Breakage mechanics in large granular flow problems

Abstract

This thesis makes a first attempt to tackle large granular flow problems with grain crushing within a continuum mechanics framework. That is, a special finite element (FE) technique, the Eulerian method, is employed to allow the modelling of granular materials to flow through fixed meshes. The flowing materials are modelled using a linear elastic breakage model, which is derived from the continuum breakage mechanics theory (Einav 2007a, b). This enables the macroscopic behaviour of the flowing materials to be captured, in association with the evolving grain size distribution (GSD). Two typical granular flow processes are studied: crushable granular materials displacing around a penetrating pile during installation, and mineral materials flowing through a roller mill. The former aims to study the pile end-bearing capacity at steady state penetration; while the latter focuses on the energy-size reduction relationship in mineral comminution. In addition, a cavity expansion process in a brittle granular medium is also studied, with an emphasis on the eventual dissipation of fluid in petroleum application. The study highlights the fundamental connection between micro-structure and mechanics of brittle granular materials. It is demonstrated that tracking the evolution of the GSD can be useful in the continuum modelling of many applications, which is currently missing out from most existing studies. As a result of this research, a new formula to better predict the end-bearing capacity of piles is proposed and compared with previous equations. Another finding is the derivation of a correlation between the evolving GSD and permeability reduction during undrained cavity expansions. This is followed by establishing a relationship between generation/dissipation of excess pore pressures and grain crushing. Finally, the approach of this thesis is shown to enable us to find optimum roller gaps, which represent the maximum area of new surface to be created with the minimum level of work input; and the influence of increasing grinding speeds on new surface area creation.