# Brittleness

A mode of rock failure. It is an imprecise, relative term.

## Definition

Stress-strain curve

There are several ways to look at brittleness.[1] For example:

• Brittle failure is said to occur when the ability of the rock to resist load decreases with increasing deformation. Brittle failure is associated with materials that undergo little to no permanent deformation before failure and, depending on the test conditions, may occur suddenly and catastrophically.
• Brittle rocks undergo little or no ductile deformation past the yield point (or elastic limit) of the rock. Note that some materials, including many rocks, have no well-defined yield point because they have non-linear elasticity (see Young's modulus).
• Brittle rocks absorb relatively little energy before fracturing. The energy absorbed is equal to the area under the stress-strain curve (see figure).
• Brittle rocks have a strong tendency to fracture.
• Brittle rock break with a high ratio of fine to coarse fragments.
• Brittle rocks have a higher angle of internal friction

## Brittleness index

Some authors in the mining industry define brittleness index B (loosely defined, but the concept is also called brittleness ratio, brittleness coefficient, or ductility number) as the ratio of uniaxial compressive strength to tensile strength[2][3].

${\displaystyle B={\frac {\mathrm {compressive} \ \mathrm {strength} }{\mathrm {tensile} \ \mathrm {strength} }}={\frac {\sigma _{\mathrm {C} }}{\sigma _{\mathrm {T} }}}}$

Altindag (2003[4]) also gives:

${\displaystyle B={\frac {\sigma _{\mathrm {C} }-\sigma _{\mathrm {T} }}{\sigma _{\mathrm {C} }+\sigma _{\mathrm {T} }}}}$

Altindag (2002 and 2003) further showed that the most useful measure may be the mean average of compressive and tensile strength:

${\displaystyle B={\tfrac {1}{2}}\times (\sigma _{\mathrm {C} }+\sigma _{\mathrm {T} })}$

He goes on to compare this measure with the ratio method above:

It is shown that the [mean strength brittleness] is closely related to rock drillability index, point load index, density, cone indenter, N-type Schmidt hammer, and seismic velocity. These relationships may also show the affect of [this type of] brittlenees with rock properties used on drillability analysis.

Tensile strength is usually correlated with compressive strength, and it may be possible to use just one of these measures as a proxy for brittleness[5]. This is good, because some (most?) labs only measure compressive strength as a standard test, e.g. in routine triaxial rig tests.

There's also Bažant's brittleness number, β.[6][7]

## Brittleness from seismic

Rickman et al. 2008[8] proposed using Young's modulus E and Poisson's ratio ν to estimate brittleness. This is appealing to development geophyisicists because elastic moduli are readily available from logs and accessible from seismic data via seismic inversion. Two recent examples are Sharma & Chopra 2012[9] and Gray et al. 2012[10]. Gray et al. gave the following equations for 'brittleness index' B:

${\displaystyle B=50\%\times \left({\frac {E_{\mathrm {min} }-E}{E_{\mathrm {min} }-E_{\mathrm {max} }}}+{\frac {\nu _{\mathrm {max} }-\nu }{\nu _{\mathrm {max} }-\nu _{\mathrm {min} }}}\right)}$

where subscripts min and max denote minimum and maximum values.

Only careful comparison of results from hydraulic fracturing with elastic moduli measured at the wells can tell you if this sort of proxy for brittleness is useful at all in your play. Indeed, some geophysicists are skeptical of this approach, which assumes that a shale's brittleness is (a) a tangible rock property and (b) a simple function of elastic moduli. Lev Vernik stated at the SEG Annual Meeting in 2012[11] that computing shale brittleness from elastic properties is not physically meaningful and we need to find more appropriate measures of frackability.

## References

1. Hucka V, B Das (1974). Brittleness determination of rocks by different methods. Int J Rock Mech Min Sci Geomech Abstr 1974;11:389–92. DOI:10.1016/0148-9062(74)91109-7.
2. Altindag, R, 2002. The evaluation of rock brittleness concept on rotary blast hole drills. The Journal of The South African Institute of Mining and Metallurgy Jan/Feb 2003. Online.
3. Goktan, R and N. Gunes Yilmaz (2005). A new methodology for the analysis of the relationship between rock brittleness index and drag pick cutting efficiency. The Journal of The South African Institute of Mining and Metallurgy VOLUME 105, November 2005. Available online.
4. Altindag, R (2003). Correlation of specific energy with rock brittleness concepts on rock cutting. The Journal of The South African Institute of Mining and Metallurgy, April 2003.Available online.
5. Tiryaki (2006). The Journal of The South African Institute of Mining and Metallurgy VOLUME 106, June 2006. Available online.
6. Bažant, in SEM/RILEM International Conference on Fracture of Concrete and Rock, Society for Experimental Mechanics (1987) 390-402; also Fracture of Concrete and Rock, S.P. Shah and S.E. Swartz (eds.), Springer Verlag, NY (1989) 229-241.
7. Bažant, Z and M Kazemi (1990). Determination of fracture energy, process zone length and brittleness number from size effect, with application to rock and concrete. International Journal of Fracture 44, 111–131. Available online.
8. Rick Rickman, Mike Mullen, Erik Petre, Bill Grieser, and Donald Kundert, 2008. A Practical Use of Shale Petrophysics for Stimulation Design Optimization: All Shale Plays Are Not Clones of the Barnett Shale. spe:115258.
9. Sharma, RK and S Chopra 2012, An Effective Way to Find Formation Brittleness, AAPG Explorer, September 2012. Online.
10. David Gray, Paul Anderson, John Logel, Franck Delbecq, Darren Schmidt and Ron Schmid, 2012. Estimation of stress and geomechanical properties using 3D seismic data. First Break 30, March 2012. Online.
11. Hall, M, 2012. Brittleness and robovibes. Blog post at agilegeoscience.com.