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Hoek-Brown Rock Mass Non-Linear Strength Criterion Calculator

The Hoek-Brown empirical failure criterion provides realistic non-linear triaxial strength curves for heavily jointed rock masses in tunneling and open pits.

Calculated Result
69.7 MPa

Triaxial Rock Strength (σ1)

Rock Mass UCS (σcm)

11.36 MPa

Hoek-Brown Parameter mb

4.298

Hoek-Brown Parameter s

2.047e-2

Curvature Exponent a

0.502

Calculation Breakdown

  1. Compute Hoek-Brown constants (mb, s, a) from GSI and Dmb = 4.298, s = 2.047e-2, a = 0.502
  2. Calculate major principal strength σ1 = σ3 + σci · [mb·(σ3/σci) + s]^aσ1 = 10 + 80 * [4.298 * (10/80) + 2.047e-2]^0.502 = 69.7 MPa

Failure Envelope: σ1 vs σ3 Confinement

Interactive visualization based on your current inputs

σ1 (MPa)
0.03059891190 MPa (UCS)5 MPa10 MPa20 MPaσ3 (MPa)σ1 (MPa)

What Is the Hoek-Brown Rock Mass Non-Linear Strength Criterion Calculator?

The Hoek-Brown empirical failure criterion provides realistic non-linear triaxial strength curves for heavily jointed rock masses in tunneling and open pits.

How Does the Hoek-Brown Rock Mass Non-Linear Strength Criterion Calculator Work?

The calculation evaluates user-provided measurements using recognized domain equations, converts between measurement units, and adjusts for real-world efficiency factors.

Hoek-Brown Rock Mass Non-Linear Strength Criterion Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

\sigma_1' = \sigma_3' + \sigma_{ci} \left( m_b \frac{\sigma_3'}{\sigma_{ci}} + s \right)^a

Empirical scaling constants mb, s, and a derive from field GSI ratings, accounting for interlocking rock blocks and joint surface conditions.

How to Use the Hoek-Brown Rock Mass Non-Linear Strength Criterion Calculator

  1. Enter your primary measurements in the input fields above.
  2. Select your preferred units (e.g. metric or imperial) if applicable.
  3. Review or adjust operational assumptions such as field efficiency.
  4. Click Calculate to instantly generate the full results breakdown and visual chart.
  5. Use the Reset button at any time to clear the form and test a new scenario.

Step-by-Step Example Calculation

Jointed Sandstone under 10 MPa Confinement

Input Values:

unconfinedRockStrengthUcsMpa:80
minorPrincipalStressMpa:10
gsiIndex:65
miIntactConstant:15
disturbanceFactorD:0

Understanding Your Result

Your calculated result represents the realistic operational capacity or baseline output under the specified conditions. Comparing theoretical and effective outputs reveals the direct impact of turns, overlap, and practical downtime.

Factors That Affect the Result

Field terrain, operator experience, equipment maintenance, overlap margin, and weather conditions can significantly influence real-world output.

When Should You Use This Calculator?

Use this calculator whenever you need quick, verified estimates for job planning, budgeting, equipment sizing, or project timelines.

Assumptions & Limitations

  • Uses the generalized Hoek-Brown 2002 formulation with disturbance parameter D.

Frequently Asked Questions

Calculation Accuracy & Reference Note

This calculator implements verified, deterministic mathematical equations based on published standards. Results should be treated as professional engineering estimates; always verify critical operations with local equipment manuals and site inspections.

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