How to Calculate Bench Volumes
A bench volume is the amount of material in — or removed from — one horizontal level of a pit. It sounds like a simple slab calculation and it is not, because a bench is bounded above and below by design levels but sideways by wherever the face actually is. This guide explains how the calculation is set up, what the reference surface does to the answer, and which mistakes produce a number that looks reasonable and is wrong.
What is actually being measured
A bench occupies the space between two elevations: its own floor and the floor of the bench above. Its volume is whatever material sits between those two levels inside the area you are interested in.
That last clause is the whole difficulty. The vertical bounds are known — they are design levels. The horizontal bounds are not: they are wherever the face has been mined to, which changes every period and is only known from the survey.
The three ways it is set up
Between two surveys. Take this period's surface and last period's, restrict the comparison to the bench's elevation band, and the difference is what came out of that bench. This is the production answer, and it needs no design at all.
Against a design. Compare the surveyed surface with the design surface within the bench boundary. The result is the remaining material to the design — the answer to how much is left, not how much was moved.
Against a level. Compare the surface with a flat reference at the bench floor elevation. Simple and appropriate when the floor really is flat, and misleading when it is not, because every irregularity in the floor becomes volume.
The three answer different questions. Reporting one and labelling it as another is the most common source of an argument about a bench figure.
Where the boundary comes from
The elevation band alone does not define the bench. A pit has several benches at the same elevation on opposite walls, and a comparison over the whole model will merge them.
So the calculation is always clipped: an area boundary drawn around the bench in question, combined with the elevation band. Where that boundary is placed changes the number, which is why it belongs in the report alongside the volume.
Toe and crest positions are the natural boundary, and they move as the face advances. A boundary drawn once and reused for months quietly stops describing the bench it was drawn for.
Why the numbers do not stack
Bench volumes summed over a pit rarely equal the total pit volume computed in one operation, and the gap is not necessarily an error.
Material near a boundary gets assigned to one bench or the other depending on how the clip is drawn. Overlapping or gapped boundaries produce double counting or omission. And a surface that is compared bench by bench is being sampled several times, each time with its own edge effects.
If bench figures are going to be added up, the boundaries have to be built as a partition — sharing edges, no gaps and no overlaps — rather than drawn independently.
In-situ, loose, and what to report
A bench volume computed from surfaces is in-situ: rock as it sits. Haulage records are loose volume, and the difference is the swell factor. Converting one to the other requires a material-specific number that is rarely known precisely.
A defensible bench figure therefore carries four things: the reference it was measured against, the boundary it was clipped to, whether it is in-situ or loose, and the uncertainty of the surfaces behind it. Without those, a bench volume is a number with no way to check it.
Frequently asked questions
What reference should a bench volume be measured against?
It depends on the question. Against the previous survey for production, against the design for remaining material, against a flat level only when the floor genuinely is flat. All three are valid; reporting which one was used is what makes the figure meaningful.
Why do my bench volumes not add up to the total pit volume?
Usually because the bench boundaries were drawn independently and overlap or leave gaps, so material is double counted or missed. Building the boundaries as a partition with shared edges removes most of the discrepancy.
Can a bench volume be computed without a design surface?
Yes. Comparing two surveys within the bench's elevation band gives the material moved out of that bench without any design being involved. A design is only needed when the question is how much remains.
Should a bench volume be reported as in-situ or loose?
Volumes computed from surveyed surfaces are in-situ. If they are going to be compared with haulage counts, a swell factor has to be applied and stated — otherwise the two figures will disagree by 30–60% for no real reason.
STREAM computes cut and fill against a reference surface, a level or another survey, clipped to the area you draw.
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