Page 156 - Applied Petroleum Geomechanics

Basic rock fracture mechanics 149

Kulhawy (1984) and Bhagat (1985) experimentally found that Mode I
fracture toughnesses of several types of rocks and soils are directly pro-
portional to their tensile strengths. Experimental data show that a very soft
sedimentary rock (including coal), having a low tensile strength, has either a
very low fracture toughness or a very low resistance to fracture initiation. In
contrast, a hard rock, having a high tensile strength, has accordingly a high
fracture toughness or has a very high resistance to fracture initiation.
Whittaker et al. (1992) obtained some approximate relations between
fracture toughness and tensile strength, compressive strength, point load
strength, hardness, and velocity of acoustic wave of rock on the basis of
experimental data from many references. According to Whittaker et al.
(1992), the relations between Mode I and Mode II fracture toughnesses and
tensile strengths of various types of rocks including coal can be expressed as
follows:

(4.40)
K IC ¼ 0:27 þ 0:107T 0
K IIC ¼ 0:05 þ 0:086T 0 (4.41)
where T 0 is the tensile strength (MPa); and K IC and K IIC are Mode I and
Mode II fracture toughnesses (MPa$m 1/2 ), respectively.
Using public data and their own experimental results, Zhang (2002)
obtained a relation between Mode I fracture toughness and tensile strength
for several rock types:

T 0 ¼ 6:88K IC (4.42)
1/2
where T 0 is in MPa and K IC is in MPa$m . This equation should be valid
for general rocks from soft to hard under the condition of quasi-static or
low-speed impact loading.
Chandler et al. (2016) conducted fracture toughness measurements on
the Mancos shale samples; combined with public data, they obtained a
similar correlation as Eq. (4.42), i.e., T 0 ¼ 6.76K IC
Through analyzing laboratory test data, Whittaker et al. (1992) obtained
the following relations between fracture toughness and uniaxial compres-
sive strength (UCS):

K IC ¼ 0:708 þ 0:006UCS (4.43)
K IIC ¼ 0:114 þ 0:005UCS (4.44)