Abstract
This dissertation considers a number of numerical simulations of crushable grains. It begins by describing the algorithms used in a 2-dimensional model in which grains crush according to a set of statistical rules, resulting in the emergence of fractal distributions of particle sizes and linear compression plots. In this simulation, grains were represented by closely packed triangles that fractured probabilistically on the basis of their size, number of neighbours and an overall macroscopic stress parameter. These algorithms allowed the location and identity of neighbouring elements to be determined efficiently for large numbers of elements, over size ranges of several orders of magnitude.In the initial simulation voids were not explicitly represented and these were added into a second simulation in which elements fractured according to a similar set of rules but were permitted to move according to a set of simple kinematic rules. The differences in the results obtained from each of these simulations and their limitations of are discussed.
A discrete element package PFC3D is then used to model individual particles in simple crushing tests. 3-dimensional particles are constructed from smaller, bonded elements and random variation is introduced into the construction of the particles so that the distribution of strengths of batches of particles can be reasonably represented by a Weibull distribution. The thesis ends with some preliminary stress paths conducted on assemblies of such particles. At a superficial level contours of broken bonds bear a resemblance to the ,shapes of curves predicted by the Cambridge plasticity model Cam Clay. These simulations are therefore a promising point of departure for future investigation of the physical meaning of parameters describing these more complex aspects of soil behaviour.
Keywords: fracture modelling; granular materials; numerical modelling; particle crushing.