Rock Mechanics and Rock Engineering

, Volume 47, Issue 4, pp 1411–1478 | Cite as

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

Review Paper

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.

Keywords

Rock material Strain rate Experimental techniques Mechanical behaviour Dynamic loading Rock dynamics Dynamic fracture 

List of Symbols

a

Crack length

AB, As, Ashear

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

A(v)

Universal function

Bs, Bws

Thickness of the specimen and wall thickness of the tube specimen

CB, Cs

Longitudinal wave speeds of the bar and the specimen

CL, CS, CR

Longitudinal wave speed, shear wave speed and Rayleigh wave speed

d

Grain size of the specimen

DB, Ds

Diameter of the bar and the specimen

EB, Es

Young’s modulus of the bar and the specimen

E, Ed

Quasi-static and dynamic Young’s modulus

Emax, Emin, Eavg

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

GdC

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

KIC, KIIC

Mode I and II fracture toughness

KId, KID

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

P1, P2

Forces at bar–specimen interfaces

Pc

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

t0

Transit time to travel through the specimen once

tequil

Time to reach stress equilibrium

tf

Time to fracture

tIn.

Duration of the incident pulse

trise

Rise time of the stress history

T

Temperature

Td

Dynamic torque

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

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

v, vlim, vmax

Crack propagation velocity, limit of velocity and maximum velocity

v1, v2

Velocities of fragments

V

Volume of liquid

Veject

Ejection velocity of fragment

Vp

Particle velocity

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

‘Pull-back’ velocity

Vstr

Velocity of the striker

W

Width of the specimen

WFD

Fracture and damage energy

WIn., WRe., WTr.

Strain energies of the incident, reflected and transmitted stress waves

Ws

Energy absorbed by the specimen

xf

Distance from free end to fracture position

Greek Symbols

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

Abbreviations

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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Copyright information

© Springer-Verlag Wien 2013

Authors and Affiliations

  1. 1.École Polytechnique Fédérale de Lausanne (EPFL), School of Architecture, Civil and Environmental Engineering, Laboratory of Rock Mechanics (LMR)LausanneSwitzerland
  2. 2.Department of Civil EngineeringMonash UniversityMelbourneAustralia

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