Rheology of granular materials composed of crushable particles

Duc-Hanh Nguyen, Émilien Azéma, Philippe Sornay, Farhang Radjaï

We investigate sheared granular materials composed of crushable particles by means of contact dynamics simulations and the bonded-cell model for particle breakage. Each particle is paved by irregular cells interacting via cohesive forces. In each simulation, the ratio of the internal cohesion of particles to the confining pressure, the relative cohesion, is kept constant and the packing is subjected to biaxial shearing. The particles can break into two or more fragments when the internal cohesive forces are overcome by the action of compressive force chains between particles. The particle size distribution evolves during shear as the particles continue to break. We find that the breakage process is highly inhomogeneous both in the fragment sizes and their locations inside the packing. In particular, a number of large particles never break whereas a large number of particles are fully shattered. As a result, the packing keeps the memory of its initial particle size distribution, whereas a power-law distribution is observed for particles of intermediate size due to consecutive fragmentation events whereby the memory of the initial state is lost. Due to growing polydispersity, dense shear bands are formed inside the packings and the usual dilatant behavior is reduced or cancelled. Hence, the stress-strain curve no longer passes through a peak stress, and a progressive monotonic evolution towards a pseudo-steady state is observed instead. We find that the crushing rate is controlled by the confining pressure. We also show that the shear strength of the packing is well expressed in terms of contact anisotropies and force anisotropies. The force anisotropy increases while the contact orientation anisotropy declines for increasing internal cohesion of the particles. These two effects compensate each other so that the shear strength is nearly independent of the internal cohesion of particles.

Inertial shear flow of assemblies of frictionless polygons: Rheology and microstructure

Emilien Azéma, Farhang Radjaï, Jean-Noël Roux

Motivated by the understanding of shape effects in granular materials, we numerically investigate the macroscopic and microstructural properties of anisotropic dense assemblies of frictionless polydisperse rigid pentagons in shear flow, and compare them with similar systems of disks. Once subjected to large cumulative shear strains their rheology and microstructure are investigated in uniform steady states, depending on inertial number I, which ranges from the quasistatic limit (?∼10−5) to 0.2. In the quasistatic limit both systems are devoid of Reynolds dilatancy, i.e., flow at their random close packing density. Both macroscopic friction angle ?
, an increasing function of I , and solid fraction ?, a decreasing function of I, are larger with pentagons than with disks at small I, but the differences decline for larger I and, remarkably, nearly vanish for ?∼0.2. Under growing I , the depletion of contact networks is considerably slower with pentagons, in which increasingly anisotropic, but still well-connected force-transmitting structures are maintained throughout the studied range. Whereas contact anisotropy and force anisotropy contribute nearly equally to the shear strength in disk assemblies, the latter effect dominates with pentagons at small I, while the former takes over for I of the order of 10^-2. The size of clusters of grains in side-to-side contact, typically comprising more than 10 pentagons in the quasistatic limit, very gradually decreases for growing I.

Method for evaluating the compactness of a layer of railway line ballast (patent)

Gilles Saussine, Juan Carlos Quezada, Pierre Breul, Franck Radjai

The method for evaluating the compactness of a layer of railroad ballast near a railroad tie includes at least one step of taking at least two measurements of the penetration resistance of the ballast  near one and the same railroad tie, and a step of calculating the mean value of these measurements of penetration resistance. Also provided are a device for implementing such a method and a method for predicting the settlement of the ballast of a railroad track including a step of evaluating the compactness of a ballast near a railroad tie.

Shear strength and microstructure of polydisperse packings: The effect of size span and shape of particle size distribution

Emilien Azéma, Sandra Linero, Nicolas Estrada, Arcesio Lizcano

By means of extensive contact dynamics simulations, we analyzed the effect of particle size distribution (PSD) on the strength and microstructure of sheared granular materials composed of frictional disks. The PSDs are built by means of a normalized $\beta$ function, which allows the systematic investigation of the effects of both, the size span (from almost monodisperse to highly polydisperse) and the shape of the PSD (from linear to pronouncedly curved). We show that the shear strength is independent of the size span, which substantiates previous results obtained for uniform distributions by packing fraction. Notably, the shear strength is also independent of the shape of the PSD, as shown previously for systems composed of frictionless disks. In contrast, the packing fraction increases with the size span, but decreases with more pronounced PSD curvature. At the microscale, we analyzed the connectivity and anisotropies of the contacts and forces networks. We show that the invariance of the shear strength with the PSD is due to a compensation mechanism which involves both geometrical sources of anisotropy. In particular, contact orientation anisotropy decreases with the size span and increases with PSD curvature, while the branch length anisotropy behaves inversely.