Experimental Study of Crater Formation in Plastically Deforming Synthetic Rocks
Authors: Garner N.E. , Gatlin Carl 
Published: December 2007

Introduction
The resistance of solid materials to indentation or perforation by projectiles or other penetrators has been studied by workers in many areas. Despite these efforts no universally accepted laws or formulas are available for describing experimental observations. In the metals field the force-deformation behavior of impacting bodies is often analyzed by the Hertz law for clastic collisions, the Meyer law if plastic deformations occur, or some combination of both. The similarities of these expressions to empirical drilling formulas of the oil industry are apparent.Beginning with the basic contributions of Simon and co-workers at Battelle, a number of experimental papers concerning the reaction of rocks to vertical impact have appeared in the U. S. mining and petroleum literature. Most published data have, to date, been obtained at atmospheric pressure, although some early high pressure information was reported by Payne and Chippendale. Maurer has recently utilized available brittle impact data to develop a drilling rate equation based on the experimentally observed proportionality between crater volume and blow energy. His result agreed with earlier efforts by both Somerton, who used dimensional analysis, and Outmans, who used plasticity theory.It has long been known that rocks exhibit different modes of failure depending on the state of stress. The literature in this area is considerable; however, papers by Bredthauer, Handin and Hager, and Robinson are adequate to illustrate the point.Since rocks flow plastically at certain triaxial stress conditions, the mathematical theory of plasticity has been used to analyze the rock drilling problem. Cheatham has altered the wedge indentation solution of Prandtl to rocks, and has developed useful equations for penetrator forces under a variety of conditions. Outmans has utilized Hill's solution in a similar manner to develop a drilling rate equation. Both Cheatham and Outmans used the linear Mohr-Coulomb rule to relate rock strength and confining pressure.The actual stress at the hole bottom is not easily ascertained, although photoelastic studies by Galle and Wilhoit, plus the analytical treatment of Cheatham and Wilhoit provide some insight. Consequently it is not clear to what extent the highly idealized rheological model of a perfectly plastic solid can be realistically applied to the rock drilling problem.This paper is the first report on a long range experimental study of crater formation in rocks at elevated stress states. The data presented here are from the first phase of the project. Data obtained from impulsive wedge impacts on two synthetic, plastically deforming rocks are presented.

MODEL ROCKS
Geologists have long been faced with modelling the behavior of the earth and, as a consequence, have studied scaling problems in some detail. In general, their main problem is handling the wide disparity between laboratory and geologic time. In our studies the time effects (blow velocity or rate of loading, blow duration, etc.) were essentially the same for both model and prototype, as were wedge geometry and tooth penetration. Thus application of available scaling laws suggests that similarity is obtained if the stress-strain curves of model and prototype are similar.
JPT
P. 1025^