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Ultrasonic elastic‐wave velocities, as well as the stress‐strain behavior, were measured on dry dune sand from Saudi Arabia under hydrostatic loading from 0 to 50 MPa. The samples came from the dune's crest, limb, and base. The experiments included several loading and unloading cycles. All samples exhibited irreversible deformation and porosity reduction during the tests due to grain repacking in low‐stress regimes and grain breakage at higher stress. The loading behavior was plastic, while the unloading/reloading behavior was elastic. In spite of noticeable porosity variations during the experiments, the elastic‐wave velocities mainly depended on the stress rather than on porosity. Our velocity versus stress data is very close to earlier published results, although the provenance of the sand is very different, pointing at a universality of such behavior in loose sand. Our results were matched by the contact Hertz‐Mindlin theory with varying coordination number and shear‐stiffness adjustment. We also offer a new theoretical model for the static bulk modulus measured in these experiments. This model is based on the concept of stress heterogeneity (stress chains or patches) in a granular pack and uses elastic bound averaging of the respective moduli of stressed and unstressed parts of the pack. The same model is used to describe the velocity versus stress behavior. These results and theory constitute a new installment into the published sparse data of the mechanical properties of unconsolidated sand as well as theoretical analyses thereof and are the first ever such data generated in Saudi Arabia. Key Points: New dataset on dune sand, velocity and deformationNew theory for elastic‐wave velocityNew theory for static bulk modulus [ABSTRACT FROM AUTHOR]

Sand and glass bead samples were monotonically loaded from 0 to 50 MPa and then monotonically unloaded, all under hydrostatic stress conditions. Sand deformed irreversibly and its porosity loss was permanent. In contrast, the glass bead deformation was almost fully reversible with the initial porosity recovered. During loading, the static bulk modulus in all sand samples increased from 0 to about 0.5 GPa between 0‐ and 15‐MPa stress and remained constant for the remainder of the loading. Such behavior, somewhat unexpected in a granular system, means that sand deforms as a linear elastic body during loading from 15 to 50 MPa. The unloading behavior was very different—the static bulk modulus almost linearly decreased from about 4 GPa at 50 MPa to zero as the stress was reduced. Once again, this behavior was very different from that observed in glass beads, where the static bulk modulus during loading was essentially the same as during unloading and appeared to be a unique function of stress, independent of the direction of its variation. Moreover, the static and dynamic bulk moduli in glass beads, the latter computed from Vp, Vs, and density measured during the loading/unloading cycle, were very close to each other. In contrast, the dynamic bulk modulus in dry sand exceeded the static modulus during unloading by a factor of 1.5 to 2.0. We used a quantitative theory based on contact mechanics and the concept of stress heterogeneity in particulates to analytically match the observed results. Key Points: Measurements of static moduli of granular materialsDeformation of sand and glass beadsTheoretical explanation of results [ABSTRACT FROM AUTHOR]

A patchy saturated two‐layered porous rock, with each layer filled with a different fluid, is examined. We assume that this system is probed by an elastic wave having a wavelength much larger than the layers' thicknesses. We also assume that the diffusion length is smaller than the thickness of an individual layer, which implies hydraulic disconnection between layers. In the context of Gassmann's fluid substitution theory, we analytically derived an exact expression for the effective fluid bulk modulus assuming that both layers have the same porosity, dry frame, and mineral matrix properties. In addition we derived an approximate solution that works well at relatively high porosities. Both solutions are expressed as a weighted average of the arithmetic and harmonic averages of individual bulk moduli of the pore fluid. These weights are explicitly given as functions of the porosity, the fractional thicknesses of both layers, and the elastic moduli of the constituents. For the approximate solution, one does not require explicit knowledge of the shear modulus of the rock. The comparison with laboratory data showed that, in the case where a porous, isotropic rock is filled with water and gas, the approximate solution can be used to model the measured data for high values of water saturation. Key Points: We derive exact and approximate analytic solutions to model the effective fluid bulk modulus of patchy saturated porous rocksWe compare and validate the solutions with stochastic simulation and laboratory data [ABSTRACT FROM AUTHOR]

The shapes of particles play a crucial role in the transport and mechanical behavior of granular media. How densely particles of a specific shape can be arranged in a given volume has an enormous practical significance for many scientific and industrial fields. We developed a numerical workflow to investigate the effects of irregularly shaped frictionless, convex particles combined with the polydispersity of particle sizes on the porosity, permeability, and elastic bulk modulus of granular porous media. The workflow is based on the computationally generated three‐dimensional granular assemblies of both regular and irregularly shaped particles and pore‐scale simulation of physics to estimate the absolute permeability and elastic bulk modulus of the generated digital granular porous media. Our numerical results show that the porosity decreases by 14–25%, absolute permeability decreases by 45–76%, and elastic bulk modulus increases by 20–66% as we deviate from the regular‐shaped particle with the specified particle size distribution. How rapidly and to what degree these properties of granular assemblies of irregularly shaped particles change depends on particle size distribution. However, once the maximal densest packings of irregularly shaped particles with the prescribed aspect ratio are generated, any further change in the shape of particles has either a minimal impact or an opposite effects are observed. Overall, our numerical observations suggest that the irregular shape of particles has the greatest effect on permeability and the least effect on porosity in both monodisperse and polydisperse granular media. Key Points: We developed a numerical workflow to investigate the effects of irregularly shaped frictionless, convex particles combined with the polydispersity of particle sizes on the physical properties of granular porous mediaHow rapidly and to what degree the properties of granular packings of irregularly shaped particles change depends on the particle size distributionThe irregular shape of particles has the greatest impact on permeability and the least effect on porosity in both monodisperse and polydisperse granular assemblies [ABSTRACT FROM AUTHOR]