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We first phrase a boundary-value problem for a dense, steady, fully-developed, gravitational flow of identical inelastic spheres over in inclined bumpy base in the absence of sidewalls. We then obtain approximate analytical solutions for the profiles of the solid volume fraction, the strength of the velocity fluctuations, and the mean velocity of the flow. We compare these with those obtained in numerical solutions of the exact equations.

Powders &amp; Grains 2021

Analytical solutions for dense, inclined, granular flow over a rigid, bumpy base

[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

Spin rates of minor planets or asteroids are known to have been affected by several agents including but not limited to tidal fly-bys, impacts, and solar radiation. Surface processes like landslides occur as a result of such rotational changes. We study the evolution of landslides on top-shaped rubble pile asteroids like 101955 Bennu and 162173 Ryugu, with the underlying core modeled as two solid cones fused back to back. Using a depth-averaged avalanche theory applicable to granular flows we solve for axisymmetric landslides occurring at various spin rates and regolith friction. Static regions on the surface corresponding to different spin rates are identified from an equilibrium analysis. We then solve for landslides initiated at different latitudes. It is found that landslides equilibrate at lower latitudes as the spin rate is increased. Beyond a critical spin rate regolith is shed from the equator. This critical spin is higher for a lower value of the semi-apex angle of the cone.

Axisymmetric landslides on top-shaped asteroids

Coordination number controls elastic moduli, seismic velocity, and force transmission in sands and is thus a critical factor controlling the resistance of sands to deformation. Previous studies quantified relationships between coordination number, porosity, grain size, sphericity, and effective stress in pluviated or modeled sands. Here, we determine if these relationships hold in naturally-deposited beach sands. We collect samples while preserving their microstructures and use x-ray computed microtomography images to characterize grain properties. Similar to pluviated and modeled sand studies, we find that average coordination numbers and porosities for freshly deposited natural sands are 8.1 ± 2.8 and 0.37 ± 0.01, respectively. The range and standard deviation in coordination numbers of the natural beach sands are, however, significantly higher than observed in pluviated and modeled sand studies. At the same effective stress and porosities, coordination number is linearly proportional to grain surface area except for the smallest and largest grains. Coordination number depends non-linearly on sphericity. We attribute the higher ranges and standard deviations of coordination numbers in the natural sands to its broader grain size distribution, and we propose that the largest grains limit grain rearrangement, which influences spatial distributions of coordination numbers in natural sands.

Coordination numbers in natural beach sand

This presentation includes a numerical technique to prepare dense 2D disc samples with loose contact network using DEM under periodic boundary conditions. We mainly focus on a numerical procedure to control void ratio (e) and coordination number (Z*) for two kinds of samples. It has been achieved by using various interparticle friction coefficient values during isotropic compression and shearing. One dense and one loose sample has been prepared by varying the preparation procedure. For the loose sample we control interparticle friction coefficient values to control density while for the dense sample we add an extra step of dilation thus controlling void ratio and coordination number quasi-independently. As a result of this difference in preparation the dense sample macroscopic angle of friction under shearing has been dictated by its initial void ratio instead of coordination number.

Sample preparation of dense granular materials. Influence of void ratio e and coordination number Z* on the mechanical behaviour at failure

Fluid-driven grain flow through a confined channel filled with non-buoyant grains is herein observed to exist in three regimes according to total imposed flow rate. (1) At low imposed flow rates, no grain flow occurs as the fluid stress is insufficient to mobilise the grains and Darcy flow is observed. (2) At a sufficient imposed flow rate, grains begin to flow at the top of the channel with self-similar Gaussian velocity profiles that become faster and encroach deeper into the channel with increased flow rate. (3) At high flow rates, significant grain flow occurs at the base of the channel, distorting the Gaussian profile, resulting in a gradual transition towards a more symmetric, full-channel flow. Each regime, and the transitions between them, is discussed in relation to experimental grain velocity measurements.

From Darcy to Gaussian to fully mobilised grain flow in a confined channel

Granular packings exhibit significant changes in rheological and structural properties when the rotational symmetry of spherical or circular particles is broken. Here, we report on experiments exploring the differences in dynamics of a grain-scale intruder driven through a packing of either disks or pentagons, where the presence of edges and vertices on grains introduces the possibility of rotational constraints at edge-edge contacts, as well as differences in grain-scale dynamics and stress transmission through the granular material. We observe that the intruder’s stick-slip dynamics are comparable between the disk packing near the frictional jamming fraction and the pentagonal packing at significantly lower packing fractions. We connect this stark contrast in packing fraction with the average speed, rotation, and vorticity fields of grains during slip events, finding that rotation of pentagons is limited and the flow of pentagonal grains is largely confined in front of the intruder, whereas disks rotate more on average and circulate around the intruder to fill the open channel behind it. We lastly observe that the packing of pentagons does not transmit stresses as far around the system as does the packing of disks, even at comparable applied forces from the intruder, and that disks transmit back-bending stress chains more frequently and with greater spatial extent than pentagons. Measures of spatial extent of stress transmission collapse when packing fraction is rescaled with respect to the packing fraction of open channel formation, though intruder dynamics do not collapse. Our results indicate that grain-scale rotation constraints significantly modify collective motion of grains on mesoscopic scales and correspondingly enhance resistance to penetration of a local intruder.

Particle dynamics in two-dimensional point-loaded granular media composed of circular or pentagonal grains

Granular asteroids are naturally occurring gravitational aggregates (rubble piles) bound together by gravitational forces. For this reason, it is reasonable to use the theoretical concepts and numerical tools developed for granular media to study them. In this paper, we extend the field of applicability of the Contact Dynamic (CD) method, a class of non-smooth discrete element approach, for the simulation of three-dimensional granular asteroids. The CD method is particularly relevant to address the study of dense granular assemblies of a large number of particles of complex shape and broad particles size distribution since it does not introduces numerical artefacts due to contact stiffness. We describe how the open-source software LMGC90, interfaced with an external library for the calculation of self-gravity, is used to model the accretion process of spherical and irregular polyhedral particles.

A Contact Dynamics open source code for the simulation of granular asteroid with realistic regolith shapes. Application to the accretion process

Experiments on the discharge of a silo with an inclined outlet are performed using flattened seeds in order to evaluate the validity of a previous theoretical formulation developed in our work group [1]. In that description, funnel flow regime is assumed to be based on a free fall parabolic arc. The shape of this arc is described with a parameter which is the only one involved in the flow rate formulation. An experimental analysis of the behavior of this parameter is carried out based on the geometry and shape of the grains within the silo. Also, video analysis of the silo discharge is performed in order to investigate the velocity profiles at the outlet
of the hopper for these non-spherical particles. Experiments are contrasted with analytical predictions derived from the proposed formulation in order to assess and discuss its validity for the case of flattened particles.

Silo fischarge: influence of the particle shape on the velocity profiles

Through numerical simulations, we investigate impact generated seismic wave transmission in gran-ular media under extremely low pressure. This mimics the conditions in the interior of asteroids and other smallplanetary bodies. We find a dependency not only on the overburden pressure on the medium, but also on thevelocity of the impact that generates the wave. This is, at extremely low values of overburden pressure, the wavespeed depends no only on the imposed pressure, but also on the increment in pressure created by the passingof the wave. We study crystalline and random packings and find very similar behaviour though with differentwave speeds as expected. We then relate our results to different mission-related events on asteroids.

Seismic waves in the asteroid environment

In this work, we present an alternative methodology to solve the particle-fluid interaction in the
resolved CFDEM
R coupling framework. This numerical approach consists of coupling a Discrete Element
Method (DEM) with a Computational Fluid Dynamics (CFD) scheme, solving the motion of immersed particles
in a fluid phase. As a novelty, our approach explicitly accounts for the body force acting on the fluid phase when
computing the local momentum balance equations. Accordingly, we implement a fluid-particle interaction
computing the buoyant and drag forces as a function of local shear strain and pressure gradient. As a benchmark,
we study the Stokesian limit of a single particle. The validation is performed comparing our outcomes with the
ones provided by a previous resolved methodology and the analytical prediction. In general, we find that the
new implementation reproduces with very good accuracy the Stokesian dynamics. Complementarily, we study
the settling terminal velocity of a sphere under confined conditions.

Modeling particle-fluid interaction in a coupled CFD-DEM framework

We revisit the Critical State (CS) in a dynamic perspective at a mesoscopic scale to enrich the classical view of the critical state as a steady state. The dynamics of mesostructures has been characterized by recording generating and vanishing processes in discrete element simulations. Our results suggest that mesostructures have a short but regular lifespan at the critical state along a biaxial compression loading path.

Analytical solutions for dense, inclined, granular flow over a rigid, bumpy base

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