Investigating the impact of fracture orientation deviation on elastic effective properties using the non-periodic homogenization

Anais Ibourichene and Paul Cupillard and Jean-Fran├žois Barthelemy. ( 2020 )
in: 2020 RING Meeting, ASGA

Abstract

The equivalent elastic properties of a fractured medium is currently approached by various effective medium theories or numerical modelling of seismic wave propagation. However, these methods are limited by computational considerations and scale separation. This study proposes to extend the use of the non-periodic homogenization to fractured media. This method enables to go beyond size restriction and opens the path to the effective properties of multi-scale fractured media. First, the non-periodic homogenization is challenged towards well-established effective medium theories in the framework of the Eschelby problem. Elliptical fractures embedded in a 2D medium are depicted and the effective stiffness tensor obtained by the homogenization is compared to solutions predicted by effective medium theories. The non-periodic homogenization is best described by the differential scheme in the case of flat fractures whereas the NIA approximation is preferred for ellipses with an aspect ratio greater than 0.1. In a second part, the variation of the stiffness matrix induced by a fracture orientation deviation is quantified and set up against the effects of the fracture length and the aspect ratio.

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BibTeX Reference

@INPROCEEDINGS{IBOURICHENE_RM2020,
    author = { Ibourichene, Anais and Cupillard, Paul and Barthelemy, Jean-Fran├žois },
     title = { Investigating the impact of fracture orientation deviation on elastic effective properties using the non-periodic homogenization },
 booktitle = { 2020 RING Meeting },
      year = { 2020 },
 publisher = { ASGA },
  abstract = { The equivalent elastic properties of a fractured medium is currently approached by various effective medium theories or numerical modelling of seismic wave propagation. However, these methods are limited by computational considerations and scale separation. This study proposes to extend the use of the non-periodic homogenization to fractured media. This method enables to go beyond size restriction and opens the path to the effective properties of multi-scale fractured media. First, the non-periodic homogenization is challenged towards well-established effective medium theories in the framework of the Eschelby problem. Elliptical fractures embedded in a 2D medium are depicted and the effective stiffness tensor obtained by the homogenization is compared to solutions predicted by effective medium theories. The non-periodic homogenization is best described by the differential scheme in the case of flat fractures whereas the NIA approximation is preferred for ellipses with an aspect ratio greater than 0.1. In a second part, the variation of the stiffness matrix induced by a fracture orientation deviation is quantified and set up against the effects of the fracture length and the aspect ratio. }
}