Model Behavior
The Hoek-Brown model, like the Mohr-Coulomb model, belongs to the linear-elastic ideal-plastic material models and accordingly has a stress-strain relationship like the one shown in the figure below.
A. Reversible, elastic stress states
The model shows elastic behavior within the range of allowable stresses defined by the boundary condition. Within this range (the yield surface) there is an isotropic linear-elastic stress-strain relation according to Hooke's law.
B. Stiffness
The proportional relationship of the linear-elastic behavior is described by the constant modulus of elasticity.
C. Irreversible, plastic stress states
If the stress fulfills the limit condition and is on the yield surface, the behavior is changed to plastic, which is defined by the yield rule. According to Hoek-Brown, the following nonlinear failure criterion results.
The resulting yield surface is shown in the 3D principal stress space in the graphic below.
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Stress failure hypothesis
The Hoek-Brown failure criterion is a semi-empirical failure criterion that describes the rock strength by means of a nonlinear relationship between the maximum and minimum principal stresses.
A failure line is determined that approximates the values determined in triaxial tests in the laboratory, on intact rock and in observed failures in jointed rock bodies.
Input Parameters
The following input parameters are required to define the material with the Hoek-Brown model.
| Variable | Meaning |
|---|---|
| E | Modulus of elasticity |
| ν | Poisson's ratio |
| σci | Uniaxial compressive strength of intact rock |
| GSI | Geological Strength Index |
| mi | Material parameter for intact rock |
| D | Loosening/damage factor |