Strength criteria for rock

A strength criterion states the combination of stresses at which rock fails. The simplest, Mohr-Coulomb, uses a cohesion and a friction angle, and in principal-stress form gives the major principal stress at failure as the uniaxial strength plus the minor principal stress times a passive-type coefficient. It is linear, easy to use and built into most software, but real rock shows a curved strength envelope: confinement helps a lot at low stress and less at high stress.

The Hoek-Brown criterion captures that curvature. For intact rock it uses the uniaxial compressive strength and a material constant m_i, which ranges from single figures for fine-grained, weak rocks to above 30 for coarse granites. For rock masses, the generalised form reduces the constants according to the Geological Strength Index and a disturbance factor for blast damage or stress relief, so that a heavily jointed mass is much weaker than its intact blocks.

Discontinuities have their own criteria. A smooth planar joint behaves roughly frictionally. Rough joints dilate as they slide, so their strength is higher at low normal stress; Barton's relation expresses this through a joint roughness coefficient and the joint wall strength. Infilled joints may be governed by the infill clay.

Which criterion governs depends on the problem: intact rock for pillars and small blocks, the rock mass for large slopes and tunnels in jointed ground, and a single discontinuity for wedge and planar failures.