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A Review of Dynamic Experimental Techniques and Mechanical Behaviour of Rock Materials

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Abstract

The purpose of this review is to discuss the development and the state of the art in dynamic testing techniques and dynamic mechanical behaviour of rock materials. The review begins by briefly introducing the history of rock dynamics and explaining the significance of studying these issues. Loading techniques commonly used for both intermediate and high strain rate tests and measurement techniques for dynamic stress and deformation are critically assessed in Sects. 2 and 3. In Sect. 4, methods of dynamic testing and estimation to obtain stress–strain curves at high strain rate are summarized, followed by an in-depth description of various dynamic mechanical properties (e.g. uniaxial and triaxial compressive strength, tensile strength, shear strength and fracture toughness) and corresponding fracture behaviour. Some influencing rock structural features (i.e. microstructure, size and shape) and testing conditions (i.e. confining pressure, temperature and water saturation) are considered, ending with some popular semi-empirical rate-dependent equations for the enhancement of dynamic mechanical properties. Section 5 discusses physical mechanisms of strain rate effects. Section 6 describes phenomenological and mechanically based rate-dependent constitutive models established from the knowledge of the stress–strain behaviour and physical mechanisms. Section 7 presents dynamic fracture criteria for quasi-brittle materials. Finally, a brief summary and some aspects of prospective research are presented.

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Abbreviations

a :

Crack length

A B, A s, A shear :

Cross-sectional area of the bar and the specimen, and shear area of the specimen

A(v):

Universal function

B s, B ws :

Thickness of the specimen and wall thickness of the tube specimen

C B, C s :

Longitudinal wave speeds of the bar and the specimen

C L, C S, C R :

Longitudinal wave speed, shear wave speed and Rayleigh wave speed

d :

Grain size of the specimen

D B, D s :

Diameter of the bar and the specimen

E B, E s :

Young’s modulus of the bar and the specimen

E, E d :

Quasi-static and dynamic Young’s modulus

E max, E min, E avg :

Maximum, minimum and average Young’s modulus of the specimen

f :

Frequency factor

f(a/R), f(a/W), f(S/2R):

Geometric correction function

F :

Return force

G dC :

Dynamic fracture energy

h :

Initial distance between two plates

\(\dot{h}\) :

Velocity of two plates in the Stefan effect equation

H:

Loading history

K :

Kinetic energy of the fragment

K IC, K IIC :

Mode I and II fracture toughness

K Id, K ID :

Dynamic crack initiation and propagation toughness

\(K_{\text{I}}^{\text{dyn}} (t)\) :

Dynamic stress intensity factor

\(\dot{K}_{\text{I}}^{\text{dyn}}\) :

Loading rate of fracture toughness

\(L_{\text{s}}\), \(L_{\text{str}}\) :

Length of the specimen and the striker bar

n :

Number of reflections

P(t):

Applied dynamic load

P 1, P 2 :

Forces at bar–specimen interfaces

P c :

Confining pressure

Q :

Activation energy

R:

Air constant in Arrhenius equation

R :

Radius of the specimen

R(t):

Ratio of stress difference

S :

Span of bending

t 0 :

Transit time to travel through the specimen once

t equil :

Time to reach stress equilibrium

t f :

Time to fracture

t In. :

Duration of the incident pulse

t rise :

Rise time of the stress history

T :

Temperature

T d :

Dynamic torque

\(\dot{u}_{1}\), \(\dot{u}_{2}\) :

Velocities at the incident bar–specimen and specimen–transmitted bar interfaces

v, v lim, v max :

Crack propagation velocity, limit of velocity and maximum velocity

v 1, v 2 :

Velocities of fragments

V :

Volume of liquid

V eject :

Ejection velocity of fragment

V p :

Particle velocity

\(\Updelta V_{\text{pb}}\) :

‘Pull-back’ velocity

V str :

Velocity of the striker

W :

Width of the specimen

W FD :

Fracture and damage energy

W In., W Re., W Tr. :

Strain energies of the incident, reflected and transmitted stress waves

W s :

Energy absorbed by the specimen

x f :

Distance from free end to fracture position

α :

Angle of the wedge

γ :

Shear strain

\(\dot{\gamma }(t)\) :

Shear strain rate

\(\varepsilon_{ 1}\) :

Axial strain

\(\varepsilon_{\text{f}}\) :

Strain to failure

\(\varepsilon_{{{\text{In.}}}}\), \(\varepsilon_{{{\text{Re.}}}}\), \(\varepsilon_{{{\text{Tr.}}}}\) :

Incident, reflected and transmitted strains measured by strain gauges on the bars

\(\dot{\varepsilon }\), \(\dot{\varepsilon }_{\lim }\), \(\dot{\varepsilon }_{\text{cri}}\), \(\dot{\varepsilon }_{\hbox{max} }\) :

Strain rate, limit of strain rate, critical strain rate and maximum strain rate

\(\eta\) :

Viscosity of liquid

\(\dot{\theta }_{ 1} (t)\), \(\dot{\theta }_{ 2} (t)\) :

Angular velocities of the specimen ends

\(\mu\) :

Friction coefficient between the wedge and the bar

\(\nu\) :

Poisson’s ratio

\(\rho_{\text{s}}\) :

Density of the specimen

\(\sigma_{\text{d}} (t)\) :

Dynamic stress history

\(\sigma_{\text{d}}\), \(\sigma_{\text{s}}\) :

Dynamic strength and quasi-static strength

\(\sigma_{\text{spall}}\) :

Spalling strength

\(\sigma_{\text{t}}\), \(\sigma_{\text{td}}\) :

Quasi-static and dynamic tensile strength

\(\sigma_{\text{tc}}\), \(\sigma_{\text{tcd}}\) :

Quasi-static and dynamic triaxial compressive strength

\(\sigma_{\text{uc}}\), \(\sigma_{\text{ucd}}\) :

Quasi-static and dynamic uniaxial compressive strength

\(\sigma_{\text{t,max}}^{{_{{{\text{Re.}}}} }}\) :

Maximum reflected tensile stress

\({{\sigma_{\text{ucd}} } \mathord{\left/ {\vphantom {{\sigma_{\text{ucd}} } {\sigma_{\text{uc}} }}} \right. \kern-0pt} {\sigma_{\text{uc}} }}\) :

Normalized dynamic uniaxial compressive strength

\(\sigma_{ 1} - \sigma_{ 3}\) :

Differential stress

\(\dot{\sigma }\) :

Stress rate

\(\tau (t)\) :

Shear stress

\(\tau\), \(\tau_{\text{d}}\) :

Quasi-static and dynamic shear strength

\(\omega\) :

Angular velocity of fragment

ASTM:

American Society for Testing and Materials

BD:

Brazilian disc

CB:

Chevron bend

CCNBD:

Cracked chevron notched BD

CCNSCB:

Cracked chevron NSCB

CDM:

Continuum damage mechanics

CEB:

Comité Euro-International du Béton

COD:

Crack opening displacement

CPG:

Crack propagation gauge

CRD:

Commission on Rock Dynamics

CSR:

Constant strain rate

CSTFBD:

Cracked straight through FBD

CT:

Compact tension

DCA:

Dominant crack algorithm

DIC:

Digital image correlation

DIF:

Dynamic increase factor

DT:

Direct tension

FBD:

Flattened BD

FEM:

Finite-element method

HCBD:

Holed cracked BD

HCFBD:

Holed cracked FBD

HS:

High speed

HSR:

High strain rate

In-DT:

Indirect tension

IRT:

Infrared thermography

ISR:

Intermediate strain rate

ISRM:

International Society for Rock Mechanics

ITFC:

Incubation-time fracture criterion

LECEI:

Loading edge cracks by edge impact

LGG:

Laser gap gauge

MDM:

Micromechanical damage mechanics

NSCB:

Notched SCB

RST:

Rocking spalling test

SCB:

Semi-circular bending

SCM:

Sliding crack model

SCRAM:

Statistical crack mechanical model

SE:

Stress equilibrium

SEM:

Scanning electron microscope

SENB:

Single edge notched bending

SG:

Strain gauge

SHB:

Split Hopkinson bar

SHPB:

Split Hopkinson pressure bar

SHPSB:

Split Hopkinson pressure shear bar

SHTB:

Split Hopkinson tension bar

SIF:

Stress intensity factor

SM:

Suggested method

SR:

Short rod

TC:

Triaxial compression

TPB:

Three-point bending

TriHB:

Triaxially compressed Hopkinson bar

TSHB:

Torsional split Hopkinson bar

UC:

Uniaxial compression

VHSR:

Very high strain rate

WLCT:

Wedge loaded compact tension

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Acknowledgments

This work is supported by the Swiss National Science Foundation (no. 200020_129757) and the China Scholarship Council (CSC). During the preparation of this study, the authors contacted many researchers whose research is relevant to the subject matter, and we appreciate the help and support that they provided by sharing their knowledge and resources. They are Gérard Gary (École Polytechnique), Yang Ju and Ruidong Peng (China University of Mining and Technology), Tohid Kazerani (University of Nottingham), Jianchun Li (Institute of Rock and Soil Mechanics, Chinese Academy of Sciences), Xibing Li (Central South University), Xiao Li (Institute of Geology and Geophysics, Chinese Academy of Sciences), Zhuocheng Ou (Beijing Institute of Technology), Yuri Petrov (St. Petersburg State University, Russia), Fabrice Pierron (University of Southampton), Chun’an Tang (Dalian University of Technology), David Taylor (Trinity College, Ireland), Lili Wang (Ningbo University), Qizhi Wang (Sichuan University), Kaiwen Xia (University of Toronto), Songlin Xu (University of Science and Technology of China), Zhiqiang Yin (Anhui University of Science and Technology), Gaofeng Zhao (The University of New South Wales), Xiaobao Zhao (Nanjing University) and Wancheng Zhu (Northeastern University). A special acknowledgement is given to Mrs Haiying Bian (editorial office of Geomechanics and Geoengineering—An International Journal), who provided language editing for this review.

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  1. École Polytechnique Fédérale de Lausanne (EPFL), School of Architecture, Civil and Environmental Engineering, Laboratory of Rock Mechanics (LMR), Bâtiment GC D0-407, Station 18, 1015, Lausanne, Switzerland

    Q. B. Zhang & J. Zhao

  2. Department of Civil Engineering, Monash University, Building 72, Clayton, Melbourne, VIC, 3800, Australia

    J. Zhao

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  1. Q. B. Zhang
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  2. J. Zhao
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Zhang, Q.B., Zhao, J. A Review of Dynamic Experimental Techniques and Mechanical Behaviour of Rock Materials. Rock Mech Rock Eng 47, 1411–1478 (2014). https://doi.org/10.1007/s00603-013-0463-y

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