Remarks on linear and nonlinear failure criteria

To explore the nature of stress states at failure, published data are analyzed for three rock types - Dunnville sandstone, Red Wildmoor sandstone, and Taiwan siltstone - within the framework of three stress invariants. Data include a series of axisymmetric (conventional triaxial) compression, axisymmetric (conventional triaxial) extension, and multiaxial strength tests. The data are fitted to linear and nonlinear failure criteria: Paul-Mohr-Coulomb (PMC), a generalized linear criterion containing all three principal stresses; Hoek-Brown, a popular nonlinear criterion containing major and minor principal stresses; and a simplified version of PMC, where the friction angle in extension is assumed to be equal to the friction angle in compression. The results show that both versions of PMC provide a better approximation of the test data and successfully capture, in a piecewise-linear manner, the well-known nonlinear nature of the failure surface in the meridian and equipressure planes.