Page 166 - Applied Petroleum Geomechanics

Basic rock fracture mechanics 159

τ

τ = c σ tan ϕ r
+
n
τ = σ n tan(ϕ r ) i +
c
ϕ +i σ n
r
Figure 4.17 Shear failure criterion in the fractured rock compared to that in the
intact rock.

Newland and Allely (1957) developed an equation to explain and
predict the shear resistance of nonplanar rock joints based on the observed
dilatant behavior of granular material such as sand:

s ¼ s n tanðf þ iÞ (4.61)
r
where s is the maximum shear strength under the normal stress s n ; i is the
average angle of deviation of the fracture from the direction of the applied
shear stress (see Fig. 4.17), and 4 r is the angle of internal friction of the intact
rock or residual angle of internal friction used by Barton (1976).
Compared to the MohreCoulomb criterion, the cohesion in the
fractured rock is zero in Eq. (4.61). Barton (1973, 1976) proposed a similar
equation to describe the fracture shear failure based on shear tests for the
rough tension fractures:
JCS

s ¼ s n tan f þ JRC log (4.62)
r
s n
Eqs. (4.61) and (4.62) can be used as the shear failure criterion for
fractured rocks.

4.4.3 Mechanical behaviors of rock masses

Research shows that the deformation behaviors of a rock matrix and a rock
mass are different. For a simple case, if a set of structure planes (such as
bedding planes) are parallel and equally spaced in the rock mass, Young’s
moduli of rock mass and rock matrix can be expressed as:

1 1 1
¼ þ (4.63)
E m E r k n s