Stress transmission in cemented bidisperse granular materials

We analyze stress distributions in a two-dimensional bidisperse cemented granular packing for a broad range of the values of particle-size ratio, the volumes of large and small particles, and the amount of cementing matrix. In such textured porous materials, the stress concentration, which controls the fracture and fragmentation of the material under tensile loading or in grinding processes, reflects not only the porosity but also the contact network of the particle phase and the resulting stress chains. By means of peridynamic simulations under tensile loading, we show how both the texture and stress distribution depend on size ratio, volume ratio, and the amount of the cementing matrix. In particular, the volume fraction of the class of small particles plays a key role in homogenizing stresses across the system by reducing porosity. Interestingly, the texture controls not only the porosity but also the distribution of pores inside the system with its statistical variability, found to be strongly correlated with the homogeneity of stresses inside the large particles. The most homogeneous stress distribution occurs for the largest size ratio and largest volume fraction of small particles, corresponding to the lowest pore size dispersion and the cushioning effect of small particles and its similar role to the binding matrix for stress redistribution across the packing. At higher porosity, the tensile stresses above the mean stress fall off exponentially in all phases with an exponent that strongly depends on the texture. The exponential part broadens with decreasing matrix volume fraction and particle-size ratio. These correlations reveal the strong interplay between size polydispersity and the cohesive action of the binding matrix for stress distribution, which is significant for the behavior of textured materials in grinding operations.

Rheology of granular materials composed of nonconvex particles

By means of contact dynamics simulations, we investigate the shear strength and internal structure of granular materials composed of two-dimensional nonconvex aggregates. We find that the packing fraction first grows as the nonconvexity is increased but declines at higher nonconvexity. This unmonotonic dependence reflects the competing effects of pore size reduction between convex borders of aggregates and gain in porosity at the nonconvex borders that are captured in a simple model fitting nicely the simulation data both in the isotropic and sheared packings. On the other hand, the internal angle of friction increases linearly with nonconvexity and saturates to a value independent of nonconvexity. We show that fabric anisotropy, force anisotropy, and friction mobilization, all enhanced by multiple contacts between aggregates, govern the observed increase of shear strength and its saturation with increasing nonconvexity. The main effect of interlocking is to dislocate frictional dissipation from the locked double and triple contacts between aggregates to the simple contacts between clusters of aggregates. This self-organization of particle motions allows the packing to keep a constant shear strength at high nonconvexity.

Strength and failure of cemented granular matter

Cemented granular materials (CGMs) consist of densely packed solid particles and a pore-filling solid matrix sticking to the particles. We use a sub-particle lattice discretization method to investigate the particle-scale origins of strength and failure properties of CGMs. We show that jamming of the particles leads to highly inhomogeneous stress fields. The stress probability density functions are increasingly wider for a decreasing matrix volume fraction, the stresses being more and more concentrated in the interparticle contact zones with an exponential distribution as in cohesionless granular media. Under uniaxial loading, pronounced asymmetry can occur between tension and compression both in strength and in the initial stiffness as a result of the presence of bare contacts (with no matrix interposed) between the particles. Damage growth is analyzed by considering the evolution of stiffness degradation and the number of broken bonds in the particle phase. A brutal degradation appears in tension as a consequence of brittle fracture in contrast to the more progressive nature of damage growth in compression. We also carry out a detailed parametric study in order to assess the combined influence of the matrix volume fraction and particle-matrix adherence. Three regimes of crack propagation can be distinguished corresponding to no particle damage, particle abrasion and particle fragmentation, respectively. We find that particle damage scales well with the relative toughness of the particle-matrix interface with respect to the particle toughness. This relative toughness is a function of both matrix volume fraction and particle-matrix adherence and it appears therefore to be the unique control parameter governing transition from soft to hard behavior.

Multi-scale analysis of the stress state in a granular slope in transition to failure

By means of contact dynamics simulations, we analyze the stress state in a granular bed slowly tilted toward its angle of repose. An increasingly large number of grains are overloaded in the sense that they are found to carry a stress ratio above the Coulomb yield threshold of the whole packing. Using this property, we introduce a coarse-graining length scale at which all stress ratios are below the packing yield threshold. We show that this length increases with the slope angle and jumps to a length comparable to the depth of the granular bed at an angle below the angle of repose. This transition coincides with the onset of dilation in the packing. We map this transition into a percolation transition of the overloaded grains, and discuss it in terms of long-range correlations and granular slope metastability.

Self-stresses and crack formation by particle swelling in cohesive granular media

We present a molecular-dynamics study of force patterns, tensile strength, and crack formation in a cohesive granular model where the particles are subjected to swelling or shrinkage gradients. Nonuniform particle size change generates self-equilibrated forces that lead to crack initiation as soon as the strongest tensile contacts begin to fail. We find that the tensile strength is well below the theoretical strength as a result of inhomogeneous force transmission in granular media. The cracks propagate either inward from the edge upon shrinkage or outward from the center upon swelling. We show that the coarse-grained stresses are correctly predicted by an elastic model that incorporates particle size change as metric evolution.

Intermittent flow of a collection of rigid frictional disks in a vertical pipe

We study the quasistatic flow of a collection of rigid frictional disks pushed upward (against the gravity) inside a narrow vertical pipe by a compliant mechanism. The contact dynamics method was used for the numerical simulations in combination with a friction law at disk-disk and wall-disk contacts characterized by discontinuous velocity weakening from a static threshold to a dynamic coefficient of friction. The material is sheared by the rolling of particles at the walls inducing a convective motion in the bulk. We observe a transition from constant flow to an intermittent flow when the driving velocity is reduced below a characteristic velocity that scales as k(-1/2) with the stiffness k of the pushing mechanism. The intermittent flow is composed of alternating phases of creep motion, where the pressure at the bottom of the granular column rises nonlinearly with time, and sudden slip, corresponding to a fast pressure drop. We show that the mean static pressure is correctly predicted by the Janssen model. The interplay between friction mobilization at the walls and structural changes in the bulk gives rise to a broad distribution of slip amplitudes characterized by a power law with an exponent approximately -1.7 that appears to be robust with respect to our system parameters.

Model for granular texture with steric exclusion

We propose a method to characterize the geometrical texture of a granular packing at the particle scale including the steric hindrance effect. This method is based on the assumption of a maximum directional disorder (statistical entropy) compatible with both the strain-induced anisotropy of the contact network and steric exclusions. We show that the predicted statistics for the local configurations are in fairly good agreement with our numerical data.

Dynamic rearrangements and packing regimes in randomly deposited two-dimensional granular beds

We study the structural properties of two-dimensional granular packings prepared by random deposition from a source line. We consider a class of random ballistic deposition models based on single-particle relaxation rules controlled by a critical angle, and we show that these local rules can be formulated as rolling friction in the framework of dynamic methods for the simulation of granular materials. We find that a packing prepared by random deposition models is generically unstable, and undergoes dynamic rearrangements. As a result, the dynamic method leads systematically to a higher solid fraction than the geometrical model for the same critical angle. We characterize the structure of the packings generated by both methods in terms of solid fraction, contact connectivity, and anisotropy. Our analysis provides evidence for four packing regimes as a function of solid fraction, the mechanisms of packing growth being different in each regime.