The presence of multi-scaled fractures in the crust of the Earth has been largely evidenced by geological observations that support power laws to describe fracture distribution.

Two main approaches have been developed to study fractured media : numerical simulations of waves or effective medium theories that assumes an Elementary Representative Volume or ERV. Each of these methods focuses on a restricted range of fracture size because of computational or theoretical consideration.

In this work, the non-periodic homogenization is exploited to go beyond size restriction and explore the effective properties of multiscale fractured media. We first ensure that this method can be applied to various scales by comparing its solutions to those of the two previous approaches.

Then, we build a 2D medium that accommodates fractures of various lengths. The density of each fracture set is predicted by a power law function of the fracture size, as supported by geological studies. We evidenced that the non-periodic homogenization is efficient to retrieve the effective properties of fractured media and that this method is well adapted to investigate multiscale fractured medium.


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