Modelling Rock Behaviour in Rock Cutting

Prediction of rock cuttability by various excavation machines such as tunnel boring machines, road headers, rippers, picks, roller disc cutters, excavators, etc is of major concern to both civil and mining engineers and rock mechanics. In principle, the design of a rock cutting tool is based on achieving maximum excavation with minimum input energy, minimum applied force, minimum equipment weight and volume and, more importantly, minimum tool wear. When a rock material is indented by the force of a cutting tool and then unloaded several material zones form underneath and around the tool. As the tool moves into the rock the volume of its associated rock cavity (ie volume of displaced rock) expands and depending on the indenter's shape various phenomena may occur. Immediately beneath the tool a small zone in which the stress state is more or less hydrostatic, is formed which is underlain by an inelastic, or damaged, material zone. Both size and shape of this damaged zone control the magnitude of the indentation force and the chip formation mechanism during unloading. The rock is unable to store the whole strain energy induced by the tool and consequently the extra energy is expended either in forming new fracture surfaces and/or in plastic deformation in the damaged zone. Therefore, it is not surprising to see that both perfect-elastic and rigid-plastic constitutive models are not generally suitable for modelling indentation of rocks. In contrast elastoplastic constitutive models are more appropriate as they can include both elastic and plastic deformations (Kral et al, 1993). Elastic solutions for several half-space indentation problems can be found in most text books on elasticity and in particular in Timoshenko and Goodier (1951), Sneddon, (1951), Poulos and Davis (1974) and Johnson (1985a). If a failure criterion, eg the Mohr-Coulomb failure criterion, is applied to delimit elastic solutions for indentation problems, a lower bound limit of the applied indentation force (for a given indentation depth) can be estimated. It may be noted that elastic analyses, without any delimiting failure criteria, normally overestimate the indentation force. Plastic solutions for a few indentation problems may be found in Hill (1950), Johnson, (1985a) and Alehossein et al (1992). When analysing the behaviour of indented rocks the choice of an appropriate constitutive model describing effectively the behaviour of the rock at various stages and phases during indentation is a challenging issue. Several questions need to be answered before starting an effective analysis. The first question is of course: Which one of these is more appropriate for modelling zones underneath and around a cutter, elasticity or plasticity theory, continuum damage mechanics or fracture mechanics, and what is the bridging link between these various theories? Which mode is more dominant in fracturing rock, tensile or shear mode? What governs the mechanism of chip formation? What is the function, shape and the behaviour of the pulverised zone that forms just underneath a cutter? Is the hydrostatic stress state assumption reasonable for this zone? How does the rock change during the absorption and dissipation of the input energy and how does the indentation energy vary with rock type and depth of penetration? How can we model the damaged zone under the indenter? Furthermore does a plastic material form beneath the pulverised zone? When and how do radial and ring cracks form around and under an indenter?