Rock Mechanics formula solvers
Barton Q-System Rock Mass Quality
Rock MechanicsBarton, Lien and Lunde's 1974 tunnelling quality index, fitted to some 200 case records at the Norwegian Geotechnical Institute. Six ratings multiplied in three pairs: how blocky the rock is, how well the blocks interlock, and what the water and the stress field are doing to them. It spans six orders of magnitude, from 0.001 for squeezing ground to 1000 for massive unjointed rock.
Generalized Hoek–Brown Failure Criterion (2002)
Rock MechanicsThe strength of a jointed rock mass at a given confinement, in the 2002 edition of Hoek, Carranza-Torres and Corkum. Unlike Mohr–Coulomb, the envelope is CURVED: rock gains strength with confinement quickly at first and then far more slowly, which is why a straight line fitted at one stress level misleads badly at another.
Hoek–Brown Constants s and a (2002)
Rock MechanicsThe other two constants of the 2002 generalized criterion. s measures how much of the intact rock's cohesion the mass has kept — 1 for genuinely intact rock, falling to a ten-thousandth for a poor mass — and a is the curvature of the envelope, fixed by GSI alone and never by anything else.
Hoek–Brown Rock Mass Constant m_b (2002)
Rock MechanicsHow the intact rock's frictional constant m_i is knocked down to the rock mass value m_b, in the 2002 edition. Two judgement calls go in — the Geological Strength Index and the disturbance factor — and both of them make the rock look better if you are generous.
Obert–Duvall Pillar Strength
Rock MechanicsObert and Duvall's 1967 linear fit for the strength of a hard-rock pillar, scaled from the strength of a cubical specimen by the pillar's width-to-height ratio. Squat pillars are stronger than slender ones because the platens confine the middle of them, and this is the simplest honest expression of that fact.
Pillar Factor of Safety
Rock MechanicsPillar strength divided by pillar stress: the number the whole room-and-pillar exercise exists to produce. Both terms come from correlations with real scatter in them, so the factor of safety is a way of carrying that uncertainty explicitly rather than a promise about any one pillar.
Point Load Strength Index and the UCS it Implies
Rock MechanicsThe ISRM Suggested Method's field strength test: break a lump of rock between two conical platens, divide the breaking load by the square of the equivalent core diameter, correct it to a 50 mm standard size, and multiply by a conversion factor to estimate the uniaxial compressive strength. The test is cheap and portable. The conversion factor is where all the uncertainty lives, so it is an input here and not a constant.
Rock Mass Deformation Modulus (Hoek–Diederichs)
Rock MechanicsThe stiffness of a jointed rock mass, from Hoek and Diederichs' 2006 simplified expression: a sigmoid in GSI, knocked down by the disturbance factor. This is the number that governs how much a tunnel converges or a foundation settles — strength decides whether the ground fails, stiffness decides how much it moves before it does.
Rock Quality Designation (RQD)
Rock MechanicsDeere's 1964 index: of the core you pulled out of a run, what fraction came up as sound pieces at least 100 mm long. It is the oldest and cheapest measure of rock quality still in daily use, it feeds both the Q-system and RMR, and it is far cruder than the confidence usually placed in it.
RQD from Volumetric Joint Count
Rock MechanicsPalmstrom's 1982 estimate of RQD for rock you can see but cannot drill: count the joints crossing a cubic metre of the mass, and the correlation returns the RQD a core run would probably have shown. Useful in a face, a trench or an outcrop, and never a substitute for core where core exists.
Tributary Area Pillar Stress
Rock MechanicsThe load a room-and-pillar layout puts on each pillar: every pillar carries the full weight of the rock over its own area plus the rock over the openings around it. It is a statics argument with no rock mechanics in it at all, which is both why it is trustworthy and why it is crude.