Discontinuity Analysis for Rock Engineering

The previous chapter described techniques for sampling and conducting preliminary processing of discontinuity data. One of the most important characteristics of discontinuities is their orientation, relative both to each other and to any engineering structure or excavation face. Discontinuity orientation data can be presented and utilised in design by two different methods: if the rock face at the design site is readily accessible the locations and orientations of actual discontinuities can be measured and used explicitly in the design calculations. If, however, the rock face is not accessible it is necessary to measure discontinuity orientation at other rock faces, or from boreholes, and build up a statistical model that represents the discontinuity orientation characteristics of the rock mass. In most cases the statistical model is based on the fact that geological processes usually generate one or more clusters (or sets) of nearly parallel discontinuities in a given rock mass.

Although it is relatively easy to specify the size of a discontinuity in terms of its surface area, size is one of the most difficult discontinuity properties to measure accurately. This is because only by completely dismantling a given rock mass is it possible to trace and to measure the complete area of each discontinuity. This has never been done satisfactorily for a rock mass. When studying the size of discontinuities it is desirable also to consider their shape. In a completely blocky rock mass, where all discontinuities terminate at other planar discontinuities, the shapes will take the form of complex polygons whose geometry is governed by the locations of the bounding discontinuities. It was noted in Chapter 5 that discontinuity occurrence is often random, leading to negative exponential distributions in spacing. It is reasonable to suppose, therefore, that the linear dimensions of discontinuities would also be of negative exponential form. Sampling difficulties have so far made it impossible to prove or disprove this hypothesis. In view of these sampling difficulties, a number of workers have adopted the simplifying assumption that discontinuities are circular, to provide a starting point for the analysis of size (Baecher et al., 1977 and Warburton, 1980a).

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.