Rock Mechanics and Rock Engineering

, Volume 52, Issue 1, pp 61–81 | Cite as

Dynamic Characterisation of Gneiss

  • Sunita Mishra
  • Anuradha Khetwal
  • Tanusree ChakrabortyEmail author
Original Paper


The present work aims to understand the stress–strain response of a metamorphic rock, and gneiss under high loading rate for different specimen diameters and slenderness ratios through detailed tests. The high strain rate characterisation of gneiss rock is done for two different diameters and five different slenderness ratios of the rock specimens using a 76 mm-diameter split Hopkinson pressure bar (SHPB) device in an effort to understand the standard specimen dimension for gneiss in SHPB test. The stress–strain response of the rock specimens is studied by varying the length of the striker bars and the gas gun pressure values, systematically. The petrological and static characterisation of the gneiss rock is also carried out to assess the response of the rock specimens. Finally, a methodology is proposed to characterize gneiss rock specimens under high loading rate. Furthermore, numerical simulation of SHPB test on gneiss rock is performed using strain rate-dependent Johnson–Holmquist (JH-2) model available in the finite-element software package, LS-DYNA. The simulation results are compared with the experimental data, and thus, the parameters of JH-2 model for gneiss rock are determined.


Energy absorption High strain rate JH-2 model Gneiss Split Hopkinson pressure bar 



Total time duration of loading of striker bar


Length of striker bar


Longitudinal stress wave velocity in bar


Incident strain pulse


Transmission strain pulse


Reflected strain pulse


Strain in specimen

\(\dot {\upvarepsilon }(t)\)

Strain rate within specimen


Stress developed in specimen


Elastic modulus of bars


Density of bar


Cross-sectional area of bars


Cross-sectional area of specimen


Velocity of striker bar


Length of specimen


Density of specimen


Specific gravity of specimen


Uniaxial compressive strength


Tangential elastic modulus


Tensile strength


Diameter of specimen


Weight of specimen


Gas gun pressure values


Peak stress in specimen


Strains at peak stress


Dynamic modulus values


Dynamic increase factors

\(\upsigma _{{\text{p}}}^{*}\)

Peak stress from Ramesh (2008)


Energy absorbed by specimen


Displacement perpendicular to plane


Out-of-plane rotations


Poisson’s ratio of the bar


Normalized equivalent stress

\(\upsigma _{{\text{i}}}^{{\text{*}}}\)

Normalized intact equivalent stress

\(\upsigma _{{\text{f}}}^{{\text{*}}}\)

Normalized fracture strength




Actual equivalent stress


Equivalent stress at the Hugoniot elastic limit


Hugoniot elastic limit


Pressure component of the HEL


Shear modulus


Intact normalized strength parameter


Fractured normalized strength parameter


Strength parameter (for strain rate dependence)


Fractured strength parameter (pressure exponent)


Intact strength parameter (pressure exponent)

\(\upsigma _{{{{\text{f}}_{{\text{max}}}}}}^{{\text{*}}}\)

Maximum normalized fractured strength


Normalized pressure


Actual pressure


Normalized maximum tensile hydrostatic stress


Maximum tensile hydrostatic pressure

\(\dot {\upvarepsilon }\)

Actual strain rate

\({\dot {\upvarepsilon }_0}\)

Reference strain rate

\(\Delta {\upvarepsilon _{\text{p}}}\)

Change in plastic strain upon accumulation of damage

\(\upvarepsilon _{{\text{f}}}^{{\text{p}}}\)

Plastic strain to fracture under constant pressure


Parameter for plastic strain to fracture


Parameter for plastic strain to fracture (exponent)


Compressibility factor


First pressure coefficient (equivalent to the bulk modulus)


Second pressure coefficient


Third pressure coefficient


Failure criteria


Change in pressure


Amount of energy converted to potential or hydrostatic energy


Energy loss corresponding to the increased bulking pressure and reduced deviatoric stress


Energy loss in a particular strain increment


Percentage of deviation


Smallest element dimension


Speed of the sound wave



This work is a part of an ongoing research project funded by the SENS4Metro under Department of Science and Technology (DST), India, Terminal Ballistics Research Laboratory (TBRL), Chandigarh, under Defense Research and Development Organization (DRDO), India. The authors acknowledge the funding provided by DST and TBRL in this work. The authors additionally acknowledge IIT Delhi—DRDO Joint Advanced Research Center (JATC) for providing necessary funding.


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  • Sunita Mishra
    • 1
  • Anuradha Khetwal
    • 1
  • Tanusree Chakraborty
    • 1
    Email author
  1. 1.Department of Civil EngineeringIndian Institute of Technology (IIT) DelhiNew DelhiIndia

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