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 |
The 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 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:
The 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 the rock |
H | - | height of the rock slope |
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.