Understanding the evolution of micro-cracking induced during rock indentation by roller tricone drilling tools is a key aspect of maximizing drilling efficiency. Crack network patterns and interaction between neighbouring cracked zones induced by two adjacent tool bits are a challenge for drilling engineers. In this paper, a methodology based on the cavity expansion model is developed to analyse the indentation of rocks by a blunt spherical indenter. Rock elasto-plasticity behaviour is used to propose an analytical solution for the plastic zone radius and a description of stresses within and outside the plastic zone. A Maple program was written to derive the expressions of plastic zone radius and stresses when adopting either the Mohr-Coulomb criterion or the Hoek- Brown criterion. The two approaches were then compared. All analyses were conducted on two hard rock types: granite and limestone. The first is encountered in geothermal reservoirs and the second in petroleum drilling. The results were also compared with those obtained using an experimental procedure developed in a previous investigation, in which the cracked zone radius is estimated using image analysis to distinguish the indentation microcrack network in the vicinity of the tool bit.


Rock indentation has been intensively studied for more than three decades, for two main reasons:

  1. the requirements of the underground space sectors (storage tunnels, mining activities) and

  2. the development of rock excavation technology.

Drilling performance depends on the rate of penetration of the tool, which can be predicted by numerous methods, including those based on indentation tests on representative samples.

Several phenomena occur during the indentation process. The first phase of deformation is elastic; however, the loading evolution leads inevitably to the development of irreversible deformation, which proceeds to the initiation and propagation of cracks due to the tensile stresses, and then to fragmentation. This behaviour of the rock under indentation has been widely studied (Lawn and Wilshaw, 1975; Kutter and Sanio, 1982; Sanio, 1985; Nelson, Ingraffea, and O'Rourke, 1985; Wijk, 1989; Fowell, 1993, Kou et al., 1995; Tan, Kou, and Lindquist, 1996; Alhossein and Hood, 1996).

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