Permeability of deformable soft aggregated earth materials: From single pore to sample cross section

[1] Fluid flow in deformable porous media is of interest in many areas of hydrology, geophysics, and environmental engineering at scales ranging from individual pore to field scale. With increasing interest in pore-scale hydraulics, there is also the need to connect microscale with bulk material properties by suitable upscaling. In this study, fluid permeability through a stack of deforming spherical aggregates is described using analytical and finite element (FE) analyses. The permeability of an entire sample cross section was constructed from analytical estimates of individual pore permeabilities and from numerical solution to steady flow through the entire cross section of the sample. Experimental results of pore deformation within a stack of modeling clay aggregates were compared to FE calculations for two-dimensional cross sections. Results showed that pores within a cubic pack of aggregates deform isotropically even under anisotropic stress conditions. Therefore aggregate arrangement seems to be as important as stress anisotropy to predicting pore shape evolution. Observations of cross sections through a porous sample under compaction showed reduction in both the mean and variance of pore permeability with increasing compaction. Despite predominantly vertical compaction, sample permeability remained nearly isotropic (with only a slight additional decrease in the vertical direction). The Aissen analytical approximation for pore permeability was very similar to numerical results for the entire range of sample deformation, thereby providing a useful tool for estimating sample permeability from images of complex pore cross-sectional areas.