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

• The elastic moduli of bim-rocks are calculated using computational homogenization.
• High accuracy, compared to Hashin–Shtrikman solution, is attained for bim-rocks with spherical blocks.
• Elastic moduli of bim-rocks with elliptical blocks significantly deviate from the close form solution.
• Deviation increases with block volume proportion and orientation.
• Simplified approximation for estimate of elastic moduli of bim-rocks is provided.

Block-in-matrix (bim) rocks are comprised of stiff inclusions (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, ν, 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 form solution 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 form solution, with deviation from isotropy increasing with 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.