Search

[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.

[ 1] This study develops a framework for modeling deformation of individual pores in elastoviscoplastic earth material accounting for the effects of evolving pore size and shape on material hydraulic permeability. We describe the velocity field of a fluid within deforming pores of hypotrochoidal cross-sectional areas as a function of remote stress or deformation and elastoviscoplastic material properties using finite element analysis. We find that pore permeability decreases with increasing stress and deformation. Pore cross-sectional areas are mainly reduced in size while the shape remains constant. Under stress-controlled conditions, change in permeability depends on matrix constitutive laws and loading time while there is no such dependency for controlled strain. Permeability estimates based on the hydraulic radius, Saint-Venant, and Aissen approximations were in good agreement with numerical calculations for a deforming hypotrochoidal pore. We also show that permeability of a deforming hypotrochoidal pore can be modeled using a pore with equivalent elliptical cross-sectional area ( equal initial permeability and size), providing the ellipse has the correct orientation. The study shows that fluid flow in deforming elastoviscoplastic earth material can be modeled on the pore scale knowing the evolution of pore size and shape employing rather simple relations between pore cross-sectional geometry and permeability.