Conventional methods of drilling with rotary and percussive bits utilize a wedge-shaped tooth form which places a compressive line load on the rock. According to the classical theory of elasticity, the stresses caused by a compressive line loading at the surface are everywhere compressive within the interior of the rock. Paradoxically, it has been observed in the laboratory that the rock directly under the point of the bit undergoes a splitting type of failure which strongly suggests the presence of reasonably large tension stress in the rock, notwithstanding the prediction of the classical theory.
It is shown that the classical solution, for stresses under a line load does not reproduce the true condition underneath a rock bit, and a more realistic boundary condition is proposed. Having formulated a more realistic boundary condition one is still faced with the very difficult mathematical problem of solving the field equations of problem of solving the field equations of the theory of elasticity to find the state of stress in the rock. In this paper, we apply a recently developed paper, we apply a recently developed digital computer program which clearly shows the presence of tensile stresses, directly under the bit, which are of such a nature and such a magnitude as to explain the "splitting action" observed in practice.
Rock drill bits are essentially wedges, or indentors of various shapes, which load the rock over a small surface area in order to produce high contact stresses. It is therefore perhaps natural to analyze the situation by treating the applied load as a line loading (for a wedge bit) or concentrated load (e.g. for a button-bit) in an effort to estimate the stress field in the rock. This approach is all the more attractive because the stress and strain fields in a semi-infinite elastic body, subjected to a line load, as shown in Fig. 1-a, have been found by Flamant to be given by the simple expressions: