Stresses on discontinuities

Abstract

Measurement of in situ stresses forms an increasingly important part in the rock investigation stage of the design of underground openings. Over-coring techniques now make it feasible to determine the three-dimensional state of stress to an acceptable degree of accuracy, both in terms of magnitude and orientation. The relatively complex, three-dimensional, nature of the problem can make the visualisation, interpretation and application of stress measurement data a daunting task. A key aspect in the application of stress measurement data is the transformation of stress from one set of coordinate axes to another, for example from the global coordinate system of a mine to a local system that allows the calculation of normal and shear stresses in the plane of a major fault zone or some other discontinuity. In the Author’s experience, the difficulties that rock mechanics engineers have with stress transformation problems, although partly related to the tensorial nature of stress, are mainly linked to difficulties in defining three-dimensional Cartesian coordinate axes and correctly interpreting the associated sign conventions. The aim of this chapter is to present a simple, practical method for three-dimensional stress transformation, based partly upon hemispherical projection techniques and partly upon analytical methods. A brief review of the theoretical background to stress analysis is presented in Appendix E for those who are not familiar with this topic. All readers are, however, strongly urged to consult this Appendix to acquaint themselves with the sign conventions and with the stress analysis equations adopted in this chapter.