Q-System Calculator — Barton Q and the NGI Support Chart, Free

The RQD floor, and why it changes your answer

Barton et al. state that where RQD is reported or measured as 10 or less — including zero — a nominal value of 10 is used in the calculation. This is not a rounding convenience. A crushed zone logged honestly as RQD = 0 would otherwise give Q = 0 exactly: off the chart, unplottable on a log axis, and not what the method says.

It matters because it applies to precisely the ground where the answer matters most. This page applies the floor, and flags every row where it did — because a Q computed from a floored RQD and a Q computed from a measured one are different claims, and the reader is entitled to know which they are looking at.

De, ESR, and the one place the method asks what you are building

Q describes the rock. It says nothing about what you are putting in it. The bridge is the equivalent dimension, De = span (or height) ÷ ESR, where ESR is the Excavation Support Ratio — a number that encodes how much a failure would cost.

A temporary mine opening runs at ESR 3 to 5, a permanent mine opening or a hydropower water tunnel at 1.6, a minor road tunnel at 1.3, a power house or major rail tunnel at 1.0, an underground station or public facility at 0.8, and a very important cavern with a hundred-year design life at 0.5. The same rock mass carries a much larger unsupported span in the first case than in the last, because the consequence of a fall is not the same.

The 2015 table has seven rows, and it is not the five-row table most textbooks reproduce. Vertical shafts are their own entry (2.5 circular, 2.0 rectangular), which shifts every letter below them, and there is a 0.5 row that older versions simply do not have — a tool that stops at 0.8 cannot express the most demanding case in the table. One more rule the handbook adds: take ESR as 1.0 whenever Q ≤ 0.1 for shafts, permanent openings and minor tunnels. Below that quality the ground needs supporting properly whatever it is being used for. This page warns rather than silently overriding, because it cannot know which lettered category your ESR came from.

The support chart, and which of its lines are real

The chart is the point of the Q-system. Log Q across the bottom, log De up the side, and the plane divided into nine reinforcement categories: unsupported, spot bolting, then systematic bolting with progressively thicker fibre-reinforced sprayed concrete, then ribs, then a cast concrete lining, and finally a region marked "special evaluation" where the empirical data runs out. Your scenario is a point, and the region it lands in is the answer.

Only one of those boundaries is published as an equation. The maximum unsupported span is Span = 2 × ESR × Q^0.4, from Barton, Lien and Lunde (1974) and presented for design use in Barton et al. (1980) — in the chart's own coordinates, De = 2 Q^0.4. This page draws that line from the equation.

Every other boundary is a digitisation of the published figure. The handbook draws them; it does not state them, and neither does the 1993 paper the chart descends from. So they were traced off the figure, and the figure on this page says so in those words, next to the citations. The check that makes the rest trustworthy is the first line: fitting the digitised unsupported boundary gives De = 2.31 Q^0.374 against the published 2 Q^0.4 — agreement within a few per cent across the whole chart, from a curve that was traced rather than computed.

Two features of the geometry are easy to get wrong and are handled explicitly here. The spot-bolting region pinches out at a vertex near Q 31, De 8.4: below that dimension there is no category 2 at all and category 1 borders category 3 directly. And two boundaries run horizontal at large De rather than continuing to climb. Below De = 3 the published chart has no empirical data and draws its lines dashed; this page does the same, and dashes them again above De = 50 where the digitisation ends.

What else the page reports

Per scenario: the three quotients separately, so you can see which one is driving Q; the rock-mass class; De and the reinforcement category; the permanent roof support pressure p = (0.2/Jr) Q^(−1/3) MPa, with the √Jn/3 form where there are fewer than three joint sets; and the bolt length from L = 2 + 0.15 × span/ESR.

A caution on that last one, because it catches people. The support chart carries its own bolt-length axis down the right-hand side, and that axis does not follow the equation. They agree near De = 20 and drift apart either side, and the axis starts at 1.5 m, which the equation cannot produce at all — its floor is 2.15 m. This page computes the equation, because it is the citable form, and footnotes the discrepancy rather than quietly picking one.

For walls, the handbook multiplies Q before reading support off the same chart — by 5 above Q = 10, by 2.5 between 0.1 and 10, and not at all below. That adjusted value is reported but not applied, because one row here is one geometry and silently plotting a wall point at five times its Q would be exactly the kind of hidden step this page avoids.

Who uses this

Tunnel engineers choosing a support class, and the ones checking somebody else's choice. Engineering geologists mapping structural domains along a drive, where the interesting figure is three points at the same equivalent dimension and three different categories. Mining geotechnicians, who often need Q and RMR together. Students and lecturers, who need the chart and its provenance rather than a number from a black box.

It is a classification and a chart reading, not a support design. It will not size a rib or check a wedge. What it gives you is the correctly computed Q, the correctly placed point, and a clear statement of which lines around that point came from an equation and which came from a drawing.

Common questions

Is this free? What is the catch?

Free, with no account and no gated options. Enter your own scenarios, change every setting, export the figure. Free exports carry a small watermark, as they do everywhere on this site. There is no catch — Q is one equation and six tables.

Which edition of the Q-system is this?

Barton, Lien & Lunde (1974), Rock Mechanics 6(4), 189–236 for the definition, with the parameter tables, the ESR table and the reinforcement categories from the NGI (2015) handbook. That matters for the categories in particular: the 2015 chart has no standalone "systematic bolting" category — sprayed concrete begins at category 3 — the cast concrete lining moved from 9 to 8, and 9 became "special evaluation". Most textbook reproductions still show the 1993 arrangement. The 2025 edition changes them again, dropping the E500 energy class and renaming the sprayed-concrete ribs; this page targets 2015.

Where are the Jn, Jr, Ja, Jw and SRF tables?

In the handbook, which is freely downloadable from NGI, and this page takes the resulting numbers rather than reproducing five long descriptive tables in a grid. It does bound them: Jn 0.5–20, Jr 0.5–4, Ja 0.75–20, Jw 0.05–1, SRF 0.5–400. A value outside the tabulated range is refused with a message rather than quietly multiplied into a Q. Two things worth checking against the handbook rather than memory: the Ja scale runs to 20, not 24, and the modern Jw table has no water-pressure column at all — its descriptions are inflow-based, and the pressure bands people quote are a 1974 feature that NGI has dropped.

Why is my fault zone plotting at the left-hand edge?

Because Q is capped at 0.001 for support determination, and because the third quotient is unforgiving: a Jw of 0.5 against an SRF of 5 divides your Q by ten before the joints get a say. That is the method working as intended — the chart's far left is where "special evaluation" lives, and the honest reading of a point there is that the empirical database does not cover it.

Can I use this for the walls of a cavern?

Partly. Use the wall height in place of the span for De, and note the wall Q adjustment printed in the results — ×5 above Q = 10, ×2.5 between 0.1 and 10, unadjusted below. The page reports the adjusted value rather than plotting it, because one row is one geometry. If your wall height exceeds the span, the 2025 handbook directs using the wall height for the crown as well, with one Q for the whole profile.

How accurate is the RMR correlation?

Not very, and it is labelled that way. RMR ≈ 9 ln Q + 44 is Bieniawski's 1976 regression through 111 case histories; the scatter is ±50 % or more, and reviewers of both systems say plainly that there is no scientific basis for assuming a universally valid regression between two systems that characterise and weight the rock mass differently. It is a cross-check on the order of magnitude. Nothing on this page consumes it. The GSI figure in the same table comes by a better route — the published Q′ relation, using your own Jr and Ja with the water and stress terms dropped.

Does anything leave my browser?

No. The whole calculation runs in this tab, there is no account and there is no upload.