Water-saturated Granular Materials Research Articles

On unsteady flows of pore pressure-activated granular materials

We investigate mathematical properties of the system of nonlinear partial differential equations that describe, under certain simplifying assumptions, evolutionary processes in water-saturated granular materials. The unconsolidated solid matrix behaves as an ideal plastic material before the activation takes place and then it starts to flow as a Newtonian or a generalized Newtonian fluid. The plastic yield stress is non-constant and depends on the difference between the given lithostatic pressure and the pressure of the fluid in a pore space. We study unsteady three-dimensional flows in an impermeable container, subject to stick-slip boundary conditions. Under realistic assumptions on the data, we establish long-time and large-data existence theory.

Phase speed in water-saturated sand and glass beads at MHz frequencies.

Measurements of the phase velocity of compressional sound waves in water-saturated granular materials are reported for the 1.0-2.0 MHz frequency range. The sound speed estimates are based on travel times through granular layer thicknesses ranging from 8 to 17 mm. Three types of granular media were used: 336 μm median diameter glass beads and two natural sands with median diameters of 219 and 406 μm. These grain sizes and frequency range correspond to 0.5<ka<1.2, where k is the wavenumber and a the grain radius. To remove trapped air, the samples were boiled under pressure before transfer to the measurement tank. The results are compared to previously reported experimental results and to the Schwartz and Plona [J. Appl. Phys. 55(11), 3971-3977 (1984)] multiple scattering prediction, confirming negative dispersion for ka > 0.5. Scaling the data by a factor depending on porosity and grain density reduces the spread among the available phase speed estimates by nearly a factor of 2, from 12.5% to 6.9%.

Ploughing friction on wet and dry sand

The friction for sliding objects over partially water-saturated granular materials is investigated as a function of the water volume fraction. We find that ploughing friction is the main sliding mechanism: The slider leaves a deep trace in the sand after its passage. In line with previous research and everyday experience, we find that the friction force varies nonmonotonically with the water volume fraction. The addition of a small amount of water makes the friction force sharply drop, whereas too much added water causes the friction force to increase again. We present a ploughing model that quantitatively reproduces the nonmonotonic variation of the friction force as a function of water volume fraction without adjustable parameters. In this model, the yield stress of the water-sand mixture controls the depth to which the hemisphere sinks into the sand and the force that is required to plough through the water-sand mixture. We show that the model can also be used for other ploughing friction experiments, such as an ice skate that leaves a ploughing track on ice.

Attenuation and group speed in water-saturated granular materials at MHz frequencies.

Attenuation and group speed measurements are reported for water-saturated granular materials (natural sand and glass beads) at frequencies of 1.0 to 1.8 MHz. Median grain diameters were 219 to 497 μm, corresponding to kd≳1, i.e., the scattering regime. The measurements were made for different thicknesses of sediment resting on a reflective surface using a monostatic geometry. The attenuation estimates compare well with previously reported experimental results and to the predictions of multiple scattering theory, confirming in particular the tendency toward f 4 dependence for kd≳1. Group speed estimates exhibit the negative dispersion predicted by theory and are comparable in magnitude to previously reported measurements made using transmission geometries. It is found that the available data exhibit a O(10)% spread among the sound speed measurements at a given kd value, and that this spread is reduced to 2.2% when the data are scaled by a factor dependent on porosity and grain density, and that essentially all of the reduction can be attributed to differences in porosity.

Sound speed and attenuation in water-saturated granular materials at MHz frequencies

Sound speed and attenuation measurements are reported for water-saturated granular materials (natural sand and glass beads) at frequencies of 1.0 to 1.8 MHz. Median grain diameters were 0.219 to 0.497 mm, corresponding to kd&amp;gt;1, i.e., the scattering regime. The measurements were made for different thicknesses of sediment resting on a reflective surface using a monostatic geometry. The attenuation estimates compare well with previously reported experimental results and to the predictions of multiple scattering theory. The sound speed estimates exhibit the negative dispersion predicted by theory, but compared to previous measurements are biased low by 100 m/s to 200 m/s. It is argued that this bias is due to microbubbles in concentrations of O(10) ppm by volume.

A new methodology to simulate subglacial deformation of water-saturated granular material

Abstract. The dynamics of glaciers are to a large degree governed by processes operating at the ice–bed interface, and one of the primary mechanisms of glacier flow over soft unconsolidated sediments is subglacial deformation. However, it has proven difficult to constrain the mechanical response of subglacial sediment to the shear stress of an overriding glacier. In this study, we present a new methodology designed to simulate subglacial deformation using a coupled numerical model for computational experiments on grain-fluid mixtures. The granular phase is simulated on a per-grain basis by the discrete element method. The pore water is modeled as a compressible Newtonian fluid without inertia. The numerical approach allows close monitoring of the internal behavior under a range of conditions. Our computational experiments support the findings of previous studies where the rheology of a slowly deforming water-saturated granular bed in the steady state generally conforms to the rate-independent plastic rheology. Before this so-called critical state, deformation is in many cases accompanied by volumetric changes as grain rearrangement in active shear zones changes the local porosity. For previously consolidated beds porosity increases can cause local pore-pressure decline, dependent on till permeability and shear rate. We observe that the pore-water pressure reduction strengthens inter-granular contacts, which results in increased shear strength of the granular material. In contrast, weakening takes place when shear deformation causes consolidation of dilated sediments or during rapid fabric development. Both processes of strengthening and weakening depend inversely on the sediment permeability and are transient phenomena tied to the porosity changes during the early stages of shear. We find that the transient strengthening and weakening in turn influences the distribution of shear strain in the granular bed. Dilatant strengthening has the ability to distribute strain during early deformation to large depths, if sediment dilatancy causes the water pressure at the ice–bed interface to decline. Oppositely, if the ice–bed interface is hydrologically stable the strengthening process is minimal and instead causes shallow deformation. The depth of deformation in subglacial beds thus seems to be governed by not only local grain and pore-water feedbacks but also larger-scale hydrological properties at the ice base.

Modeling liquefaction of water saturated granular material under undrained cyclic shearing

The tendency of particles in a water-saturated granular mass to re-arrange into a denser state during cyclic shearing under pressure results in an increase in pore water pressure. The increase in the pore water pressure causes a reduction in the inner particle contact forces, and in turn easier re-arrangement of the particles. Eventually, the material loses its shear strength, partially or almost completely. In this paper, a general three-dimensional continuum mechanics model is presented for the deformation of granular materials. A physically based model is also presented for characterization of liquefaction of the water saturated granular material under undrained cyclic shearing. The model incorporates the fabric of the granular mass, which develops as the frictional granular mass is deformed in shear. It includes the coupling between shearing and excess pore water pressure. The model parameters are estimated, based on the results of cyclic shearing experiments on large hollow cylindrical samples of silica sand. Basically, the calculation results utilizing this model can embody liquefaction phenomena of the water saturated granular material under undrained cyclic shearing.

Effect of porosity on the properties of strain localization in porous media under undrained conditions

Abstract Within the general framework of mixture theory and by introducing the fictitious “fluid phase” as a mixture of a liquid and a gas, the conditions for localization of deformation into a shear band in the incremental response of partially saturated and fully saturated elastic–plastic porous media under undrained conditions are derived. The effect of porosity is included in the derivation. The explicit analytical expressions of the direction of shear band initiation and the corresponding hardening modulus of the porous media for the plane strain case are deduced, and a parametric analysis is made of the influence of the porosity on the properties of strain localization based on Mohr–Coulomb yield criterion. It is found that the dependence of the shear banding properties of partially saturated porous media on the porosity is related to the stress states and Poisson's ratio. However, the properties of the strain localization for the fully saturated porous media are almost independent of Poisson's ratio. Finally, on the basis of Mohr–Coulomb yield criterion, some solutions of the shear banding orientation for water-saturated granular materials are obtained, which are proved to be in good agreement with the experimental results reported by other researchers.

Dynamic Pore-Pressure Fluctuations in Rapidly Shearing Granular Materials

Results from two types of experiments show that intergranular pore pressures fluctuated dynamically during rapid, steady shear deformation of water-saturated granular materials. During some fluctuations, the pore water locally supported all normal and shear stresses, while grain-contact stresses transiently fell to zero. Fluctuations also propagated outward from the shear zone; this process modifies grain-contact stresses in adjacent areas and potentially instigates shear-zone growth.