Undercut Span Calculator
The undercut span in cave mining is characterised by the hydraulic radius (also called the shape factor), HR = plan area ÷ perimeter, in metres.
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Before you rely on this: First-pass guide only. Verify safety-critical or regulated work against the relevant standards, your project requirements and a qualified professional.
How to use this calculator
- Enter the undercut length L and width W of the plan footprint in metres.
- Read the hydraulic radius (HR), plan area and perimeter — HR is the shape factor used on a caveability (stability) chart.
- Compare HR against your site's rock-mass caveability curve to decide whether the undercut span is sufficient to cave.
How it works
The undercut span in cave mining is characterised by the hydraulic radius (also called the shape factor), HR = plan area ÷ perimeter, in metres. For a rectangle of length L and width W this is HR = (L × W) ÷ (2 × (L + W)). A larger HR means a larger, more slender-perimeter footprint that is more likely to cave under a given rock mass strength.
Hydraulic radius normalises span for shape: a long thin undercut and a square undercut of the same area have different HR values, and the square (more compact) shape gives the larger HR. Geotechnical engineers plot HR against a stability/caveability chart (such as Laubscher's) using the rock mass rating to find whether the span sits in the caving, transitional or stable zone. This tool computes the geometry only — it does not assess rock strength, and results must be verified against site geotech and a competent professional.
Worked example
40 m × 30 m block-cave undercut. For a rectangular undercut 40 m long by 30 m wide, the plan area is 40 × 30 = 1,200 m² and the perimeter is 2 × (40 + 30) = 140 m. The hydraulic radius HR = 1,200 ÷ 140 = 8.571 m. This HR value is then plotted against the rock mass caveability chart to judge whether the span is large enough to initiate and sustain caving.
Common mistakes
- Confusing hydraulic radius with a simple half-span. HR = area ÷ perimeter, not L ÷ 2 — for a 40 × 30 m undercut HR is 8.571 m, not 20 m.
- Entering dimensions in metres but expecting the result to reflect a non-rectangular or stepped footprint. This tool assumes a flat rectangular plan; irregular footprints need the actual plan area and true perimeter.
- Treating a favourable HR as proof the block will cave. HR is only the geometric input to a caveability chart — the rock mass rating and site geotech determine the actual caving outcome.
Frequently asked questions
What is hydraulic radius in cave mining?
Hydraulic radius (HR), also called the shape factor, is the undercut plan area divided by its perimeter, measured in metres: HR = area ÷ perimeter. It is the standard way to express undercut span because it accounts for the footprint's shape as well as its size.
Why not just use the width as the span?
A raw width ignores the shape of the footprint. A long, narrow undercut and a compact square undercut of the same width behave very differently. Hydraulic radius combines area and perimeter into a single number that caveability charts are calibrated against.
Does a bigger hydraulic radius mean the rock will definitely cave?
No. A larger HR increases the likelihood of caving for a given rock mass, but whether caving actually initiates depends on the rock mass rating and site geotechnical conditions. HR is only the geometric input to a caveability (stability) chart — always confirm with site geotech and a competent professional.
Can I use this for a non-rectangular undercut?
This calculator assumes a flat rectangular footprint. For an irregular or stepped undercut, compute HR separately using the true plan area and true perimeter of the actual footprint.
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