Effective Elastic Properties of Cracked Rocks — An Overview

  • Yves Guéguen
  • Mark Kachanov
Part of the CISM Courses and Lectures book series (CISM, volume 533)


Upper crustal rocks contain cracks of diverse sizes, shapes and orientations. Predicting their influence on the effective elastic properties of a rock poses a challenging problem of considerable interest, in particular to seismologists. In geophysics, theoretical work on this problem is usually complicated by the presence of pore fluids or when the defect-free matrix of a rock is elastically anisotropic, as in the case of shales for example. The first challenge arising in this context is the identification of microstructure-sentive parameters in terms of which the effective elastic constants are to be expressed. Simple parameters such as volume fraction or crack density (as usually defined) may not suffice for capturing the way in which the complex microstructure of a rock determines its effective elasticity. Defect interactions present another challenge and a number of approximate theoretical schemes have been designed to deal with this problem, but their applicability is not always clear. This chapter offers a critical assessment of these questions, putting the emphasis on microcracks as microstructural elements that often have a dominant effect on the overall elasticity. The issues of matrix anisotropy and frequency effects are examined. Because elastic wave velocities carry microstructural information, it is possible and of great interest to extract from them information on pore and crack content, as well as on the presence and properties of pore fluids. Problems related to multiple defects have been discussed in a broader context of mechanics of materials for over half a century. One of the goals of the present work is to bridge a gap in this area between geophysics and the general mechanics of materials. The former does not always utilize the results of the latter; the latter often neglects specific complexities of the former.


Representative Volume Element Geophysical Research Crack Density Porous Rock Transversely Isotropic 
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© CISM, Udine 2011

Authors and Affiliations

  • Yves Guéguen
    • 1
  • Mark Kachanov
    • 2
  1. 1.Laboratoire de GéologieCNRS, Ecole Normale SupérieureParisFrance
  2. 2.Department of Mechanical EngineeringTufts UniversityBostonUSA

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