Failure criteria for rocks based on smooth approximations to Mohr–Coulomb and Hoek–Brown failure functions

Existing experimental evidence from true triaxial test (also referred to as poly-axial test) indicates that the influence of the intermediate principal stress (σ2) on rock strength is substantial. In order to consider this effect in rock engineering design, an adequate 3D failure criterion, which takes into account the effect of σ2, is required. Such a criterion should not only be a convex but also a smooth function of stress state; the latter …