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Hoek - Brown

Hoek-Brown failure criterion describes the failure of a rock mass (based on the performed analyses of hundreds of underground structures and rock slopes) as:

where:

σ1ef

-

major principal stress during rock failure

σ3ef

-

minor principal stress during rock failure

σc

-

strength of the intact rock in simple compression

σci

-

uniaxial compressive strength of intact pieces of rock

mb,s

-

nonlinear material constant depending on the rock quality

a

-

coefficient depending on the rock breaking

Basic parameters of the modified Hoek-Brown model should be determined from in-situ and laboratory measurements. To become more acquainted with this model, a brief list of ranges of individual parameters is provided. If rock mass classification using GSI is known then it is possible to let the program to determine the H-B parameters by itself.

For actual analysis the H-B parameters are transformed into the M-C parameters. The solution procedure then becomes identical to that of the Mohr-Coulomb criterion.

For conversion of Hoek-Brown parameters is used solution according to Hoek, Carranza-Torres and Corkum (2002) in case of the analysis of rock slope stability:

Angle of internal friction φ:

Cohesion (shear strength) c:

where:

The maximum value of a smaller principal stress σ‘3max is given by:

where:

γ

-

unit weight of rock

H

-

height of rock slope

σc

-

strength of the intact rock in simple compression, or uniaxial compressive strength of intact rock mass

Literature:

Stability analysis of rock slopes with a modified Hoek-Brown failure criterion, ANG Xiao-Li ; LIANG LI ; YIN Jian-Hua International journal for numerical and analytical methods in geomechanics. ISSN 0363-9061, 2004, vol. 28, no2, pp. 181-190.

Hoek E, Carranza-Torres CT, Corkum B.: Hoek–Brown failure criterion—2002 edition. Proceedings of the 5th North American Rock Mechanics Symposium, Toronto, Canada, vol. 1, 2002, pp. 267 – 273.