Hoek-Brown Failure Criterion
Also known as: Generalized Hoek-Brown Criterion, HB Criterion
The Hoek-Brown Criterion, developed by Evert Hoek and E. T. Brown starting in 1980, is an empirical failure criterion that predicts the shear strength of rock masses as a function of confining pressure. It accounts for rock quality (via the Geological Strength Index, GSI) and thus bridges laboratory rock mechanics and field behavior. The criterion is widely used in mining for slope stability, pillar design, and stress analysis.
Key highlights
- Accounts for confining pressure nonlinearity, matching real rock behavior better than Mohr-Coulomb
- Links rock quality (GSI) to strength, connecting field and lab data
- Empirically validated on thousands of case studies; reliable for mining engineering
- Applicable across wide range of rock types and qualities
- Integrates with numerical modeling software; widely implemented
Intuition
This section is available to Pro members. Upgrade to Pro
How it works
This section is available to Pro members. Upgrade to Pro
When to use it
Use Hoek-Brown for slope stability, pillar design, and underground excavation stress analysis. Works for hard to moderately weak rock. Requires GSI or RMR estimate for site characterization. Preferred over Mohr-Coulomb for nonlinear behavior.
Strengths & limitations
- Accounts for confining pressure nonlinearity, matching real rock behavior better than Mohr-Coulomb
- Links rock quality (GSI) to strength, connecting field and lab data
- Empirically validated on thousands of case studies; reliable for mining engineering
- Applicable across wide range of rock types and qualities
- Integrates with numerical modeling software; widely implemented
- Empirical correlations may not apply to rock types outside the database (very weak clay, highly cemented carbonate)
- GSI estimation is subjective; different geotechnicians may assign different GSI values
- Does not account for anisotropy (strength variation with direction) explicitly
- Failure surface is implicit; no direct formula for cohesion and friction angle
- Temporal effects (weathering, strength degradation over years) are not captured
Common pitfalls
This section is available to Pro members. Upgrade to Pro
Applications
This section is available to Pro members. Upgrade to Pro
Frequently asked
How do I estimate GSI if I don't have RMR?
Use field observations: rate Rock Structure (from unfractured to intensely fractured) and Surface Condition (from fresh to heavily altered/slickensided). Combine using GSI lookup chart. Alternatively, convert RMR to GSI: GSI ≈ RMR - 5 (approximate).
How do I apply Hoek-Brown in limit equilibrium slope stability analysis?
Convert HB to equivalent Mohr-Coulomb parameters: c = (m_b·σci·s) / (m_b + 2·a·s^(a-1)), φ = arctan(tan(β) / 2^a / (1 + m_b)) where β depends on confining stress. This gives c,φ for use in standard LE codes.
Does higher GSI always mean higher strength?
Yes, within HB framework. Higher GSI (better rock quality) gives higher m_b and s, thus higher strength for given σci. However, real rock quality also depends on discontinuity spacing and persistence, which GSI attempts to capture.
Can I use HB for very weak rock (GSI<25)?
Yes, but with caution. At very low GSI, the criterion is extrapolated beyond original validation range. Consider also Mohr-Coulomb or other methods for comparison. Empirical validation is weak at GSI<20.
How do I account for scale effects (e.g., large pillar vs. lab sample)?
The generalized HB includes a size parameter; scaling is partially accounted for. However, for very large excavations, apply size corrections (e.g., pillar strength degradation formulas). HB is not a substitute for explicit size analysis.
Sources
- 1.Hoek, E., & Brown, E. T. (2002). The Hoek-Brown failure criterion and GSI: 2018 update. Journal of Rock Mechanics and Geotechnical Engineering, 10(2), 445-463.
- 2.Carter, T. G., Marinos, V., & Marinos, P. (2018). Guidelines for the classification of rock masses in Turkey. Bulletin of Engineering Geology and the Environment, 77(4), 1639-1681.
You have read it. What now?
Cite this page
ScholarGate. (2026, June 3). Hoek-Brown Criterion. ScholarGate. https://scholargate.app/mining-engineering/hoek-brown-criterion