Hoek–Brown Rock Mass Constant m_b (2002)

$m_i$ belongs to the intact rock and you look it up: roughly 4 for claystone, 7 for shale and slate, 10 for limestone and sandstone, 15 to 25 for most metamorphic rock, 25 to 33 for granite, gabbro and basalt. $m_b$ belongs to the rock MASS, and this equation is the bridge — an exponential knock-down driven by two numbers that are both judgements rather than measurements.

The Geological Strength Index is a chart you read by looking at a rock face. Two axes: how blocky the mass is down one side, how good the joint surfaces are along the other, and you place the ground in a cell. Evert Hoek introduced it precisely because the earlier practice of converting RMR to Hoek–Brown constants broke down in weak rock, and he wanted something a geologist could apply by eye at a face without a rating sheet. That is a strength, not a weakness. But it means GSI is engineering judgement wearing a number, and two competent geologists at the same face routinely differ by ten points.

Ten points is not a rounding error. Take a limestone at $m_i = 10$, undisturbed. At GSI 45, $m_b = 10\,e^{-55/28} = 1.403$. At GSI 55, $m_b = 10\,e^{-45/28} = 2.005$. Forty-three percent, on a parameter that goes straight into the strength equation — and the direction of the disagreement is always the one that makes the ground look better, because a face that has been cleaned up for inspection looks blockier than the ground behind it. The right response is not to argue about the true GSI. It is to run the design at both ends and see whether the answer changes anything.

And then there is $D$, the most abused parameter in the system. It runs from 0 for an undisturbed mass to 1 for heavy production blasting, and it sits in the DENOMINATOR of the exponent, shrinking $28 - 14D$ from 28 down to 14. The same GSI 55 limestone at $D = 0.7$ gives $m_b = 0.844$ against 2.005 at $D = 0$ — a 58% reduction, from a number chosen by describing how the ground was excavated. Every temptation runs one way: a generous $D$ makes any rock mass look better, and nobody can prove you wrong from an office.

Hoek's own guidance is that $D$ applies to the BLAST-DAMAGED ZONE and not to the whole mass — typically a few metres behind a blasted face, essentially zero for a machine-bored tunnel, and zero again for material well inside a slope. Applying $D = 1$ everywhere is as wrong as applying $D = 0$ everywhere; it is simply wrong in the safe direction. The defensible practice is to say in writing which zone you applied it to and why.

One last time: the 28 and the 14 are the 2002 numbers. Earlier editions used different ones and had no $D$ at all. An $m_b$ lifted from a pre-2002 paper does not belong in the 2002 strength equation.