It may be seen from Maurer's survey (Maurer, 1 1966) that most of the common methods used in rock drilling today depend upon mechanical loading of the rock. In order to predict the behavior of rock under an imposed system of stresses, it is necessary to have a valid criterion which delineates those combinations of stress which cause macroscopic rock failure from those which do not.
Admittedly, the conditions under which brittle materials fracture depend very much upon statistically variable local effects such as inclusions, grain boundaries, minute imperfections, etc. However, it is extremely desirable to be able to predict fracture under complex states of stress by means of a stress-criterion of failure, where, for a given material, the effects of the other variables mentioned are incorporated into a small number of experimentally observable parameters. One of the most successful of these "macroscopic stress criteria" has been the Coulomb-Mohr theory 2,3 (also see Jaeger 4 and Terzaghi5 ), modified by the addition of tension cutoffs (Paul 6). At first thought it might seem rather odd that a macroscopic theory is capable of predicting fractures which originate at highly localized random imperfections at an atomic level (or more likely at the level of individual mineral grains in rocks). However, Griffith7 showed that fractures originating near the tips of randomly oriented elliptical cracks lead to the macroscopic stress criterion of failure indicated in Fig. l(a). Fig. l (a) is to be interpreted in the following way: P and Q represent the maximum and minimum principal stresses (compression is considered positive) in a macroscopically isotropic body; fracture will not occur for any combination of principal stresses lying within the 'fracture curve' shown, but fracture will occur for any combination of principal stresses which lie on the curve.
Table I. List of Nomenclature (Available in full paper)
One obvious defect of the original Griffith criterion is that it leads to the conclusion that the compressive strength must be exactly eight times the tensile strength. It is well known that this is not generally the case, particularly in rocks, where compressive strengths in excess of 100 times the tensile strength have been reported. This particular defect in the original Griffith conception has been partially removed through a modification due to McClintock and Walsh8 wherein it is assumed that the cracks close up under pressure, enabling sliding friction to develop on the crack surfaces. However, as they point out, the coefficient of friction at the surface would have to be unreasonably high in order to explain compressive strengths in excess of ten times the tensile strength. Since there is only one free parameter in the expression for the Griffith curve (see Eqs. 5 through 8) the curve can be made to agree with experiments on uniaxial tension as shown by the solid line in Fig. l(a), or the curve can be made to agree with uniaxial compression, as shown by the dotted line in Fig. 1 (a). In either case, one or the other strength is predicted poorly for most materials.
