Rock Mass Rating (RMR89) Calculator — Bieniawski Geomechanics
Calculate Bieniawski’s Geomechanics Rock Mass Rating (RMR₈₉), rock quality class (I–V), stand-up time, and estimated rock mass modulus.
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How to Use the Rock Mass Rating (RMR89) Calculator — Bieniawski Geomechanics
Developed by Z.T. Bieniawski between 1973 and 1989, the Rock Mass Rating (RMR₈₉) geomechanics classification system is a global standard in tunneling, mining, and foundation engineering. It synthesizes five basic geological parameters—intact rock compressive strength (UCS), drill core quality (RQD), joint spacing, joint surface condition, and groundwater inflow—plus a sixth orientation adjustment based on tunnel or slope alignment.
Formula and Calculation Methodology
- R_UCS: Uniaxial Compressive Strength or Point Load Index rating (0 to 15)
- R_RQD: Rock Quality Designation drill core recovery rating (3 to 20)
- R_spacing & R_condition: Discontinuity spacing (5 to 20) and joint surface condition (0 to 30)
- R_groundwater & R_orientation: Pore water inflow rating (0 to 15) and strike/dip adjustment (0 to -12)
Engineers use the resulting 0-to-100 RMR score to classify rock masses into five distinct stability categories (Class I Very Good to Class V Very Poor). Beyond empirical rock bolt and shotcrete support charts, RMR directly correlates with the in-situ deformation modulus (E_m), rock mass cohesion, and internal friction angle required for numerical finite-element slope stability modeling.
Bieniawski (1989) Rock Mass Classification & Engineering Properties
| RMR Range | Rock Class | Description | Cohesion (c) | Friction Angle (φ) |
|---|---|---|---|---|
| 81 – 100 | Class I | Very Good Rock | > 400 kPa | > 45° |
| 61 – 80 | Class II | Good Rock | 300 – 400 kPa | 35° – 45° |
| 41 – 60 | Class III | Fair Rock | 200 – 300 kPa | 25° – 35° |
| 21 – 40 | Class IV | Poor Rock | 100 – 200 kPa | 15° – 25° |
| 0 – 20 | Class V | Very Poor Rock | < 100 kPa | < 15° |
Frequently Asked Questions
What is the difference between Basic RMR and Adjusted RMR?
Basic RMR is the sum of the first five intrinsic rock mass parameters (UCS, RQD, spacing, condition, and groundwater) before applying the sixth tunnel/foundation/slope orientation deduction.
How is Deformation Modulus (Em) estimated from RMR?
For RMR > 50, Bieniawski’s formula estimates rock mass modulus as Em = 2 × RMR – 100 (in GPa). For weaker rock (RMR ≤ 50), Serafim and Pereira’s equation Em = 10^((RMR – 10)/40) is used.
How does RMR relate to the Q-System?
Barton’s Q-index and Bieniawski’s RMR are correlated by the empirical equation RMR ≈ 9 × ln(Q) + 44.
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