Shearing tools are used to mobilise and transport granular materials in the mining, civil, agricultural and bulk solids handling industries. Examples of widely used shearing tools in these industries are dragline buckets, bucket wheel excavators, bulldozers, ploughs, scoops, tines, and graders. The use of these tools to break, shear and transport granular materials is energy intensive. It is estimated that processes using these tools consume at least 5 per cent of the worlds' gross annual energy expenditure. As energy usage becomes more expensive, which is mainly due to environmental and economic constraints, the engineering and design of shearing tools becomes more important.
The engineering of shearing tools is presently undertaken with either scaled physical models or the continuum theories of granular science. However, in general these approaches do not allow for accurate predictions of the important
behaviours of shearing tools. For example, a key problem with scaled physical models is the calibration of the constitutive behaviour in the scaled granular material, to the actual granular material. Other problems with scaled physical models are the considerable difficulties associated with measuring, interpreting, and building models of large and complex tool-medium systems. In these systems, the continuum theories of granular science are often used to predict behaviour in conjunction with scaled physical modelling. However, the use of continuum theories in tool shearing has two important limitations. The first limitation is that, for the most part, continuum theories do not allow for self-organisation phenomena in the tool surcharge i.e. the discrete mass transport and build-up of the surcharge over and behind the tool. A second limitation is that the micro-mechanics of a granular medium with large and frequent shear bands and dislocations are not well represented in standard
continuum models. For these reasons, the behaviour predicted from scaled physical models and continuum theories is often inconsistent with the behaviour of the real system. There is however a strongly contrasting approach in the granular science called discontinuum mechanics. In this thesis it is shown that discontinuum mechanics has considerable advantages over the standard continuum mechanics in predicting the behaviour of a tool-medium system.
The aim of this thesis is to improve the prediction of tool-medium behaviour through the extension, calibration and application of the discontinuum methods. However to achieve this objective, two principal goals must first be considered. These goals are the basis of two distinct hypotheses made in this thesis. The first goal is the comparison of phenomena observed in laboratory experiments, against simulations undertaken with the discontinuum methods (Hypothesis One). The second goal is comparing
and contrasting the accuracies of the continuum and discontinuum methods with laboratory results (Hypothesis Two). Both of these goals are achieved in a four-stage procedure, which is described as follows.
In the first stage, a tool-medium system is defined with similar parametric values to those encountered in the mining, civil or bulk solids handling industries. This system is called the Idealised Tool-Medium System (ITMS), and is composed of a constant velocity tool, and a cohesionless, frictional granular material.
In the second stage, the ITMS is subjected to a series of detailed experiments designed to formulate a baseline of empirical relations ("the experimental relations"). The aim of these experiments is to relate tool parameters to surcharge parameters, for three granular materials with different constitutive properties. Tool parameters are inclination, speed, and
stress. Surcharge parameters are area, shear-zone inclination, front slope inclination, and height. The constitutive properties are material friction angle, particle shape, particle size distribution, bulk density, and voids ratio.
In the third stage, the ITMS is analysed with two continuum methods, known as Coulomb's Method of Wedges (CMW), and the Theory of Plasticity of Geomaterials (TPG). In the CMW study, closed form mathematical relations are derived and solved, for the parametric values defining the ITMS. In the TPG analyses, the commercial computer code FLAC2D, is used to numerically construct the same relations. Thus, an outcome of the third step is an assessment of the performance of CMW and TPG in capturing the mechanisms, phenomena, and relations defining the ITMS.
In the fourth stage, the ITMS is analysed using two discontinuum methods; the Cellular Automaton Method
(CAM), and the Discrete Element Method (DEM). In these methods, several new theoretical extensions are proposed and coded into computer programs. These programs are called the Tool Shearing Cellular Automaton Method (TSCAM), and the Tool Shearing Discrete Element Code (TSDEC). The theoretical extensions in TSCAM include constant velocity boundaries, particle size distributions, and frictional behaviour. In TSDEC, a new calibration procedure is demonstrated that relates laboratory measured particle parameters (i.e. size distribution and shape factor), to an equivalent discontinuum of disc clusters. Hence, an outcome of the fourth step is an assessment of the performance of CAM and DEM in capturing the mechanisms, phenomena and relations defining the ITMS. The key results from stages two, three and four, are summarised, in turn, in the next three paragraphs.
A key result from the experiments is that the
ITMS initially has a transient state, which converges over time to a steady state. In the transient state, the surcharge shape is constantly changing, or self-organising into the final time-independent state; the steady state. The steady state has five zones; the static, shearing, shear flow, avalanching, and convection zones. Each zone has distinctly different mechanisms, and the zone size and shape varies with the tool parameters and medium constitutive properties. To facilitate comparison, the mechanisms, phenomena, and relations observed in the experiments are grouped into a list of 27 ITMS behaviours. It is reasoned that, the percentage of these ITMS behaviours captured by each method is a quantitative measure of its predictive accuracy. The predictive accuracy of each method and their dominant causal factors are discussed in the next two paragraphs.
The key results from continuum analyses on the ITMS are as follows. CMW captures about 20 per cent of ITMS behaviours, while TPG captures about 60 per cent. The poor predictive ability of CMW is primarily a result of the simplified representation of the granular medium i.e. the effects of stress and particle micro-mechanics are not included. Even so, the relations predicted by CMW follow trends that are in general agreement with experiment, albeit with different magnitudes. However, in comparison to CMW, TPG captures significantly more ITMS behaviours, although the relations for tool stress are inconsistent with the experimental relations. An important limitation of TPG, which is shared by CMW, is that the surcharge shape does not emerge from the simulations; it must be experimentally determined, and used as an initial condition. Hence a key finding from the continuum analyses is the importance of accurately predicting the self-organisation of the surcharge
into the correct steady state geometry.
The key results from discontinuum analyses on the ITMS are as follows. CAM captures about 75 per cent of the ITMS behaviour, while DEM captures approximately 95 per cent. Both CAM and DEM are successful in capturing the transient and steady state conditions, although the accuracy of the relations varies with tool speed, and medium type. For example, highly nonspherical or angular mediums are poorly represented in CAM. The main cause for this poor representation results from the use of discs rather than non-circular particles. In the DEM analysis, it is shown that particle shape significantly influences the accuracy of the representation of ITMS behaviours. This analysis indicates that, when simulating non-spherical media, carefully calibrated assemblies of disc clusters capture more ITMS behaviours than discs.
The two main conclusions from this thesis are
summarised as follows. First, the discontinuum methods, in contrast to the continuum methods, are more successful in capturing key behaviours in the ITMS. Overall, the continuum methods capture approximately 40 per cent of the ITMS behaviours, while the discontinuum methods capture about 85 per cent. These key behaviours include:
• The formation of five distinct zones in the steady state condition that are categorised by distinctly different mechanisms and phenomena. These are the static, shearing, shear flow, avalanching, and convection zones.
• The transient build-up or self-organisation of the surcharge (size and shape).
• The magnitude of the shear and normal stresses on the tool surface and their strong dependence on tool inclination.
Second, of the two discontinuum methods used (i.e. CAM and DEM), the DEM produced the most accurate simulation of the ITMS behaviours. The success of the DEM is
by and large attributed to the new and improved calibration of the micro-mechanics of the equivalent discontinuum developed in this thesis. Consequently, as a result of the overall investigations, a general philosophy for DEM modelling of steady state tool-medium systems is proposed. The development of this philosophy is an important step towards the improved design and engineering of shearing tools.