Acta Mechanica Solida Sinica

, Volume 22, Issue 3, pp 251–260 | Cite as

Theoretical model of effective stress coefficient for rock/soil-like porous materials

  • Kai Zhang
  • Hui Zhou
  • Dawei Hu
  • Yang Zhao
  • Xiating Feng


Physical mechanisms and influencing factors on the effective stress coefficient for rock/soil-like porous materials are investigated, based on which equivalent connectivity index is proposed. The equivalent connectivity index, relying on the meso-scale structure of porous material and the property of liquid, denotes the connectivity of pores in Representative Element Area (REA). If the conductivity of the porous material is anisotropic, the equivalent connectivity index is a second order tensor. Based on the basic theories of continuous mechanics and tensor analysis, relationship between area porosity and volumetric porosity of porous materials is deduced. Then a generalized expression, describing the relation between effective stress coefficient tensor and equivalent connectivity tensor of pores, is proposed, and the expression can be applied to isotropic media and also to anisotropic materials. Furthermore, evolution of porosity and equivalent connectivity index of the pore are studied in the strain space, and the method to determine the corresponding functions in expressions above is proposed using genetic algorithm and genetic programming. Two applications show that the results obtained by the method in this paper perfectly agree with the test data. This paper provides an important theoretical support to the coupled hydro-mechanical research.

Key words

rock/soil-like porous materials generalized model for effective stress coefficient tensor equivalent connectivity index of pore genetic algorithm 


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  1. [1]
    Terzaghi, K.V., Die Berechnung der durchassigkeitsziffer des Tones aus dem Verlauf der hydrodynamischen Spannungserscheinungen. Sitzungsber. Akad. Wiss. Wien Math Naturwiss, 1923, 132(2A): 105–126.Google Scholar
  2. [2]
    Biot, M.A., General theory of three-dimensional consolidation. Journal of Application Physics, 1941, 12: 155–160.CrossRefGoogle Scholar
  3. [3]
    Walsh, J.B., Effect of pore pressure and confining pressure on fracture permeability. International Journal of Rock Mechanics and Mining Sciences & Geomechanic Abstract, 1981, 18(3): 429–435.CrossRefGoogle Scholar
  4. [4]
    Kranz, R.L., Frankel, A.D., Engelder, T. and Scholz, C.H., The permeability of whole and jointed barre granite. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1979, 16: 225–234.CrossRefGoogle Scholar
  5. [5]
    Lade, P.V. and Boer, R.D., The concept of effective stress for soil, concrete and rock. Geotechnique, 1997, 47(1): 61–78.CrossRefGoogle Scholar
  6. [6]
    Nur, A. and Byerlee, J.D., An Exact Effective Stress Law for Elastic Deformation of Rock with Fluids. Journal of Geophysical Research, 1971, 76(26): 6414–6419.CrossRefGoogle Scholar
  7. [7]
    Shao, J.F., Poroelastic behaviour of brittle rock materials with anisotropic damage. Mechanics of Materials, 1998, 30(1): 41–53.MathSciNetCrossRefGoogle Scholar
  8. [8]
    Shao, J.F., Lu, Y.F. and Lydzba, D., Damage modeling of saturated rocks in drained and undrained conditions. Journal of Engineering Mechanics, ASCE, 2004, 130(6): 733–740.CrossRefGoogle Scholar
  9. [9]
    Karami, H., Experimental Investigation of Poroelastic Behaviour of a Brittle Rock. 1998, University of Lille I: Lille.Google Scholar
  10. [10]
    Bart, M., Shao, J.F. and Lydzba, D., Coupled hydromechanical modeling of rock fractures under normal stress. Canadian Geotechnical Journal, 2004, 41(4): 686–697.CrossRefGoogle Scholar
  11. [11]
    Bernabe, Y., The effective pressure law for permeability in Chelmsford granite and Barre granite. International Journal of Rock Mechanics and Mining Sciences, 1986, 3(3): 267–275.CrossRefGoogle Scholar
  12. [12]
    Sun, P.D., Sun Model and Its Application. Hangzhou: Zhejiang University Press, 2002 (in Chinese).Google Scholar
  13. [13]
    Sun, P.D., Xian, X.F. and Qian, Y.M., Experiment study on the effective stress in coal. Mining Safety & Environmental Protection, 1999, 2: 16–19 (in Chinese).Google Scholar
  14. [14]
    Zhao, Y.S., Hydromechanics in Coal Rock. Beijing: China Coal Industry Publishing House, 1993 (in Chinese).Google Scholar
  15. [15]
    Zhao, Y.S. and Hu, Y.Q., Experimental study of the law of effective stress by methane pressure. Chinese Journal of Geotechnical Engineering, 1995, 17(3): 26–31 (in Chinese).Google Scholar
  16. [16]
    Feng, Z.C., Wu, H. and Zhao, Y.S., The numerical study of effective stresses law of rock mass. Journal of Tai Yuan University of Technology, 2003, 34(6): 713–715 (in Chinese).Google Scholar
  17. [17]
    Zhang, Y.T., Rock Hydraulics and Engineering. Beijing: China Waterpub Press, 2005 (in Chinese).Google Scholar
  18. [18]
    Bear, J., Dynamics of fluids in Porous Media. New York: American Elsevier Publishing Company, 1972.zbMATHGoogle Scholar
  19. [19]
    Qian, J.H. and Yin, Z.Z., Geotechnique Principle and Computing. BeiJing: China Water Power Press, 1996 (in Chinese).Google Scholar
  20. [20]
    Yang, C.X., Evolutionary Identification of Nonlinear Material model. ShenYang: Northeastern University, 2001 (in Chinese).Google Scholar
  21. [21]
    Lu, Y.F., Modelisation de l’endommagement anisotrope des roches saturees in laboratoire de mecanique de lille. University des Sciences et Technologies de Lille, 2002.Google Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2009

Authors and Affiliations

  • Kai Zhang
    • 1
  • Hui Zhou
    • 1
  • Dawei Hu
    • 1
  • Yang Zhao
    • 1
  • Xiating Feng
    • 1
  1. 1.State Key Laboratory of Geomechanics and Geotechnical EngineeringInstitute of Rock and Soil Mechanics, Chinese Academy of SciencesWuhanChina

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