Granular systems are not always homogeneous and can be composed of grains with very different mechanical properties. To improve our understanding of the behavior of real granular systems, in this experimental study, we compress 2D bidisperse \md{systems} made of both soft and rigid grains. By means of a recently developed experimental set-up, \md{from the measurement of the displacement field we can} follow all the mechanical observables of this granular medium from the inside of each particle up to the whole system scale. We \md{are able to} detect the jamming transition from these observables and study their evolution deep in the jammed state for packing fractions as high as $0.915$. We show the uniqueness of the behavior of such a system, \md{in which way} it is similar to purely soft or rigid systems and how it is different from them. This study constitutes the first step toward a better understanding of the mechanical behavior of granular materials that are polydisperse in terms of grain rheology.

Highly strained mixtures of bidimensional soft and rigid grains: an experimental approach from the local scale

The shape of the particles and local friction, separately, are known to strongly affect the macroscopic properties of an assembly of grains. But the combined effects of these two parameters still remain poorly described. By means of extensive two dimensional contact dynamics simulations, we perform a systematic analysis of the interplay between friction and shape on strength properties of granular systems.
The shape of the particles is varied from disks to triangles, while the friction is varied from 0 to 0.7. We find that the macroscopic friction first increases with angularity, but it may decline (for low friction values), saturate (for intermediates friction values), or continue to increase (for large friction values) for the most angular shapes. In other words, the effect of the particle's angularity on the shear strength depends on the level of sliding friction. In contrast, the effect of local friction on the shear strength does not depend on the specific properties of shape. The results presented here highlight the subtle coupling existing between shape and friction effects.

Shape or friction? Which of these characteristics drives the shear strength in granular systems?

Using a numerical approach based on the coupling of the discrete and finite element methods, we explore the variation of the bulk modulus K of soft particle assemblies undergoing isotropic compression. As the assemblies densify under pressure-controlled boundary conditions, we show that the non-linearities of K rapidly deviate from predictions standing on a small-strain framework or the, so-called, Equivalent Medium Theory (EMT). Using the granular stress tensor and extracting the bulk properties of single representative grains under compression, we propose a model to predict the evolution of K as a function of the sample’s solid fraction and a reference state as the applied pressure P-> 0. The model closely reproduces the trends observed in our numerical experiments confirming the behavior scalability of soft particle assemblies from the individual particle scale. Finally, we present the effect of the interparticle friction on K’s evolution and how our model easily adapts to such a mechanical constraint.

Bulk modulus of soft particle assemblies under compression

A very staggering result that has been constantly highlighted in granular media is that the shear strength of granular assemblies is independent of the particle size dispersity. In other words, a packing com- posed of monodisperse particles has similar strength properties to those of polydisperse systems. This has been shown numerically for the simplified case of disc and polygon assemblies in 2D and spheres in 3D. In this pa- per, we use three-dimensional contact dynamics simulations to revisit these results for the more complex case of assemblies composed of highly polydisperse rigid polyhedra. Although non-spherical shapes induce more intricated spatial correlations than spherical shapes because of the multiple contact types (i.e., vertex-face, edge- edge, edge-face, face-face), our numerical data provide evidence that the shear strength independence as the particle size dispersity increases still holds up for assemblies of polyhedra. We explain this finding from com- pensation mechanisms at the micro-scale between geometrical and mechanical anisotropies developed within the assemblies.

Independence of shear strength with particle size dispersity still valid in polyhedral particle assemblies

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

Using a discrete-element approach and a bonding interaction law, we model and test crushable inherently anisotropic structures reminiscent of the layering found in sedimentary and metamorphic rocks. By systematically modifying the level of inherent anisotropy, we characterize the evolution of the failure strength of circular rock samples discretized using a modified Voronoi tesselation under diametral point loading at different orientations relative to the sample’s layers. We characterize the failure strength, which can dramatically increase as the loading becomes orthogonal to the rock layers. We also describe the evolution of the macroscopic failure modes as a function of the loading orientation and the energy consumption at fissuring. Our simulation strategy lets us conclude that the length of bonds between Voronoi cells controls the energy being consumed in fissuring the rock sample, although failure modes and strength are considerably changing. We end up this work showing that the microstructure is largely affected by the level of inherent anisotropy and loading orientation.

Strength and energy consumption of inherently anisotropic rocks at failure

Size limitations of geotechnical testing equipment often require that samples of coarse granular materials have to be scaled in order to be tested in the laboratory. Scaling implies a convenient modification of the particle size distribution (PSD) to reduce particle sizes. However, it is well known that particle size and shape may be correlated in nature, due to geological factors (as an example). By means of two-dimensional contact dynamics simulations, we analyzed the e↵ect of altering the size span on the shear strength of granular materials when particle size and shape are correlated. Two di↵erent systems were considered: one made of only circular particles, and the second made of size-shape correlated particles. By varying systematically the size span we observed that the resulting alteration of material strength is not due to the change in particle sizes. It results instead from the variation of the particle shapes induced by the modification of the PSD, when particle size and particle shape are correlated. This finding suggests that particle shape distribution is a higher order factor than PSD for the shear strength of granular materials. It also highlights the importance of particle shape quantification in soil classification and the case for its consideration in activities such as sampling, sub- sampling, and scaling of coarse materials for geotechnical testing

Impact of sample scaling on shear strength: coupled effects of grains size and shape

We use bi-dimensional non-smooth contact dynamics simulations to analyze the isotropic compaction of mixtures composed of rigid and deformable incompressible particles. Deformable particles are modeled using the finite-element method and following a hyper-elastic neo-Hookean constitutive law. The evolution of the packing fraction, bulk modulus, and particle connectivity, beyond the jamming point, are characterized as a function of the applied stresses for a different proportion of rigid/soft particles and two values of friction coefficient. Based on the granular stress tensor, a micro-mechanical expression for the evolution of the packing fraction and the bulk modulus are proposed. This expression is based on the evolution of the particle connectivity together with the bulk behavior of a single representative deformable particle. A constitutive compaction equation is then introduced, set by well-defined physical quantities, given a direct prediction of the maximum packing fraction $\phi_{max}$ as a function of the proportion of rigid/soft particles.

Emilien Azéma

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