Estimating the elastic moduli and isotropy of block inmatrix (bim) rocks by computational homogenization

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29 Scopus citations


Block-in-matrix (bim) rocks are comprised of stiffinclusions (blocks) in softer matrix. The heterogeneity and multi-scale nature of bim-rocks makes the evaluation of their mechanical properties a challenging task. In this research we study the elastic moduli (E, v, K. μ) and isotropy of bim-rocks using finite elements based computational homogenization and multi-scale approach. The influence of volumetric block proportion (VBP), block shape and block orientation is presented. Application of multi-scale homogenization method to estimate the elastic moduli of a naturally occurring conglomerate is also reported. When compared to close formsolution of Hashin-Shtrikman the computational homogenization approach shows good agreement for bim-rocks with spherical blocks. For bim-rocks with elliptical blocks the elastic moduli show tangible difference from the closed formsolution, with deviation fromisotropy increasingwith VBP and preferred orientation of blocks. Based on the results of our numerical study we propose a simplified approximation for estimation of elastic moduli of bim-rocks, together with estimates of deviation from isotropy.

Original languageEnglish
Pages (from-to)58-65
Number of pages8
JournalEngineering Geology
StatePublished - 1 Jan 2016


  • Bim-rocks
  • Computational homogenization
  • Elastic moduli
  • Isotropy
  • Multi-scale analysis

ASJC Scopus subject areas

  • Geotechnical Engineering and Engineering Geology
  • Geology


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