Farhang Radjai

Contact forces in a granular packing

We present the results of a systematic numerical investigation of force distributions in granular packings. We find that all the main features of force transmission previously established for two-dimensional systems of hard particles hold in three-dimensional systems and for soft particles, too. In particular, the probability distribution of normal forces falls off exponentially for forces above the mean force. For forces below the mean, this distribution is either a decreasing power law when the system is far from static equilibrium, or nearly uniform at static equilibrium, in agreement with recent experiments. Moreover, we show that the forces below the mean do not contribute to the shear stress. The subnetwork of the contacts carrying a force below the mean thus plays a role similar to a fluid surrounding the solid backbone composed of the contacts carrying a force above the mean. We address the issue of the computation of contact forces in a packing at static equilibrium. We introduce a model with no local simplifying force rules, that allows for an exact computation of contact forces for given granular texture and boundary conditions. (c) 1999 American Institute of Physics.

Shear strength properties of wet granular materials.

We investigate shear strength properties of wet granular materials in the pendular state (i.e., the state where the liquid phase is discontinuous) as a function of water content. Sand and glass beads were wetted and tested in a direct shear cell and under various confining pressures. In parallel, we carried out three-dimensional molecular dynamics simulations by using an explicit equation expressing capillary force as a function of interparticle distance, water bridge volume, and surface tension. We show that, due to the peculiar features of capillary interactions, the major influence of water content over the shear strength stems from the distribution of liquid bonds. This property results in shear strength saturation as a function of water content. We arrive at the same conclusion by a microscopic analysis of the shear strength. We propose a model that accounts for the capillary force, the granular texture, and particle size polydispersity. We find fairly good agreement of the theoretical estimate of the shear strength with both experimental data and simulations. From numerical data, we analyze the connectivity and anisotropy of different classes of liquid bonds according to the sign and level of the normal force as well as the bond direction. We find that weak compressive bonds are almost isotropically distributed whereas strong compressive and tensile bonds have a pronounced anisotropy. The probability distribution function of normal forces is exponentially decreasing for strong compressive bonds, a decreasing power-law function over nearly one decade for weak compressive bonds, and an increasing linear function in the range of tensile bonds. These features suggest that different bond classes do not play the same role with respect to the shear strength.

Turbulentlike Fluctuations in Quasistatic Flow of Granular Media

We analyze particle velocity fluctuations in a simulated granular system subjected to homogeneous quasistatic shearing. We show that these fluctuations share the following scaling characteristics of fluid turbulence in spite of their different physical origins: (i) scale-dependent probability distribution with non-Gaussian broadening at small time scales; (ii) spatial power spectrum of the velocity field showing a power-law decay, reflecting long-range correlations and the self-affine nature of the fluctuations; and (iii) superdiffusion of particles with respect to the mean background flow.

Quasistatic rheology, force transmission and fabric properties of a packing of irregular polyhedral particles

By means of contact dynamics simulations, we investigate a dense packing composed of polyhedral particles under quasistatic shearing. The effect of particle shape is analyzed by comparing the polyhedra packing with a packing of similar characteristics except for the spherical shape of the particles. The polyhedra packing shows higher shear stress and dilatancy but similar stress-dilatancy relation compared to the sphere packing. A harmonic approximation of granular fabric is presented in terms of branch vectors (connecting particle centers) and contact force components along and perpendicular to the branch vectors. It is found that the origin of enhanced shear strength of the polyhedra packing lies in its higher force anisotropy with respect to the sphere packing which has a higher fabric anisotropy. Various contact types (face-vertex, face-face, etc) contribute differently to force transmission and fabric anisotropy. In particular, most face-face contacts belong to strong force chains along the major principal stress direction whereas vertex-face contacts are correlated with weak forces and oriented on average along the minor principal stress direction in steady shearing.

Stress-strain behavior and geometrical properties of packings of elongated particles

We present a numerical analysis of the effect of particle elongation on the quasistatic behavior of sheared granular media by means of the contact dynamics method. The particle shapes are rounded-cap rectangles characterized by their elongation. The macroscopic and microstructural properties of several packings subjected to biaxial compression are analyzed as a function of particle elongation. We find that the shear strength is an increasing linear function of elongation. Performing an additive decomposition of the stress tensor based on a harmonic approximation of the angular dependence of branch vectors, contact normals, and forces, we show that the increasing mobilization of friction force and the associated anisotropy are key effects of particle elongation. These effects are correlated with partial nematic ordering of the particles which tend to be oriented perpendicular to the major principal stress direction and form side-to-side contacts. However, the force transmission is found to be mainly guided by cap-to-side contacts, which represent the largest fraction of contacts for the most elongated particles. Another interesting finding is that, in contrast to shear strength, the solid fraction first increases with particle elongation but declines as the particles become more elongated. It is also remarkable that the coordination number does not follow this trend so that the packings of more elongated particles are looser but more strongly connected.

Identification of rolling resistance as a shape parameter in sheared granular media.

Using contact dynamics simulations, we compare the effect of rolling resistance at the contacts in granular systems composed of disks with the effect of angularity in granular systems composed of regular polygonal particles. In simple shear conditions, we consider four aspects of the mechanical behavior of these systems in the steady state: shear strength, solid fraction, force and fabric anisotropies, and probability distribution of contact forces. Our main finding is that, based on the energy dissipation associated with relative rotation between two particles in contact, the effect of rolling resistance can explicitly be identified with that of the number of sides in a regular polygonal particle. This finding supports the use of rolling resistance as a shape parameter accounting for particle angularity and shows unambiguously that one of the main influencing factors behind the mechanical behavior of granular systems composed of noncircular particles is the partial hindrance of rotations as a result of angular particle shape.

Force chains and contact network topology in sheared packings of elongated particles.

By means of contact dynamic simulations, we investigate the contact network topology and force chains in two-dimensional packings of elongated particles subjected to biaxial shearing. The morphology of large packings of elongated particles in quasistatic equilibrium is complex due to the combined effects of local nematic ordering of the particles and orientations of contacts between particles. The effect of elongation on shear behavior and dilatancy was investigated in detail in a previous paper [Azéma and Radjai, Phys. Rev. E 81, 051304 (2010)]. Here, we show how particle elongation affects force distributions and force-fabric anisotropy via various local structures allowed by steric exclusions and the requirement of force balance. We find that the force distributions become increasingly broader as particles become more elongated. Interestingly, the weak force network transforms from a passive stabilizing agent with respect to strong force chains to an active force-transmitting network for the whole system. The strongest force chains are carried by side-side contacts oriented along the principal stress direction.

Features of static pressure in dense granular media

Abstract It is shown that the partial pressure, i.e. the contribution of contacts with a given force to the total average pressure, in a granular packing in quasistatic flow increases linearly from zero with the force level both in two and three dimensions. It reaches its maximum for the average force and decays for larger forces. We found that a well-defined sub-texture, composed of the contacts carrying a force below the average force, does not contribute to the shear stress, so that its contribution to the average pressure is mechanically similar to a hydrostatic pressure.

Stress transmission in wet granular materials.

Abstract.We analyze stress transmission in wet granular media in the pendular state by means of three-dimensional molecular-dynamics simulations. We show that the tensile action of capillary bonds induces a self-stressed particle network organized in two percolating “phases” of positive and negative particle pressures. Various statistical descriptors of the microstructure and bond force network are used to characterize this partition. Two basic properties emerge: 1) the highest particle pressure is located in the bulk of each phase; 2) the lowest pressure level occurs at the interface between the two phases, involving also the largest connectivity of the particles via tensile and compressive bonds. When a confining pressure is applied, the number of tensile bonds falls off and the negative phase breaks into aggregates and isolated sites.

Cohesive granular texture

We investigate the textural properties of cohesive 2D granular packings simulated by means of the molecular dynamics and contact dynamics methods involving simple contact laws with adhesion. We find that, while tensile forces appear naturally in response to external tensile loading, they appear only for a strong adhesion when the applied load is compressive in all directions. We introduce an adhesion index which represents the extent of activation of attractive forces compared to an external loading. The evolution of the tensile pressure and the average coordination number with the adhesion index suggests a transition between two regimes. In a first regime, the adhesion gives mainly rise to a geometrical rearrangement of the texture. In particular, the coordination number increases with the adhesion index. In a second regime, the adhesion entails a force reorganization involving tensile force chains and a partial crystallization of the contact network. Finally, we analyze the contribution of the tensile and compressive forces to shear stress and fabric anisotropy. An interesting result is that tensile forces play the same role in the stability of a cohesive packing as weak compressive forces.