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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. [ABSTRACT FROM AUTHOR]

In situ determination of stress, strength, and deformation of soils for direct assessment of trafficability and susceptibility to compaction has been a long-standing problem in soil mechanics and agricultural engineering. Despite considerable progress in development of sophisticated probes, data interpretation remains in its infancy due to incomplete understanding of soil-probe interaction. In this study we developed a novel theoretical framework for describing pressure and deformation of fluid inclusions within an elasto-plastic soil matrix subject to anisotropic remote stresses that provides the basis for development of in situ probes for stress and deformation measurement. Results showed that for a compressible fluid inclusion (e.g., air) embedded in an elastic matrix, inclusion pressure is determined primarily by the matrix mean stress, Poisson's ratio, and the product of matrix bulk modulus and fluid compressibility. For incompressible fluids (e.g., water), inclusion pressure becomes independent of matrix stiffness. Differences in remote stress affect inclusion shape and influence probe pressure for large deformation due to increasing stress concentration. The solution for an elastic matrix also provides upper and lower bounds for inclusion pressure in an elasto-plastic matrix under isotropic stress. For the more common anisotropic remote stress, inclusion pressure and deformation differ considerably for elastic and elasto-plastic soil matrix. We found that elastic rubber membranes, often used to separate the fluid inclusion from the matrix, do not influence inclusion pressure or shape as long as membrane and soil stiffness are of similar magnitude. Pressure measurements from laboratory and field experiments using the so-called Boiling probe agreed well with inclusion pressures predicted by the proposed model. [ABSTRACT FROM AUTHOR]

A new conjugate gradient algorithm is presented for extracting eigenvalues from large systems of equations encountered in finite element analysis. The new algorithm involves applying the conjugate gradient method (CGM) to a static problem to generate an equivalent tridiagonal matrix used for eigenvalue computation. The eigenvalues of the tridiagonal matrix are then extracted using a QR factorization. The similarity of the new CGM with the Lanczos method is discussed regarding the need for matrix inversion and reorthogonalization. Several examples using the new method are presented to illustrate its performance. [ABSTRACT FROM AUTHOR]