Abstract
A new approach to the calculation of the elastic bulk modulus of low consolidated porous media is developed based on a physical consolidation model of rocks and the classical Hertz contact theory. The derived analytical relationships for the elastic bulk modulus, which take into account some micro-structural characteristics of packing, are compared with theoretical predictions from various micromechanics theories, Hashin-Shtrikman strict bounds as well as with experimental results available for low consolidated granular materials. The latter comparison demonstrates a good agreement.
Similar content being viewed by others
References
Bedrikovetsky P. (1993) Mathematical Theory of Oil and Gas Recovery: With Applications to ex-USSR Oil and Gas Fields 1st ed. Kluwer Academic Publishers, London-Boston-Dodrecht
Digby P.J. (1981) The effective elastic moduli of porous granular rocks. ASME Journal of Applied Mechanics 48: 803–808
Chang C.S., Chao S.J., Chang Y. (1995) Estimates of elastic moduli for granular material with anisotropic random packing structure. International Journal of Solids and Structures 32(14): 1989–2008
Dvorkin J., Nur A., Yin H. (1994) Effective properties of cemented granular materials. Mechanics of Materials 18(4): 351–366
Gibson, L.J. & Ashby, M.F., 1999. Cellular Solids: Structure and Properties 2nd ed., Cambridge University Press.
Han G., Dusseault M.B. (2003) Description of fluid flow around a wellbore with stress-dependent porosity and permeability. Journal of Petroleum Science and Engineering 40(1-2): 1–16
Hashin Z., Shtrikman S. (1961) Note on a variational approach to the theory of composite elastic materials. Journal of the Franklin Institute 271(4): 336–341
Hertz, H., 1896. Miscellaneous papers. D. E. Jones & G. A. Schott, eds., New York: MacMillan.
Iwata H., Homma T. (1974) Distribution of coordination numbers in random packing of homogeneous spheres. Powder Technology 10(1-2): 79–83
Johnson K.L. (1985) Contact Mechanics. Cambridge University Press, Cambridge [Cambridgeshire]
Johnson K.L. (1982) One hundred years of hertz contact. ARCHIVE: Proceedings of the Institution of Mechanical Engineers 1847-1982 (vols 1-196) 196(1982): 363–378
Kachanov M., Tsukrov I., Shafiro B. (1994) Effective Moduli of Solids With Cavities of Various Shapes. Applied Mechanics Reviews 47(1S): S151–S174
Kováčik J. (2008) Correlation Between Elastic Modulus, Shear Modulus, Poisson’s Ratio and Porosity in Porous Materials. Advanced Engineering Materials 10(3): 250–252
Kováčik J. (1999) Correlation between Young’s modulus and porosity in porous materials. Journal of Materials Science Letters 18(13): 1007–1010
Krajcinovic D. et al (1992) Elastic moduli of perforated plates in the neighborhood of critical state. International Journal of Solids and Structures 29(14-15): 1837–1847
Mallick K. et al (1993) Critical state of a two-dimensional elastic continuum containing elliptical voids. Engineering Fracture Mechanics 46(4): 553–570
Markov K. (2000) Elementary micromechanics of heterogeneous media. In: Markov K., Preziosi L. (eds) Heterogeneous Media: Micromechanics Modeling Methods and Simulations. Birkhäuser, Boston, pp 1–162
Mori T., Tanaka K. (1973) Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metallurgica 21(5): 571–574
Nur A. et al (1998) Critical porosity: a key to relating physical properties to porosity in rocks. The Leading Edge 17(3): 357–362
Panayiotopoulos K. (1989) Packing of sands - A review. Soil and Tillage Research 13(2): 101–121
Sevostianov I., Kachanov M. (2004) Connection between elastic and conductive properties of microstructures with Hertzian contacts. Proc. R. Soc. Lond. A 460: 1529–1534
Smith W.O., Foote P.D., Busang P.F. (1929) Packing of Homogeneous Spheres. Physical Review 34(9): 1271
Tsukamoto H., Kotousov A. (2006) Transformation Toughening in Zirconia-Enriched Composites: Micromechanical Modeling. International Journal of Fracture 139(1): 161–168
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Neto, L.B., Kotousov, A. & Bedrikovetsky, P. Application of Contact Theory to Evaluation of Elastic Properties of Low Consolidated Porous Media. Int J Fract 168, 267–276 (2011). https://doi.org/10.1007/s10704-010-9574-6
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10704-010-9574-6