Modelling rock strength in three dimensions

A general, three-dimensional failure criterion for rock is proposed. This criterion is formulated in terms of the first and third stress invariants of the stress tensor, and it involves only three independent material parameters. Although these parameters interact with one another, each parameter corresponds to one of the three failure characteristics of rock behaviour. These material parameters may be determined from simple tests such as uniaxial compression and triaxial compression tests. For the purpose of including reasonable values of tensile strengths in the failure criterion, it may be advantageous to include the uniaxial tensile strength in the parameter determination. A simple expression for evaluation of the uniaxial tensile strength on the basis of the uniaxial compressive strength is given. Thirty-six sets of good quality data for different types of rock have been included in this study, and comparisons between the proposed failure criterion and the experimental data are made in triaxial, biaxial and octahedral planes. The ability of this criterion to capture the characteristics of failure in rock appears to be quite good with accuracies within the range of the natural scatter of the test data.