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In this paper, an assembly of disordered packings is considered as a suitable set of packing cells of ordered spheres. In consequence, any of its parameters can be obtained by averaging the values of the set. Namely, the density of a packing of ordered spheres is described by two variables: the angle of the base, and the angle of the inclined edge of the associated parallelepiped. Then, the density of a packing of disordered spheres is obtained by averaging the angle of the base, and the subsequent averaging of the other angle, according to the kind of strain induced by the experiment. The average packing yields the density limits of loose sphere assemblies achieved by a process of fluidization and sedimentation in air, in water, and in viscous liquid at zero gravitational force. It also models the close sphere assemblies shaped by gentle tapping, vertical shaking, horizontal and multidirectional vibrations. The theory allows to elucidate the mechanism of each of the limits, as, for example, the metastable columns of spheres in the loosest packing, as well as the random close packing, and crystallization. The limits obtained coincide very well with the published experimental, numerical and theoretical data.

Powders &amp; Grains 2021

An average model for disordered sphere packings

[EPJ Web of Conferences, Volume 249 (2021)](https://www.epj-conferences.org/articles/epjconf/abs/2021/03/contents/contents.html)

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Powders & Grains 2021

Powders & Grains 2021 will be held in Buenos Aires (Argentina, VIRTUAL) July 5, 13, 21, 29 and Aug 6, 2021. The aim of the conference is to give an up-to-date picture of the broad research field of granular media, powders and grains. Contributions from experts around the world will focus on research topics that cover a wide range of open problems in the field.

poster

Knowledge transfer from micromechanics of granular media failure to geohazard forecasting and mitigation has been slow. But in the face of a rapidly expanding data infrastructure on the motion of individual grains for laboratory samples – and ground motion data at the field scale – opportunities to accelerate this knowledge transfer are emerging. In particular, such data assets coupled with data-driven approaches enable a re-examination of granular failure with ‘new eyes’. To this end, effective strategies that can jump scales from bench to field are urgently needed. Here we demonstrate one strategy that focusses on the study of deformation patterns in the precursory failure regime using kinematic data. Unlike previous studies which focus on regions of high strains, here we probe the development and evolution of near- undeforming regions through the lens of explosive percolation. We find a common dynamical signature in which undeforming regions, which are initially transient in the precursory failure regime, become persistent from the time of imminent failure. We demonstrate the robustness of these findings for data on individual grain motions in a classical laboratory test and ground motion in two real landslides at vastly different scales.

Dynamics of undeforming regions in the lead up to failure: jumping scales from lab to field

DEM-simulated model cohesive assemblies of spherical grains of diameter d, with contact tensile strength F_0, once prepared in loose states, are quasistatically subjected to growing isotropic pressure P, and then to triaxial compression, maintaining lateral stresses sigma_2 = sigma_ 3 = P_0 while increasing axial stress 1 = P + q and strain epsilon_1. Reduced pressure P*= d^2 P/F_0 varies from 0.1 (cohesion dominated case, for which systems typically equilibrate with solid fraction Phi = 0.35), to large values for which the cohesionless behavior is retrieved. In triaxial compression, while the moderate strain response (e.g. epsilon_1 = 0.1) is influenced by initial coordination numbers and mesoscale heterogeneities, the approach to the critical state, as both q (deviator) and Phi steadily increase, gets slower for smaller P*. Critical ratio q/p strongly increases for decreasing P* as roughly predicted in an “effective stress” scheme. Anomalously small elastic moduli are observed in the gel-like structures. While extensive geometric rearrangements take place, no shear banding is observed. Loose cohesive granular assemblies are thus capable of large quasistatic stable plastic strains and ductile rupture.

Quasistatic response of loose cohesive granular materials

An average model for disordered sphere packings

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Dynamics of undeforming regions in the lead up to failure: jumping scales from lab to field

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