Shear flow of dense granular materials near smooth walls. II. Block formation and suppression of slip by rolling friction

Fabric-based jamming phase diagram for frictional granular materials

A jamming phase diagram maps the phase states of granular materials to their intensive properties such as shear stress and density (or packing fraction). We investigate how different phases in a jamming phase diagram of granular materials are related to their fabric structure via three-dimensional discrete element method simulations. Constant-volume quasi-static simple shear tests ensuring uniform shear strain field are conducted on bi-disperse spherical frictional particles. Specimens with different initial solid fractions are sheared until reaching steady state at a large shear strain (200%). The jamming threshold in terms of stress, non-rattler fraction, and coordination numbers (Z's) of different contact networks is discussed. The evolution of fabric anisotropy (F) of each contact network during shearing is also examined. By plotting the fabric data in the F-Z space, a unique critical fabric surface (CFS) becomes apparent across all specimens, irrespective of their initial phase states. Through the correlation of this CFS with fabric signals corresponding to jamming transitions, we introduce a novel jamming phase diagram in the fabric F-Z space, offering a convenient approach to distinguish the various phases of granular materials solely through the direct observation of geometrical arrangements of particles. This jamming phase diagram underscores the importance of the microstructure underlying the conventional jamming phenomenon and introduces a novel standpoint for interpreting the phase transitions of granular materials that have been exposed to processes such as compaction, shearing, and other complex loading histories.

Strain localization in planar shear of granular media: the role of porosity and boundary conditions

Shear strain localization into shear bands is associated with velocity weakening instabilities and earthquakes. Here, we simulate steady-state plane-shear flow of numerical granular material (gouge), confined between parallel surfaces. Both constant shear stress and constant strain-rate boundary conditions are tested, and the two types of boundary conditions are found to yield distinct velocity profiles and friction laws. The inertial number, I, exerts the largest control on the layers' behavior, but additional dependencies of friction on normal stress and thickness of the layer are observed under constant stress boundary condition. We find that shear-band localization, which is present in the quasistatic regime ([Formula: see text]) in rate-controlled shear, is absent under stress-controlled loading. In the latter case, flow ceases when macroscopic friction coefficient approaches the quasistatic friction value. The inertial regime that occurs at higher inertial numbers ([Formula: see text]) is associated with distributed shear, and friction and porosity that increase with shear rate (rate-strengthening regime). The finding that shear under constant stress boundary condition produces the inertial, distributed shear but never quasistatic, localized deformation is rationalized based on low fluctuations of shear forces in granular contacts for stress-controlled loading. By examining porosity within and outside a shear band, we also provide a mechanical reason why the transition between quasistatic and inertial shear coincides with the transition between localized and distributed strain.

Numerical investigation on effect of particle aspect ratio on the dynamical behaviour of ellipsoidal particle flow

Flow of ellipsoidal particles in a modal shear cell was investigated at the microdynamic level based on discrete element method simulations. In a stress-controlled double-shear condition, the flow was studied by varying the aspect ratio of ellipsoidal particles and comparing with the flow of spherical particle assembly in terms of some key properties, including particle alignment, linear velocity, angular velocity, porosity, contact force and contact energy. It was found that particle elongation impacts the rotational displacement around the axis perpendicular to the shear direction, which causes that the ellipsoidal particles with higher elongation are more aligned with the direction of the shear velocity, with more uniform force network. This then affects other particle properties. The fluctuation of linear velocity and the angular velocity decreases with an increase in particle aspect ratio, although the particle elongation does not significantly affect the flow velocity gradient. There is a reduction in both normal and tangential forces per contact with an increase of particle elongation. Due to the variation of the particle alignment with elongation, the standard deviation of the contact energies increases and then reduces when an increase in particle aspect ratio occurs, and on contrary, the porosity has an opposite variation trend.

Frictional active Brownian particles

Frictional forces affect the rheology of hard-sphere colloids, at high shear rate. Here we demonstrate, via numerical simulations, that they also affect the dynamics of active Brownian particles and their motility-induced phase separation. Frictional forces increase the angular diffusivity of the particles, in the dilute phase, and prevent colliding particles from resolving their collision by sliding one past to the other. This leads to qualitatively changes of motility-induced phase diagram in the volume-fraction motility plane. While frictionless systems become unstable towards phase separation as the motility increases only if their volume fraction overcomes a threshold, frictional systems become unstable regardless of their volume fraction. These results suggest the possibility of controlling the motility-induced phase diagram by tuning the roughness of the particles.

Unsteady granular flows down an inclined plane

The continuum description of granular flows is still a challenge despite their importance in many geophysical and industrial applications. We extend previous works, which have explored steady flow properties, by focusing on unsteady flows accelerating or decelerating down an inclined plane in the simple shear configuration. We solve the flow kinematics analytically, including predictions of evolving velocity and stress profiles and the duration of the transient stage. The solution shows why and how granular materials reach steady flow on slopes steeper than the angle of repose and how they decelerate on shallower slopes. The model might facilitate development of natural hazard assessment and may be modified in the future to explore unsteady granular flows in different configurations.

Coexistence and transition between shear zones in slow granular flows

We report experiments on slow granular flows in a split-bottom Couette cell that show novel strain localization features. Nontrivial flow profiles have been observed which are shown to be the consequence of simultaneous formation of shear zones in the bulk and at the boundaries. The fluctuating band model based on a minimization principle can be fitted to the experiments over a large variation of morphology and filling height with one single fit parameter, the relative friction coefficient μ(rel) between wall and bulk. The possibility of multiple shear zone formation is controlled by μ(rel). Moreover, we observe that the symmetry of an initial state, with coexisting shear zones at both side walls, breaks spontaneously below a threshold value of the shear velocity. A dynamical transition between two asymmetric flow states happens over a characteristic time scale which depends on the shear strength.

Shear-induced alignment and dynamics of elongated granular particles

The alignment, ordering, and rotation of elongated granular particles was studied in shear flow. The time evolution of the orientation of a large number of particles was monitored in laboratory experiments by particle tracking using optical imaging and x-ray computed tomography. The experiments were complemented by discrete element simulations. The particles develop an orientational order. In the steady state the time- and ensemble-averaged direction of the main axis of the particles encloses a small angle with the streamlines. This shear alignment angle is independent of the applied shear rate, and it decreases with increasing grain aspect ratio. At the grain level the steady state is characterized by a net rotation of the particles, as dictated by the shear flow. The distribution of particle rotational velocities was measured both in the steady state and also during the initial transients. The average rotation speed of particles with their long axis perpendicular to the shear alignment angle is larger, while shear aligned particles rotate slower. The ratio of this fast/slow rotation increases with particle aspect ratio. During the initial transient starting from an unaligned initial condition, particles having an orientation just beyond the shear alignment angle rotate opposite to the direction dictated by the shear flow.