Abstract
With the rapid development of computer technology, numerical simulations of rock dynamics have been widely carried out. The accuracy of numerical simulations depends on the parameters of the constitutive model. In this paper, the parameters of a Johnson–Holmquist-II (JH-2) constitutive model for granite were determined. First, mechanical and penetration tests were carried out on granite specimens. The mechanical tests included a quasi-static compression test and Brazilian disc splitting test to obtain the basic mechanical parameters and failure modes of granite under impact loading. Then, using the experimental results combined with the existing literature data, the parameters of the JH-2 constitutive model were determined through theoretical derivation. Finally, by comparing the numerical simulation results with the test results, the validity of the parameters was verified. These parameters can better simulate the mechanical response and failure modes of granite under different loads. The material model parameters can provide references for subsequent experiments and related numerical simulations.
Highlights
-
The parameters of a Johnson–Holmquist-II (JH-2) constitutive model for granite were obtained.
-
Various mechanical tests and penetration tests were performed on granite.
-
The model parameters have a wide range of applications.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Availability of Data and Materials
Not applicable.
Code Availability
Not applicable.
Abbreviations
- JH-2:
-
Johnson–Holmquist-II
- HEL:
-
Hugoniot elastic limit
- CRH:
-
Caliber radius head
- σ i :
-
Current equivalent stress
- σ HEL :
-
Equivalent stress at the HEL
- \(\sigma_{i}^{*}\) :
-
Normalized complete strength
- A :
-
Intact material constants
- N :
-
Intact material constants
- C :
-
Strain rate coefficient
- B :
-
Fracture material constants
- M :
-
Fracture material constants
- P :
-
Hydrostatic pressure
- P HEL :
-
Pressure at the HEL
- P * :
-
Normalized hydrostatic pressure
- T :
-
Maximum tensile strength
- T*:
-
Normalized tensile strength
- \(\dot{\varepsilon }\) :
-
Strain rate
- \(\dot{\varepsilon }_{0}\) :
-
Reference strain rate
- \(\dot{\varepsilon }^{*}\) :
-
Dimensionless strain rate
- \(\sigma_{{\text{f}}}^{*}\) :
-
Normalized fracture strength
- SFMAX:
-
The upper limit of the breaking strength
- \(\sigma_{D}^{*}\) :
-
Normalized damaged strength
- D :
-
Damage
- μ :
-
Volumetric strain
- \(\Delta P\) :
-
Pressure variation
- K 1 :
-
Bulk modulus
- K 2 :
-
Pressure coefficient 2
- K 3 :
-
Pressure coefficient 3
- \(\beta\) :
-
Bulk factor
- \(\rho\) :
-
Current density of the material
- \(\rho_{0}\) :
-
Initial density
- \(\varepsilon_{{\text{P}}}^{{\text{f}}}\) :
-
The plastic strain at fracture
- D 1 :
-
Damage parameters
- D 2 :
-
Damage parameters
- \(\Delta \varepsilon_{{\text{p}}}\) :
-
Increment of equivalent plastic strain
- L :
-
Length
- v :
-
Compression rate
- \(\sigma_{x}\) :
-
Stress component
- \(\sigma_{y}\) :
-
Stress component
- t :
-
Thickness
- d :
-
Diameter
- U s :
-
Shock wave velocity
- u p :
-
Particle velocity
- C :
-
Volume sound velocity
- S :
-
Slope of the fitted straight line
- G :
-
Shear modulus
- E :
-
Elastic modulus
- ν :
-
Poisson’s ratio
- μ HEL :
-
Volumetric strain at the HEL
References
Ai HA, Ahrens TJ (2006) Simulation of dynamic response of granite: a numerical approach of shock-induced damage beneath impact craters. Int J Impact Eng 33:1–10. https://doi.org/10.1016/j.ijimpeng.2006.09.046
Cai Y, Yu S, Lu Y (2015) Experimental study on granite and the determination of its true strain-rate effect. Lat Am J Solids Struct 12:675–694. https://doi.org/10.1590/1679-78251331
Dai F, Xia K, Tang L (2010) Rate dependence of the flexural tensile strength of Laurentian granite. Int J Rock Mech Min Sci 47:469–475. https://doi.org/10.1016/j.ijrmms.2009.05.001
Forrestal MJ, Longcope DB (1998) Target strength of ceramic materials for high velocity penetration. J Appl Phys 67(8):3669–3672. https://doi.org/10.1063/1.345322
Forrestal MJ, Tzou DY (1997) A spherical cavity-expansion penetration model for concrete targets. Int J Solid Struct 34(31–32):4127–4146. https://doi.org/10.1016/S0020-7683(97)00017-6
Gomez JT, Shukla A, Sharma A (2001) Static and dynamic behavior of concrete and granite in tension with damage. Theor Appl Fract Mech 36:37–49. https://doi.org/10.1016/s0167-8442(01)00054-4
Grady DE, Kipp ME (1980) Continuum modelling of explosive fracture in oil shale. Int J Rock Mech Min Sci Geomech Abstr 17:147–157. https://doi.org/10.1016/0148-9062(80)91361-3
Holmquist TJ, Johnson GR (2011) A computational constitutive model for glass subjected to large strains, high strain rates and high pressures. J Appl Mech 78:051003. https://doi.org/10.1115/1.4004326
Holmquist TJ, Johnson GR, Lopatin CM, Grady DE, Hertel ES Jr (1995) High strain rate properties and constitutive modeling of glass. Office of Scientific and Technical Information (OSTI), Oak Ridge
Holmquist TJ, Johnson GR, Gerlach CA (2017) An improved computational constitutive model for glass. Philos Trans Math Phys Eng Sci 375:20160182. https://doi.org/10.1098/rsta.2016.0182
Johnson GR, Holmquist TJ (1994) An improved computational constitutive model for brittle materials. AIP Conf Proc 309:981–984
Johnson GR, Holmquist TJ (1999) Response of boron carbide subjected to large strains, high strain rates, and high pressures. J Appl Phys 85:8060–8073. https://doi.org/10.1063/1.370643
Kenkmann T, Poelchau MH, Wulf G (2014) Structural geology of impact craters. J Struct Geol 62:156–182. https://doi.org/10.1016/j.jsg.2014.01.015
Kingsbury SJ, Tsembelis K, Proud WG (2004) The dynamic properties of the Atlanta Stone Mountain granite. AIP Conf Proc 706:1454–1457
Li XB, Lok TS, Zhao J (2004) Dynamic characteristics of granite subjected to intermediate loading rate. Rock Mech Rock Eng 38:21–39. https://doi.org/10.1007/s00603-004-0030-7
Martin DC (1997) Seventeenth Canadian geotechnical colloquium: the effect of cohesion loss and stress path on brittle rock strength. Can Geotech J 34(5):698–725. https://doi.org/10.1139/cgj-34-5-698
Mishra S, Chakraborty T (2019) Determination of high-strain-rate stress–strain response of granite for blast analysis of tunnels. J Eng Mech 145(8):04019057. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001627
Muralha J, Grasselli G, Tatone B, Blümel M, Chryssanthakis P, Yujing J (2014) ISRM suggested method for laboratory determination of the shear strength of rock joints: revised version. Rock Mech Rock Eng 47:291–302. https://doi.org/10.1007/s00603-013-0519-z
Murray YD (2007) Users manual for LS-DYNA concrete material model 159. US Department of Transportation, McLean
Pawel B, Michal K, Roman G, Michal S et al (2020) Fracture and fragmentation of dolomite rock using the JH-2 constitutive model: Parameter determination, experiments and simulations. Int J Impact Eng. https://doi.org/10.1016/j.ijimpeng.2020.103543
Petersen CF (1969) Shock wave studies of selected rocks. Ph.D. Thesis, Stanford University, Stanford, CA
Ramsey JM, Chester FM (2004) Hybrid fracture and the transition from extension fracture to shear fracture. Nature 428(6978):63. https://doi.org/10.1038/nature02333
Riedel W, Thoma K, Hiermaier S (1999) Penetration of reinforced concrete by BETA-B-500 numerical analysis using a new macroscopic concrete model for hydrocodes. In: Proc 9. ISIEMS, Berlin, pp 315–322
Shang JL, Shen LT, Zhao J (2000) Hugoniot equation of state of the Bukit Timah granite. Int J Rock Mech Min Sci 37:705–713. https://doi.org/10.1016/s1365-1609(00)00002-2
Taylor LM, Chen E-P, Kuszmaul JS (1986) Microcrack-induced damage accumulation in brittle rock under dynamic loading. Comput Methods Appl Mech Eng 55:301–320. https://doi.org/10.1016/0045-7825(86)90057-5
Wang H, Shou L, Zhang J (2014) Experiment and numerical analysis of destruction effect of granite target under projectile impact. Chin J Rock Mech Eng 33:366–375
Wang J, Yin Y, Luo C (2018a) Johnson–Holmquist-II(JH-2) constitutive model for rock materials: parameter determination and application in tunnel smooth blasting. Appl Sci 8:1675. https://doi.org/10.3390/app8091675
Wang J, Yin Y, Esmaieli K (2018b) Numerical simulations of rock blasting damage based on laboratory-scale experiments. J Geophys Eng 15:2399–2417. https://doi.org/10.1088/1742-2140/aacf17
Wang Z, Li Y, Huang Y (2020) Determination of JH-2 model parameters and numerical analysis of repeated penetration of granite. J Harbin Inst Technol 52:133–142
Xia K, Nasseri MHB, Mohanty B, Lu F, Chen R, Luo SN (2008) Effects of microstructures on dynamic compression of Barre granite. Int J Rock Mech Min Sci 45:879–887. https://doi.org/10.1016/j.ijrmms.2007.09.013
Xu S, Huang J, Wang P, Zhang C, Zhou L, Hu S (2015) Investigation of rock material under combined compression and shear dynamic loading: an experimental technique. Int J Impact Eng 86:206–222. https://doi.org/10.1016/j.ijimpeng.2015.07.014
Yang R, Bawden WF, Katsabanis PD (1996) A new constitutive model for blast damage. Int J Rock Mech Min Sci Geomech Abstr 33:245–254. https://doi.org/10.1016/0148-9062(95)00064-x
Acknowledgements
Not applicable.
Funding
Not applicable.
Author information
Authors and Affiliations
Contributions
HXH implemented the numerical simulation and wrote the first draft of this paper. WJY and WBL conceptualized the research and contributed to paper revision. XMW provided the research funds. ZYL and XJZ contributed to the experiment implementation and provided relevant data.
Corresponding author
Ethics declarations
Conflict of Interest
The authors know that there is no conflict of interest concerning the publication of this technical note.
Ethics Approval
Not applicable.
Informed Consent
Not applicable.
Statements and Declarations
Not applicable.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Huang, H.X., Yao, W.J., Li, W.B. et al. Determination of and Experimental Research on the Parameters of the Johnson–Holmquist-II (JH-2) Constitutive Model for Granite. Rock Mech Rock Eng 55, 3901–3917 (2022). https://doi.org/10.1007/s00603-022-02845-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00603-022-02845-4