Core recovery parameters

2013-12-05T07:26:37Z

121.243.11.72: /* Classification table */

The '''Hoek–Brown failure criterion''' is an empirical [[stress (mechanics)|stress]] [[yield surface|surface]] that is used in [[rock mechanics]] to predict the [[material failure theory|failure]] of [[Rock (geology)|rock]].<ref name=Hoek/><ref name=Pariseau/> The original version of the Hoek–Brown criterion was developed by Evert Hoek and E. T. Brown in 1980 for the design of [[underground mining|underground excavation]]s.<ref name=Hoek80/> In 1988, the criterion was extended for applicability to [[slope stability]] and [[surface mining|surface excavation]] problems.<ref name=Hoek88/> An update of the criterion was presented in 2002 that included improvements in the correlation between the model parameters and the [[Geological Strength Index|geological strength index]] (GSI).<ref name=Hoek02/>

The basic idea of the Hoek–Brown criterion was to start with the properties intact rock and to add factors to reduce those properties because of the existence of joints in the rock.<ref name=Hoek88/> Although a similar criterion for concrete had been developed in 1936, the significant tool that the Hoek–Brown criterion gave design engineers was a quantification of the relation between the stress state and Bieniawski's [[Rock Structure Rating|rock mass rating]] (RMR).<ref name=Bien/>
The Hoek–Brown failure criterion is used widely in [[mining engineering]] [[design]].

== The original Hoek–Brown criterion ==
The Hoek–Brown criterion has the form<ref name=Pariseau/>
:<math>
\sigma_1 = \sigma_3 + \sqrt{A\sigma_3 + B^2}
</math>
where <math>\sigma_1</math> is the effective maximum [[principal stress]], <math>\sigma_3</math> is the effective minimum principal stress, and <math>A,B</math> are materials constants. In terms of the mean [[normal stress]] (<math>\sigma_m</math>) and maximum [[shear stress]] (<math>\tau_m</math>)
:<math>
\tau_m = \tfrac{1}{2}\sqrt{A(\sigma_m - \tau_m) + B^2}
</math>
where
:<math>
\tau_m = \tfrac{1}{2}(\sigma_1-\sigma_3) ~;~~ \sigma_m = \tfrac{1}{2}(\sigma_1+\sigma_3) ~.
</math>
We can convert the above relation into a form similar to the [[Mohr–Coulomb failure criterion]] by solving for <math>\tau_m</math> to get
:<math>
\tau_m = \tfrac{1}{8}\left[-A \pm \sqrt{A^2 + 4(A\sigma_m + B^2)}\right]
</math>
The material constants <math>A,B</math> are related to the [[uniaxial compressive strength|unconfined compressive]] (<math>C_0</math>) and [[tensile strength]]s (<math>T_0</math>) by<ref name=Pariseau/>
:<math>
A = \cfrac{C_0^2 - T_0^2}{T_0} ~;~~ B = C_0 ~.
</math>

=== Symmetry issue ===
If we set <math>\sigma_m = 0</math> in the above equation, we get the [[pure shear]] Hoek–Brown criterion:
:<math>
\tau_m = \tfrac{1}{8}\left[-A \pm \sqrt{A^2 + 4B^2}\right]
</math>
The two values of <math>\tau_m</math> are unsymmetric with respect to the <math>\sigma_m</math> axis in the <math>\sigma_m-\tau_m</math>-plane. This feature of the Hoek–Brown criterion appears unphysical<ref name=Pariseau/> and care must be exercised when using this criterion in [[finite element method|numerical simulation]]s.

== See also ==
* [[Failure theory (material)]]
* [[Mohr–Coulomb theory]]

== References ==
<references>
<ref name=Hoek>{{Cite book
| author = Hoek E. and Brown E.T.
| year = 1980
| title = Underground Excavations in Rock
| location = London
| publisher = Institution of Mining and Metallurgy
}}</ref>
<ref name=Pariseau>{{Cite book
| author = Pariseau, W. G.
| year = 2009
| title = Design Analysis in Rock Mechanics
| publisher = Taylor and Francis
| pages = 499
}}</ref>
<ref name=Hoek80>{{Cite journal
| author = Hoek E. and Brown E.T.
| year = 1980
| title = Empirical strength criterion for rock masses
| journal = J. Geotechnical Engineering Division ASCE
| pages = 1013–1025
}}</ref>
<ref name=Hoek88>{{Cite journal
| author = Hoek, E. and Brown
| year = 1988
| title = The Hoek-Brown failure criterion - a 1988 update
| journal = Proc. 15th Canadian Rock Mech. Symp.
| pages = 31–38
| url = http://www.rocscience.com/library/pdf/RL_2.pdf
}}</ref>
<ref name=Hoek02>{{Cite journal
| author = Hoek E, Carranza-Torres CT, Corkum B
| year = 2002
| title = Hoek-Brown failure criterion-2002 edition
| journal = Proceedings of the fifth North American rock mechanics symposium
| volume = 1
| pages = 267–273
| url = http://www.rockeng.utoronto.ca/downloads/rocdata/webhelp/pdf_files/theory/Hoek-Brown_Failure_Criterion-2002_Edition.pdf
}}</ref>
<ref name=Bien>{{Cite journal
| author = Bieniawski, Z. T.
| year = 1976
| title = Rock mass classification in rock engineering
| journal = Proc. Symposium on Exploration for Rock Engineering
| editor = Z. T. Bieniawski
| pages = 97–106
| location = Balkema, Cape Town
}}</ref>
</references>

== External links ==
*[http://www.rocscience.com/hoek/pdf/history%20of%20the%20hoek%20brown%20criterion.pdf History of the Hoek–Brown criterion]

{{DEFAULTSORT:Hoek-Brown failure criterion}}
[[Category:Solid mechanics]]

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Core recovery parameters