Page 97 - Applied Petroleum Geomechanics

Rock strengths and rock failure criteria 89

where P max is the maximum load exerted on the rock sample; A is the area
of the cross section of the sample.
ISRM (1979) recommends that the test specimen should be a right
circular cylinder, having a diameter approximately 54 mm, and a
height-to-diameter ratio of 2.5e3. If thesamplesizedoesnot meet this
requirement, the strength test results obtained from Eq. (3.2) will need to
be corrected. Based on an analysis of a series of laboratory test data, Hoek
and Brown (1980) found that rock UCS decreases as the sample size
increases. They proposed that the UCS should be normalized by dividing
individual strengthofeachsampletothe strength of asamplewitha
diameter of 50 mm. The proposed correction is determined by the
following equation:

0:18
50
s c ¼ s c50 (3.3)
d
where s c is the corrected UCS for rock specimen with a diameter of
d (mm); s c50 is the UCS for rock specimen with a diameter of d ¼ 50 mm.
Based on laboratory studies the rock failure process can be broken down
into a number of stages characterized by changes in the measured axial and
lateral strain response recorded during uniaxial and triaxial compression tests
(Fig. 3.3). In the figure the axial and lateral strains are measured and the
volumetric and crack volumetric strains are calculated. These stages include
(Eberhardt et al., 1999):
(1) Crack closure (at stress of s cc ).
Crack closure, at stress of s cc , occurs during the initial stages of loading
when existing cracks orientated at an angle to the applied load close. During
crack closure, the stressestrain response is nonlinear, exhibiting an increase
in axial stiffness.
(2) Linear elastic deformation (from s cc to s ci ).
Once the majority of existing cracks have closed, linear elastic defor-
mation takes place.
(3) Crack initiation and stable crack growth (from s ci to s cd ).
Crack initiation, s ci , represents the stress level where the loading-
induced microfracturing begins. The growth of these cracks has been
shown to occur in the direction of the major principal stress, s 1 , and cracks
grow along a curved path to align themselves with s 1 . The opening of
cracks with faces parallel to the applied load is therefore detected as a
departure from linear lateral and volumetric strain behaviors.