1. Hoek-Brown Failure Criterion in Rock Mechanics
   1. 1. Understanding the Hoek-Brown Criterion
   2. 3. Key Takeaways

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Hoek-Brown Failure Criterion in Rock Mechanics

The Hoek-Brown failure criterion is a widely used empirical model in rock mechanics that describes the strength of rock materials based on the major and minor principal stresses. It was developed by Edward Hoek and J. A. E. Brown and is particularly useful for assessing rock mass stability in underground excavations and slopes.

1. Understanding the Hoek-Brown Criterion

The Hoek-Brown criterion extends the Mohr-Coulomb failure theory by incorporating the rock’s strength, deformability, and cohesion.

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Hoek-Brown Failure Criterion

Hoek-Brown Failure Criterion

The Hoek-Brown failure criterion is given by the equation:

σ₁ = σ₃ + σᵢ (mᵢ + s (σ₃ / σᵢ)^a)

Variables:

• σ₁ = Major principal stress (MPa)
• σ₃ = Minor principal stress (MPa)
• σᵢ = Uniaxial compressive strength of intact rock (MPa)
• mᵢ = Material constant for intact rock
• s and a = Empirical constants for rock mass properties

This equation helps predict rock strength under different loading conditions and is widely applied in geotechnical engineering for underground excavation, tunneling, and slope stability analysis.

Solved Example:

Given:

• mᵢ = 24
• σᵢ = 100 MPa
• σ₃ = 50 MPa
• s = 1, a = 0.5

Using the equation:

σ₁ = 50 + 100 × (24 + 1 × (50 / 100)^0.5)

Solving step-by-step:

(50 / 100)^0.5 = √0.5 = 0.707

24 + (1 × 0.707) = 24.707

100 × 24.707 = 2470.7

σ₁ = 50 + 2470.7 = 2520.7 MPa

Final Result:

σ₁ ≈ 2520.7 MPa

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3. Key Takeaways

✅ The Hoek-Brown criterion is an empirical model designed specifically for rock masses.
✅ It accounts for rock material properties, making it more realistic than traditional models like Mohr-Coulomb.
✅ It is widely used in mining, tunneling, and slope stability analysis.
✅ The criterion is not suitable for all rock types and must be calibrated based on geotechnical surveys.