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Ground Support Design Calculator

Calculate rock bolt spacing, length, and shotcrete thickness from RMR and excavation dimensions.

About this calculator

The Bieniawski Rock Mass Rating (RMR) system -- published by Z.T. Bieniawski in Engineering Rock Mass Classifications (John Wiley & Sons, 1989) -- scores rock quality on a 0-100 scale from measured properties like intact rock strength, discontinuity spacing, and groundwater condition, and that single score maps to broad support classes ranging from Class V (very heavy support, steel sets, RMR 0-20) up to Class I (generally unsupported, RMR 81-100). This calculator uses that classification to look up a starting bolt spacing, bolt length, and shotcrete thickness for each class, then combines the resulting bolt spacing with the entered excavation span to estimate how many bolts fit across one row and how many rows are needed per meter of tunnel advance.

Support requirements are STEP-classified, not smoothly scaled -- RMR 61 and RMR 80 fall in the same "Spot Bolting" class and get identical support figures, even though 80 is close to crossing into the unsupported Class I band -- so a small RMR difference near a class boundary can matter more than a larger difference within one class. Once RMR reaches 81, the classification stays "Generally Unsupported" all the way to 100 -- no rock bolts or shotcrete are recommended at all in this band (bolt spacing and shotcrete thickness are reported as 0 only as a placeholder for "not applicable," not as a real spacing value), and there is no further reduction in support requirements above that threshold, since the model treats the entire 81-100 band as one uniform class. The rock load estimate is a simplified Terzaghi-style approximation scaled by RMR, span, and rock density, and every output here is meant as a preliminary design input to be checked and finalized by a geotechnical engineer, not a stand-alone final design.

Inputs

m
m
kg/m³

Results

Support Class

Systematic Bolting + Shotcrete

Bolt Spacing1.5 m
Bolt Length4 m
Shotcrete Thickness50 mm
Bolts per Row5
Rows per Meter1
Rock Load59.6 kPa
Shotcrete Vol/m0.65 m³

Figures current as of 1989. Source: Z.T. Bieniawski, Engineering Rock Mass Classifications (John Wiley & Sons, 1989)

How to Use This Calculator
  1. Enter the RMR Value from your Rock Mass Rating Calculator output.
  2. Set the excavation span (m) and height (m) for the tunnel or opening being designed.
  3. Enter rock density (kg/m³) for load calculations.
  4. Review Support Class, Bolt Spacing (m), Bolt Length (m), and Shotcrete Thickness (mm) for design specifications.
  5. Use these outputs as preliminary design inputs to be verified by a geotechnical engineer.

What each input means

RMR Value
Bieniawski Rock Mass Rating score (0-100)
Excavation Span
Width of the underground opening
Excavation Height
Height of the underground opening
Rock Density
Rock unit weight in kg/m³

How this is calculated

Worked example, using the default values

  1. Identify Input Parameters
    4 parameters
    RMR Value = 55, Excavation Span = 5, Excavation Height = 4, Rock Density = 2700 = 4 input(s) provided
  2. Calculate Support Class
    Support Class
    Systematic Bolting + Shotcrete = Systematic Bolting + Shotcrete
  3. Calculate Bolt Spacing
    Bolt Spacing
    1.5 = 1.5
  4. Calculate Bolt Length
    Bolt Length
    4 = 4

Figures and sources

Engine last updated . Checked against 3 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.

Frequently Asked Questions

Why does support requirement stay the same for RMR 81 through 100?

This calculator groups RMR into five discrete support classes rather than scaling continuously, and the entire 81-100 range falls into a single "Generally Unsupported" class -- no rock bolts are recommended anywhere in that band (bolt spacing and shotcrete thickness show 0 as a "not applicable" placeholder, not an actual spacing value). Once a rock mass crosses that top threshold, the model has no further reduction in support requirements to apply -- RMR 85 and RMR 100 produce identical figures.

Does a higher RMR score always mean less support is needed?

Yes, and the bolt spacing figures move consistently with that: within Class V through Class II (RMR 0-80), bolt spacing widens as RMR improves -- 0.75 m, then 1.0 m, then 1.5 m, then 2.5 m -- because a wider spacing means fewer bolts per row, i.e. less support. The only place this looks like it reverses is the jump into Class I (RMR 81-100), where the reported spacing drops back to 0 m; that 0 isn't a tighter spacing than Class II's 2.5 m, it's a "no bolts needed" sentinel for the best-supported class of all. Read as bolt-count-per-row rather than raw meters, support strictly decreases as RMR increases across every class boundary.

How does excavation span affect the estimated rock load?

Rock load scales directly with excavation span in this formula -- a wider opening is assumed to mobilize a proportionally taller zone of loosened rock above it, which increases the estimated load in direct proportion to span, holding RMR and rock density fixed. A wider tunnel or cavern therefore always carries a higher estimated rock load than a narrower one under otherwise identical conditions.

Is this calculator's output sufficient for a final tunnel support design?

No -- it produces preliminary reference figures from a simplified RMR-to-support- class lookup and a simplified rock-load formula, not a substitute for a full geotechnical analysis. A qualified geotechnical engineer needs to verify ground conditions, review site-specific data, and finalize the actual support design before it's used for construction.

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