Generalized Hoek-Brown

The Generalized Hoek-Brown criterion describes the non-linear (curved) failure envelope of a rock mass. JW Slope uses the generalized form and converts it to an equivalent Mohr-Coulomb cohesion and friction angle at each slice's normal stress.

Parameters

These are edited on the LEM tab of the Define Material Properties modal once Generalized Hoek-Brown is selected.

Derived rock-mass constants

From the four inputs the solver computes the standard Hoek-Brown rock-mass constants:

mb = mi * exp( (GSI - 100) / (28 - 14*D) )
s  = exp( (GSI - 100) / (9 - 3*D) )
a  = 0.5 + ( exp(-GSI/15) - exp(-20/3) ) / 6

and the major principal stress at failure:

sigma'_1 = sigma'_3 + sigma_ci * ( mb * sigma'_3 / sigma_ci + s )^a

Conversion to equivalent Mohr-Coulomb

Because the limit-equilibrium solvers work with a linear envelope, the Hoek-Brown envelope is linearized at the actual normal stress acting on each slice base:

1. For a slice base effective normal stress sigma'_n, the solver searches for the minor principal stress sigma'_3 whose Hoek-Brown tangent point produces that normal stress.
2. The instantaneous tangent to the envelope at that point gives the local friction angle phi, and the tangent line's intercept gives the local cohesion c.
3. That (c, phi) pair is used as the slice's Mohr-Coulomb strength for the factor of safety.

Each evaluation is cached per normal stress (rounded to 0.1 stress units) on the slice, so repeated solver iterations at similar stresses reuse the result.

When to use

Use Generalized Hoek-Brown for slopes in rock masses, where strength is governed by intact-rock strength, rock-mass quality (GSI), and blast/excavation disturbance rather than by a constant cohesion and friction angle. For intact rock with strong structural control, consider the Generalized Anisotropic model instead.