What is the generalised Hoek-Brown criterion?

σ'1 = σ'3 + σci × (mb × σ'3/σci + s)^a, where σ'1 and σ'3 are major and minor principal stresses at failure, σci is uniaxial compressive strength of intact rock (MPa), and mb, s, a are rock mass constants derived from mi (intact rock constant) and GSI via: mb = mi × exp((GSI-100)/(28-14D)), s = exp((GSI-100)/(9-3D)), a = 0.5 + (e^(-GSI/15) - e^(-20/3))/6, where D is disturbance factor (0–1). Per Hoek et al. (2002).

How are Mohr-Coulomb parameters estimated from Hoek-Brown?

For a specified confining stress range, Hoek et al. (2002) provide equations for equivalent cohesion c' and friction angle φ'. Approximate: φ' = arcsin[(6amb(s+mbσ'3n)^(a-1))/(2(1+a)(2+a)+(6amb(s+mbσ'3n)^(a-1))]). The rock mass deformation modulus Em = (1 - D/2) × √(σci/100) × 10^((GSI-10)/40) GPa when σci < 100 MPa.

Hoek-Brown Rock Strength Criterion Calculator

Apply the generalised Hoek-Brown criterion to calculate rock mass strength envelope, equivalent Mohr-Coulomb parameters, and deformation modulus from GSI, mi, and σci.

2D stress state at a point. All stresses in MPa.

σx — Normal Stress X (MPa)

σy — Normal Stress Y (MPa)

τxy — Shear Stress (MPa)

⚙ Mechanical Note: Results are based on standard textbook formulas and ISO/AASHTO references. Always verify critical designs with applicable codes (ISO 898, AASHTO 1993, AISC, Eurocode 3) and a qualified engineer.

How It Works

Apply the generalised Hoek-Brown criterion to calculate rock mass strength envelope, equivalent Mohr-Coulomb parameters, and deformation modulus from GSI, mi, and σci

Each component has a specific meaning:

GSI — The gsi recorded for the patient or scenario being assessed.
Mi — The mi recorded for the patient or scenario being assessed.
Σci — The σci recorded for the patient or scenario being assessed.

Note: Interpret the hoek-brown criterion result against the clinical thresholds and context described above.

How to Use

Enter the GSI, mi, σci for the patient or scenario you are assessing. Apply the generalised Hoek-Brown criterion to calculate rock mass strength envelope, equivalent Mohr-Coulomb parameters, and deformation modulus from GSI, mi, and σci. Use the hoek-brown criterion result to inform your clinical assessment.

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Frequently Asked Questions

What is the generalised Hoek-Brown criterion?

How are Mohr-Coulomb parameters estimated from Hoek-Brown?