Vertical stress is the weight of what is above: ρgz, about 27 kilopascals for every metre of ordinary rock. Horizontal stress is not — it can be half the vertical or three times it, and which one it is decides whether a tunnel squeezes or spalls.
A rock mass is far softer than the rock in it, because most of the movement happens on the joints. Two published relations turn a rating into a modulus, and the honest thing is to run both — where they agree you have a number, and where they diverge you have a warning.
On competent rock a footing almost never fails in bearing — it fails the settlement check first, or it fails because of one discontinuity nobody logged. The elastic settlement is straightforward; the discontinuity is the reason a geologist is there at all.
Cut a hole in stressed ground and the ground moves into it. How much, in the elastic case, is u = p·a/(2G) — a closed form that needs no software. Beyond that the rock yields, and then the support does not resist the load so much as control the deformation.
Barton's relation is fitted to case histories, not derived, and it is quoted here with its inputs on show. It tells you the order of the support, not the design — and the Q value itself is worth more argument than the arithmetic that follows it.
Whether ground can be dug, ripped or must be blasted is decided in the field and settles the programme and the price. Seismic velocity is the usual proxy because it can be measured over a whole site in a morning, and because it responds to the joints as well as to the rock.
| velocity m/s | usually |
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RMR and Q themselves are computed in Geotechnical, from the joints you logged; the UCS behind them belongs in Rock strength; and on soil rather than rock, bearing and settlement are in Soil. This instrument takes those numbers and asks what can be built.