Skip to main content

Geological Strength Index (GSI) Rock Mass Modulus Calculator (Hoek-Diederichs)

Jointing and fracturing dramatically reduce the in-situ stiffness of a rock mass compared to laboratory core samples.

Young modulus of intact core specimen

GSI rating from structural surface character

Calculated Result
20.8 GPa

Rock Mass Deformation Modulus (Erm)

Modulus Ratio (Erm/Ei)

0.52

Calculation Breakdown

  1. Hoek-Diederichs Empirical EquationErm = Ei · [0.02 + (1-D/2)/(1 + e^((60+15D-GSI)/11))] => 20.8 GPa

Rock Mass Modulus vs GSI

Interactive visualization based on your current inputs

Erm
0.09.4192838GSI = 30 (Blocky/Seamy)GSI = 60 (Fair)GSI = 85 (Massive)GSI RatingErm (GPa)

What Is the Geological Strength Index (GSI) Rock Mass Modulus Calculator (Hoek-Diederichs)?

Jointing and fracturing dramatically reduce the in-situ stiffness of a rock mass compared to laboratory core samples.

Hoek and Diederichs developed an improved sigmoidal empirical relation for estimating deformation modulus Erm directly from GSI.

How Does the Geological Strength Index (GSI) Rock Mass Modulus Calculator (Hoek-Diederichs) Work?

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

Geological Strength Index (GSI) Rock Mass Modulus Calculator (Hoek-Diederichs) Formula & Variables

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

E_{rm} = E_i \left( 0.02 + \frac{1 - D/2}{1 + e^{\frac{60 + 15D - \text{GSI}}{11}}} \right)

Hoek-Diederichs rock mass deformation modulus equation.

How to Use the Geological Strength Index (GSI) Rock Mass Modulus Calculator (Hoek-Diederichs)

  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 Basalt Dam Abutment

Input Values:

intactModulusEiGpa:50.0
geologicalStrengthIndexGsi:55

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

  • Assumes blast damage disturbance factor D = 0 for mechanical TBM excavation.

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.

Explore more tools and calculators in Math Calculators