6.2 Failure Criteria

We do not know exactly how a rock fails, either in terms of the precise details of each microcrack initiation and propagation, or in terms of the total structural breakdown as many microcracks propagate and coalesce. In both cases, the process is extremely complex and not subject to convenient characterization through simplified models. Nevertheless, as engineers we should like some measure of the failure properties and the ability to predict when failure will occur. It was mentioned earlier that stress has been traditionally regarded as the cause and strain as the effect in materials testing: as a consequence, early testing and standards utilized a constant stress rate application. It was then natural to express the strength of a material in terms of the stress present in the test specimen at failure. Since uniaxial and triaxial testing of rock are by far the most common laboratory procedures in rock mechanics and rock engineering, the most obvious means of expressing a failure criterion is

With the advent of stiff and servo-controlled testing machines and the associated preference for strain rate control, perhaps the strength could be expressed in the form

We also discussed the possibility of more eclectic forms of control such as constant rate of energy input, leading to more sophisticated possibilities for strength criteria expressed in the form

Despite this possibility, the number and variation of the failure criteria which have been developed, and which are in some degree of everyday use, are rather limited. The Mohr-Coulomb...