We study through numerical simulations the dependence of the hydraulic permeability of granular materials on the particle shape and the grain size distribution. Several models of sand are constructed by simulating the settling under gravity of the grains; the friction coefficient is varied to construct packs of different porosity. The size distribution and shapes of the grains mimic real sands. Fluid flow is simulated in the resulting packs using a finite element method and the permeability of the packs is successfully compared with available experimental data. Packs of nonspherical particles are less permeable than sphere packs of the same porosity. Our results indicate that the details of grain shape and size distribution have only a small effect on the permeabilty of the systems studied.
An algorithm is presented for representing irregular particles as clusters of overlapping spheres, for use within discrete element method (DEM) simulations of particulates. The algorithm is sufficiently fast to be implemented on desktop computers. Although volume and moment of inertia comparisons of resulting clusters with prototypical geometric data show that in the region of 50 to 100 spheres may be needed to represent a particle, actual DEM simulations of an unstable pile of simulated particles show that only 10 or so spheres may be sufficient to capture the mechanics of the system.
When Hertz-Mindlin force laws are considered in the context of the effective-medium theory, the predictions yield a constant Poisson coefficient and bulk/shear elastic moduli that scale with pressure with a 1/3 power law exponent (P 1/3 ). This prediction contradicts early and recent experimental findings that conclude moduli grow faster with a 1/2 power law exponent (P 1/2 ). Such a conclusion is also reached by recent second-order corrections to linear elastic theory. In this work we use a discrete-particle method to study the elastic response of a model of sand that is unconsolidated because of cyclic loading. We use a detailed molecular dynamics simulation that accounts for Hertz-type grain interactions and history-dependent shear forces. The porous sand model is constructed from spherical particles whose size distribution mimics well-sorted unconsolidated sands. The geometry of the model is obtained by simulating critical processes in sedimentary rock formations. Hysteretic behavior and relations between the sample bulk modulus, strain, and stress are obtained. The simulated sample reproduces experimental transient and stationary loading-unloading behavior. We find good correspondence of pressure and strain dependence of elastic moduli in our model with semilinear elasticity theory predictions. Simple arguments explain low coordination numbers observed on force-transmitting samples and the tendency to reduce dissipation under cyclic loading. Our approach clearly shows that a Hertz-Mindlin grain interaction is not inconsistent with the experimental P 1/2 behavior of the bulk modulus.
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