Internal state of granular assemblies near random close packing

The structure of random sphere packings in mechanical equilibrium in prescribed stress states, as studied by molecular dynamics simulations, strongly depends on the assembling procedure. Frictionless packings in the limit of low pressure are devoid of dilatancy, and consequently share the same random close packing density, but exhibit fabric anisotropy related to stress anisotropy. Efficient compaction methods can be viewed as routes to circumvent the influence of friction. Simulations designed to resemble two such procedures, lubrication and vibration (or ``tapping'') show that the resulting granular structures differ, the less dense one having, remarkably, the larger coordination number. Density, coordination number and fabric can thus vary independently. Calculations of elastic moduli and comparisons with experimental results suggest that measurable elastic properties provide information on those important internal state variables.Comment: March 12, 200

Internal states of model isotropic granular packings. II. Compression and pressure cycles

This is the second paper of a series of three investigating, by numerical means, the geometric and mechanical properties of spherical bead packings under isotropic stresses. We study the effects of varying the applied pressure P (from 1 or 10 kPa up to 100 MPa in the case of glass beads) on several types of configurations assembled by different procedures, as reported in the preceding paper. As functions of P, we monitor changes in solid fraction \Phi, coordination number z, proportion of rattlers (grains carrying no force) x0, the distribution of normal forces, the level of friction mobilization, and the distribution of near neighbor distances. Assuming the contact law does not involve material plasticity or damage, \Phi is found to vary very nearly reversibly with P in an isotropic compression cycle, but all other quantities, due to the frictional hysteresis of contact forces, change irreversibly. In particular, initial low P states with high coordination numbers lose many contacts in a compression cycle, and end up with values of z and x0 close to those of the most poorly coordinated initial configurations. Proportional load variations which do not entail notable configuration changes can therefore nevertheless significantly affect contact networks of granular packings in quasistatic conditions.Comment: Published in Physical Review E 12 page

Incremental response of granular materials: DEM results

We systematically investigate the incremental response of various equilibrium states of dense 2D model granular materials, along the biaxial compression path (\sigma 11 < \sigma 22, \sigma 12 = 0). Stress increments are applied in arbitrary directions in 3- dimensional stress space (\sigma 11, \sigma 22, \sigma 12). In states with stable contact networks we compute the stiffness matrix and the elastic moduli, and separate elastic and irreversible strains in the range in which the latter are homogeneous functions of degree one of stress increments. Without principal stress axis rotation, the response abides by elastoplasticity with a Mohr-Coulomb criterion and a non-associated flow rule. However a nonelastic shear strain is also observed for increments of \sigma 12, and shear and in-plane responses couple. This behavior correlates to the distribution of friction mobilization and sliding at contacts.Comment: 4 page

How granular materials deform in quasistatic conditions

Based on numerical simulations of quasistatic deformation of model granular materials, two rheological regimes are distinguished, according to whether macroscopic strains merely reflect microscopic material strains within the grains in their contact regions (type I strains), or result from instabilities and contact network rearrangements at the microscopic level (type II strains). We discuss the occurrence of regimes I and II in simulations of model materials made of disks (2D) or spheres (3D). The transition from regime I to regime II in monotonic tests such as triaxial compression is different from both the elastic limit and from the yield threshold. The distinction between both types of response is shown to be crucial for the sensitivity to contact-level mechanics, the relevant variables and scales to be considered in micromechanical approaches, the energy balance and the possible occurrence of macroscopic instabilitie

Tracer Dispersion in Rough Open Cracks

Tracer dispersion is studied in an open crack where the two rough crack faces have been translated with respect to each other. The different dispersion regimes encountered in rough-wall Hele-Shaw cell are first introduced, and the geometric dispersion regime in the case of self-affine crack surfaces is treated in detail through perturbation analysis. It is shown that a line of tracer is progressively wrinkled into a self-affine curve with an exponent equal to that of the crack surface.This leads to a global dispersion coefficient which depends on the distance from the tracer inlet, but which is still proportional to the mean advection velocity. Besides, the tracer front is subjected to a local dispersion (as could be revealed by point measurements or echo experiments) very different from the global one. The expression of this anomalous local dispersion coefficient is also obtained

Slow quench dynamics of a trapped one-dimensional Bose gas confined to an optical lattice

We analyze the effect of a linear time-variation of the interaction strength on a trapped one-dimensional Bose gas confined to an optical lattice. The evolution of different observables such as the experimentally accessible onsite particle distribution are studied as a function of the ramp time using time-dependent exact diagonalization and density-matrix renormalization group techniques. We find that the dynamics of a trapped system typically display two regimes: for long ramp times, the dynamics are governed by density redistribution, while at short ramp times, local dynamics dominate as the evolution is identical to that of an homogeneous system. In the homogeneous limit, we also discuss the non-trivial scaling of the energy absorbed with the ramp time.Comment: 4 pages, 4 figures, version published in PR

Flow of wet granular materials: a numerical study

We simulate dense assemblies of frictional spherical grains in steady shear flow under controlled normal stress $P$ in the presence of a small amount of an interstitial liquid, which gives rise to capillary menisci, assumed isolated (pendular regime), and to attractive forces. The system behavior depends on two dimensionless control parameters: inertial number $I$ and reduced pressure $P^*=aP/(\pi\Gamma)$, comparing confining forces $\sim a^2P$ to meniscus tensile strength $F_0=\pi\Gamma a$, for grains of diameter $a$ joined by menisci with surface tension $\Gamma$. We pay special attention to the quasi-static limit of slow flow and observe systematic, enduring strain localization in some of the cohesion-dominated ($P^*\sim 0.1$) systems. Homogeneous steady flows are characterized by the dependence of internal friction coefficient $\mu^*$ and solid fraction $\Phi$ on $I$ and $P^*$. We record fairly small but not negligible normal stress differences and the moderate sensitivity of the system to saturation within the pendular regime. Capillary forces have a significant effect on the macroscopic behavior of the system, up to $P^*$ values of several units. The concept of effective pressure may be used to predict an order of magnitude for the strong increase of $\mu^*$ as $P^*$ decreases but such a crude approach is unable to account for the complex structural changes induced by capillary cohesion. Likewise, the Mohr-Coulomb criterion for pressure-dependent critical states is, at best, an approximation valid within a restricted range of pressures, with $P^*\ge 1$. At small enough $P^*$, large clusters of interacting grains form in slow flows, in which liquid bonds survive shear strains of several units. This affects the anisotropies associated to different interactions, and the shape of function $\mu^*(I)$, which departs more slowly from its quasistatic limit than in cohesionless systems.Comment: 20 pages, 29 figures with 39 subfigure

Experimental study of the transport properties of rough self-affine fractures

An experimental study of the transport properties of fluid-saturated joints composed of two complementary rough fracture surfaces, translated with respect to each other and brought in contact, is reported. Quantitative roughness measurements on different fractured granite samples show that the surfaces have a self-affine geometry from which the dependence of the mean aperture on the relative displacement of fracture surfaces kept in contact can be predicted. Variations of the hydraulic and electrical conductances of the joint are measured as functions of its mean aperture. A simple parallel plane model accounts for the global trend of the measurements, but significant deviations are observed when a relative lateral displacement of the surfaces is introduced. A theoretical analysis of their origin shows that they are due both to the randomness of the aperture field and to a nonzero local slope of the surface near the injection hole; the corresponding conductivity fluctuation amplitudes have power law and linear variations with the lateral displacement, and are enhanced by the radial injection geometry