Acta Mechanica Solida Sinica

, Volume 29, Issue 1, pp 13–21 | Cite as

A Dynamic Micromechanical Constitutive Model for Frozen Soil under Impact Loading

  • Qijun Xie
  • Zhiwu Zhu
  • Guozheng Kang


By taking the frozen soil as a particle-reinforced composite material which consists of clay soil (i.e., the matrix) and ice particles, a micromechanical constitutive model is established to describe the dynamic compressive deformation of frozen soil. The proposed model is constructed by referring to the debonding damage theory of composite materials, and addresses the effects of strain rate and temperature on the dynamic compressive deformation of frozen soil. The proposed model is verified through comparison of the predictions with the corresponding dynamic experimental data of frozen soil obtained from the split Hopkinson pressure bar (SHPB) tests at different high strain rates and temperatures. It is shown that the predictions agree well with the experimental results.

Key Words

frozen soil dynamic micromechanical model debonding damage theory SHPB 


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  1. 1.
    French, H.M., The Periglacial Environment (2nd edition). England, 1996.Google Scholar
  2. 2.
    Fossum, A.F. and Fredrich, J.T., Cap plasticity models and compactive and pliant pre-failure deformation. In: Proceedings of the Fourth North American Rock Mechanics Symposium, NARMS2000, Seattle, Washington, 2000: 1169–1176.Google Scholar
  3. 3.
    Ma, Q.Y., Experimental analysis of dynamic mechanical properties for artificially frozen clay by the split Hopkinson pressure bar. Journal of Applied Mechanics and Technical Physics, 2010, 51(3): 448–452.CrossRefGoogle Scholar
  4. 4.
    Zhang, H., Zhu, Z., Song. S., et al., Dynamic behavior of frozen soil under uniaxial strain and stress conditions. Applied Mathematics and Mechanics, 2013, 34: 229–238.CrossRefGoogle Scholar
  5. 5.
    Lee, M.Y., Fossum, A., Costin, L.S., et al., Frozen Soil Material Testing and Constitutive Modeling. Report No. SAND2002-0524. Sandia National Laboratory, USA, 2002.Google Scholar
  6. 6.
    Ma, Q.Y., Study on the Dynamic Mechanical Properties of Frozen Soil under Impact Loading. Beijing University of Science and Technology, 2005.Google Scholar
  7. 7.
    Tohgo, K. and Chou, T.W. Incremental theory of particulate-reinforced composites including debonding damage. JSME International Journal. Series A, Mechanics and Material Engineering, 1996, 39(3): 389–397.CrossRefGoogle Scholar
  8. 8.
    Tohgo, K. and Weng, G.J., A progressive damage mechanics in particle-reinforced metal-matrix composites under high triaxial tension. Journal of Engineering Materials and Technology (United States), 1994, 116(3): 414–420.CrossRefGoogle Scholar
  9. 9.
    Eshelby, J.D., The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1957, 241(1226): 376–396.MathSciNetCrossRefGoogle Scholar
  10. 10.
    Mori, T. and Tanaka, K., Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metallurgica, 1973, 21(5): 571–574.CrossRefGoogle Scholar
  11. 11.
    Chen, J.K., Huang, Z.P. and Mai, Y.W., Constitutive relation of particulate-reinforced viscoelastic composite materials with debonded microvoids. Acta Materialia, 2003, 51(12): 3375–3384.CrossRefGoogle Scholar
  12. 12.
    Ning, J.G., Wang, H., Zhu, Z.W. and Sun, Y.X., Investigation of the constitutive model of frozen soil based on meso-mechanics. Transactions of Beijing Institute of Technology, 2005, 25(10): 847–851.Google Scholar
  13. 13.
    Ning, J.G. and Zhu, Z.W., Constitutive model of frozen soil with dynamic and numerical simulation of the coupled problem. Chinese Journal of Theoretical and Applied Mechanics, 2007, 39: 70–76.Google Scholar
  14. 14.
    Chen, L.J., Research on Constitutive Model of Frozen Soil Based on Composite Mechanics. Northwest A&F University, 2010.Google Scholar
  15. 15.
    Tohgo, K., Itoh, Y. and Shimamura, Y., A constitutive model of particulate-reinforced composites taking account of particle size effects and damage evolution. Composites Part A: Applied Science and Manufacturing, 2010, 41(2): 313–321.CrossRefGoogle Scholar
  16. 16.
    Wang, J., Damage Evolution and Constitutive Relation of Particulate-reinforced Composites. Yanshan University, 2011.Google Scholar
  17. 17.
    Wang, W.B. and Shenoi, R.A., Investigating high strain rate behaviour of unidirectional composites by a visco-elastic model. Journal of Ship Mechanics, 2009, 13(3): 406–415.Google Scholar
  18. 18.
    Karim, M.R., Constitutive Modeling and Failure Criteria of Carbon-fiber Reinforced Polymers under High Strain Rates. The University of Akron, 2005.Google Scholar
  19. 19.
    Qu, G.Z., Zhang, J.M., Zhang, B. and Qin, Y.H., Thermodynamic theory to unfrozen water content of frozen soil under heat exchange. Science Technology and Engineering, 2008, 18(5): 1671–1891 (in Chinese).Google Scholar
  20. 20.
    Liu, B. and Li, D.Y., Test study of unfrozen water content in artificial frozen silt. Chinese Journal of Rock Mechanics and Engineering, 2012, 31: 3696–3702.Google Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2016

Authors and Affiliations

  1. 1.School of Mechanics and EngeeringSouthwest Jiaotong UniversityChengduChina
  2. 2.State Key Laboratory of Frozen Soil Engineering, Cold and Arid Regions Environmental and Engineering Research InstituteChinese Academic SciencesLanzhouChina
  3. 3.State Key Laboratory of Explosion Science and TechnologyBeijing Institute of TechnologyBeijingChina

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