Multi-scale analysis of the influence of particle shape on the mechanical response of granular materials

Abstract

Particle-scale characteristics govern the behaviour of particulate materials at the macroscale. An important factor that dominates the interaction of individual particles is shape, which generates particle interlocking. The resulting geometric interlocking affects the contact force network and the particle motion which lead to change in rheology, as well as stress distribution in the granular system. Accordingly, both numerical, by means of Discrete Element Modelling (DEM) simulations, and experimental, by use of direct shear and silo discharge tests, approaches are considered to determine the influence of particle shape on the mechanical response of granular assemblies at the micro- and macro-scales.

The Discrete Element Modelling (DEM) has been utilized to track the interaction of particles and obtain particle-scale information. In DEM simulations, shape factor is addressed through multiple approaches, but most of the studies use spherical particles due to the simplicity of contact detection algorithm resulting in faster simulation times. However, the lack of interlocking in spheres necessitates the need to better capture the shape effect. This is usually done by applying a rotational constraint at contacts, which is referred to as a rolling resistance model. The first part of this study investigates the influence of such implementations, through considering two different rolling resistance models, on the flow characteristics of spherical particles in a silo. Using a coarse-graining technique, the particle-scale DEM data was converted to continuum fields, which allowed a better understanding of stress and density distribution. It is seen that the flow profiles, packing density and stress distribution are highly dependent on the applied rolling resistance. Morevover, the possibility of obtaining comparable bulk response through both models is investigated. Accordingly, a procedure has been suggested to compensate for the differences in the calculation of torque for the two models using a proposed dimensionless parameter.

Meanwhile, there exist other approaches which try to simulate the most representative shape by allowing to adjust surface or edge properties and also aspect ratio of a particle. Two of the most widely used approaches, namely ‘Multi-spheres’ and ‘Superquadrics’, are employed here and the influence of changing particle surface and edge complexities on the micro- and macro- scale response is assessed for the two cases: direct shear test and silo flow. For direct shear test, the density of the sample determines the level of change in bulk response due to the shape factor. In the case of silo flow, beyond a certain level of shape complexity, the edge and surface properties show no significant influence on the material flow. The comparison between the two methods of shape description provides useful insights into the particle shape effect during shearing and flow.

Additionally, it is not yet fully known whether introducing a rolling resistance in spherical particle contacts can adequately capture the granular friction in non-spherical particles. In this respect, the response of spherical particles with restricted rotational freedom is compared to the particles simulated using the multi-sphere and superquadric approaches. The results indicate that certain characteristics of the particles with complex shapes can be replicated with spherical particles, such as: angle of repose (AoR), dilative behaviour and shear strength (only with the Elastic-Plastic Spring-Dashpot model).

Lastly, in order to validate the numerical observations, experiments were performed including angle of repose, Jenike shear and silo discharge (at 1g and also different accelerations with flat-bottom and wedge shape hopper). Additionally, the validity of Beverloo’s assumption for predicting the mass flow rate and velocity profiles inside the silo (at higher accelerations) is analysed in detail (Beverloo suggests that the mass flow rate at increased acceleration is proportional to the square root of the gravity). The results from AoR, Jenike and 1g silo discharge showed a great dependency on the particle shape factor. Comparing the mass flow rate at 1g with those of at different gravitational accelerations (in normalized form) suggest the validity of Beverloo’s approach only in case of spherical particles. Additionally, analysis of the normalized velocity of the particles shows that while the mass flow region for the spherical particles follows Beverloo’s assumption, the region near the outlet diverges to some extent. Furthermore, particles with shape irregularity show different flow profiles in presence of high gravitational forces compared to those of the 1g case.

In summary, this thesis presents an extensive investigation of the particle shape parameter on DEM simulation of granular assemblies. On the numerical side, the influence of different rolling resistance models on the interaction of the spherical particles is clarified. Moreover, the effect of the particle surface and edge characteristics of multi-sphere and superquadrics shapes is quantified at both micro and macroscales. The comparison of the three shape descriptors suggests that spherical particles together with rolling resistance can mimic several key mechanical properties of complex shape particles. Finally, the experimental observations have provided further insights into the particle flow at different gravitational stress states. Results suggest that it is yet challenging to predict the flow profiles of the discharging granular material with complex shapes, at different gravitational levels.