Strength criterion
Generalized Hoek–Brown criterion
A transparent introduction to the empirical rock-mass strength criterion, its inputs and the boundary between a preliminary calculation and an engineering design decision.
Core relationship
σ₁ = σ₃ + σci · (mb · σ₃/σci + s)ᵃ
Inputs & units
- Intact uniaxial compressive strength σci [MPa]
- Material constant mi [–]
- Geological Strength Index GSI [0–100]
- Disturbance factor D [0–1]
- Confining stress σ₃ [MPa]
Assumptions
- Rock mass can be represented by the generalized isotropic criterion for the question being asked.
- Compression-positive stress convention is used consistently.
- GSI, mi, σci and D come from documented observations, tests or justified references.
Limitations
- It is an empirical rock-mass failure criterion, not a complete excavation, support or deformation model.
- Input quality, disturbance, anisotropy, groundwater, scale and stress-path effects may dominate the result.
- Any equivalent Mohr–Coulomb parameters depend on the selected confining-stress range and application.
Synthetic worked example
Synthetic check: enter a documented parameter set, evaluate several σ₃ values, and verify that the generated envelope is monotonic over the selected range. The numbers are a software check—not site evidence.
Engineering use boundary
This page is educational and supports preliminary assessment. It does not replace site investigation, competent engineering judgement, final design, independent review or permitting requirements.