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

  • Q. B. Zhang
  • J. ZhaoEmail author
Review Paper


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.


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

List of Symbols


Crack length

AB, As, Ashear

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


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


Longitudinal wave speed, shear wave speed and Rayleigh wave speed


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


Frequency factor

f(a/R), f(a/W), f(S/2R)

Geometric correction function


Return force


Dynamic fracture energy


Initial distance between two plates


Velocity of two plates in the Stefan effect equation


Loading history


Kinetic energy of the fragment


Mode I and II fracture toughness


Dynamic crack initiation and propagation toughness

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

Dynamic stress intensity factor


Loading rate of fracture toughness

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

Length of the specimen and the striker bar


Number of reflections


Applied dynamic load

P1, P2

Forces at bar–specimen interfaces


Confining pressure


Activation energy


Air constant in Arrhenius equation


Radius of the specimen


Ratio of stress difference


Span of bending


Transit time to travel through the specimen once


Time to reach stress equilibrium


Time to fracture


Duration of the incident pulse


Rise time of the stress history




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


Volume of liquid


Ejection velocity of fragment


Particle velocity

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

‘Pull-back’ velocity


Velocity of the striker


Width of the specimen


Fracture and damage energy

WIn., WRe., WTr.

Strain energies of the incident, reflected and transmitted stress waves


Energy absorbed by the specimen


Distance from free end to fracture position

Greek Symbols


Angle of the wedge


Shear strain

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

Shear strain rate

\(\varepsilon_{ 1}\)

Axial strain


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


Viscosity of liquid

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

Angular velocities of the specimen ends


Friction coefficient between the wedge and the bar


Poisson’s ratio


Density of the specimen

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

Dynamic stress history

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

Dynamic strength and quasi-static strength


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


Angular velocity of fragment



American Society for Testing and Materials


Brazilian disc


Chevron bend


Cracked chevron notched BD


Cracked chevron NSCB


Continuum damage mechanics


Comité Euro-International du Béton


Crack opening displacement


Crack propagation gauge


Commission on Rock Dynamics


Constant strain rate


Cracked straight through FBD


Compact tension


Dominant crack algorithm


Digital image correlation


Dynamic increase factor


Direct tension


Flattened BD


Finite-element method


Holed cracked BD


Holed cracked FBD


High speed


High strain rate


Indirect tension


Infrared thermography


Intermediate strain rate


International Society for Rock Mechanics


Incubation-time fracture criterion


Loading edge cracks by edge impact


Laser gap gauge


Micromechanical damage mechanics


Notched SCB


Rocking spalling test


Semi-circular bending


Sliding crack model


Statistical crack mechanical model


Stress equilibrium


Scanning electron microscope


Single edge notched bending


Strain gauge


Split Hopkinson bar


Split Hopkinson pressure bar


Split Hopkinson pressure shear bar


Split Hopkinson tension bar


Stress intensity factor


Suggested method


Short rod


Triaxial compression


Three-point bending


Triaxially compressed Hopkinson bar


Torsional split Hopkinson bar


Uniaxial compression


Very high strain rate


Wedge loaded compact tension



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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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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