internal and external forces and dynamic dis-
turbances. Understanding the 3D dynamic fracture behavior
of rocks is essential for the study of seismic crustal faulting,
reservoir reconstruction of geothermal energy and oil and
gas resources exploitation, rock blasting, rock crack propa-
gation and arrest, and safety and stability assessment of rock
engineering projects such as rock slope, mining structure,
tunnel, dam-base rock structure, etc. Although studies have
been conducted to investigate the dynamic fracture behavior
of rocks subjected to dynamic impact (Freund 1998; Rosakis
etal. 2020), to the best of our knowledge, no research has
been performed to study the 3D dynamic fracturing of rocks
with consideration of the coupled insitu static and dynamic
stress and real-time thermal conditions.
Therefore, based on the TEHB, the dynamic fractur-
ing tests are proposed to explore the 3D dynamic fracture
mechanics of rocks subjected to the coupled insitu static and
dynamic and/or thermal loads. Figure5 shows the two pro-
posed examples of 3D dynamic fracturing tests conducted
on rock specimens with double pre-existing elliptical cracks
under the coupled static and dynamic compression/tension.
With the aid of the advanced measurement and analysis tech-
niques (e.g., high-speed photograph, digital image correla-
tion, electromagnetic radiation, infrared radiation, X-ray CT,
and scanning electron microscope, etc.), the influences of
the confining pressure, the dynamic loading types and pat-
terns, the strain rate, the thermal condition, the specific crack
systems, etc., on the dynamic fracture strength, dynamic
stress intensity, mixed-mode crack initiation, propagation
and termination, rate-dependent fracturing and 3D dynamic
fracture criterion can be determined and established.
4 Summary
The novel TEHB system provides a cutting-edge testing plat-
form for rock dynamics testing with the consideration of the
coupled triaxial dynamic impact under strain rates between
101s−1 and 103s−1, and triaxial static insitu stress. It is supe-
rior over conventional SHBs in precisely, repeatedly and syn-
chronously generation of multiple identical half-sine stress
pulse, multi-directional dynamic impact with the consideration
of the insitu conditions, and in the quick and easy achieve-
ment of stress equilibrium in the rock specimen as well as
achieving higher strain rate. Based on the TEHB, three novel
and essential 3D dynamic tests that could be only performed
using the TEHB are introduced and analyzed in detail. The
3D dynamic compression tests are proposed to determine and
establish the 3D dynamic constitutive models and the strength
and failure criteria of rocks under the coupled multi-directional
dynamic compression and multi-directional static confining
pressure. The 3D dynamic tension tests are to build dynamic
tensile constitutive models and dynamic tensile failure criteria
of rocks considering the coupled multi-directional dynamic
tensile stress and multi-directional static confining pressure.
The 3D dynamic fracturing tests aim to determine and estab-
lish the dynamic fracture strength, mixed-mode crack propaga-
tion, rate-dependent fracturing and 3D dynamic fracture crite-
rion subjected to the coupled insitu static and dynamic loads.
The expected findings from this work could pave the way for
future rock dynamics study and promote the development of
3D rock dynamic theories, which can provide basic dataset
and theoretical support for the design, construction, operation
and stability assessment of rock engineering built in regions
where severe dynamic disturbance and complex tectonic stress
present.

Novel Three-dimensional Rock Dynamic Tests Using theTrue Triaxial Electromagnetic Hopkinson…
1 3
Three types of representative 3D rock dynamic tests are
proposed and introduced in this paper. Note that additional
novel dynamic tests, e.g., the loading and unloading test, the
dynamic repetitive impact test and dynamic direct shear test
considering specific insitu environmental conditions, etc., can
also be further designed and performed with the TEHB.
Fig. 5 Schematic diagram of two typical 3D dynamic fracturing tests
on rock specimens containing pre-existing defect (e.g., cracks, joints,
tunnel shaped holes, etc.) under the coupled static and dynamic load
conditions: a Specimen under the coupled static biaxial confining
pressure and the biaxial and four-directional compression; b, c the
typical loading paths of synchronous and asynchronous biaxial and
four-directional compression, respectively; d specimen under the
coupled static biaxial confining pressure and the symmetric/bidirec-
tional dynamic tensile load; e a typical loading path of the coupled
static compression and dynamic tensile loads. The black points on the
surface of the specimen are speckles for the full-field strain evolution
measurement using the digital image correlation technique

H.Xie et al.
1 3
Acknowledgements This research is financially supported by the
Program for Guangdong Introducing Innovative and Entrepreneurial
Teams (No. 2019ZT08G315) and the Natural Science Foundation of
China (No. 51827901).
Compliance with Ethical Standards
Conflict of Interest We declare that there is no conflict of interest.
Appendix
Supplementary material
A supplementary video is provided for a better under-
standing of the construction and some potential applications
of the true triaxial electromagnetic Hopkinson bar sys-
tem, which can be found online at https ://doi.org/10.6084/
m9.figsh are.11473 737.v1.
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