Advertisement

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
  • 292 Downloads

Abstract

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.

Keywords

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

Abbreviations

t

Total time duration of loading of striker bar

Lst

Length of striker bar

cbar

Longitudinal stress wave velocity in bar

εi(t)

Incident strain pulse

εt(t)

Transmission strain pulse

εr(t)

Reflected strain pulse

ε(t)

Strain in specimen

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

Strain rate within specimen

σs(t)

Stress developed in specimen

Ebar

Elastic modulus of bars

ρb

Density of bar

Ab

Cross-sectional area of bars

As

Cross-sectional area of specimen

Vst

Velocity of striker bar

ls

Length of specimen

ρs

Density of specimen

SG

Specific gravity of specimen

σcs

Uniaxial compressive strength

Et

Tangential elastic modulus

σts

Tensile strength

ds

Diameter of specimen

Ws

Weight of specimen

Pg

Gas gun pressure values

σp

Peak stress in specimen

εp

Strains at peak stress

Ed

Dynamic modulus values

DIF

Dynamic increase factors

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

Peak stress from Ramesh (2008)

WT

Energy absorbed by specimen

U

Displacement perpendicular to plane

UR

Out-of-plane rotations

υbar

Poisson’s ratio of the bar

σ*

Normalized equivalent stress

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

Normalized intact equivalent stress

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

Normalized fracture strength

D

Damage

\(\upsigma\)

Actual equivalent stress

σHEL

Equivalent stress at the Hugoniot elastic limit

HEL

Hugoniot elastic limit

PHEL

Pressure component of the HEL

G

Shear modulus

A

Intact normalized strength parameter

B

Fractured normalized strength parameter

C

Strength parameter (for strain rate dependence)

M

Fractured strength parameter (pressure exponent)

N

Intact strength parameter (pressure exponent)

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

Maximum normalized fractured strength

P*

Normalized pressure

P

Actual pressure

T*

Normalized maximum tensile hydrostatic stress

T

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

D1

Parameter for plastic strain to fracture

D2

Parameter for plastic strain to fracture (exponent)

µ

Compressibility factor

K1

First pressure coefficient (equivalent to the bulk modulus)

K2

Second pressure coefficient

K3

Third pressure coefficient

FS

Failure criteria

P

Change in pressure

β

Amount of energy converted to potential or hydrostatic energy

U

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

U(D)

Energy loss in a particular strain increment

derror

Percentage of deviation

le

Smallest element dimension

cs

Speed of the sound wave

Notes

Acknowledgements

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.

References

  1. Anuradha, Mishra S, Chakraborty T, Matsagar V, Chandel P, Singh M (2016) High strain rate response of himalayan quartzitic gneiss by using split Hopkinson pressure bar. In: Rock dynamics: from research to engineering—2nd international conference on rock dynamics and applications, ROCDYN 2016, pp 93–98Google Scholar
  2. ASTM D2113–99 (1999) Standard practice for rock core drilling and sampling of rock for site investigation. American Society for Testing and Materials, West ConshohockenGoogle Scholar
  3. ASTM D7012-14 (2014) Standard test methods for compressive strength and elastic moduli of intact rock core specimens under varying states of stress and temperatures. American Society for Testing and Materials, West ConshohockenGoogle Scholar
  4. Blanton TL (1981) Effect of strain rates from 10– 2 to 10 s– 1 in triaxial compression tests on three rocks. Int J Rock Mech Min Sci Geomech Abstr 18(1):47–62CrossRefGoogle Scholar
  5. Brosch FJ, Schachner K, Blümel M, Fasching A, Fritz H (2000) Preliminary investigation results on fabrics and related physical properties of an anisotropic gneiss. J Struct Geol 22(11–12):1773–1787CrossRefGoogle Scholar
  6. Burger D, Donadon MV, Cristovao F, Muller SF (2009) Formulation and implementation of a constitutive model for brittle materials in Abaqus explicit finite element code. In: Proceedings of COBEM—20th international congress of mechanical engineering, GramadoGoogle Scholar
  7. Chakraborty T, Larcher M, Gebbeken N (2014) Performance of tunnel lining materials under internal blast loading. Int J Protect Struct 5(1):83–96CrossRefGoogle Scholar
  8. Chakraborty T, Mishra S, Loukus J, Halonen B, Bekkala B (2016) Characterization of three himalayan rocks using a split Hopkinson pressure bar. Int J Rock Mech Min Sci 85:112–118CrossRefGoogle Scholar
  9. Chen W, Song B (2011) Split Hopkinson (Kolsky) bar—design, testing and applications. Springer, New YorkCrossRefGoogle Scholar
  10. Chong KP, Hoyt PM, Smith JW, Paulsen BY (1980) Effects of strain rate on oil shale fracturing. Int J Rock Mech Min Sci Geomech Abstr 17(1):35–43CrossRefGoogle Scholar
  11. Cronin DS, Bui K, Kaufmann C, McIntosh G, Berstad T (2003) Implementation and validation of the Johnson–Holmquist ceramic material model in LS-DYNA. In: 4th European LS-DYNA users conference, D-I-47-60Google Scholar
  12. Dai F, Xia KW, Tang LZ (2010) Rate of dependence of the flexural tensile strength of Laurentian granite. Int J Rock Mech Min Sci 47:469–475CrossRefGoogle Scholar
  13. Doan ML, Billi A (2011) High strain rate damage of Carrara marble. Geophys Res Lett 38:1–6CrossRefGoogle Scholar
  14. Dusenberry DO (2010) Handbook for blast resistant design of buildings. Wiley, New York, p 512CrossRefGoogle Scholar
  15. Field JE, Walley SM, Proud WG, Goldrein HT, Siviour CR (2004) Review of experimental techniques for high rate deformation and shock studies. Int J Impact Eng 30(7):725–775CrossRefGoogle Scholar
  16. Grady DE (1995) Shock wave properties of brittle solids. In: Schmidt S (ed) Shock compression of condensed matters. AIP Press, New York, USA, pp 9–20Google Scholar
  17. Hakala M, Kuula H, Hudson JA (2007) Estimating the transversely isotropic elastic intact rock properties for in situ stress measurement data reduction: a case study of the Olkiluoto mica gneiss, Finland. Int J Rock Mech Min Sci 44(1):14–46CrossRefGoogle Scholar
  18. Hao Y, Hao H (2013) Numerical investigation of the dynamic compressive behaviour of rock materials at high strain rate. Rock Mech Rock Eng 46(2):373–388CrossRefGoogle Scholar
  19. Hokka M, Black J, Tkalich D, Fourmeau M, Kane A, Hoang N-H, Li CC, Chen WW, Kuokkala V-T (2016) Effects of strain rate and confining pressure on the compressive behavior of Kuru granite. Int J Impact Eng 91:183–193CrossRefGoogle Scholar
  20. Hong L, Zhou Z, Yin T (2009) Energy consumption in rock fragmentation at intermediate strain rate. J Central South Univ Technol 16:677–682CrossRefGoogle Scholar
  21. Holmquist TJ, Johnson GR (2011) A computational constitutive model for glass subjected to large strains, high strain rates and high pressures. J Appl Mech 78:051003CrossRefGoogle Scholar
  22. ISRM (2014) Suggested methods for determining the dynamic strength parameters and mode-I fracture toughness of rock materials. In: International society for rock mechanics commission on testing methods. The ISRM Suggested Methods for Rock Characterization, Testing, and Monitoring: 2007–2014Google Scholar
  23. Johnson GR, Cook WH (1983) A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. In: Proceedings of 7th international symposium on ballistics, Hague, 19–21 April 1983, pp 541–547Google Scholar
  24. Johnson GR, Holmquist TJ (1994) An improved computational constitutive model for brittle materials. High-pressure science technology. Am Inst Phys 12:981–984Google Scholar
  25. Jiao Y, Hudson JA (1998) Identifying the critical mechanism for rock engineering design. Geotechnique 48(3):319–335CrossRefGoogle Scholar
  26. Kang HM, Kang MS, Kim MS, Kwak HK, Park LJ, Cho SH (2014) Experimental and numerical study of the dynamic failure behavior of rock materials subjected to various impact loads. Struct Under Shock Impact XIII 141:357–367CrossRefGoogle Scholar
  27. Kang M, Cho JW, Kim YG, Park J, Jeong MS, Lee S (2016) Dynamic compressive properties obtained from a split Hopkinson pressure bar test of Boryeong Shale. Met Mater Int 22(5):764–770CrossRefGoogle Scholar
  28. Kimberley J, Ramesh T (2011) The dynamic strength of an ordinary chondrite. Meteor Planet Sci 46:1653–1669CrossRefGoogle Scholar
  29. Klepaczko JR (1990) Behavior of rock-like materials at high strain rates in compression. Int J Plast 6:415–432CrossRefGoogle Scholar
  30. Lankford J (1976) Dynamic strength of oil shale. OnePetro (Society of Petroleum Engineers) 16(1):17–22CrossRefGoogle Scholar
  31. Li XB, Lok TS, Zhao J (2005) Dynamic characteristics of granite subjected to intermediate loading rate. Rock Mech Rock Eng 38(1):21–39CrossRefGoogle Scholar
  32. Li X, Hong L, Yin T (2008) Relationship between diameter of split Hopkinson pressure bar and minimum loading rate under rock failure. J Central South Univ Technol 15:218–223CrossRefGoogle Scholar
  33. Liu S, Xu J (2015) Effect of strain rate on the dynamic compressive mechanical behaviors of rock material subjected to high temperatures. Mech Mater 82:28–38CrossRefGoogle Scholar
  34. Lu YB, Li QM, Ma GW (2010) Numerical investigation of the dynamic compressive strength of rocks based on split Hopkinson pressure bar tests. Int J Rock Mech Min Sci 47(5):829–838CrossRefGoogle Scholar
  35. Lundberg B (1976) A split hopkinson bar study of energy absorption in dynamic rock fragmentation. Int J Rock Mech Mining Sci Geomech Abs 13:187–197CrossRefGoogle Scholar
  36. Martin BE, Heard WF, Loeffler CM, Nie X (2017) Specimen size and strain rate effects on the compressive behavior of concrete. Exp Mech.  https://doi.org/10.1007/s11340-017-0355-2 CrossRefGoogle Scholar
  37. Ming L, Xian-biao M, Li-li C, Rong-rong M, Guang-hui Z (2014) High strain rate effects on mechanical behavior of coal-serial gneiss. Electron J Geotech Eng 19:6035–6046Google Scholar
  38. Mishra S, Meena H, Parashar V, Khetwal A, Chakraborty T, Matsagar V, Chandel P, Singh M (2017) High strain rate response of sedimentary rocks under dynamic loading using split Hopkinson pressure bar. Geotech Geol Eng.  https://doi.org/10.1007/s10706-017-0345-2 CrossRefGoogle Scholar
  39. Ngo T, Mendis P, Gupta A, Ramsay J (2007) Blast loading and blast effects on structures—an overview. Electron J Struct Eng Spec Issue Load Struct 7:76–91Google Scholar
  40. Qi CZ, Wang MY, Qihu Q (2009) Strain-rate effects on the strength and fragmentation size of rocks. Int J Impact Eng 36:1355–1364CrossRefGoogle Scholar
  41. Ramesh KT (2008) High strain rate experiments. Springer handbook of experimental solid mechanics, Part D. Springer, New York, p 33Google Scholar
  42. Shan R, Jiang Y, Li B (2000) Obtaining dynamic complete stress–strain curves for rock using the split Hopkinson pressure bar technique. Int J Rock Mech Min Sci 37:983–992CrossRefGoogle Scholar
  43. Wang ZG, Meyer LW (2010) On the plastic wave propagation along the specimen length in SHPB test. Exp Mech 50:1061–1074CrossRefGoogle Scholar
  44. Wu C, Hao H, Lu Y, Zhou Y (2003) Characteristics of stress waves recorded in small-scale field blast tests on a layered rock–soil site. Géotechnique 53(6):587–599CrossRefGoogle Scholar
  45. Yang SQ, Tian WL, Huang YH, Ranjith PG, Ju Y (2016) An experimental and numerical study on cracking behavior of brittle gneiss containing two non-coplanar fissures under uniaxial compression. Rock Mech Rock Eng 49(4):1497–1515CrossRefGoogle Scholar
  46. Zhang QB, Zhao J (2013) Determination of mechanical properties and full-field strain measurements of rock material under dynamic loads. Int J Rock Mech Min Sci 60:423–439CrossRefGoogle Scholar
  47. Zhang QB, Zhao J (2014) A review of dynamic experimental techniques and mechanical behaviour of rock materials. Rock Mech Rock Eng 47(4):1411–1478CrossRefGoogle Scholar
  48. Zhou YX, Xia K, Li XB, Li HB, Ma GW, Zhao J, Zhou ZL, Dai F (2011) Suggested methods for determining the dynamic strength parameters and mode-I fracture toughness of rock materials. In: The ISRM suggested methods for rock characterization, testing, and monitoring: 2007–2014. International Society for Rock Mechanics Commission on Testing MethodsGoogle Scholar
  49. Zhou Z, Cai X, Zhao Y, Chen L, Xiong C, Li X (2016) Strength characteristics of dry and saturated rock at different strain rates. Trans Nonferrous Met Soc China 26:1919–1925CrossRefGoogle Scholar
  50. Zhu WC, Bai Y, Li XB, Niu LL (2012) Numerical simulation on rock failure under combined static and dynamic loading during SHPB tests. Int J Impact Eng 49:142–157CrossRefGoogle Scholar
  51. Zhu JB, Liao ZY, Tang CA (2016) Numerical SHPB tests of rocks under combined static and dynamic loading conditions with application to dynamic behavior of rocks under in situ stresses. Rock Mech Rock Eng 49(10):3935–3946CrossRefGoogle Scholar
  52. Zou C, Wong LNY (2016) Size and geometry effects on the mechanical properties of Carrara marble under dynamic loadings. Rock Mech Rock Eng 49(5):1695–1708CrossRefGoogle Scholar

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

Personalised recommendations