Self‐similar heterogeneity in granular porous media at the representative elementary volume scale

Abstract

Geometrical measurements of sandstone pore microstructure (e.g., Katz and Thompson, 1985) indicated that both the surface and volume of pores are self‐similar and exhibit the same fractal dimension. This result yields the microscale hydraulic conductivity to be given as a function of the inner and outer cutoffs and fractal dimension. Accordingly, the fractal dimension can be viewed as the imprint of the process responsible for shaping the structure of voids in a porous medium. We show that the same approach can be extended to different porous media, e.g., to granular aggregates, and it can also be used to describe the soil structure at the scale of the representative elementary volume. For this purpose the fractal rock fragmentation model proposed by Turcotte (1986) has been used to derive the particle size distribution for a fractal mixture. Sedimentation of this mixture is then simulated using a ballistic aggregation algorithm, and both the solid phase and the void space geometry of the resulting aggregate are analyzed. The results show that the same fractal dimension embedded in the fragmentation process is preserved by the sedimentation mechanism and it also characterizes the volume of the pore space and the spatial distribution of the particles.