Aaron Graves, PhDude (Replica)

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Rock Mass Rating (RMR) Calculator

Published on October 24, 2023 by Dr. Aaron Graves

Determine the quality of rock masses for tunneling, mining, and foundation engineering using the Bieniawski (1989) RMR system. This tool provides an instant Geomechanics Classification score and rock class description.

A) What is a Rock Mass Rating (RMR) Calculator?

A Rock Mass Rating (RMR) Calculator is a specialized geotechnical engineering tool used to quantify the quality of a rock mass. Developed by Z.T. Bieniawski in 1973 and significantly updated in 1989, the RMR system (also known as the Geomechanics Classification) provides a numerical value between 0 and 100.

This score allows engineers and geologists to communicate complex geological conditions through a standardized metric. It is essential for determining support requirements in tunnels, assessing slope stability, and designing foundations for large structures like dams or bridges.

B) Formula and Explanation

The RMR score is the sum of six basic parameters. The fundamental formula is:

RMR = P1 + P2 + P3 + P4 + P5 + P6

Where:

  • P1: Strength of intact rock material.
  • P2: Rock Quality Designation (RQD).
  • P3: Spacing of discontinuities (joints, bedding planes).
  • P4: Condition of discontinuities (roughness, weathering).
  • P5: Groundwater conditions.
  • P6: Rating adjustment for discontinuity orientation.

C) Practical Examples

Example 1: Hard Granite Tunnel

A tunnel is being bored through fresh granite. The UCS is 160 MPa (Rating: 12), RQD is 85% (Rating: 17), joint spacing is 0.7m (Rating: 15), joints are slightly rough (Rating: 25), and the site is damp (Rating: 10). The orientation is favorable (-2).
Total RMR: 12 + 17 + 15 + 25 + 10 - 2 = 77 (Class II: Good Rock).

Example 2: Weathered Shale Slope

Excavating a road cut in shale. UCS is 30 MPa (Rating: 4), RQD is 40% (Rating: 8), spacing is 50mm (Rating: 5), joints are slickensided (Rating: 10), and water is flowing (Rating: 0). Orientation is unfavorable (-10).
Total RMR: 4 + 8 + 5 + 10 + 0 - 10 = 17 (Class V: Very Poor Rock).

D) How to Use Step-by-Step

  1. Collect Lab Data: Obtain the Unconfined Compressive Strength (UCS) of the rock core.
  2. Measure RQD: Calculate the percentage of intact core pieces longer than 10cm.
  3. Field Observation: Note the average distance between joints and their surface characteristics (roughness, infilling).
  4. Check Water: Observe if the face is dry, damp, or has flowing water.
  5. Determine Orientation: Use a Brunton compass to find the strike and dip of joints relative to your engineering work.
  6. Input Values: Enter these into the calculator above to get your final classification.

E) Key Factors Affecting Rock Quality

  • RQD
    • Factor Impact on RMR Significance
    Joint Condition Up to 30 points Rougher joints provide better interlocking and shear strength.
    Up to 20 points Indicates the degree of fracturing in the rock mass.
    Groundwater Up to 15 points High water pressure reduces effective stress and destabilizes rock.

    F) FAQ

    1. What is the difference between RMR and Q-System?
    RMR is additive and simpler for general engineering, while the Q-System is multiplicative and specifically tailored for tunnel support design.

    2. Can I use RMR for soil?
    No, RMR is specifically designed for rock masses. Use soil mechanics classifications like USCS for soil.

    3. What does a score of 45 mean?
    A score of 45 falls into Class III (Fair Rock), typically requiring systematic rock bolting in tunnels.

    4. How is RQD calculated?
    RQD = (Sum of length of core pieces > 10 cm / Total length of core run) * 100.

    5. Does RMR change with depth?
    Indirectly, as groundwater and stress levels change, but the basic geological parameters usually stay consistent unless the lithology changes.

    6. Is RMR 89 different from RMR 76?
    Yes, the 1989 version updated the ratings for joint conditions and water to be more precise.

    7. What is the "Stand-up Time"?
    RMR predicts how long an unsupported tunnel span will stay open. Class I rock can stand for years; Class V for only minutes.

    8. Is orientation always negative?
    In the RMR system, orientation adjustments range from 0 (very favorable) to -12 (very unfavorable).

    G) Related Tools