Speaker: Paul Cupillard

Date: Thursday 19th of January 2023, 1:15pm.

Abstract:

Tectonic processes and the industrial exploitation of the subsurface induce brittle deformations in the earth crust, leading to fractures at all scales. Geological observations have evidenced that a power law is appropriate to describe the density of a fracture set as a function of the fracture size. Nevertheless, for either theoretical or computational reasons, studies on seismic wave propagation in fractured media have been restricted to a short range of fracture sizes so far. In particular, effective medium theories all rely on an Elementary Representative Volume (ERV) consisting of a host matrix in which cracks are included. Assuming the ERV small with respect to the wavelength, then it is in a quasi-static regime of stress so that techniques from micromechanics can be used to compute an equivalent medium.
In the frame of a 18-month post-doc, Anaïs Ibourichène started working on the application of the non-periodic homogenization method to fractured media to go beyond the ERV setting and explore the effect of a wide distribution of crack sizes on seismic wave propagation. I here present the preliminary results obtained by Anaïs in 2D. First, the effective properties computed using the homogenization in the case of Eshelby problems are compared to analytical solutions provided by various effective medium theories. Then, the homogenization is applied to a synthetic mass rock which contains different fracture sets, each set being characterized by a length l (up to λmin/4) and a density d ∼ l−3. Finally, some short-term and long-term perspectives of this work are discussed.