# Generalized Hoek-Brown Criterion

The Generalized Hoek-Brown criterion is an empirical failure criterion which establishes the strength of the rock in terms of major and minor principal stresses. It predicts strength envelopes that agree well with values determined from laboratory triaxial tests of intact rock, and from observed failures in jointed rock masses.

**RSData** implements the most recent update (the 2002 edition) of the Generalized Hoek-Brown criterion. This edition resolves some formerly troublesome issues including:

- The applicability of the criterion to very weak rock masses, and
- The calculation of equivalent Mohr-Coulomb parameters from the Hoek-Brown failure envelope

The Generalized Hoek-Brown criterion is non-linear and relates the major and minor effective principal stresses (sigma1 and sigma3) according to the following equation:

where:

- and are the axial (major) and confining (minor) effective principal stresses respectively

- is the uniaxial compressive strength (UCS) of the intact rock material
- mb is a reduced value (for the rock mass) of the material constant mi (for the intact rock)
- s and a are constants which depend upon the characteristics of the rock mass

In most cases, it is practically impossible to carry out triaxial tests on rock masses at a scale which is necessary to obtain direct values of the parameters in the Generalized Hoek-Brown equation. Therefore some practical means of estimating the material constants mb, s and a is required. According to the latest research, the parameters of the Generalized Hoek-Brown criterion [Hoek, Carranza-Torres & Corkum (2002)], are given by the following equations:

where:

- GSI (the Geological Strength Index) relates the failure criterion to geological observations in the field
- mi is a material constant for the intact rock
- the parameter D is a "disturbance factor" which depends upon the degree of disturbance to which the rock mass has been subjected by blast damage and/or stress relaxation. It varies from 0 for undisturbed in situ rock masses to 1 for very disturbed rock masses.

## Rock Mass Deformation Modulus

If you are using the Generalized Hoek-Brown strength criterion, the rock mass deformation modulus is automatically calculated. See the Rock Mass Modulus topic for details.

## Recommended Reading

The Generalized Hoek-Brown calculations in RocData are based on the latest version of the criterion, as detailed in the following paper:

Hoek-Brown failure criterion â€“ 2002 edition

The following document provides a chronological overview of the evolution of the Hoek-Brown failure criterion, and provides references to all of the significant papers which have been published:

A Brief History of the Hoek-Brown Failure Criterion

Finally, a set of notes by Dr. Evert Hoek:

is available on the Rocscience website, www.rocscience.com. Practical Rock Engineering is recommended reading for all students of rock mechanics. Chapter 11 (Rock Mass Properties) should be read by users of RocData.

**Additional information regarding Generalized Hoek-Brown criterion:**

For the triaxial test:

* Hoek-Brown criterion for intact rock

It is important to note that for intact rock, the parameters of the Generalized Hoek-Brown criterion are as follows:

- s = 1
- GSI = 100
- a = 0.5

therefore the Generalized Hoek-Brown equation reduces to the following:

This is the equation which is used for the curve fitting of triaxial lab data (intact rock) to the Hoek-Brown criterion. Note that the curve fitting variables are sigci (the uniaxial compressive strength of the intact rock) and mi (the Hoek-Brown "m" parameter for intact rock).

Also, check out the Rock Mass Modulus page for more information on how rock mass modulus is calculated in RSdata.