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Rock strengths and rock failure criteria 103

30

25
y = 14.859x 0.4639
R² = 0.6999
20
UCS (MPa) 15

10
Plumb, 1994
5 Bradford et al., 1998
GoM sandstone
Power (GoM sandstone)
0
0 1 2 3 4 5 6
E (GPa)
Figure 3.14 Correlations and laboratory-measured uniaxial compressive strengths
versus Young’s moduli in sandstones from ultradeep Gulf of Mexico wells.

rocks in oil field cores and quarries. The upper bound UCS is a strong
negative function of porosity in the low to intermediate porosity range, but
it becomes relatively independent of porosity at high porosity where sand
production is a problem. The average upper bound is approximated by:
2
UCS ¼ 357ð1 0:028fÞ (3.25)
In Eqs. (3.24) and (3.25), UCS is in MPa and porosity f is in %. Eq.
(3.25) represents an upper bound UCS of sandstones and predicts a higher
UCS than that from Eq. (3.24). For sandstones which contain clays, the
strength falls well below the trend suggested by Eq. (3.25).
Weingarten and Perkins (1992) presented the following relation to
predict sandstone internal friction angle 4 (degrees) using porosity f (fraction):
4 ¼ 57:8 105f (3.26)

3.2.3 Empirical equations of rock strengths in carbonate
rocks
3.2.3.1 From sonic velocity
Milizer and Stoll (1973) obtained the following relation between the UCS
and compressional transit time for the limestone and dolomite (Chang et al.,
2006):
1:82
UCS ¼ð7682=DtÞ 145 (3.27)